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The Narrative structure of scientific theorizing Rosales, Alirio 2014

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 The Narrative Structure of Scientific Theorizing    by  Alirio Rosales    B.A., Philosophy, Universidad Central de Venezuela, 1994 M.A., Central University of Venezuela, 2006     A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Philosophy)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  August 2014  © Alirio Rosales, 2014 	   ii	  Abstract  I argue that many scientific theories and explanations are irreducibly narrative in character. To this end I propose an account of a generalized narrative, which goes against the widespread view that narratives are by definition particularized. On my account, generalized narratives are sequences of causally connected event-types in the duration of a system, with a beginning, middle and end (whereas particularized narratives are causally connected sequences of event-tokens). Many important scientific theories have a narrative structure that is not reducible to the kinds of formal statements typically identified with theory formulations, i.e., equations and “if-then” conditionals. Similarly, some scientific explanations have a narrative structure that is not reducible to the structure of an “argument” with premises and a conclusion. Narratives, generalized or particularized, play a threefold role in theorizing: heuristic, structural, and explanatory: 1) Through narratives, scientists explore imaginative scenarios where possible causal connections and outcomes are explored before a mathematical or otherwise formal framework is in place; 2) Narratives constitute the core of some theories, and can embed formal elements in them; 3) The causal order of event-types or event-tokens forms the basis of explanations. Throughout, I motivate and illustrate my proposal with examples from evolutionary biology and physics. 	   iii	   Preface   This dissertation is an original, unpublished, intellectual work of Alirio Rosales.           	   iv	   Table of Contents 	  Abstract ............................................................................................................................. ii	  Preface............................................................................................................................... iii	  Table of Contents ............................................................................................................. iv	  Acknowledgements ......................................................................................................... vii	  Dedication......................................................................................................................... ix	  Chapter 1: Introduction ....................................................................................................1	  1.1 Introduction..............................................................................................................1	  1.2. The Narrative Turn and Narrative Structure......................................................5	  1.3 Narratives Can be Generalized ............................................................................12	  1.4 The Threefold Role of Narratives.........................................................................16	  1.4.1 Heuristic Role. ..................................................................................................17	  1.4.2. Structural Role. ................................................................................................21	  1.4.3. Explanatory Role. ............................................................................................22	  1.4.4 An Observation on the Threefold Role of Narratives.......................................23	  1.5 Mary Morgan on Narrative Theorizing in Economics.......................................25	  1.6 Concluding Remarks .............................................................................................32	  Chapter 2: Theories as Narratives .................................................................................33	  2.1 Introduction............................................................................................................33	  2.2. Generalizations: Generalized Narratives vs. Algebraic Equations, Dynamical Equations and Conditionals........................................................................................34	  2.3 Approaches to Theory Structure..........................................................................46	  	   v	  2.4 Concluding Remarks .............................................................................................50	  Chapter 3: Narratives and the Problem of Explanation ..............................................52	  3.1 Introduction............................................................................................................52	  3.2 Hempel on “Genetic Explanation”.......................................................................55	  3.2.1 The D-N Model.................................................................................................55	  3.2.2. D-N and Genetic Explanation..........................................................................62	  3.3 An Evolutionary Story...........................................................................................67	  3.4 Goudge on Narrative Explanation .......................................................................75	  3.5 Ruse on Narrative Explanation ............................................................................78	  3.6 Mary B. Williams on Darwin’s Historical Methodology....................................86	  3.7 Narratives and the Problem of Explanation........................................................89	  3.8 Concluding Remarks .............................................................................................95	  Chapter 4: Narratives in Physical Theorizing ..............................................................97	  4.1. Introduction...........................................................................................................97	  4.2 Narratives of Quarks and of Electron Gases.......................................................98	  4.2.1 Narratives in Models of Quarks........................................................................98	  4.2.2 Narratives and the Behavior of Electrons in Metals .......................................108	  4.3 Taking Stock.........................................................................................................117	  4.4 Concluding Remarks ...........................................................................................120	  Chapter 5: Narratives in Biological Theorizing..........................................................122	  5.1. Introduction.........................................................................................................122	  5.2. Darwin’s Theory of the Origin of Species by Means of Natural Selection....124	  5.2.1 The Narrative Theory of Speciation ...............................................................124	  	   vi	  5.2.2 Fleming Jenkin and the If-Then Formulation.................................................129	  5.3 Fisher’s and Wright’s Theories. .........................................................................141	  5.3.1 Fisher’s Mass Selection Theory. ......................................................................142	  5.3.2 Wright’s Shifting Balance Theory...................................................................148	  5.4 The Debate............................................................................................................159	  5.4.1 The Rate of Decay of Genetic Variability. .....................................................159	  5.4.2 The Evolution of Dominance..........................................................................168	  5.4.3 Panaxia dominula. ..........................................................................................176	  5.4.4. Interpreting the Fisher-Wright Debate...........................................................182	  5.5. Concluding Remarks. .........................................................................................185	  Chapter 6: Concluding Remarks .................................................................................188	  References.......................................................................................................................194	   	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	   vii	  	  Acknowledgements 	  My greatest debt is to my family: my wife Patricia and my daughter Maria Valentina. Their infinite love and support kept me going, day by day. They have been my highest inspiration in this journey.  My second greatest debt is to my supervisor, John Beatty, and my co-supervisor, Sarah Otto. They have taught me how to do original work. Their inspiration, guidance and support are reflected in each and every page of this work.   The dedication and advice of Paul Bartha and Christopher Stephens, my dissertation committee members, were crucial in giving shape to the project. Their different approaches to doing philosophy of science combined in very helpful and fruitful ways.  I am indebted to Dominic Lopes (Philosophy External Examiner), Michael Doebeli (University Examiner), and Mary Morgan (External Examiner-LSE) for providing me with questions, comments, and suggestions that will help me improve future versions of the present work.  John Woods, Andrew Irvine, Adam Morton, Alan Richardson, and Steve Savitt, from philosophy, and Mike Whitlock from Zoology, discussed with me the core ideas of the dissertation, and provided more than valuable advice.  I am indebted to my great philosophy and zoology teachers: Murat Aydede, Roberta Ballarin, Paul Bartha, John Beatty, Sylvia Berryman, Dominic Lopes, Alan Richardson, Steven Savitt, and Christopher Stephens; Michael Doebeli, Sally Otto, Dolph Schluter, and Mike Whitlock.  	   viii	   I thank Dolph Schluter for several discussions on species and speciation. I also thank Leticia Aviles and Darren Irwin, for very stimulating discussions.  For discussions and correspondence on the scientists and the science of this dissertation, I am indebted to Nick Barton, Anthony Edwards, Warren Ewens, Ulf Dieckmann, David Jablonski, and Mark Kirkpatrick, and Patrick Phillips. I have discussed the history and the philosophy of science with Otavio Bueno, Steven French, Jon Hodge, Jim Lennox, and Andrea Woody.   I thank Yair Wand and Carson Woo, from the Sauder School of Business, for their stimulating discussions and support.  My graduate colleagues (past and present) at the Otto and Doebeli Labs and at the Philosophy Graduate Program provided a very supportive, stimulating and congenial atmosphere. I would like to especially mention Dilara Ally, Yuichi Amitani, Alistair Blachford, Tyler DesRoches, Eric Desjardins, Leithen M’Gonigle, Rich FitzJohn, Andrew Inkpen, Jasmine Ono, Liz Kleynhans, and Carl Rothfels.  I thank UBC Family Housing, in particular Autumn Fowles, for understanding and support.  Last but not least, this journey started in Caracas, Venezuela. I would have not been able to make it without the inspiration, the teachings, the guidance, and support of Jesus Alberto Leon, Ezra Heymann, Diego Rodriguez, and Carlos Di Prisco.  	  	  	  	  	  	  	  	  	   ix	  	  Dedication 	  	  	  	  	  	  To Patricia and Maria Valentina, in love.  To Jamie Avis; too bad you are not here, my friend.  To David Hull; who got everything started.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	   1	   Chapter 1: Introduction   1.1 Introduction.  Storytelling and scientific theorizing are usually taken to be fundamentally different, or even opposed, human activities. Narrative thinking is portrayed as capturing particular events and circumstances, while scientific thinking is portrayed as capturing general patterns and trends. Even those philosophers who have defended narrative forms of explanation in history and evolutionary biology have done so on the grounds that their particularity circumvents any appeal to general laws.  I argue in this thesis, instead, that narratives, or stories, are essential to how scientists investigate general patterns in the complexity of the world. Through narratives, scientists represent how processes begin, how they unfold in time, and how they end in certain outcomes. This leads to theories, to the invention of experiments, to derivation of theorems, to computer simulations, and so on. By ignoring narrative, or relegating it solely to particularized stories, philosophers do not capture how scientists theorize about the world.   Given the tendency to minimize the role of narratives in scientific theorizing, as particularistic (or as “only verbal theory” or “just so stories”), this dissertation must address a number of entrenched assumptions and rhetorical questions, such as: How can general scientific theories possibly have a narrative structure? While narratives may figure prominently in history and in non-mathematized sciences, what role do narratives play in highly mathematical sciences, such as theoretical physics or theoretical evolutionary biology? After all, where is the narrative in an equation?  	   2	  Even if narratives do have a role in theoretical physics or in theoretical evolutionary biology, surely many would argue that this role is only heuristic; there is no need for narratives once a mature, mathematical theory is arrived at, replacing “only verbal theory” with sound mathematics. Even non-mathematical theories, like Darwin’s theory of natural selection, supposedly have a logical, if-then formulation, and where is the narrative in a set of conditional statements?   I argue that these questions make sense only under what can be called the particularity assumption about narratives and under the assumption that narratives are explanatorily inert. I argue that narratives can be generalized and that they embody an explanatory structure. Furthermore, I argue that far from being dispensable, they are constitutive of scientific theorizing, along with the familiar equations and if-then conditional statements. My claim is not just an existence claim, i.e., that there are narratives in scientific theorizing and in explanation. We simply cannot account for science as it is practiced without taking into account its often irreducibly narrative character. Scientists represent certain kinds of relations as events in a narrative and not as deductions within a formal framework.  More specifically, I will show how narratives are consistent with formal mathematical and logical elements and how these formal elements do their job embedded in a narrative context. While the narrative elements coexist with the formal elements, the former are not fully reducible to the latter, i.e., subsequent events are not deductive consequences of previous ones. Narratives represent the overall structure of processes as a sequence of causally connected events.  	   3	  Only when viewed in this way can we make sense of the fact that the same mathematical equations – the same dynamics – can hold in different processes. And only when we contrast the narratives of different scientists can we fully appreciate the nature of their scientific controversies. This thesis is devoted to exploring the fundamental roles that narratives play in science.  I am not implying that the kinds of narratives studied here exhaust the kinds of narratives that are in play in all scientific fields. Within the limitations of the present work, I am leaving out narratives in mathematics (Doxiadis and Mazur eds. 2012), and narratives in theoretical economics (Morgan 2001, 2012).  Although a mathematical proof can be considered a sequence of stages in narrative (Doxiadis 2012; Lloyd 2012), the connection between events cannot be said to be causal. In Mary Morgan’s case studies in economics, narratives represent sequences of connected events that that underlie implicit causal links in models of economic processes.1  I am also leaving out work on cognitive approaches to narratives, which have already established connections with the sciences of the mind (Ryan 1991, Herman ed., 2003, Herman 2013), and cognitive linguistics (Dancygier 2012). That said, the present work looks at narratives as strategies of representation of the natural world, and as theories of the world. In this chapter, I argue for a threefold role of narratives: heuristic, structural, and explanatory. Such roles are not played in isolation, and they will have different weights in the chapters to follow. In Chapter 2, using the notion of a generalized narrative I introduce the notion of a narrative theory. This involves what I call the structural role of 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  1 Isabelle Peschard (2007) has discussed stories in an account of epistemic values in science. 	   4	  narratives. To illustrate, I show the irreducible narrative character of evolutionary theory that has figured prominently in the history of evolutionary biology ever since the 1930s and 40s: Sewall Wright’s “shifting balance theory.” In Chapter 3, I deal with the explanatory role, and show that narrative explanation and Deductive-Nomological kinds of explanation are not at odds.2  In Chapter 4 I present case studies from physics. The physics case studies will illustrate the fact that narratives are also integral components of physical theories, and not only of the less mathematized or historical sciences. It will illustrate mainly the heuristic and structural roles of narratives.  In Chapter 5, I will analyze the structure of Darwin’s theory of natural selection, to argue that it has a fascinating narrative structure.  And I will present and discuss R. A. Fisher’s mass selection theory, and Wright’s shifting balance theory, already introduced in Chapter 4, as narrative theories in population genetics. We will see how a controversy arose between Fisher and Wright over their different narrative theories, even though they shared the same mathematical principles. Chapter 5 will also illustrate the heuristic, structural and explanatory role of narratives. Again in the present chapter, I present a modest account of narratives, and provide an initial characterization of their heuristic, structural, and explanatory roles. In section 1.2, I situate my project in the context of the “narrative turn” in the humanities, and introduce my characterization of a narrative as a representation of a sequence of causally 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  2I the course of this dissertation I will be using Deductive-Nomological explanation not so much to refer to explanations that fulfills the conditions of Hempel’s D-N model, but to explanations that involve deductive derivations from general laws (sometimes formulated as equations) of principles plus certain initial conditions. I will be referring to Hempel’targets of analysis without worrying whether the actual explanations fulfill the Hempel conditions. For critical appraisals on this see, for example, Cartwright (1983) and Hughes (2010).   	   5	  connected events or states with a beginning, middle, and end, in the duration of a system. The events or states are causally connected in the sense that one event leads to the next. In section 1.3, I introduce the notion of a generalized narrative as a sequence causally connected event-types. This goes against the widespread and entrenched view that narratives are necessarily about particular events. I do so by referring to previous accounts that involved, if not explicitly, a distinction between particularized and generalized stories.  In 1.4, I introduce the heuristic, structural, and explanatory roles of narratives in scientific theorizing. Taking the roles together, I claim that narratives are constitutive of scientific practice. The ensuing picture is one of narrative exploration as a critical means by which scientists investigate the causal structure of the world.3   1.2. The Narrative Turn and Narrative Structure In the last 20 years or so, a “narrative turn in the humanities” (Kreiswirth 1995), has led to the “narrative turn everywhere (politics, science studies, law, medicine, and last, but not least, cognitive science) …” (Ryan 2007). Such a turn has been associated, for example, with the “breakdown of transcendental truth claims” and the overturning of the hegemony of “logico-deductive and patriarchal modes or reasoning and knowledge” (Kreiswirth, op. cit., p. 63).  Distinctions have been made between “grand” or metanarratives vs. local, contingent narratives of our culture (ibid.). What I want to emphasize is that the narrative turn has been understood as “a general turn against theory and toward narrative” (Rorty, 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  3 A point of qualification is in order. Although what follows is about the theoretical side of science, the view presented in it is in no way restricted to theory. Analyses of narrative exploration can perfectly be applied to experimental work as well. 	   6	  cited in Kreiswirth op. cit.). This has not been without parallel in science studies, where narratives are prominent in “science without laws” approaches, e.g., work on model organisms (Creager, Lunbeck, Wise eds., 2007).  The motivation of the present project is exactly the opposite: rather than to turn against theory, my proposal is to rethink theory, and more generally, scientific theorizing, in the light of narrative. I understand previous work by philosophers of science on narratives discussed here as moving towards that project. If there is a narrative turn in recent philosophy of science, it is a turn to better understand scientific theories, e.g., the work of Mary Morgan from her 2002 paper, “Models, Stories and the Economic World,” to her book The World in the Model. This dissertation can be understood as a first step in setting that narrative agenda for the philosophy of science. Let us start to think about narrative structure. Minimally speaking, a narrative is “the representation of an event or a series of events” (Porter Abbott 2008, p. 13). By “event,” many narratologists have in mind an object undergoing a change of state; so saying that a narrative is the representation of an event is not as strange as it sounds. 4 As David Herman has put it, narrative theorists “attribute to stories the core property of representing events or changes of state …” (Herman 2002).  In contrast, the usual philosophical understanding of event involves something more like an object being in a state (Kim 1969, 1973). For my purposes, this difference is inconsequential. That said, I will follow the more standard philosophical use, mainly for 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  4 This definition of narrative has been proposed, for example, by Gerald Prince (1973, 1982, 1987), and by Seymour Chatman (1978, 1990). For discussion and further references, see Chapters 1 and 2 of Herman (2002). As changes of state, events are “actions,” or “happenings” (Chatman 1978, Herman 2002). So, when a narratologist says that a narrative can consist of a single event, this really involves two time periods (or stages). In the narratives I will analizing here, there are indeed actions or happenings at a given event or state. 	   7	  the ease of analysis. According to the usual philosophical characterization, an event has the structure : “object  has property  at time ” (Kim 1969, 1973), e.g., “the water in the glass having a temperature of 10°C at noon on October 24, 2014.” I will think of a narrative as a representation of a sequence of events in this sense of the term. Since I am concerned with narratives that represent natural processes, I add that the sequence of events is causally linked: one event causally leads to the next.5 Some narratologists would think this is too restrictive.6 But others would agree that causal connection is what differentiates a narrative from a mere chronicle.  More specifically, I will articulate the notion of event as a particular state of a system that undergoes change through time. Examples of such systems are: a particle, a collection of interacting particles, a collection of molecules in a gas, an organism, a species, etc. The state of a system is characterized by certain determinable properties: position, momentum, temperature; fitness; population structure, gene frequency; etc, which can be assigned determinate values.7   Thus, by “event” I mean a system being in a particular state, and by “being in a particular state,” I mean the system having determinate values for the determinable properties at a particular time, e.g., having the determinate value 27 °C for the determinable property “temperature at time ;” having the determinable value 0.5 for the determinable property “gene frequency,” at time , etc.8 So, for my purposes, to speak of 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  5 As I will indicate below, this does not presuppose a particular account of causation, and it meant to b compatible with whatever turns out to be the right description of physical processes at the quantum level. 6 See Chapter 4 of H. Porter Abbott’s The Cambridge Introduction to Narrative (Abbott 2008), for a discussion. Porter Abbott prefers to leave the definition without causation. For Noel Carroll, in contrast, “the first necessary condition for what constitutes a narrative representation is that it refer at least to two, though possibly many more, events and states of affairs” (Carroll 2001, p. 119). The second is that the events are causally connected. I return to Carroll below.  7 In what follows, I can speak interchangeably of “properties” or “variables” of the system.  8 Thus, I interpret in Kim’s formula as the determinate value of a determinable variable.  	   8	  the event, “the water in the glass having a temperature of 10°C at noon on October 24, 2014,” is the same as speaking of the state of the water at noon on October 24, 2014.9  With this in mind, here is a first version of a working definition: a narrative is the representation of a causally connected sequence of events in the duration of a system. Or alternatively, a narrative is a representation of a causally connected sequence of the states of a system.  In contrast with determinable property temperature, whose determinate values are numerical values, the specification of determinate values that occurs in a narrative does not necessarily occur numerically. A given state or event is characterized by a setting that fixes the configuration of the system at that state, e.g., there is a rare mutant, low mutation and migrations rates, selection is stronger that genetic drift, etc. In this way, a combination of such values can fix the beginning state of a process, e.g., evolution by natural selection, the production of quark confinement. Further determination of the determinate values is left open in the course of research, for example, via mathematical modeling.   The idea that narratives involve causal ordering has a long tradition.  We can take Aristotle’s account of tragedy in the Poetics and think of a narrative as having the structure of a “properly constructed plot.” As he argued, a proper “plot” is a “whole” that has “a beginning, a middle, and an end” (Poetics, Chapter 7) such that “if any one of [the incidents] is displaced or removed, the whole will be disjointed and disturbed” (Poetics 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  9 With the following qualification: whereas the notion of an event includes an object having a determinate value of a determinable property at a particular time, the notion of the state of an object or system is characterized in terms of some set of determinate values of determinate variables, but those variables may or may not include time, e.g., the state of a Newtonian particle system specified by  in Newton’s second law. I am mostly interested in states that include time in their specification. 	   9	  Chapter 8). Later events follow from earlier events “by the laws of probability and necessity” (Poetics, Chapters 8-9).10  Noel Carroll analyzes narratives in terms of the “narrative connection,” which he explains in causal terms (Carroll 2001). He asks: “What is the connection that obtains between events and/or states of affair in a narrative proper? One popular candidate is causation. This seems eminently plausible, since narratives represent changes in states of affairs [changes in the states of a system], and change implies some subtending causal process” (op. cit. p. 122).  For example, “The king died, and then the queen died,” may be considered a narrative but only in a minimal sense; it is not much of a narrative unless the king’s death contributes to the queen’s.11 As Robert Richards has expressed it: “Narratives fix events along a temporal dimension, so that prior events are understood to have given rise to subsequent events and thereby to explain them – that is, in brief what narratives do” (Richards 1992, 23). For the sequence of causally connected events to be a narrative, it has to have the structure that Aristotle thought a proper plot had: “a beginning, middle, and end” (Poetics, Chapter 7). The following passage by Gerald Prince nicely expresses the view at hand: The story always involves temporal sequence (it consists of at least one modification of a state of affairs obtaining at time  into another state of affairs obtaining at )…Moreover, in a “true” narrative as opposed to the mere 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  10 This way of understanding a narrative is not without critics. J. David Velleman criticizes analyses of narrative form in terms of Aristotle’s account of a plot in Velleman (2003). 11 The example is due to E.M. Forster cited in Porter-Abbott (2008). He contrasts between “The king died and then the queen died,” with “The queen died and then the king died of grief.” The latter exhibits causation. I take the quotes from Potter-Abbott (2008). For some authors, the degree of “narrativity” of the mere temporal ordering of events is less than it would be if the earlier events were alleged to cause the latter. Carroll (2002) and Currie (2010) discuss narratives and causation. For narrativity and degrees of it, see Currie (2010), and Ryan (2007). 	   10	  recounting of a series of changes of state, these situations and events also make up a whole, a sequence…having – to use Aristotle’s terminology – a beginning, a middle, and an end. (Prince 1987, p. 58-59. Quoted in Herman 2002, p. 44).12   I can now offer a second version of my working definition of a narrative: a narrative is a representation of a causally connected sequence of states of a system having a beginning, middle, and an end.  In “The Structure of Historical Narrative,” Hayden White has provided a characterization of history of the “narrativist” kind that puts together the previous elements: In the first place, it [the narrativist history] tells a story with a beginning, middle, and end. Secondly, its subject is an entity that is undergoing a process of change from one condition to another while remaining identifiably what it was all along. (White 1972, p. 6)  I hasten to add that there is nothing absolute about “beginning” or “end,” nor there is any implication that there have to be exactly three stages. Where a process begins or where it ends is set by the problem situation in which the theorist finds herself and does not necessarily correspond to an absolute beginning or end of a process in the world. As Seymour Chatman remarks: Aristotle’s discussion of the terms “beginning,” “middle,” and “end” apply to the narrative, to story-events as imitated, rather than to real actions themselves, simply because such terms are meaningless in the real world. No end, in reality, is ever the final in the way “The End” of a novel is or film is. (Chatman 1978, p. 47)   I won’t adopt the sort of naïve realism about beginnings and ends that Chatman has in mind. I will assume, as Richard Healey does, that “Any finite process has a beginning and an ending (Healey 1994, 341), and that “processes occur in definite sequences in 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  12 Notice that Prince is using “event” is the narrative sense of change of state. See note 3 above.  	   11	  certain enduring systems, exhibiting certain patterns. Natural processes such as photosynthesis, radioactive decay, continental drift, evolution by natural selection, and speciation are examples at hand” (Healey, ibid.).  I will also assume that scientists understand causation from an understanding of how processes interact, how they are modified, and what outcomes they lead to.13 In this sense, I adopt a perspective akin to the one embodied in James Griesemer’s account of “process following” in science: Following processes is a key project for understanding causality in the world. Where, when, and how processes originate; what interactions happen to them along the way; and how they terminate is, in a word, what there is according to process ontologies. Regardless of the metaphysical standing of process ontologies, there is no doubt that scientists do follow processes, that this is an important and central activity in their work, and that they achieve causal understanding as a result of doing it. (Griesemer 2006, p. 377)  In a like manner, my claim that narratives represent sequences of causally connected events leaves open the account of causation that best applies in a given explanatory context. I take at face value that scientists provide representations of processes as sequences of events, one event leading to the next. Based on the order of events, scientists provide explanations of phenomena, which I will call narrative-based explanations. As we shall see in Chapter 3, narrative-based explanations can accommodate different philosophical accounts of explanation (Salmon 1984, 1998; Dowe 2000). Let us now move on to the following section, where I claim that narratives can be general representations of processes.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  13 This includes the quantum domain, even if what we mean by causation is more complicated due to the nature of physical processes at that level, e.g., how physical interaction is to be understood depends on how separability and non-locality are understood.  In these matters, I subscribe to the approach taken by Healey (op. cit.).  	   12	  	  1.3 Narratives Can be Generalized The notion of a generalized narrative has not been given a proper characterization so far, but that does not mean that the distinction between particularized and more general narrative structures does not have antecedents in the literature. I provide an example from the work by Hayden White, which Paul Ricoeur discusses in Time and Narrative (1983/1984, p. 161-168). Ricoeur focuses on White’s account of explanation by “emplotment” in history: “Providing the “meaning” of a story by identifying the kind of story that has been told is explanation by emplotment” (White 1973, p. 7).  Emplotment involves identifying a particular story as a story of a certain kind: it “is the way by which a sequence of events fashioned into a story is gradually revealed to be a story of a particular kind (ibid.). A given story can be emplotted, and explained differently, as a Tragedy, Romance, Comedy or Satire. As Ricoeur puts it: “By emplotment, he [White] means much more than the simple combination of the linear aspect of the story … He means the kind of story …” (Ricoeur 1983/1984, p. 166).  Thus in his notion of explanation by emplotment, we can see that White is appealing to a more general, encompassing narrative structure in which, a historian “is forced to emplot the whole set of stories making up his narrative in one comprehensive or archetypal story form” (White op.cit. p. 8. Italics in the original. Cited by Ricoeur, ibid.).  The emplotment of stories makes them “recognizable as stories of a particular type” (White 1972, p. 9). In sum, according to White: … historical narratives achieve a secondary explanatory affect, over and above whatever arguments they advance, by the progressive identification of the story they tell as belonging to a certain class of stories. In short, in historical narrative plot “explains” not the events of the story, but the story itself by identifying it as a certain kind of story. (ibid.) 	   13	   I claim that something like White’s emplotment happens outside of literature or history, in natural science, and restrict my analysis to narratives that establish causal connections between stages of a process. Just as in White’s emplotment, I am not interested in particular stories or particular causal connections, but in kinds of stories that represent kinds of events.   More specifically, the narratives I am concerned with here represent sequences of generic events or event-types. A generic event or event-type involves a kind of object being in a particular state, i.e., having a determinate value of a determinate variable (in the sense explained above) at an unspecified time. Consequently, such generalized narratives, are capable of representing kinds of causal connections between the events.  Having claimed that, I have already suggested that among the few areas of agreement about the character of narratives in previous work is that they are not general. For example, in his Narratives and Narrators, Gregory Currie writes “theories stress generality, law-likeness, and abstraction, while narratives focus on the particular, the contingent, and the concrete” (Currie 2010, p. 28).  I opened this chapter with this entrenched view, which has been taken for granted in discussions over whether narratives count as explanations of their outcomes, in history and evolutionary biology, as we shall see in Chapter 3.  Those opposed to narratives as explanations have agued that explanations require generalizations. Narrative “explanations” fall short in this regard. Those in favor have argued that explanations do not require generalizations.14  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  14 It is an open problem in contemporary narratology whether narratives can be considered generalized (David Herman, per. comm.). For discussion’s sake, my emphasis is on the clear statements to the effect that narratives are particularized. 	   14	  Narratologist David Herman, grants narratives some explanatory capacity, but distinguishes it from the kind of explanation provided by general scientific theories: Rather than focusing on general, abstract situations or trends, stories are accounts of what happened to particular people – and of what it is like for them to experience what happened – in particular circumstances and with specific consequences. Narrative, in other words, is a basic human strategy for coming to terms with time, process, and change – a strategy that contrasts with, but is in no way inferior to, “scientific” modes of explanation that characterize phenomena as instances of general covering laws. Science explains how in general water freezes when (all other things being equal) its temperature reaches zero degrees centigrade; but it takes a story to convey what it was like to lose one’s footing on slippery ice one late afternoon in December 2004, under a steel-grey sky. (Herman 2007, p. 3)    Herman exemplifies the view that when we think of scientific theory we think of regularities, recurrent patterns, and when we think of narratives, particular events usually come to mind. Newton’s Principia Mathematica Philosophia Naturalis is about regularities in nature, whereas Cervantes’s El Quijote, is about the particular circumstances in the life of a particular individual, Alonso Quijano. On the contrary, I will argue that many scientific theories tell us about regularities and recurrent patterns in nature in part through the generalized narratives they possess, in contrast with the particularized narratives of the historian, the paleoantropologist, or the author of fiction.15 The contrast of narratives with generalizations is also found in Jacob Bruner’s Actual Minds, Possible Worlds, where he distinguishes between the logico-scientific or “paradigmatic” and the narrative “modes of thought.”16 Interestingly, however, Bruner 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  15 We saw, however, how White argues that the historian explains through narrative generalizations. Misia Landau (1993) has convincingly argued and documented how generic pattern of explanation are present in evolutionary paleoantropology. The same can be said of paleontology (Raup and Stanley 1978).  16 Bruner has provided us with the most sustained contrast between narrative and scientific thinking. 	   15	  acknowledges that narratives come in genres or types that are realized in particularized stories: Narratives deal with (or are “realized” in) particulars. But particularity seems only to be the vehicle of narrative realization. For particular stories are construed as falling into genres or types; bad-boys-woos-nice girl, bully-gets-his comeuppance, power-doth-corrupt, whatever. From Aristotle to today, thoughtful students of drama and narrative have puzzled over the chicken-egg question of whether genres “generate” particular stories, in the sense of leading us to construe sequences of events according to their generic prescription, or whether genres are mere afterthoughts that occur to tidy academic minds. (Bruner 1996, p. 133-134)   Bruner suggests the idea that narratives can be generic prescriptions of the order in which events are organized in particular stories. He has in mind literary narratives, but the same can be said of White’s “archetypical narratives,” or the narratives that represent regularities and patterns in nature. Bruner’s “generic prescription” can be spelled out: generalized narratives represent a causal order between generic events: an initial event-type causally leads to a second event-type that in turn leads to a third event-type, and so on.   Let us now make more precise the distinction between generalized and particularized narratives. A generalized narrative represents a causally connected sequence of event-types or states undergone by a kind of system. A spatiotemporally particularized narrative represents a causally connected sequence of events-tokens or states in the duration of a particular system. Having argued that narratives can be generalized, let us now move to their threefold role in science.    	   16	  1.4 The Threefold Role of Narratives In the rest of this chapter, I argue that narratives, as I have characterized them, play a threefold role: heuristic, structural and explanatory. Philosophers of science are no longer only concerned with the products of scientific theorizing, e.g., models, theories, and explanations, but also with the cognitive processes and practices that lead to them. Understanding the narrative dimension of scientific thinking requires one to consider both aspects. Doing so reveals the heuristic role of narratives. Nancy Nersessian has asserted, regarding the role of analogies in Maxwell’s formulation of his equations of the electromagnetic field, that analogies are “not “merely” guides to reasoning, but form the creative heart of the reasoning process in which they are employed” (Nersessian 2002, p. 138). I assert a parallel claim regarding narratives, in their heuristic role. Authors have expressed something like the structural role of narratives by saying that stories are an “essential part of […] models […]” (Morgan 2001), or that a story is “an integral part of a model […]” (Hartmann 1999). That theories have a narrative structure has received comparatively less attention, perhaps because the mathematical parts get all the theoretical attention.  Narratives also play an explanatory role by fixing an order of events that brings about a given outcome. Narrative explanation has been widely discussed in the philosophy of history and the philosophy of biology, but less so in the context of contemporary views on explanation. As indicated above, that discussion has contemplated only particularized narratives, and the possibility of explanations based on narrative generalizations was left unexplored. I further argue that by representing the 	   17	  structure of processes, narratives contribute to scientific understanding. Let us consider each role briefly and separately.   1.4.1 Heuristic Role.  The term “heuristic” usually refers to strategies of decision making or problem solving of cognitive agents with limited or “bounded” rationality living in certain kinds of environments. This is not the sense in which I am using the term here. Rather, I use the term to refer to research as an exploration of possibilities, rather than as deductions within an established model or theory.  I borrow this use from Thomas Nickles work on the “heuristic appraisal” (HA) of theories, versus what he calls the “epistemic appraisal” (EA) of theories. The first concerns the evaluation of the “actual problem solving and predictive success to date of a model, theory research program, etc., whereas HA evaluates its possibilities, what we may call its problem-solving potential or exploratory potential (in the case of pure experimental or theoretical exploration)” (Nickles 2006, p. 166).  HA, according to Nickles employs modes of reasoning that are “rhetorical” rather than logical; examples of which are analogy, simile, and metaphor, and I would add narrative. In HA, certain salient ideas or experimental procedures are chosen as worth pursuing in terms of their fertility and potential.  Although I don’t deal with methodology here, I suggest that Nickles’s sense of heuristic refers to that dimension of research where scientists are theorizing without yet having a specific model or theory. Narrative thinking plays a major role in how such theorizing leads to mathematical models or theories, as we shall see below.  	   18	  I argue that narratives allow scientists to explore a space of outcomes, before committing to specific model formulations, and suggest what needs to be proven; narratives define what "makes sense" and what doesn't -- what is interesting and what isn't worth the time.  This I argue is akin to the kind of “model based reasoning” that has been characterized by Nancy Nersessian, to differentiate it from the kind of logical reasoning that takes place once models and theories are in place. The basis for such model-based reasoning is “the human capacity for simulative reasoning through mental modeling” (Nersessian 2008, p. 91).  Such capacity in turn “is rooted in the ability to imagine – to depict in the mind – both real world and imaginary situations, and to make inferences about future states of these situations based on current understandings, with and in the absence of physical instantiations of the things being reasoned about” (ibid).  Presented with a problem, e.g., moving a large sofa through a doorway, subjects imaginatively project alternative movements that would lead to the outcome of a sofa-like object going through a doorway. In this sense, they mentally “simulate” a situation instead of engaging in logical operations between propositions (ibid). I claim that the construction of narrative scenarios (“situations” in Nersessian’s terms) is a form of model-based reasoning so understood. By constructing narrative scenarios, i.e., representing a sequence of causally connected event-types or states of a kind of system, scientists explore a space of possible outcomes and investigate the causal structure of a process without yet having a model or a theory.  Let us imaging a post-Mendelian scientist exploring the process of natural selection. She could envisage a process beginning with the appearance of a new gene in a 	   19	  large population, or beginning with a population subdivided into groups evolving in their local environments through deterministic and random processes.  The different beginnings lead to different middle and end stages (or events) of the process. Our theorist can predict, for example that a single gene could become extinct by chance; but how fast that would happen would require mathematical modeling. As we shall see later on, narratives draw the attention of theorizers to problems that merit mathematical (or experimental) investigation. Thus, heuristically, narrative thinking can narrow down the directions of research worth pursuing, reveal novel problems, reformulate questions, suggest what needs to be proved, establish connections with previous domains, and investigate causal dependencies.  That narratives play a heuristic role in science may not be a controversial claim after all.  Perhaps more so is the theoretical significance of such a role. My example comes from Bruner again, who has distinguished between narrative and scientific, or “paradigmatic,” thinking.  There are “two modes of cognitive functioning, two modes of thought, each providing distinctive ways of ordering experience, of constructing reality” (1986, p. 11). They are “irreducible to one another,” and at the same time complementary. One is about well-formed logical arguments and the other “well-wrought” stories. Paradigmatic thinking “leads to a search for universal truth conditions,” and “deals in general causes,” whereas narrative thinking leads to “likely particular connections between two events – moral grief, suicide, foul play” (1986, p. 12). Bruner contrasts paradigmatic with narrative imagination: 	   20	  The imaginative application of the paradigmatic mode leads to good theory, tight analysis, logical proof, sound argument, and empirical discovery guided by reasoned hypothesis. But paradigmatic “imagination” or (intuition) is not the same as the imagination of the novelist or a poet. Rather, it is the ability to see possible formal connections before one is able to prove them in any formal way. (Bruner 1986, p. 12. Italics added)  Given the heuristic role of narratives in scientific thinking, the imagination of the novelist or a poet is not all there is to narrative imagination, for narrative imagination manifests itself in precisely the kind of ability Bruner attributes to paradigmatic imagination: the ability to see relations worth formalizing before one has a mathematical framework in place. In that way, the narrative mode of thought can definitely contribute to the formulation of general theories of nature.  Bruner actually leaves room for narrative imagination to be involved in scientific thinking, but its role is entirely preliminary and provisional: We all know by now that many scientific and mathematical hypotheses start their lives as little stories or metaphors, but they reach their scientific maturity by a process of conversion into verifiability, formal or empirical, and their power at maturity does not rest upon their dramatic origins (Bruner 1986, p. 12)    In another passage he writes:  There is a heartlessness to logic: one goes where one’s premises and observations take one, give or take some of the blindnesses that even logicians are prone to. Scientists, perhaps because they rely on familiar stories to fill the gaps of their knowledge, have a harder time in practice. But their salvation is to wash the stories away when causes can be substituted for them” (Bruner 1986, p. 13)     According to Bruner, narratives are a sign of immature science or not fully formed science.  I argue that this is not the case. The “power at maturity” of theories does depend on their “dramatic origins,” and stories are not always washed away when general causes are found. In many cases, the role of narratives does not end with their heuristic role.  	   21	  Indeed, they remain at the very core of many mature models and theories, and there lies their structural role.17   1.4.2. Structural Role.  I will assume that theories capture certain fundamental relations in their domain of phenomena, e.g., the relation between mass and distance in Newton’s gravitational theory.18 Those relations are represented by equations that lie at the core of the theory, e.g., Newton’s law of gravitation. So far, talk of structure of theories in science has taken for granted that the only structure worth considering is mathematical structure. But this is not right. Some theories establish relations in a domain also by means of generalized narratives that lie at its core, and that cannot be reduced to or replaced by equations or other kinds of formal statements, e.g., if-then conditionals. In these cases, narratives, and not equations or conditionals, represent the structure of the world. Instead of relations of proportionality between properties of a system, i.e., mass and distance in Newton’s inverse square gravitation law, narratives express relations between causally ordered events as stages of a process. Let us return to our imaginary theorizer. Besides imagining different narrative scenarios, and exploring different outcomes, she may formulate a full-fledged theory that establishes an order that certain kinds of events follow in nature.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  17 There are cases where narratives don’t make it to the actual formulation and presentation of theories, and seem to drop out once their heuristic role is fulfilled. Once full-fledged theoretical systems are in place, narrative are no longer needed and can be disposed of. Newton’s presentation of his theory of motion and his system of the world in Principia Mathematica tends to minimize the narrative elements that were surely present in his struggles to understand the force of gravity. For the latter, see McMullin (1978). 18 I think of theories in structuralist terms, downplaying the role of objects an emphasizing knowledge of relations. The best place for structuralism in the philosophy of science is now French (2014).  	   22	  In other words, she would formulate her theory as a generalized narrative that would be representing the structure of the world. In such structure, different kinds of processes are linked through the events or stages of a narrative. Moreover, the narrative theory – as I shall cal it – can embed different pieces of mathematical structure, e.g., equations that apply at different stages.  The structure of the world is not only expressed in mathematical or conditional terms. It is also expressed in narrative terms, in particular when it comes to causal structure. But, since structure has been synonymous with mathematical or conditional structure, narratives have been a missing element in extant philosophical approaches to theories.19 Chapter 2 aims to rectify this situation.   1.4.3. Explanatory Role.  In addition to their heuristic and structural roles, narratives also play an explanatory role in science. When our imaginary theorizer applies her narrative theory to explain phenomena in the world, she comes up with explanations that follow of the causal order of events represented in the theory. As we shall see, narrative-based explanations – as I shall call them – can have formal elements, e.g., deductive arguments with laws as premises, but narratives will not be reduced to them. Indeed, in Chapter 3 we will see how defenders of the Deductive-Nomological (D-N) model of explanation, when trying 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  19 As I will discuss in Chapter 2, this is particularly true regarding the philosophy of theory structure, i.e., “syntactic” and “semantic” approaches. More recently, Carl Craver has presented an account of theories that do not have a formal structure, e.g., theories of mechanisms in neuroscience. I will argue that such theories have in fact a narrative structure. Narratives have entered recent philosophy of science mainly through the philosophy of models. To my knowledge, the first papers to argue that narratives, or stories, are integral components of models are Stephan Hartmann (1999) and Mary Morgan (2001). Both Hartmann and Morgan can be read as arguing for what I call the structural role of narratives. I read Margaret Morrison (2009) as suggesting that theories have stories at their core.  	   23	  to reduce narrative explanation to D-N explanation, end up showing that deductive arguments are embedded in a narrative structure.   I will argue that attempts by philosophers of science to reduce narratives to DN arguments actually only succeed in reducing narratives to an irreducibly narrative sequence of DN arguments. Such narratives have DN features, but their overall narrative structure is as important to their explanatory success as their DN features.  The narrative structure of these accounts is irreducible in the sense that the later DN stages do not follow deductively from the earlier stages. The later stages (or at least the conditions invoked in the later stages) need to be specified at the appropriate points in the narrative.20 Although my discussion centers on the D-N model, the irreduciblity claim would apply to the statistical version of Hempel’s model.  Then I will claim that narratives play an explanatory role precisely by virtue of the order of events in which they represent the stages of a process. This causal order of events forms a basis for explanation. I am particularly interested in explanations that are based in generalized narratives.  1.4.4 An Observation on the Threefold Role of Narratives I have characterized three roles narratives play in scientific theorizing. These roles express different facets of scientific practice. I hasten to emphasize that the fact that they can be conceptually distinguished does not imply that they can be so neatly distinguished in the process of theorizing. In this and next section, I will distinction made by Mary Morgan (2012) between model creation and model use helps to further characterize the 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  20 Hempel considered explanations based on deterministic laws and those based on probabilistic laws as arguments (Hempel1962/2001, 1965) . Although my discussion centers on the D-N model, the irreducibility claim would apply also to the statistical explanation. 	   24	  threefold role. For my purposes, I will assume that Morgan’s distinction applies indistinctively to models or theories.  The heuristic role is clearly at play in model or theory creation, which. In this role narratives play a theoretical role before the model or theory is in place. The structural role presupposes that a model or theory is in place, and pertains the context of model use. This, however, does not fully detach the structural role from the heuristic role.  In the heuristic exploration of possibilities, the theorizer identifies features of processes that will become part of the models or theories that are eventually formulated; those features go from model creation to model use. In addition, my distinction does not imply that the heuristic exploration of possibilities stops once the model or theory is in place. I suggest that the structural role occurs in the domain of model or theory use.  The explanatory role does not make things any easier. The kind of features that the theorizers heuristically identifies and that make it to the model or theory, are very likely to be explanatory when the model or theory is applied to the world. Again, the explanatory role is not clearly detached from the heuristic role, even if it clearly belongs to the context of model or theory use.  Thus, in the reality of the research process, these roles may be in flux, and not so sharply detached from one another.  This flux is to be seen, especially in Chapter 5. In the next section, I further develop Morgan’s distinction, and present her account of the role of narratives in economic theorizing.     	   25	   1.5 Mary Morgan on Narrative Theorizing in Economics In work that preceded this dissertation, Mary Morgan has offered account of narratives in scientific theorizing in her book The World in the Model: How Economist Work and Think (Morgan 2012). Indeed, she offers an account in terms of the roles that narratives play in economic theorizing. Without going into the details of her case studies, in this section I focus on the essentials of her account, and suggest ways in which Morgan’s roles can be understood using my threefold distinction.  Morgan’s account is presented in Chapter 6, “Question and Stories: Capturing the Heart of Matters; and Chapter 9, “Model Situations, Typical Cases, and Exemplary Narratives,” which draw on Morgan (2001), and Morgan (2007). She thinks about narratives in the context of modeling and theories in economics. In Chapter 6, Morgan deals with narratives in the development of classical macroeconomic theory. In Chapter 9, with the applications of game theory in economics that led to the Prisoner’s Dilema game.  Models, Morgan asserts, “are objects to enquire into and enquire with: economists enquire into the world of the economic model, and then use them to enquire with into the economic world that the model represents” (Morgan 2012, p. 217). Economists use models to ask certain questions; then they “use the resources of the model to demonstrate something, and tell stories in the process (op. cit., p. 218).  Morgan distinction is between the “theoretical,” or “idealized” world of the model, and economic world that the world-in-the-model represents. Narratives are going to play a role in how economists inquire into the model world, and how they inquire with the latter 	   26	  into the economic world. Stories, according to Morgan, shape the building up or creation of the models, and also serve “as a means of relating the modeling result back to the world to offer an economic explanation of why the economic world behaves as it does” (op. cit., p. 221).   A particular aspect of Morgan’s account is that the narratives’ role in shaping the creation of a model is in a continuum with the exploration of the world-in-the-model. To use my terms, narratives helps the theorizer explore a space of outcomes in the construction of the model, and this role continues once the model is in place. For Morgan, economists tell stories creating a model and with the model.  In the exploration of the world-in-the-model, some stories depict scenarios that have no counterparts in the economic world. In these cases, another story explains, in terms of processes in the economic world, the kind of behavior represented in the model-world. In exploring the world-in-the-model, the theorizer captures some central features of the economic world. Stories are critical in the creation of the model and in “joining the elements [of the model] together” (op. cit. p. 221). And stories are critical “for pointing to the way the model could be used to provide explanations. It is this latter role of stories that features regularly in the way economists use their models” (op. cit., p. 221. Emphasis in the original).  The exploration of the world-in-the-model starts out in the very creation of the model. But once the model is in place, economists tell other stories with the model as they continue exploring the world-model. In doing so, the theorizer “traces the effects of changing one thing in the model (while holding others constant) to see the outcomes of such changes on all the intervening elements … (op. cit. p. 223).”   This involves offering 	   27	  “a narrative sequence of connected events as each change alters the value of some other element in the model; this requires tracing all these changes through the various relationships in the model (op. cit., p. 224). Narratives, in effect, help the theorizer explore a space of outcomes in the model-world that will provide insights about a feature of the economic world. And narratives bridge economic behavior in the model-world to behavior in the economic world, thus making the model explanatory.  As Morgan nicely puts it: “economists seek to capture the heart of the matter in two senses, in two domains: the world of the model and the world that the model represents or denotes” (op. cit., p. 239).” Narratives help the theorizer understand the world of the model, and they also help to link the latter to the economic world: Model questions are designed to prompt explorations of the relationships represented in the model. And since economic models are not only pieces of mathematics, but also pieces of economics, so their demonstrations [via the formal resources of the model] need to be interpreted, understood, and explained in economic terms. These model narratives provide not only the means to understand the economic world of the model, but also to link the model with the economics of the world. (op. cit., p. 239)   As we see, narratives or stories perform a dual role for Morgan. On the one hand, they are crucial in the investigation of the structure of theoretical economic system (world-in-the-model) that represents the economic world. In this sense, stories provide what Morgan calls the identity of the world of the model: “By identifying the specific stories that could be told with their models (and the ones that they could not tell), these economists came to understand the identity of the world that had been captured in their models” (op. cit. p. 242). On the other,  In model usage, narratives provide the possible correspondence links between the demonstration made with the model and the events, processes and behavior of the world that the model represents. Narratives may show how to apply the model to the world, and to offer potential insights, understandings, or even explanations of 	   28	  how the world (that the model represents) works. (op. cit. p. 243. Emphasis in the original).   In this role, narratives provide the theoretical model with an interpretive link with the world it represents. This interpretive link creates a match between the model-world and the real economic world that allows the model to be explanatory. Theorizers in economy use narratives in the modeling process that encompasses the creation and development of the model (that generates the identity of the world of the model), and the application of the model to the world.  Morgan further develops her account in Chapter 9 where she deals with the application of game theory to economics and the development of the Prisoner’s Dilemma game. In Chapter 6, whose core ideas I just discussed, narratives were crucial in the creation of the model and in the formation of the identity of the model as the exploration of the world in the model is carried out. In Chapter 9, the new case study allows Morgan to reinforce her point in a novel modeling context that involves the construction of generic, or “typical,” scenarios or “situations.” In such cases, narratives “are built into the identity of the model from the start of the model” (op. cit. p. 362. Emphasis in the original). In Chapter 6, the identity of the model was a result of the use of narratives with the model. In Chapter 9, narratives provide identity from the creation of the model.  As in Chapter 6, “the role of narrative does not stop once the model or game has been created. Rather, … , narrative work continues as a flexible way of matching a game situation to an economic situation in applying game theory to the world” (op. cit., p. 362). In the game-theoretic case study, model application receives a more sustained consideration.  	   29	  In the context of Chapter 9, the other role of narrative as a “matching device” between the world in the model and the economic world results, in a “smoothing out” of the differences between them. This occurs because in the case of the Prisoner’s Dilemma model, the “narratives translate the prisoners’ situation into the economic situation – real or hypothetical – and viceversa. Narratives link the particular of the economic situation to the typical situation depicted in the game and so ‘explain’ how it is, for example, that two large firms can end up doing damage to each other just as the prisoners end up with the double-defect outcome (op. cit., p. 365).  There is a third role that narratives play in game theory modeling of  “typical situations.” In “constructing and shaping an account of the economic world that locates the typical features of such situations, and so, by characterizing what is particular about different situations, contributes to the categorizing and classifying activity of modelling … . Narratives, in defining and giving structure to these typical situations, sometimes point to problems – as indeed the Prisoner’s Dilemma narrative did” (op. cit. p. 363).  The modeling context of Chapter 9 illustrates in a more acute and novel ways roles that Morgan has already discussed in Chapter 6. For instance, the third role just characterized by Morgan, is related to how the world in the model relates to the economic world.  Narratives help in locating what is typical about the situations modeled by exhibiting their particularities across different situations. In this way, they are central to game theory modeling – and to modeling in general – as a categorizing and classifying activity. Narratives in this case, link the world in the model (the game situation) and the economic world (interaction between large firms). And we have seen that the interpretive 	   30	  role (via the “corresponding link” above) that narratives play for Morgan as “matching devices,” is crucial for the explanatory capacity of models.  Summing up, narratives play three main roles in theorizing for Morgan: 1) a role in the construction of a model; 2) a role in the development of a model; 3) a role as “matching devices” between models and the world they represent. How these roles are manifested varies in the contexts of Chapter 6 and 9, e.g., narratives contribute to the identity of the model as the model is used (and developed) by economists in Chapter 6, whereas they ate built into the identity of the model right from its creation in Chapter 9. Clearly for Morgan, economic theorizing has a narrative structure expressed in these three roles. How do they relate to my proposal? I hope it can be seen from my brief discussion that central to Morgan is to argue that narratives do not stop their role in theorizing once the model is in place. The same consideration led me to the structural role of narratives. I have called their role in model creation, heuristic role. This latter consideration led me to the structural role of narratives. Morgan sees narratives as constitutive of the modeling processes that she analyzes in Chapters 6 and 9. That is, she sees narratives as essential elements of economic modeling in the exploration of the world in the model, and the definition of the identity of the model. I suggest that insofar as narratives are integral to how economists use models and do not stop once models have been created, they can be said to play a structural role in Morgan’s account.  That said, a remark is in order. Morgan’s emphasis on narratives as built into the identity of the model from its creation in her Prisoner’s Dilemma case study suggests, I believe, that my distinction between heuristic and structural roles is a fluid one; in their heuristic role narratives identify structural features of processes that will be represented 	   31	  by narratives that are told once the model is in place. Even if the three roles can be distinguished for the purposes of analysis, they may not be as sharply distinguished in scientific practice. Indeed, Morgan’s case studies illustrate the roles of narratives in the process of model making and development. I leave it to future work to substantiate this last suggestion.  I come to narratives as “branching devices.” This introduces a role that is not in principle captured, at least explicitly, by my threefold classification of the role of narratives. Narratives build “correspondence links” between the world in the model and the economic world. This, I have suggested, involves providing the model with further interpretation in terms of events and processes of the economic world.  I now emphasize that for Morgan, the explanatory role of narratives is derivative from their role as matching devices. It is because narratives bridge the two domains distinguished by Morgan, i.e., the world in the model and the economic world, that models can be explanatory of the world they represent. As matching devices, narratives make economic models explanatory. This would be their explanatory role in Morgan’s account.  We see how Morgan’s presents an account of the narrative structure of scientific theorizing in terms of her distinction between model creation and model use. I have suggested a correspondence between her roles for narrative and my threefold role. The result further elaborates the kind of roles narrative play in the contexts Morgan distinguishes, and it has allows me to further elaborate the kinds of distinctions I am proposing.   	   32	  In particular, it was not clear where Morgan’s role of narratives as matching devices fits into my threefold distinction. I have suggested that it is connected to the explanatory role of narratives. In work that will follow this dissertation, I will provide a detailed discussion of Morgan’s case studies and a comparison with the case studies presented herein.  Finally, I owe the reader a more complete account of the heuristic role of narratives. That study would require doing history of science to track the process of creation and the narratives involved. Morgan has a nice example of this in Chapter 6 of her book cited above. Morgan distinction has helped me make my threefold distinction more precise, and my threefold role has help to further elaborate what roles narratives play in model creation and model use.   1.6 Concluding Remarks  My project is not a turn to narrative against theory, but a turn to narrative to better understand theory: narrative heuristics as a guide to theory, theories as narratives, and theories used to explain phenomena. As we shall see in the next chapters, narrative is not at odds with general laws, or with the formal elements that have traditionally characterized scientific theorizing. Quite to the contrary, my main message is that by paying attention to the narrative dimension of scientific theorizing, we understand the formal better. In that spirit I offer the chapters that follow.   	   33	   Chapter 2: Theories as Narratives  2.1 Introduction In Chapter 1, I characterized the notion of a generalized narrative, as a sequence of causally linked generic events, or event-types. Such generic events are spatio-temporally unrestricted. In this Chapter I argue that some scientific theories are formulated as generalized narratives.  I give an example of a narrative theory from evolutionary biology, which will be developed into a full case study in Chapter 5: Wright’s “shifting balance” theory. I highlight the narrative structure of Wright’s theory by contrasting it with other theories, like Newton’s theory of motion and the mathematical theory of selection in population genetics, whose generalizations take the form of certain types of equations, and Darwin’s “if-then,” generalized conditional formulation of natural selection.  Discussions of theory structure have focused on latter sorts of theories, which may be one reason that theories with narrative structure haven been largely overlooked; the other reason being that narratives have long been considered to be necessarily particularized rather than general, or relegated to the status of bad science, as was observed in Chapter 1.  A central focus of this chapter then is on how the standard generalizations of theories differ from narrative generalizations, as exemplified by Wright’s theory. This is particularly interesting in the case of equations that have a story-like character, e.g., dynamical equations. The discussion will also include algebraic equations and “if-then” 	   34	  conditional statements. As we will see, the narrative character of a theory is crucial to how the theory represents processes.  Having contrasted narratives with the garden variety of scientific generalizations, I discuss three views on theory structure, namely, the syntactic and the semantic views and a recent proposal on “mechanistic theories.” I emphasize that narrative theories can be accommodated under all three approaches. The remainder of the chapter is as follows: in section 3.2, I make the contrast between Wright’s narrative theory, Newton’s theory and its equations, and a simple conditional formulation of Darwin’s theory. Section 3.3 discusses the other views on theories, and section 3.4 presents some concluding remarks.  The take home message of the chapter is that equations or if-then conditionals are no substitute for narratives in the representation of the action of processes in nature. Narratives are not reduced to these kinds of statements.  . 2.2. Generalizations: Generalized Narratives vs. Algebraic Equations, Dynamical Equations and Conditionals Theories are general. In their usual format, theories are general in virtue of “laws” or “principles” that they contain, i.e., Newton’s laws, Maxwell’s equations, Darwin’s principle of natural selection. I submit that theories can also be general also in virtue of generalized narratives that lie at their core.  In order to bring the distinction home, I emphasize the way in which Sewall Wright’s narrative theory of evolution differs from algebraic equations like those associated with Newtonian mechanics, dynamical equations of mathematical population 	   35	  genetics, and conditional (if-then) statements like those at the core of Darwin’s theory of evolution. Wright’s theory will be expanded into a case study in Chapter 5.  Let’s start with the kinds of generalizations exemplified by Newton’s theory. Here are Newton’s three laws of motion, just as he formulated them: Law 1. Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.  Law 2. A change of motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed. Law 3. To any action there is always an opposed and equal reaction; in other words, the actions of two bodies upon each other are always equal and always opposite in direction. (Newton 1726/1999, p. 416-417)  The first law establishes how a body moves in the absence of any forces whatsoever. It is called the law or principle of inertia. It can be formulated as the conditional statement: if no forces are acting on a body, the body continues at rest or in rectilinear motion.  The second law establishes that a change of motion (from rest or from rectilinear motion) occurs proportionally to, and in the direction of the impressed force. It can also be formulated as the conditional statement: if a force is applied to a body, the body accelerates with the same magnitude and in the same direction as the force. In its modern formulation, the second law states that if a force is applied to a body, the latter accelerates in the direction of the force at a rate that is inversely proportional to the mass of the object. It is expressed in the usual equation form as the algebraic equation:  21 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  21 Two observations are in order. First, as I.B. Cohen remarks, Newton “expressed the principles of motion in proportions in a retorical [verbal] style and not in equations (1999, p. 117).” Second, as indicated in the text, Newton formulates his second “Axiom” or “Law of Motion” in terms of change in the quantity of motion, or what we call momentum, . A literal mathematical transcription of the second law is (Cushing 1989, Torretti 1999); now, as Feynman notes, the second law can be written 	   36	  The third law establishes how bodies interact: between two bodies there is an action with the same magnitude and opposite sign. Together with the law of gravitation, the Newtonian principles establish how all bodies on earth and the heavens behave. Newton’s law of gravitation has been called “one of the most far-reaching generalizations of the human mind” (Feynman et al. 1963/1989, p. 7-1). It states that “every object in the universe attracts every other object with a force which for any two bodies is proportional to the mass of each and varies inversely as the square of the distance between them” (ibid.).   It is expressed as the algebraic equation:   What is the content of this generalization? The first thing to notice is that it postulates that a certain type of physical interaction occurs in the universe: a “gravitational attraction.”22 The second aspect of it is that it characterizes the gravitational interaction in terms of certain dependencies between physical quantities: force (F), mass ( , ), and distance ( ). The magnitude of the “force” of attraction increases as the mass increases and decreases as the distance between any two objects increases. The law of universal gravitation combines with Newton’s second law of motion to unify motions on the earth and in the heavens.23  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  , which can be rewriten  (Feynman et.al., 1963). It was Leonard Euler who included  as the basic principle of mechanics  (Cushing 1998, Truesdell 1960).  22 This of course was a very controversial postulation; it involved instantaneous action at a distance. See McMullin (1989) 23 As Roberto Torretti aptly remarks, the gravitational generalization is “doubly universal in that, by virtue of it, every body is accelerated toward every body at once” (Torretti 1999, p. 57). The unification though, 	   37	  Commenting on the third law, Lawrence Sklar nicely describes the nature of the whole Newtonian generalization. Sklar remarks that the principle applies to “all interactions of one body with another, including the hand which pulls on the rope being matched by the rope pulling on the hand, and most importantly, those “tugs” at a distance responsible for the interaction of the Earth with falling objects and the Moon and of the Sun with the planets” (Sklar 2013, p. 51).  My point is that these powerful generalizations do not have a narrative structure.24 They do not specify a sequence of events; they do not even involve the passage of time.25 They can be thought of as laws of coexistence, i.e., laws that restrict positions in the space of possible states of the system.26 But there are also laws of succession, i.e., those that restrict the trajectories of the system, which, as we shall see below, are more story-like. For now, the non-narrative character of the Newtonian theory is perhaps most easily seen by contrasting it with a theory of a different kind, which postulates the causal 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  involved equating inertial masses, i.e., resistance to being accelerated on the surface of the earth, with gravitational mass. A theoretical justification of this equality was only given by Einstein in his path from spcial to general relativity. No better place to see this than Einstein’s own account in Einstein (1920/1954). 24 No doubt Newton conceived narrative scenarios to describe physical interaction and gravitational attraction between bodies; but those narratives dropped out of the picture as he formulated his laws of motion. For Newton’s thinking on these matters, see McMullin (1978).  25 Let me clarify. Acceleration is change of velocity over time, and velocity is change of position over time. Time is then implicit in , which can be rewritten as a second order differential equation  . In this form, the second law is converted into a dynamical equation whose solutions are trajectories in the in the state space of the system; it is a law of succession. But  expresses an equality between three physical quantities. In the case of the law of gravitation, one obtains the dynamical equations by making the gravitational law equal to the differential equation just obtained, thus obtaining a system of two second order differential equations for a two-body system. For expositions and discussions see Hirsh, et al., (2004), and Diacu (2000).  26 This terminology has been philosophically used by Bas van Fraassen in developing his “state-space” version of the semantic approach to theory structure. A state-space represents all the possible states a system is capable of; such states are restricted by laws of coexistence and laws of succession. The former kind of laws restrict the states at which a given system can be found; the latter restrict the trajectories the system is capable of (van Fraassen 1970, 1972, 1989, 1991). Another example of a law of coexistence is the ideal gas law, . As it will be apparent in what follows, I will be using a state-space description of Wright’s shifting balance theory of evolution. John Beatty (1980a,b), Paul Thompson (1989) and Elizabeth Lloyd (1994) apply the semantic approach to evolutionary theory. I particular, Lloyd analyses the structure of mathematical population genetics using the state-space approach. 	   38	  structure of a process as a beginning event-type that leads to a middle event-type that leads to an end event-type and thus has a narrative structure.  My example of a narrative theory is the shifting balance theory of evolution, developed by Sewall Wright, one of the "founding fathers" of theoretical population genetics (Wright 1932).27 Wright's shifting balance theory represents a typical evolutionary episode from beginning to end. It represents evolution as the result of an interaction between random drift, migration, and natural selection acting within and among groups (Barton 1992), and moreover as a succession of three “phases:” each phase showing the predominant action of one process over another and leading to the next phase. Wright depicted the evolution of a species in its environment as a trajectory through a multi-dimensional state-space, whose points represent the fitness values of many possible gene combinations. In this space, there are multiple “peaks,” representing alternative gene combinations associated with relatively high fitness.28 But some peaks are higher than others, and there are “valleys,” representing gene combinations of lower fitness, between the peaks.  Depending on where a species begins – with what range of gene combinations – it will be driven by natural selection up the nearest peak. But that peak might be considerably lower than another peak that is not too far distant in the space, but is separated by a valley.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  27 The other founding fathers were Ronald Aylmer Fisher, and J.B.S Haldane. Our best account of the emergence of theoretical population genetics is Provine (1971/1978). The best paper’s length account of the contributions of Fisher, Haldane, and Wright can be found in Edwards (2001). For an exposition of the shifting balance theory and its significance in Wright’s work, see Crow (1990/1992). 28 “Epistatic” interactions between genes produce peaks with different fitness or “selective values,” as Wright use the term. For a review of the theory and evidence of how genetic interactions create multiple fitness peaks, see Whitlock et al. (1995).  	   39	  In other words, evolving from one range of relatively fit gene combinations to another range of more fit gene combinations – without any means of peak-hopping – would require some gene substitutions along the way that results in less fit combinations. So natural selection alone cannot be relied upon to get species to higher and higher fitness states.   Wright’s “shifting balance” theory was an attempt to show how this was done in nature. He presented it in terms of three “phases.” Applying the framework introduced in Chapter 1, I suggest that Wright characterizes each phase by qualitatively specifying a certain combination of determinate values of the determinate variables of the system. Let us see how the specification goes. In the first – i.e., when the narrative begins – a species is divided into subpopulations with a minimal amount of migratory exchange of genes between them. These evolve relatively independently from each other, thus exploring different regions of the state space and landing on different peaks. But the subpopulations are small enough that their gene frequencies are subject to random drift as well as natural selection, so they do not get stuck on low peaks and they may wander into nearby valleys and thereby into the vicinity of higher peaks.  In phase two, subpopulations in the vicinity of higher, steeper peaks are driven by selection close to the top of those peaks. In phase three, the group at the highest peak will grow in size and contribute highly fit migrants to the other subgroups. Selection, this time acting between, in addition to within, groups – favoring those groups with the fittest gene combinations – will soon bring the genetic composition of the whole cluster to that of the group at the higher peak.  	   40	  In each phase, a combination of determinate values of determinable variables will determine which causal process (drift, selection, migration), or combination of processes, plays the predominant role, leading to the next phase. Wright first formulated the narrative in 1932. As he summarized:  With many local races [sub-groups] each spreading over a considerable field [of gene combinations] and moving relatively rapidly in the more general field about the controlling peak [current fitness peak], the chances are good that one at least will come under the influence of another peak [first phase]. If a higher peak, this race [sub-group] will expand in numbers [by natural selection, second phase] and by crossbreeding with the others [exchanging migrants] will pull the whole species toward the new position [the new, higher peak; third phase] (Wright 1932, 168)29  As we see, the beginning stage corresponds to a certain qualitative specification of determinate values. As stated in Chapter 1, a given qualitative specification can be given a quantitative (mathematical) specification. Indeed, Wright did this for his first phase; most of this theory applied to the first phase of his narrative.  As James Crow (1990/1992) has observed, most of Wright’s mathematical theory applied to the first phase of his narrative. Further theoretical work on Wright’s theory was later developed by Russell Lande (1985), and Nick Barton, in joint work with Shahid Rouhani (Barton and Rouhani 1987, 1991, 1993; Rouhani and Barton 1987a, 1987b, 1993). Phase 2 involved the mathematics of natural selection, developed mainly by R. A. Fisher (1922, 1930/1999) and J.B.S Haldane. Mathematical work on phase 3 was initiated in 1990 (Crow et al., 1990). I will return to this in Chapter 5; suffice it to say by now that narratives can embed different equations and if-then conditionals at different stages. 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  29 In this paper, Wright does not yet tell the story in terms of phases. A clear exposition of his "Three-Phase Shifting Balance Theory" can be found in Wright (1965, p. 85-86).  	   41	  Wright’s narrative has had an enormous heuristic power in generating and guiding further mathematical developments within evolutionary biology. It integrates different evolutionary processes into a single causal structure.  Also in Chapter 5 we will see that Wright’s shifting balance theory played a heuristic, a structural and an explanatory role in the development of his mathematical theory of evolution, and posed novel problems for theoretical work. The other examples of narrative theories to be discussed later are Darwin’s theory of natural selection, and R.A. Fisher’s “mass selection” theory. Let us now compare our two examples of generalization.  Wright’s own formulation of his theory makes transparent its narrative structure. The “phases” of the shifting balance processes are event-types in the sense I have characterized the notion; a given phase represents a particular event-type in which a kind of system – a species – finds itself during its evolution; at each phase the determinable variables that characterize the system possess a set of determinate values.  Thus, for the properties population structure, migration, drift, and selection, the theory establishes that at the beginning, the species has a certain kind of population structure, and certain levels of migration, drift and selection. The states of the system – the values of those properties – change in a particular way in the middle and end of the sequence. As we see, Wright’s theory is formulated as a generalized narrative that represents the evolutionary sequence of any species as a series of causally connected event-types.  The evolution of any biological species starts with the event-type that Wright’s theory qualitatively specifies, which causally leads to event-type (phase) 2, which 	   42	  causally leads to event-type (phase) 3. It is important to remark that phase 2 does not necessarily follow from phase 1, and neither phase 3 from 2. The theoretical force of the narrative lies in the postulation of a certain order in which different processes are involved at different events of stages. This is entirely different from those versions of Newtonian mechanics based on algebraic equations that tell us nothing about the general order of events in the duration of Newtonian systems. True enough, based on the equations one can say that forces regularly produce changes in motion, but no determinate values of the determinable variables are specified that fix the beginning of a narrative; it only establishes the proportionality between the magnitude and the direction of a force with the acceleration a body acquires. One could just as well say that changes in force begin with changes in mass. To reiterate, as laws of coexistence, the Newtonian equations discussed above do not specify any regularly occurring beginnings, middle, and endings.  Up to now I have contrasted Wright’s narrative theory with algebraic equations that express laws of coexistence, such as , that clearly do not have a narrative structure. I announced above that there were other sorts of equations that seemed more promisingly story-like. Those are dynamical equations that express laws of succession.  As Sarah Otto and Troy Day put it: “Conceptually, dynamical equations track all the factors that cause a variable to increase or decrease over time” (Otto and Day 2007, 33). We solve dynamical equations to find numerical values for such increments or decrements of a variable, given certain background factors that produce it. A good example of a theory based on dynamical equations, and that will be important in Chapter 5, is mathematical population genetics. Among other things, this 	   43	  theory allows us to calculate the frequency  of a particular gene in the next generation , from data from the previous one, . We use an equation of the form  pt+1 = f(pt) . For example, where  be the frequency of allele  in generation , p is the frequency of  at time t,  is the frequency of allele  at time ,  is the fitness of the  genotype,  the fitness of the  genotype, and  the weighted average genotype fitness of the population, then   Dynamical equations such as these track changes of the values of the variables over time; they have this characteristic of narratives. But they do not represent any particular, causally connected sequence of events in the duration of a system, or any particular, causally connected sequence of states of a system.  The problem is not just with the “causally” part (I will return to that part shortly). What is non-narrative about these equations is that they do not specify any beginning events or states, and no ending states.  It may look as though the right hand side of the equation specifies the beginning states, since this is the side associated with the earlier time  while the left hand side specifies the ending states since it is associated with the later time . But no determinate values of the determinable properties are specified. Only the determinable properties of gene frequency, genotype fitness, and average population fitness are presented in the equation. This does not correspond to any state of the system.  In a similar way, one may think that giving an initial value for a dynamical equation specifies a beginning, and then an equation would be just like a narrative – a sequence of events with a beginning, middle and end. This overlooks the way in which 	   44	  the states of a system are characterized in a narrative. A narrative provides a setting with a combination of values of the determinable variables of the system that fixes a generalized beginning, e.g., there are many strongly interacting gluons, populations are subdivided into smaller groups and drift is stronger than selection in each group. At all times the processes in question begin at that configuration. The narrative fixes a generalized trajectory of the system with a beginning, middle, and end.  Dynamical equations can be compatible with stories where evolution starts with the frequency of  being very slow, and the fitness of  being negligible; they are also consistent where beginning states where the opposite is the case. There is generalization here, but no generalized trajectory through a state space. A narrative gives such generalized trajectory.  Dynamical equations such as the one above are story-like, since they “speak of time” (McCloskey 1991, p. 22). But they fall short. As Deirdre McCloskey so aptly remarks: “A differential equation involving time is in this sense neither fish nor fowl, neither a timeless metaphor nor pure story” (ibid.). Dynamical equations speak of time, but they are not stories. They are in the middle ground between zero narrativity and pure narrativity.30 In contrast, algebraic equations, exemplified by , exhibit zero narrativity, since they don’t even include the passage of time.31   	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  30 Perhaps when modellers are using those equations to study kinds of systems they have a full-fledged story in their mind. In this case the equations are already embedded in a narrative structure that encompasses the mathematical trajectories in state-space. Surely, there will be contexts where equations stand alone and what matters is to find a more general solution, a simpler formulation of a theorem, or the novel application of a mathematical technique.  31 But see note 4 above. Another context that shows how algebraic equations do not represent causal relations is that of structural equations modelling. As Judea Pearl has put it, such equations, e.g., linear regression equations, do not represent causal relations because they are symmetrical objects (…)” Pearl 2010, p. 84). They have to be supplemented with further representational structure that can capture the “directionality of the underlying processes” (Pearl 2012, p. 74). Either the equal sign has to be replaced with another symbol, or the equation has to be augmented with a “path diagram.” In a path diagram, 	   45	  Now, it is customary to read dynamical equations as representing the causal contributions of factors on the  side of the equation to the outcome on the  side. But, as we have seen, dynamical equations do not literally represent that. It is indicative of the importance of narrative causal thinking in science that we take for granted what is actually an added interpretation (added to the interpretation of the variables and signs of the equation).  There is one other sort of generalization thought to give scientific theories their generality, namely “if-then” conditional statements. Again, there is no question that such conditionals are indeed the basis of important scientific theories. But generalized narratives are different sorts of generalizations from conditional statements, and it is worth seeing how and why.  Take for example the standard, conditional version of Darwin’s theory of evolution by natural selection. Darwin’s theory will be discussed in much greater detail in Chapter 5. But a rough-and-ready, modernized (Mendelized), purely conditional version would be: in a large population, if genotype  makes its bearer fitter than either or , then allele  will increase to fixation.  Again, there is no particular, causally connected sequence of event-types or states specified here, although it may seem that there is. Note first that the conditional “if-then” is not the temporal or causal “if-then.” To be sure, temporality can be built in: “If  is in a state  at time , then  will be in state  at time .” Now it looks as if the specified beginning state or event is “  being in state .” But the conditional does not 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  “arrows are drawn from causes to effects (…)” (Ibid.). If we are investigating the possible causal influence of a variable X on a variable Y, “the diagram encodes the possible existence of (direct) causal influence of X on Y, while the equations encode the quantitative relationships among the variables involved, to be determined from the data” (Ibid.). Algebraic equations require a “causal reading” (ibid.), or a “causal interpretation” as James Woodward has put it (Woodward 1999, p. 199). Woodward and Christopher Hitchcock have put structural equation to work jointly and independently, in developing a counterfactual theory of causal explanation (Woodward 1999, Woodward and Hitchcok 2003). I leave a discussion of how such causal interpretation can be given in term of stories for another time.  	   46	  state that systems of the appropriate kind really do begin in state . The conditional states, “ If ….” Narratives, on the other hand, do not begin with “If….” They begin with particular events or states or a system – particular happenings.  As we have seen, generalized narratives like Wright’s theory specify particular events or states that a system of a certain kind begins with, e.g., population of intermediate size divided into subgroups of small size, small emigration and immigration values, etc. Wright’s theory does not state, “If a species is subdivided into small populations with minimal migration between them….” It specifies that evolutionary episodes begin with that state.  Having compared narrative with non-narrative generalizations in theories, let us now proceed to discuss approaches to theory structure that focused on theories formulated with the latter kind of generalizations.	   2.3 Approaches to Theory Structure Newton’s theory of motion and theories of mathematical population genetics have been paradigmatic examples of scientific theories for the two main philosophical approaches to theory structure, the so-called “received” or “syntactic” and the “semantic” views (Da Costa and French 2003).32 Those two analyses do not figure prominently in my thesis, mainly because narrative theories can be accommodated under either. It is worth briefly 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  32 The standard reference for an account of the development of the syntactic and the semantic approaches is Suppe (1977). An insightful and succinct discussion of the different approaches that comprise the semantic view can be found in Hughes (1996); and an equally insightful discussion of the two approaches and their applications to understanding physical theories can be found in chapters 1 and 3 of Hughes (2010). Hughes observes that the terms “syntactic” and “semantic” are often misleading when trying to differentiate the two approaches to theory structure. I agree, but will follow the standard use (Hughes 2010, p. 3, n. 9)   	   47	  showing how both approaches work as well for theories based on generalized narratives as for theories like Newtonian mechanics.  Let’s start with Newton’s theory (what can be said for Newton’s theory can be also said for mathematical population genetics, so I will only address Newton’s theory here. We can consider it as a system of axioms (Newton’s laws), and the empirical interpretation of those axioms. Newton’s theory is then regarded as a formal system with an empirical interpretation. 33 This, simply put, is the “syntactic” or “received view” of theories. Alternatively, theories can be viewed as “definitions or stipulations of kinds of systems” (Beatty 1980). Newton’s theory can be understood as a definition of the class of systems governed by Newton’s laws. As Ronald Giere has put it: “A Newtonian particle system is a system that satisfies the three laws of motion and the law of universal gravitation” (Giere 1984, p. 81).  Take now Wright’s theory. Under a syntactic characterization, it would consist of statements expressing that all organisms evolve in three phases, and specifying the beginning, middle, and end phases. Under the semantic approach, the theory would define a kind of system that evolves in the three stages stipulated by Wright’s narrative, just as I have presented Wright’s theory above.  Traditionally however, both the syntactic and the semantic views focus on general principles that take the form of equations or “if-then” conditionals. As we have seen, both of these kinds of statements are inadequate to express narratives as I have characterized then. And, as we shall see in Chapter 3, and again in Chapter 5, narratives may have equations and/or “if-then” conditionals embedded in them. But those narratives cannot be 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  33 The interpretation was partial; only of the so-called theoretical terms. For details see Suppe (1977).  	   48	  reduced to the equations and conditionals they include; those equations and conditionals are not substitutes for the narratives that embed them.  As an alternative to the syntactic and the semantic approaches, Carl Craver has suggested a third alternative, in order to account for what he calls “non-formal patterns” in scientific theories (Craver 2002). Craver is motivated by “theories about mechanisms,” which according to him exhibit such patterns. His examples from such theories come from brain neurophysiology.34  In his proposal for non-formal theory patterns, Craver states what he and other authors understand by a mechanism: “Mechanisms are entities and activities organized in such that they realize regular changes from start or set up conditions to finish or terminating conditions” (Craver 2002, p. 69). However, he does not explain what he means by a non-formal pattern of theory structure, other than saying that such theories are about mechanisms.  In making his proposal, Craver assumes that the syntactic and the semantic views are only applied to mathematized theories; and thus focus on formal patterns. While this is true historically speaking,35 the preceding paragraphs suggest that both conceptions of theories can be applied to non-formal theories, e.g., narrative theories. In arguing for a non-formal pattern of theory structure, Craver is really suggesting that philosophers should pay attention to theories of mechanisms as the latter notion is understood by him and the other proponents of the “new mechanistic philosophy” (Skipper and Millstein 2005, p. 327).  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  34 For more on the philosophy of mechanisms and its burgeoning literature, and how it provides a philosophy of neuroscience, see Craver (2007). The initial paper is Machamer, Darden, and Craver (2000).  35 In the sense that classical mechanics and quantum mechanics were the initial targets of analysis.  	   49	  My aim is not to discuss Craver’s account of mechanisms, but to highlight its narrative character. RIG Hughes (2010) has also highlighted the narrative character of mechanistic explanations.  More specifically, my claim is that the theories of mechanisms are formulated as generalized narratives, but not all narrative theories are theories of mechanisms in Craver’s sense. In particular, in Chapter 5 I will argue that Darwin’s theory of natural selection is a narrative theory but this does not imply that natural selection is a “mechanistic theory”.36   In order to see the narrative character of mechanistic explanations, let take a closer look at Craver’s example. He refers to the mechanism for producing action potentials, which are the electrical signals that propagate through neurons: Here is how the mechanism works (…). First a small initial depolarization of the membrane (resulting from electrical transmission at synapses or spreading from everywhere in the cell) repels the evenly spaced positive charges composing the α-helix. Second, the alpha helix rotates in each of the four proteins subunits composing the channel. The rotation of the helix changes the conformation of the channel, creating a pore through the membrane. Third, the pore is lined with a “hairpin turn” structure containing charges that select specifically Na+ ions to flow into the cell by diffusion. (Craver 2002, p. 69).   The mechanism, writes Craver, has active and temporal organization, and “shows an orderly sequence of steps (repelling, rotating, opening, and diffusing), each systematically dependent on, and productively continuous with, its predecessor” (ibid).  The generalized narrative structure is apparent: there is sequence of beginning, middle, and end event-types which Craver calls “steps.” And, as Craver remarks, each stage 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  36 Robert Skipper and Roberta Millstein have thrown convincing doubts, I think, on the applicability of the Machamer et al. (2000) notion of mechanism to natural selection. In arguing that Darwin’s is a narrative theory, I view natural selection as a process rather than as a mechanism in chapter 5. As I explained in Chapter 1, I agree with James Griesemer’s view that science tracks processes. Narratives contribute to that through representing  them. 	   50	  causally leads to the next. For Craver, mechanisms are systems than undergo changes of states. The narrative represents neuronal transmission as a sequence of causally connected event-types. Indeed, Stuart Glennan independently suggested that the narratives involved in mechanistic explanations are generalized narratives (2010, p. 263). I argue that Craver’s non-formal pattern of mechanistic theories is a narrative pattern. But as I remarked above, not all generalized narratives are representation of mechanisms of the Machamer, Darden, and Craver kind. In the rest of this dissertation, I will use “process” and “mechanism” interchangeably, e. g., the process or mechanism of natural selection.   2.4 Concluding Remarks Some scientific theories have generalized narratives at their core; and not equations, or “if-then” conditionals. This does not make them lesser theories; on the contrary, narrative theories are crucial to how scientists represent the general structure of processes by providing specific combinations of determinable values that characterize the states or events of a kind of system.  A narrative theory specifies a generalized trajectory in the space of states of a kind of system that begins at a certain kind of event, and ends at another kind of event. The trajectory is a story where each kind of event causally leads to the next.  As we saw, Wright termed “phases,” the events in his story, and Craver called them “steps.” In any case, the causal structure of processes is represented as a sequence of causally connected beginning, middle, and ending event-types in the duration of a kind of system.   	   51	  Theories with equations or if-then conditionals are used for explaining phenomena. This kind of explanation has been widely analyzed by philosophers of science, e.g., Carl Hempel’s deductive-nomological model. What has been hitherto overlooked is that scientists also use narrative theories to explain phenomena as the result of a sequence of causally connected event-types. This will be the subject matter of Chapter 3.  Accounts of narrative explanation in history and evolutionary biology have implicitly assumed that such explanations are based on particularized narratives, i.e., narratives that represent sequences of spatiotemporally bounded event-tokens. Consequently, narrative explanation has been pitched against explanations that use generalizations expressed as equations of if-then conditional statements.  Defenders of such explanations, e.g., Carl Hempel, attempted to reduce narrative structure to deductive arguments, and thought that narrative structure was explanatorily inert. As we will see, deductive arguments end up embedded in narrative structure. Narrative-based explanations are not at odds with D-N explanations, whether in particularized or generalized form. In both cases, D-N explanations will be embedded in narrative structure. I will argue that narrative structure does not reduce to the structure of a logical argument.         	   52	  Chapter 3: Narratives and the Problem of Explanation   3.1 Introduction  In this chapter, I return to the discussion of narratives in the literature of philosophy of science where that discussion ended, perhaps prematurely, in the 1970s.37 At that point it was argued that narrative explanation – to the extent that it really explained – could be reduced to Deductive-Nomological (D-N) or Covering-Law explanation, i.e., it could be shown to have the structure of an argument with general laws and particular conditions as premises and the event to be explained as conclusion.  I show that attempts by Carl G. Hempel and by philosophers of biology Michael Ruse and Mary Williams to reduce narrative to D-N arguments actually only succeed in reducing narratives to an irreducibly narrative sequence of D-N arguments.  The overall narrative structure of the resulting explanation is as important for its success as the D-N structures embedded in it, and it is irreducible in the sense that D-N arguments at later stages of the narrative do not follow deductively from D-N arguments at earlier stages. In general, narrative-based explanations, as I shall call them, will be consistent with certain laws or theoretical principles that together with suitable particular conditions will form the basis of D-N derivations within it.  In contrast, Hempel, Ruse, and Williams thought that narrative structure was explanatorily inert, and their explanatory role was parasitic on D-N structure.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  37 As we shall see, it was revisited by Mary Williams (1986).  	   53	  Philosophers working in other fields, notably history and evolutionary biology, argued that explanation in these sciences did not conform to Hempel’s model. They proposed a narrative form of explanation in response.  Defenders of the D-N model, beginning with Hempel himself, responded by showing how those narrative explanations could be made to conform to the D-N mold; they really had an implicit D-N structure. One just had to make it explicit. Two University of Toronto philosophers, William Dray and Thomas Goudge, propounded accounts of narrative explanation, the former in history (Dray 1954), and the latter in evolutionary biology (Goudge 1961).38  Although I will continue to use the term narrative explanation, I introduce the more general term “narrative-based explanation,” to think about any form of explanation that employs narrative representations of phenomena, i.e., sequences of causally connected event-tokens or event-types.  I will discuss only Goudge’s account, since it deals with explanation in evolutionary biology. Goudge’s example of narrative explanation is paleontologist Alfred Sherwood Romer’s “drying-pool” story of the evolution of land-life (Romer 1959, Clack 2002). Such story as we shall see, represents a sequence of spatiotemporally bounded event-tokens. Chapter 5, we will see examples of explanations based on generalized narratives that represent spatio-temporally unbounded events.  The crux of the debate to which I return centered around the question of whether narrative-based explanation such as Romer’s “drying-pool” account, could be reduced to 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  38 William Dray (1989) has provided an engaging account of the significance of Hempel’s work for the philosophy of history. James Lennox (1999) has done the same for the philosophy of biology. Paul Riceour offers a penetrating analysis of the discussion of the D-N model in the philosophy of history, and in the philosophy of narrative (Ricoeur 1983/1984, Part II, “History and Narrative”) 	   54	  a D-N argument. Following Hempel, supporters of the D-N model saw narrative explanations as concealed deductive arguments.  In section 3.2, I revisit Hempel’s formulation of the D-N model, and his defense of the latter from what W.B. Gallie called “genetic explanation.” In section 3.3 I present and discuss Romer’s account of the evolution of land animals. This sets the stage for my discussion of Thomas Goudge’s account of narrative explanation in 3.4, Michael Ruse’s criticism of Goudge in 3.5, and Mary B. Williams account of the logical structure of narrative explanation in 3.6.   I argue, that, contrary to their intentions Hempel, Ruse, and Williams end up embedding arguments within a narrative.39 Different D-N structures are embedded in the stages of the narrative; we end up with an irreducibly narrative sequence of D-N arguments. This is the subject of section 3.7, where I expand on the explanatory role of narratives. Specifically, in a narrative based explanation, the phenomenon to be explained is shown to be the end-event or stage of a sequence of events leading to it.  Narratives represent different kinds of processes acting at each event or stage, and leading to the next. In this sense, in their heuristic role, they are crucial in the exploration of causal structure. Interesting causal connections are identified, and the scientists can make sense of otherwise disconnected facts, as aspects of a single narrative (causal) structure.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  39 This holds for both particularized and generalized narratives. Romer’s narrative is restricted to a certain period of time, i.e., the Devonian, and to certain forms of organisms whose existence is supported by fossil evidence. Consequently, it represents a sequence of spatiotemporally restricted events  that took place during that period (which lasted millions of years), in particular kinds of systems. It is an example of a particularized narrative. In contrast, Sewall Wright’s narrative presented in Chapter 2, is not so spatiotemporally restricted, i.e., it is a generalized narrative. Narrative-based explanations employ both kinds of narratives. 	   55	  In this sense, I argue that studying narrative theorizing sheds light how scientists make causal sense of the world. Some concluding remarks are presented in 3.8.  3.2 Hempel on “Genetic Explanation” 3.2.1 The D-N Model  The philosophical discussion of explanation in the 20th century begins with Carl Hempel’s deductive-nomological model of scientific explanation, also called “covering-law” by William Dray (1971). Hempel formulated the main ideas of his account in 1942, in his paper “The Function of General Laws in History,” and presented a more formal account in his 1948 classic “Studies in the Logic of Explanation.”40  As we shall see below, Hempel’s view that historical explanation conformed to his view of explanation as a deductively valid argument with at least one general law and statements describing particular conditions as premises, and the event to be explained as conclusion, was a major input for the formulation of accounts of narrative explanation. But let us now see how, in their presentation of the D-N model, Hempel and Paul Oppenheim, perhaps inadvertently presented an explanation in narrative form. As an example of a phenomenon to be explained, Hempel and Oppenheim offer the following description: “A mercury thermometer is rapidly immersed in hot water; there occurs a temporary drop of the mercury column, which is then followed by a swift rise. How is this phenomenon to be explained?” (Hempel and Oppenheim 1948/1965, p. 246).  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  40 Coauthored with Paul Oppenheim, and published in 1948 (Hempel and Oppenheim 1948). It is included, along with Hempel (1942), in Hempel (1965). All citations in what follows are from Hempel (1965). Wesley Salmon has termed Hempel and Oppenheim (1948) the “fountainhead” of the problem of scientific explanation in his magisterial Four Decades of Scientific Explanation (Salmon 1990). 	   56	  The answer is as a sequence of causally linked events:  The increase in temperature affects at first only the glass tube of the thermometer; it expands and thus provides a larger space for the mercury inside, whose surface therefore drops. As soon as by heat conduction the rise in the temperature reaches the mercury however, the latter expands, and as its coefficient of expansion is considerably larger than that of a glass, a rise of the mercury level results. (ibid.)   Another example equally narrative in character is given in by Hempel (1965). In How We Think, Dewey (1933) describes a phenomenon he observed while washing the dishes. After removing glass tumblers from the hot suds and placing them upside down on a plate, soap bubbles emerged from underneath the tumblers, grew, came to a stand still and receded into the tumblers. Why did this happen? Here is Hempel’s rendering of Dewey’s explanation:  Transferring the tumblers to the plate, he had trapped cool air in them; that air was gradually warmed by the glass, which initially had the temperature of the hot suds. This led to an increase in the volume of the trapped air, and thus to the expansion of the soap film that had formed between the plate and the tumblers’s rims. But gradually, the glass cooled off, and so did the air inside, and as a result, the soap bubbles receded. (Hempel 1965, p. 336)  Again, there is a sequence of causally connected events that leads to a certain end-event. Hempel’s concern is with abstracting a common structural pattern of explanation in both cases: The explanation here outlined may be regarded as an argument to the effect that the phenomenon to be explained, the explanandum phenomenon, was to be expected in virtue of certain explanatory facts. These facts fall into two groups: (i) particular facts and (ii) uniformities expressible by means of general laws. (ibid.)41  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  41 In Hempel and Oppenheim (1948/1965), we can read: “From the preceding sample cases [of explanation] let us now abstract some general characteristics of scientific explanation” (p. 247). 	   57	  The first group of explanatory facts include, respectively: a) the thermometer is made of glass, it is partly filled with mercury, and it is immersed in water; b) the tumblers are immersed in soap suds at a higher temperature than the surroundings and they are placed upside down on a plate containing a puddle of soapy water. The second group of uniformities would be expressed by, respectively: a) laws of thermal expansion of the mercury and the glass; b) “(…) the gas laws and by various other laws concerning the exchange of heat between bodies of different temperature, the elastic behavior of soap bubbles, and so on” (Hempel 1965, p. 336).  The conjunction of statements expressing these kinds of explanatory facts forms the explanans (what explains). In short, the explanandum is a logical consequence of the explanans.  Hempel emphasizes that laws are not always explicit; they are only hinted at “by such phrasings as ‘the warming of the trapped air led to an increase in its pressure’” (p. 336). He asserts that even if laws are not mentioned in “this oblique fashion, they are clearly presupposed in the claim that certain stages in the process yielded others as their results” (ibid. Italics added).42  The italicized claim expresses the narrative character of the explanations in Hempel’s own words: an event is the result of a series of events or stages. But as it will recur in this chapter, this is not explanatory for Hempel. One stage leads to the next in virtue of laws that may be implicit, or only obliquely referred to in the narrative (my terms). Once laws are made explicit, the narrative sequence can conform to the logical pattern of a D-N argument.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  42 In his 1942 paper, one of Hempel’s main points was that even if historians did not appeal to laws explicitly, the latter were implicit in their explanations.  	   58	  For Hempel, narrative structure collapses into argument-structure. This makes the narrative superfluous, and leaves narrative structure explanatorily inert. Below, I present a D-N reconstruction of Dewey’s explanation, in anticipation of Hempel’s own reconstruction of “genetic explanation” in history. I will argue, to the contrary, that later stages of some narratives do not deductively follow from the beginning, and that not all narrative explanations are reducible to D-N arguments. Narrative structure does not collapse into D-N structure. I call this the no-collapse thesis.  Let’s introduce the well-known D-N schema. According to Hempel, explanations may or may not make explicit reference to laws, but if  “we imagine the various explicit or tacit explanatory assumptions to be fully stated, then the explanation can be “rationally reconstructed” as a deductive argument of the form:   (p. 336)   The L’s are laws, and the C’s particular conditions. The D-N schema lays out the structure of a D-N argument, as described above.43 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  43 Hempel uses “particular facts” or “antecedent conditions.” As Wesley Salmon (1984) has pointed out, the term “antecedent condition” does not necessarily have  a causal connotation. However, it is easily forgotten that the original formulation of the D-N model by Hempel  was explicitly causal (Kim 1999). Hempel  regarded explanations that employed deterministic laws, which are properly called “deductive-nomological,” or “covering-laws,” and explanation that employ “statistical, or probabilistic laws,” as arguments (Hempel 1962/2001). He expanded his deductive-nomological model into what he called “deductive-statistical” explanation, and “inductive-statistical” explanation. For my purposes, it doesn’t matter whether the explanation at hand is deductive or inductive-nomological. Indeed, the generalized narratives that we will discuss in the next chapter, embed statistical laws at the initial stage, and deterministic ones in the second stage. For discussion of the Hempelian models, see Salmon (1984, Chapter 2: and 1989), and the contributions by James Fetzer and Ilkka Niiniluoto to Fetzer (ed.) (2000). 	   59	  A D-N explanation “effects a deductive subsumption of the explanandum under principles that have the character of general laws” (Hempel 1965, p. 336). By pointing out this relation between the explanandum and the explanans, a D-N argument shows that “the occurrence of the phenomenon was to be expected; and it is in this sense that the explanation enables us to understand why the phenomenon occurred” (Hempel 1965, p. 337).  In other words, within the argument structure, the explanans confers “nomic expectability” on the explanadum (Salmon 1984), i.e., the latter is expected to occur in virtue of the laws or theoretical principles and certain particular facts.  Let us now reconstruct in Dewey’s narrative explanation as D-N argument. The first step is to make explicit the laws involved at each stage.44 In the first stage, cool air is trapped in hot glass and it is gradually warmed up (laws of heat transfer); in the second stage, there is an increase in the volume of the trapped air and an expansion of the soap film that had formed (gas laws); in the third stage, the glass and the air inside of it cool, causing the soap bubbles to recede (laws of heat transfer and laws of elastic behavior).  In this way, Dewey’s narrative would be reduced to a D-N argument, but notice that the resulting explanation is actually a series of D-N arguments embedded in a narrative sequence, or in other words, a narrative sequence of D-N arguments.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  44 But, as Hempel emphasizes (Hempel 1965, p. 412), the D-N and  “Inductive-Statistical” models “are not meant to describe how working scientists actually formulate their explanatory accounts (Hempel 1965, ibid.). They are logical reconstructions. Indeed, Erich Reck has recently argued, convincingly I think, that Hempel’s analysis of explanation is a case of Carnapian “explication” (Reck 2102, 2013).  How good the Hempelian model conforms to real life explanations is a problem I will ignore for the sake of discussion. Hempel himself admitted caveats, as deductions from laws needed further assumptions, which he called the problem of “provisos” (Hempel 1988, 1988/2000).  Hughes (2010), Chapter 1, offers a lucid critical discussion of Hempel’s model in the case of Einstein’s explanation of the perihelion of Mercury, and argues that idealizing and abstracting assumptions, different types of approximations, and unstated assumptions, make Einstein’s explanation a far instance of a D-N argument.  	   60	  As stated above, the overall narrative is not reduced to the argument; at subsequent stages, new laws and new particular conditions are introduced which are not deduced from the laws and particular conditions of the first stage.   Let  represent a stage of the narrative; we can symbolize the narrative sequence with the embedded D-N arguments as follows:   At each stage, , we have a D-N argument with laws, and initial conditions. For the narrative to be reduced to a D-N argument, the C’s of one stage correspond to the e’s of the previous one. If this holds, then the whole genetic (narrative) sequence reduces to the first stage. But as we saw above, this is not the case. New C’s are introduced together with new laws at each stage.  The explanandum event is not simply a logical consequence of the laws, the initial conditions, and the outcome of the first stage. It is the end event of a narrative sequence.  Still, it may seem as if, even if new laws are introduced, one can still express a narrative sequence as a D-N sequence. What one has is a logical sequence from the first to the end stage of the narrative; what matters is that there is a connecting law at each stage, just as Hempel supposed. The problem with this is that a representation of a narrative sequence as a D-N logical sequence abstracts from the different causal contexts that the narrative sequence connects. Contexts that take precedence over whatever laws that could come into play. As we shall see in the example of narrative explanation presented below, a narrative sequence connects different processes that occur at different events or stages. At such different events, different laws can be invoked. The resulting 	   61	  explanation is not a chain of deductions, but a story that connects causal scenarios. Moreover, for the explanation to be a chain of deductions, each new law and initial conditions have to be a deductive consequence of laws and initial conditions at the previous stage. But this, I argue, is not the case.  Dewey’s reasoning is not a logical deduction but a narrative that depicts a system undergoing a sequence of changes that end with the event to be explained: warming of the air, increase in volume, cooling of the air.  What is important is to see that the example that Hempel takes from Dewey involves both narrative and D-N elements. In How We Think, Dewey presents it as an example of “explaining an unexpected event” (Dewey 1933, p. 73), where an observer with some scientific education is capable of detecting “something odd or exceptional with the behavior of the bubbles” (ibid.).  The explanation is given in terms of “processes supposed to be operative” (ibid.). The connection between these processes is made by representing sequences of events in a narrative, and not by logical argument. Furthermore, different laws are applied in the order fixed by the narrative. To summarize: the D-N elements of the explanation do not make its overall narrative structure superfluous or explanatorily inert. A given D-N derivation, on the other hand, would leave unspecified which stage will follow out of several possible that could. What gives the D-N sequences coherence, what in the end makes them explanatory, is the narrative in which the multiple deductions are embedded.45 In the next section, we will see Hempel confronting narrative explanation via genetic explanation in history.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  45 That said, I am granting that D-N explanations can stand alone in some contexts, e.g., explanation using conservation or symmetry principles. 	   62	   3.2.2. D-N and Genetic Explanation  Hempel originally formulated the D-N or covering law model in a paper on the role of general laws in history (Hempel 1942). Philosopher of history William Dray has remarked that when “The Function of General Laws in History” appeared, “English speaking philosophy of history was in a somnolent state” (Dray 2000, p. 217), and has recounted how Hempel’s “simple and tough minded” message made an immediate impact in the field.46  The message was this: even if historians are concerned with particular events, their explanations – to the extent that they are explanations at all – make an implicit appeal to laws. For Hempel, as Dray points out, laws “must have a theoretical function in the explanation of historical events which is quite analogous to the one they have in explanation in the natural sciences” (op. cit., p. 218).   Hempel writes that, “in history no less than any other branch of empirical enquiry, scientific explanation can be achieved only by means of suitable general hypothesis, or by theories, which are bodies of systematically related hypotheses” (Hempel 1942/1965, p. 239).  Hempel’s message prompted reactions pro and con that Dray reviews (2000, p. 218-221). Interestingly, Dray observes that towards the mid 1970s, the discussion was beginning to shift gears toward narrative explanation: An early sign of the change was an increased preoccupation with narrative, first as the vehicle of explanation generally favored by historians themselves, but then for 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  46 This quote comes from “Explanation in History,” Dray’s contribution to a volume honoring Hempel, Science, Explanation and Rationality, edited by James Fetzer. Dray offers a superb analysis of the impact of Hempel (1942) on the field of the philosophy of history, and an effective and insightful guide to his vast literature. My debt to this paper, in setting the stage of this section, will be apparent in what follows. 	   63	  its own sake; and good work was done by Danto (1965, pp. 112-182), Mink 1970, and others in exploring the ways narratives can make a human subject matter intelligible, this both supplementing and challenging the view of it as serial covering law explanation that some of Hempel’s remarks had suggested. Reservations about the viability of narrative history expressed by Mandelbaum (1967; 1977, pp. 24-39) only served to fuel the discussion. (Dray 2000, p. 220)47    Dray observes that Hempel discusses “genetic explanation,” as a form of narrative explanation:  He [Hempel] doesn’t, however, consider the explanatory significance of narrative as such: he attends only to one form of it which he calls genetic explanation, in which a development is traced from a point of origin through a series of stages to a final result; and he endeavors to show that the explanatory force of such reconstructions is fully accounted by his general theory of explanation. (Dray 2000, p. 232)  The term “genetic explanation” was coined by W. B. Gallie to refer to explanations in history, and in the natural and social sciences, in terms of a developmental succession of stages, that didn’t conform to Hempel’s D-N model of explanation (Gallie 1955). This indeed suggests narrative structure, as a developmental succession can be thought as a causally ordered sequence of events.48 In this sense genetic explanation can be seen as a form of narrative explanation.  Here is Hempel’s description of genetic explanation:  One explanatory procedure, which is used widely in history, though not in history alone, is that of genetic explanation; it presents the phenomenon under study as the final stage of a developmental sequence, and accordingly accounts for the phenomenon by describing the successive stages of that sequence. (Hempel 1965, p. 447)  He cites an example from ecclesiastic history, namely the explanation of the practice of selling indulgences by the Christian Church. The explanation is made in terms of a 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  47 I include Dray’s references in the quote in the bibliography. 48 Since Gallie’s paper concerns historical explanation, I won’t enter into the details of his account to simplify matters.  	   64	  succession of events starting with the crusades, where promises were made for the absolution of the sins of those crusaders who died in battle, and proceeding through the times when the crusades were in decline, where new forms of indulgences were created to raise funds, and eventually the practice became established.   Hempel grants the importance of this kind of explanation in producing scientific understanding, but he is skeptical that mere temporal succession is explanatory: “the mere enumeration in a yearbook of “the year’s important events” in the order of their occurrence clearly is not a genetic explanation of the final event or of anything else” (Hempel 1965, p. 448).  Temporal succession has to be supplemented with nomological connection. Hempel sees genetic accounts as “basically nomological in character” (op.cit., p. 448). Explanations in terms of nomologically connected stages includes explanations of physical phenomena:   In a genetic explanation each stage must be shown to “lead to” the next, and thus to be linked to its successor by virtue of some general principle which makes the occurrence of the latter at least reasonably probable, given the former. But in this sense, even successive stages in a physical phenomenon such as the free fall of a stone may be regarded as forming a genetic sequence whose different stages – characterized let us say, by the position and the velocity of the stone at different times – are interconnected by strictly universal laws; and the successive stages in the movement of a steel ball bouncing its zigzaggy way down a Galton pegboard may be regarded as forming a genetic sequence with probabilistic connections. (Hempel 1963/2001)  The stages of a genetic explanation are connected by general principles that make a stage at least a probabilistic outcome of the previous one. Physics provides examples of genetic sequences governed by deterministic (“strictly universal”) and probabilistic laws. The genetic explanations of the physicist, Hempel would say, are “purely nomological” 	   65	  (ibid.); the complex genetic explanations of historians “combine a certain measure of nomological interconnecting with more or less large amounts of straight description” (ibid.).  It is not deduction plus particular conditions alone; further descriptions are needed that fundamentally define the relevant processes and their developmental links or connections. Hempel plugs in such additional descriptions into his schema to argue that genetic explanation has an argument structure.  A given intermediate stage in a genetic account will have some aspects of it evolving from the preceding stage by virtue of “connecting laws,” and it will have other aspects that are descriptively added because they are relevant to understanding subsequent stages. Here is Hempel’s D-N reconstruction of a genetic explanation: Thus schematically speaking a genetic explanation will begin with a pure description of an initial stage; thence, it will proceed to an account of a second stage, part of which is nomologically linked to, and explained by, the characteristic features of the initial stage, while the balance is simply added descriptively because of its relevance for the explanation of some parts of the third stage, and so forth. (ibid.)   Hempel presents in diagrammatic form “the way nomological explanation is combined with straightforward description” (Hempel 1965, p. 449) in genetic explanation, which I modify slightly:    Genetic explanation involves nomological and descriptive components (the D’s). Arrows indicate nomic connections between successive stages; the laws involved are not stated 	   66	  fully and explicitly and could be of a statistical kind. The S’s describe facts about a given stage that together with the laws explain the transition to a next stage S; the D’s represent additional descriptions of “further facts which are adduced without explanation, because of their explanatory significance for the next stage” (Hempel 1965, p. 450).  We have Hempel’s reconstruction of a genetic (narrative) explanation as a D-N argument. As in the Dewey example, what the reconstruction shows is a series of D-N arguments embedded in a narrative sequence. New particular conditions and descriptions are added at subsequent stages that are not strictly deduced from the laws and particular conditions at the first stage; D-N arguments do their work in a narrative sequence. The overall narrative does not reduce to a single D-N argument, and thus does not collapse into the latter. The collapse of the narrative (into a D-N argument) may be true in very simple cases in physics, such as that of free fall. One only writes Galileo’s law of free fall and the initial position of the body, no new laws need to be introduced or initial conditions added at subsequent stages. A narrative representation of the physical movement would clearly be superfluous.  But, as we saw in the Dewey example, different laws and different initial conditions have to be introduced at successive stages; later stages do not deductively follow from the first. There was not a single law + initial conditions connecting the first with the final stage. The same can be said of the case studies in Chapter 4, where the narratives were not deductively obtained from the equations plus particular conditions of the relevant theories (QCD, and QM).  	   67	  What Hempel obtains then is an explanation that consists in an irreducibly narrative sequence of D-N arguments, and in which the overall narrative structure is as important as the D-N structures embedded in them. A narrative-based explanation is not at odds with D-N explanation. Let’s recall that Hempel’s analysis of “genetic explanation” in history was a response to the challenge that such type of explanation did not conform to the D-N model of explanation. Another challenge to the D-N model came also from the philosophy of biology in the late 1960s, when the latter was only a nascent field. I now turn to analyze the scientific context of that discussion. The analysis will provide an illustration of how, in practice, narratives used for explanatory purposes can embed laws. The narrative-based explanation in question is Alfred Sherwood Romer’s “drying pool idea” of how land-life began (Clack 2002).   3.3 An Evolutionary Story  The example of narrative explanation that is discussed by the philosophers involved is Alfred Sherwood Romer’s account of why the early amphibians began to venture onto dry land. Here, I will give the reader a detailed view of what Romer’s explanatory project was about, so that we can appreciate its narrative nature, before we get to Thomas Goudge’s discussion of it.49  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  49 A discussion and assessment of Romer’s “drying-pool idea” in the light of subsequent and more recent developments can be found in Jennifer A. A. Clack’s superb Gaining Ground (Clack 2012), Chapter 4, p. 132-141. Clack highlights that several theories were proposed to answer the question, ““Why did the tetrapods come out of the water onto the land?” or as an alternative, “Why did tetrapods evolve limbs with digits?” (Clack 2012, p. 132), “at a time when data were even scarcer than they are now …” (ibid.).    	   68	  A central focus of Romer’s work was to explain large-scale events and trends in evolution in terms of the adaptive value of certain structures, as those could be discerned in the fossil record. His view of evolution is synthesized in this paragraph:   Evolution as seen in the fossil record is in its entirety a study of continual adaptive processes, for any feature of mutational nature which becomes well enough established in a group to appear in the fossil record is surely sufficiently advantageous to be considered an adaptation or is associated genetically with adaptive features in other structures and its functions. (Romer 1949, p. 103)50  A crucial event in the history of life was the invasion of land by vertebrates living in freshwater. This seems to have taken place 416 million years ago (Clack 2012), in the Devonian period, where primitive amphibians ventured onto land for the first time. Romer’s story is a response to the general question: “Why land life?” (Romer 1959, p. 93).  Land life involved the development of limbs, and the general question boils down to: Why should the amphibians have developed these limbs and become potential land dwellers?” (ibid.). For Romer, the answer has to involve the attribution of survival value to certain structures. The problem is how such attributions are made.51 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  50 I am quoting from “Times Series and Trends in Animal Evolution,” Romer’s contribution to the important volume Genetics, Paleontology, and Evolution, whose preparation was supervised by the Committee on Common Problems of Genetics, Paleontology and Systematics, established in February of 1943. As its name indicates, the committee’s mission was to foster interactions between biologists working on evolution at different time scales. It led to the foundation of the Society for the Study of Evolution, and the launching of its journal, Evolution, in 1946.  51 This is a problem for both the explanation structures of existing species, and in fossil structures. The relation between Darwin’s theory of natural selection and the fossil record has been problematic since the Origin of Species. The interest reader should consult the volume Adaptation, edited by Michael Rose and George Lauder (Rose and Lauder, eds., 1996), especially Chapter 10, “Paleontological Data and the Study of Adaptation,” by Michael Novacek. Romer’s story reflects his advocacy to the use of Darwin’s theory in paleontology.  	   69	  In 1941, Romer published Man and the Vertebrates, which was later revised and enlarged as The Vertebrate Story (Romer 1959). In the introduction to the latter book, he writes:  The story we are to tell is essentially an evolutionary one. We will be concerned mainly with the facts of the case, but one’s thoughts naturally turn to the problem of how these many marvelous changes and adaptations seen in vertebrate history have been brought about. A full discussion of evolutionary theory would take a volume in itself, but we may here give the bare outline of the situation. (Romer 1959, p. 4-5)  In emphasizing that the story is evolutionary, Romer attacks teleological accounts in terms of the “future adaptive value” of traits, which he deems unscientific. He wants to make an appropriate use of Darwin’s theory of natural selection in paleontological explanation.52   A passage from his 1967 presidential address to the American Association for the Advancement of Science (AAAS) is telling in this regard: How did the major evolutionary step from water toward and to land take place? Those who favor teleological interpretation insist that some divine or mystical driving force must have underlain this radical shift in habitus and structure since, they say, the development of adaptations fitting the fish descendants for future life on dry land would have no immediate adaptive value to a water dweller. Here, however, as in other cases, there is no need to call upon the supernatural, for it can be shown that under some special condition such adaptations could have been of immediate selective value. This special condition seems to have been seasonal drought.  (Romer 1967, p. 1633)53    Romer cites evidence from previous work on the late Paleozoic that shows the prevalence of seasonal droughts. Such droughts became prominent in the Devonian period, when amphibians made their first steps onto dry land: there was alternation between seasons of 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  52 This is, at any rate, how I interpret Romer’s project. 53 Romer gives as an example of such teleological interpretations L. du Nouy, Human Destiny (New American Library, NY, 1947). 	   70	  abundant rainfall and seasons where the “rains would cease, streams slow down, and ponds become stagnant” (Romer 1967, p. 1633).  The problem then is how to understand the evolution of legs in terms of their immediate, and not “teleological,” future adaptive value. “Why should a water dweller have these structures, so essential to land life?” (Romer 1967, p. 1633). The answer – writes Romer – seems to be that legs evolved “as structures which would aid a water dweller, under drought conditions, to continue his life in its own proper element” (Romer 1967, p. 1634). Romer succinctly expresses it:  The development of limbs and the consequent ability to live on land seem, paradoxically, to have been adaptations for remaining in the water, and true land life seems to have been, so to speak, only the result of a happy accident. (Romer 1959, p. 94)  Life on land was a not a direct consequence of the presence of limb-like structures in early amphibians. Such structures enabled those creatures to escape death out of a drying pond and seek other remaining bodies of water. They were not adaptations for future life on land. This came to be known as the “drying-pool idea” (Clack 2012). Romer’s story involves two types of organisms: primitive amphibians with moderately developed legs, which lived in the Carboniferous and Devonian times, and lobe-finned fish possessing lungs, crossopterygians, which had less developed limbs. It is a sequence of two events: first, there are organisms that have developed proto-limbs and use them to survive the drying pools by finding other bodies of water; second, limbs further develop as land was invaded.  It invokes particular environmental conditions in which early tetrapods lived. These have to do with the presence of “red beds” in sediments from the late Devonian 	   71	  period. The red color in layers of sandstone was due to the presence of iron, and it was taken as evidence of arid or semiarid conditions (Clack 2012, p. 133). As Jennifer Clack describes it: “Early theories of the origin of tetrapods suggested that these arid conditions caused a general drying up of the pools and lakes in which the lobe-fined ancestors of tetrapods lived, leaving the creatures stranded” (ibid.).  If pools remained under crowded conditions for extended periods of time, food supplies would be exhausted, and the water would dry out completely. The crossopterygians would die, but “the amphibian, with his newly-developed land limbs, could crawl out of the shrunken or dried-up pool, walk up or down the stream bed or overland, and reach another pool where he might take up his aquatic existence again. Land limbs were developed to reach the water, not to leave it” (Romer 1959, p. 94). The search for water opened up the possibility of the exploration of land: Once this development of limbs has taken place, however, it is not hard to imagine how true land life eventually resulted. Instead of immediately taking to the water again, the amphibian might have learned to linger about the drying pools and devour stranded fish. Insects were present by cold-swamps days and would have afforded the beginning of a diet for a land form. Later, plants were taken up as a source of food supply, while (as is usually the case) the larger forms on land probably took to eating their smaller or more harmless relatives. Finally, through these various developments, a land fauna would have been established. (ibid.)    Romer’s scenario was widely discussed in the light of new evidence and some its central aspects questioned. Clack has provided an instructive perspective:  The drying pool hypothesis was nevertheless widely accepted for many years. It gave rise to a variety of scenarios about how the changes to the limbs may have occurred, assuming that those changes took place between a fin like that of Eusthenopteron and a pentadactyl limb like that of the Permian temnospondyl Eryops …” (Clack 2012, p. 134).   	   72	  Romer’s story generated further stories on how limb-like fins changed into fully-fledged limbs. Some authors argued that Romer got the story wrong, e.g., that limbs were first acquired to burrow in the mud, and then to live on land (Orton 1954, cited in Clack 2012, p. 100). Clack gives a reconstruction of Romer’s story simplifying the scenario to just one kind of form: Building on the red-beds scenario, the next suggestion, by A.S. Romer (1933, 1945), was that those fishes whose fins were strongest and most resembled the structure of limbs, such as the lobed limbs of Sauripterus or Eushernopteron [both crossopterygians], were favored by a strong selective pressure on the animals to get back into the water. Those with more limblike legs were able to better to struggle over the dry surface and so were more likely to reach another pool. According to this idea [the “drying pool” idea], limbs actually arose to enable the animals to get back into the water, not to be better able to leave it, and Romer argued that it is not until the Carboniferous that truly terrestrial tetrapods are found (Romer 1958)” (Clack op. cit., p. 133).    Clack’s reconstruction highlights how the development of limbs was not prima facie an adaptation to terrestrial life. As it can be seen in Romer’s previous quotation, terrestrial life was a by-product of limb-like structures as adaptations that enabled their bearers to survive in water. The story depicts a scenario where limbs can have an early selective advantage before vertebrates were fully adapted to land; and where that early selective advantage opened of the possibility of land dwelling by the early amphibians. This is the theoretical significance of Romer’s story.  Romer’s explanation of the emergence of life on land is based on a narrative; a sequence of two events-tokens that are spatiotemporally localized (in a time span of 60 million years); first, the acquisition of limbs to get from pool to pool, and second (much later) the further development of limbs for life on land.  	   73	  We can see this most clearly when Romer replies to a critique by Robert F. Inger (Inger 1957) by appealing to the narrative structure of his account. Inger emphasizes the ecological factors involved in the origin of tetrapods, thinking that Romer’s account was a one-stage development. Romer replies:  Dr. Inger's views and mine are not actually as divergent as might be assumed at first sight. I heartily agree with him, as discussed below, in his major thesis that the development of vertebrate terrestrial life took place under favorable conditions of temperature, humidity and other environmental factors. The seeming contrast is due to the fact that he has synapsed into a supposed single event two chapters in tetrapod history: (1) the development of limbs giving the potentiality of terrestrial existence, and (2) the utilization of these limbs for life on land. These two steps need not have been taken synchronously and, I believe, were separated in time by many millions of years.” (Romer 1958, p. 365. Italics added.)  Inger contests the “red beds scenario,” and argues: “The ecological requirements of contemporary fishes and amphibians indicate that the continuously humid climate is the more favorable for invasion of the land. Furthermore the behavior and distribution of contemporary air-breathing, terrestrial fishes demonstrate that terrestrial habits are adopted in a continuously humid climate” (Inger 1957, p. 376).  Recall that the presence of limb-like structures in the first event opened up the possibility of life on land that took place millions of years later; it gave early amphibians “the potentiality of terrestrial existence,” to use Romer’s suggestive terms.    On the face of it, there is nothing in the second event, where proto-tetrapods invade land, that rules out the kind of ecological conditions that Inger is arguing for. On the contrary, ecology is a determinant factor in the second event of Romer’s narrative. If the full narrative structure of Romer’s account is taken into account, Inger’s criticism looses its force.  	   74	  As already stated, we have a sequence of event-tokens, in the duration of a particular system at a period of time in the past (the Devonian). In this sense it is a particularized narrative, even if the period of time lasted some 63 millions years.   The story allows Romer to establish a relation between two events that are million years apart, and in which limbs were not favorably selected for life on land in the first event. And it is compatible with biological laws; the first stage involves laws of anatomy and physiology that govern what animals with limb-like structures can do, and laws of inheritance and evolution, plus particular conditions that have to be specified regarding mutations of certain sorts and environmental conditions under which ponds can dry up. The second stage involves some of the same laws, and different values for the same kinds of initial conditions as in the first stage; different kinds of mutations and environmental conditions favorable for invasion of the land. The particular conditions of the second stage are added anew, and are not deduced from the particular conditions specified in the first stage, plus the laws of the second stage. Thus, the second stage is not deductively connected via laws and initial conditions with the first.  Even if the relevant laws were explicitly incorporated, Romer’s narrative would not collapse into a D-N argument. We would obtain the same kind of explanation of the preceding section: one with a narrative sequence of D-N arguments. Narrative structure is not explanatory inert.  In the discussion that follows, we will see an example of how Romer’s narrative can embed principles of population genetics, prompted by Michael Ruse’s pro D-N criticism of Thomas Goudge’s account of narrative explanation. Meanwhile, the discussion so far supports and generalizes a point that Marc Ereshefsky has made to the 	   75	  effect that “evolutionary theory and the Hempelian model are not at odds…” (op.cit., p. 96). Indeed, narrative-based explanation and D-N explanation are not at odds; a narrative-based explanation can have D-N elements embedded in it, but it is not reduced to a D-N argument.54  Let’s now move on to Thomas Goudge’s account of narrative explanation in evolutionary biology.   3.4 Goudge on Narrative Explanation  An initial proposal to show that narrative explanation did not conform to the D-N model was made by Thomas Goudge in Chapter 3 of The Ascent of Life (Goudge 1961).55 I have argued that the problem of narrative explanation vs. D-N explanation is best posed as the problem of whether narrative structure collapses into D-N structure. I have advanced a no collapse thesis in this respect.  I suggest that Goudge’s account is an early instance of a no collapse approach to narrative explanation. Goudge own’s motivation was to show that narrative explanation does not appeal to laws since, as a form of historical explanation, it appeals to unique, contingent conditions. That laws were not needed was the typical anti-DN move at the time, but as we have seen, laws and narrative explanation are not at odds.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  54 Marc Ereshefsky has addressed the “laws” side of the discussion I am to revisit here in Ereshefsky (1992, p. 83-39), in the context of clarifying what makes evolutionary theory distinctively historical (and distinct from physics). For Goudge, and more recently John Beatty (1985), evolutionary theory does not have laws. Goudge, on the other hand, and David Hull (1992) and Robert Richards (1992) after him, argued for the centrality of narratives in evolutionary explanations. Although I don’t emphasize the historical nature of evolutionary theory, Ereshefsky’s paper can be profitably read in conjunction with the next subsections. Ereshefsky’s argues, correctly I think, that both physics and evolutionary biology give explanations in terms of “incomplete generalizations,” and that this does not make the Hempelian model a “useless paradigm” (op. cit., p. 87-88). In my view, a narrative-based explanation can have D-N features, and the D-N arguments that are embedded in the narrative can all use incomplete generalizations as premises.  55 This chapter is based on his paper “Causal Explanation in Natural History” (Goudge 1958). 	   76	  As I read Goudge, his main point is that in a narrative, the event to be explained is not necessitated by the preceding events in the narrative, given the “contingent conditions.” As a causal explanation, narrative explanation involves both necessary and what Goudge calls “contingent contributory conditions.”  He characterizes the explanation in question: […] the explanation consists not in deducing the event from a law or sets of laws, but in proposing an intelligible sequence of occurrences such that the event to be explained ‘falls into place’ as the terminal phase of it. The event ceases to be isolated and is connected in an orderly way with states of affairs which led up to it. Thus the explanation proposed is a historical one (Goudge 1961, p. 72).   The event to be explained is the end-event of “an intelligible sequence of occurrences.” Goudge first outlines the necessary and contributory conditions that figure in Romer’s explanation. Statements of necessary conditions include “that amphibians must have emerged from water to become land-dwellers, that they must have found suitable food after they emerged, etc” (p. 73); statements of contingent contributory conditions, “that the amphibians walked up or down the stream or overland, etc” (ibid.). Those conditions are arranged in a “broadly continuous” temporal sequence. Such an explanation conforms to a mode of explanation adopted by historians. In order to explain particular episodes of human affairs, historians produce a “coherent narrative” of the relevant events. The historian arranges the events in a “significant order” to tell a likely story. “The narratives ‘pictures’ a certain temporal sequence of events” (Goudge 1958, p. 198). Goudge sees a parallel between the historian’s narratives and Romer’s own explanation: The aim is to make the sequence of events intelligible as a relatively independent whole. In a similar way, the explanatory pattern we are considering forms a coherent or connected narrative which represents a number of possible events in 	   77	  an intelligible sequence. Hence the pattern is appropriately called a ‘narrative explanation.’ (p. 75)  Romer’s narrative explanation is a sequence of events that constitute necessary and contributory conditions for the occurrence of the event to be explained. In terms of the preceding discussion, the contributory conditions have to be added at each event or stage of the narrative. A given stage does not deductively follow from the conditions of the previous one; new necessary and contributory conditions are added at each stage. In particular, the end stage is not a deductive consequence from the first. As we saw above,  Romer’s narrative-based explanation can embed different laws and different conditions (initial and contributory) at every stage.  Whatever necessary or contributory conditions there are, those would occur both in the first and in the second stage of Romer’s narrative. Goudge is right to argue the character of Romer’s account is not that of a deductive derivation, and in this sense I consider his a no-collapse approach. That a narrative is a “non-deductive sequence of events” is best understood as the thesis that narrative structure does not collapse into deductive structure. This happens because the initial conditions of the next stage do not follow from the laws and the end result of the previous stage.  Goudge early non-collapse approach was criticized by Michael Ruse (1971, 1973), who attempted to show that narrative explanation could be reduced to D-N arguments. Some years later, Mary B. Williams (1988), made another, very explicit attempt at reducing narrative explanation to D-N arguments. In the following section, I will argue that the no-collapse thesis applies both to both Ruse and Williams.   	   78	  3.5 Ruse on Narrative Explanation Michael Ruse’s analysis of Goudge’s account of narrative explanation is best understood within the context of his early philosophical project on evolutionary theory. Beginning with Michael Scriven in 1959, philosophers writing on evolutionary theory defied the then dominant physics-based, logical empiricist philosophy of science, of which Hempel’s D-N model was a prominent part. According to these writers, evolutionary theory didn’t fit the deductive mold, and evolutionary explanations were not of the D-N kind.56  Ruse reacted against this state of affairs, and his main motivation was to argue that evolutionary theory had a deductive structure and that evolutionary biologists didn’t have to abjure the D-N model of explanation. Central to this enterprise was the idea that, at the core of evolutionary theory were the laws and principles of the discipline of population genetics, which in turn contained the principles of Mendelian genetics. As Ruse expressed it: “Population genetics is presupposed by all other evolutionary studies” (Ruse 1973, p. 48). For Ruse, evolutionary theory was really not that different from physical theories.57  Evolutionary explanations, however, often didn’t make explicit use of the principles of population genetics, and for Ruse this only meant that those explanations were only part of a more complete evolutionary explanation that would incorporate 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  56 Besides Goudge (1961), see Scriven (1959), and Beckner (1968).  57 See Ruse (1977). The problem of whether population genetics principles are the basis for the rest of evolutionary theory, including macroevolution, was revived by the theory of “punctuated equilibria” in paleobiology (Cf. Charlesworth et al. 1982) 	   79	  them.58 D-N explanation in evolutionary biology applies the principles of population genetics.  At the beginning of Chapter 5 of The Philosophy of Biology Ruse writes: No one would deny that most evolutionary explanations as actually given do not satisfy the covering law model; but, one might want to ask, why should anyone deny that the model is in some sense an ideal – the ultimate goal of evolutionists? (Ruse 1973, p. 70)  And he eloquently summarizes what he hopes to achieve:  I hope that my criticisms reveal positive reasons for accepting the covering-law model in the context of evolutionary studies; but to conclude the chapter I shall explain why I find it intuitively implausible to suppose that evolutionary explanations have a model which is not that of the explanations of the physical sciences (whose model I take to be the covering-law model). (In this chapter I shall be arguing for the necessity of covering-law explanation, for it is against this that evolutionary theory has been used). (ibid.)59   These quotes hardly need interpretation. Ruse’s goal is to “see whether Romer’s explanation seems better understood in terms of the narrative or covering-law model […]” (op.cit., p. 83). As it turns out, given our discussion so far, Ruse’s critique of Goudge is hardly a problem for narrative-based explanation; moreover, it will allow us to show how population genetics principles can be embedded to Romer’s narrative.  According to Ruse, for Romer’s account to be explanatory, some questions it leaves open ought to be answered, and this requires appeal to laws (population genetic principles). Romer’s narrative leaves open why other possible outcomes did not evolve in response to the presence of droughts, such as the lung fish’s strategy for remaining in a dehydrated state of suspended animation at the bottom of dried-up pools.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  58 Ruse presents an example from David Lack’s Darwin’s Finches (1947) to this effect. 59 The applicability of the D-N model has been contested for physics itself, beginning with Cartwright’s “The Simulacrum Account of Explanation,” in Cartwright (1983), and continuing with, for example, Chapter 1 in Hughes (2010).   	   80	  Why did the amphibians not evolve that strategy is not answered by Romer’s account, and until this question is answered we won’t have explained the evolutionary event that did actually occur. Romer’s account, “taken in isolation,” is not an adequate explanation (ibid).  Examples of related questions are: “Why should the amphibians be able physically to develop limbs at all? Why, at first, was it so important for the amphibians to stay in water? Why later, even though there was food on land, did the amphibians not remain far more tied to their pools than they did?” (op. cit., p. 85).  I suggest that Romer would agree with Ruse that his story leaves these questions unanswered, and that answering them would require the principles of evolutionary theory. And he would remark that it was not the goal of his story to answer them; as we have seen, a central role of narratives is to generate questions that pose modeling problems.  Ruse’s main objection to Goudge’s is that he “fails to see how any of the questions posed can be answered without making some reference to laws” (ibid).60 This means the laws of population genetics: Consider the first question, why amphibians should be able to develop limbs at all? To answer this, even briefly, one must necessarily sketch some of the principles of genetics (particularly population genetics). One must explain the nature of mutations, how these affect the physical characteristic of organisms, how these can be passed on from one generation to the next, and how such new characteristics can spread throughout a group. (p. 85)  The answer is going to be based on the assumption that such principles also held for early amphibians; given that mutations today occur randomly relative to the “needs” of organisms, one would suppose that the capacity to develop land-limbs had nothing to do with the “needs” of the amphibians. Ruse goes on: 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  60 But note that even if there were reference to population genetic laws; the transition to legs won’t be the only possible outcome.  	   81	  Suppositions of this nature are clearly lawlike, since they are generalizations which one believes hold even in unexamined instances. That is, they are generalizations which are held to be empirically or nomically necessary. Hence, it would seem that one must appeal to laws to answer the question of why amphibians were able to develop limbs, and until this question is answered we do not have a sufficient condition for the evolution of land vertebrates. (ibid.)61  The same applies to the other two questions. For example, in order to explain why amphibians left water, one would have to invoke the notion of an adaptive advantage, which in turn requires the principles of the theory of natural selection as these figure “within that law-network known as ‘population genetics’” (p. 86).  So, for Ruse, as for Hempel, narrative explanation does appeal to laws. Ruse would agree with Hempel to the effect that laws make the connection between stages explanatory, and the narrative ends up collapsing into a D-N argument. In addition, Ruse introduces a novel twist into the discussion with his observation that the narrative raises some question whose answer requires the applications of the principles of population genetics. Romer’s narrative is compatible with the laws of population genetics, and can have D-N features embedded in it.  That narratives can have laws is not problematic; what is problematic is that this implies that narrative collapses into a D-N argument structure. This of course, was Ruse’s (and Hempel’s) unstated assumption.  Indeed, Ruse goes on to argue that narrative explanation has the structure of a deductive argument. Even if laws are not included in a narrative explanation, as the Hempelian schema requires, Goudge would need to use rules of inference that do include them. Otherwise, we would not have a way to ensure that the explanans be relevant to the explanandum. The rule in question (i.e. modus ponens) would appeal to laws in virtue of 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  61 The appeal to laws is “dual:” a) laws from which we infer that past organisms have genetic systems similar to those of contemporary organisms; b) laws of how such systems change over time. 	   82	  which, conditions forming the explanandum would be obtained from conditions that figure in the explanans.  Ruse’s proposal then is that an evolutionary explanation would have the structure:  Instance of s  Whenever we have an instance of s, we have an instance of E (Explanans) --------------------------------------------------------------------------- Instance of E (Explanandum)  In contrast, Goudge’s account in terms of a series of events with necessary and contributory conditions would force something like the following schema:  s. (Explanans) ---------------- E (Explanandum)   Goudge would be using an odd rule to the effect that if one has s one immediately has E.  Without laws, we must rely, says Ruse, on “esoteric rules of inference” (p. 93).62 On the face of this, Goudge has argued that the events in a narrative sequence did not follow deductively from one another, but his support for this was the absence of laws because of the contingent, contributory conditions.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  62 Recall my remark that Goudge was making narrative explanation depend on a deductive relation between the complex sufficient condition and the event to be explained. This is precisely the target of Ruse’s criticism. 	   83	  This, I emphasize was misleading. What blocks the reduction is the addition of new initial conditions, contingent or not, at each event of the narrative. A given event is not a deductive consequence of the previous event, and the end event is not a deductive consequence of the initial conditions and the laws of the first stage. Goudge’s emphasis on “contingent” conditions was in the direction of a no-collapse approach. Let us now discuss the other aspect of Ruse’s analysis that I have highlighted.  Ruse posed a series of questions arising in Romer’s narrative whose answers required the principles of population genetics. The questions pertain different stages of Romer’s story. Take for example, “Why, at first. Was it so important for the amphibians to stay in water?” (op. cit., p. 85); this question makes sense in the context of the second stage, together with he laws and the particular conditions used to answer it. Answering the question, leads to a D-N argument in the second stage.  Or consider “Why should the amphibians be able physically to develop limbs at all? This question pertains the first stage, as does the D-N derivation to which it leads. Ruse, as Hempel, hasn’t shown that Romer’s narrative is a D-N argument; rather he has shown how a sequence of D-N arguments can be embedded in a narrative order, where a D-N argument in the second stage is not deduced from a D-N argument in the first stage; the narrative does not collapse into a D-N sequence.  In asking questions that lead to D-N arguments within the narrative, Ruse allows me to emphasize that a narrative leaves open which specific laws to use. The specification of laws narrows down the narrative to a single course of processes from a range of alternatives. 	   84	  For example, Ruse’s appeal to population genetics and the spread of specific mutations assumes that the evolutionary transition was driven by discrete genetic changes. But it need not have been. Ruse could equally well have appealed to quantitative genetics, where limbs evolved by increasing musculature from the fins from standing variation. Or there could be a combination of large-scale discrete mutations and fine-scale changes in allele frequencies at numerous sites.  The point is that Romer’s narrative did not need to specify these choices, other than to say that whatever happened had to be consistent with evolutionary theory. This is why Ruse’s questions are left open.  Ruse clearly shares with Hempel the view that narratives are explanatorily inert, and that they collapse into a D-N argument once laws are made explicit.  Ruse, as Hempel, views the explanatory role of narratives as parasitic on whatever laws they might contain.  I have argued instead that narratives don’t collapse into D-N arguments and that they allow scientists to make causal links between processes without any commitments to specific laws or mathematical frameworks. In the case of Romer’s narrative, the phenomenon to be explained is not a deductive consequence of the theory of natural selection, but the by-product of selective pressures for continued survival in water.  Thus, contrary to what Ruse concludes, specifying the laws in a narrative explanation does not make the latter a D-N explanatory argument. Quite to the contrary, D-N explanation acquires a narrative character; D-N arguments are embedded in an irreducible narrative sequence. And, as we can see, D-N arguments bolster specific claims – support specific transitions – in Romer’s narrative-based explanation.  	   85	  What results is a picture that, I argue, is common in the explanatory practices of evolutionary biology and other natural sciences. Narratives capture causal connections in terms of a sequence of events, each event leading to the next. This allows scientists to represent the action of processes leading (although not necessarily) to certain outcomes, just as in Romer’s story. As we have seen, in order to answer such questions, the scientist develops new theory or appeals to an existing background theory.  In this regard, Ruse and Hempel before him were simply wrong. Narratives play an explanatory role by establishing a causal order of events that lead to a certain outcome. And they can have D-N elements embedded in them.  In closing, I note that Ruse comes close to admitting the co-existence of non-deductive and deductive forms of explanations. He refers to David Lack’s explanations of the origins and distribution of the Galapagos bird fauna, in his classic Darwin’s finches (1947/1983), a pioneer study of speciation and adaptive radiation. Lack does not make use of population genetics, and his explanations are not deductive derivations of the D-N type. They are, I hasten to observe, given in narrative form.  Just as he does in the case of Romer’s narrative, Ruse shows how Lack’s accounts can incorporate population genetic principles that flesh out a number of details that have been left out. Again, the problem with Ruse’s view is that narrative structure is explanatory inert.  Let us now move to Mary Williams’s account of the logical structure of a narrative explanation.   	   86	  3.6 Mary B. Williams on Darwin’s Historical Methodology In a paper published in 1986, Mary B. Williams presented an account of the logical structure of narrative explanation. Assuming the centrality of narrative explanation for Darwin’s historical methodology and the methodology of contemporary evolutionary biology, Williams will “delineate its logically respectable structure” (Williams 1986, p. 514). This already reflects the hidden assumption that narratives structure is explanatorily inert. Williams takes her clue from David Hull’s view that: “In historical narratives, an event is not explained by subsuming it under a generalization. Instead, it is explained by integrating it into an organized whole” (1975, p. 274).  For Hull, the “integration of an element into an overall pattern” is as, and perhaps more important than subsuming it under a law. Williams’s analysis “will give some insight into how an element is integrated into an overall pattern via narrative explanations” (op. cit., p. 514). I note that this is precisely the kind of explanations of biological phenomena we will find in Chapter 5 where, e.g., dominance will be explained by fitting it into the overall pattern of a generalized narrative. Investigating the logical structure of a narrative explanation, just as Hempel and Ruse did, Williams shows how narrative explanation integrates multiple D-N structures. This is right; but she concludes, “narrative explanations are covering law explanations” (p. 515). Narrative structure is reduced to D-N structure, and that the latter is what makes narrative structure explanatory.   In the light of the previous sections, I argue that Williams’s conclusion should be inverted; it is not that narrative explanations are covering law explanations. Rather, D-N 	   87	  explanations become and element of a narrative based-explanation. Indeed, narratives can sometimes encompass a multitude of alternative D-N arguments, as I argued above when applying population or quantitative genetic laws to limb evolution. They are integrated into the stages of a narrative.  Williams’ example of narrative explanation is again Romer’s narrative. She introduces a notion of “generic explanation,” as the D-N form underlying Romer’s narrative account. In a generic explanation, Williams argues, laws are involved in explaining the development of land limbs as a result of a selective process, which describes how a mutation conferring more efficient land limbs comes to be fixed in the species.  According to Williams, a generic explanation “is a sketch of a D-N explanation of the fixation of a single mutation which makes whatever limbs the population has slightly more efficient on land” (p. 517).  Like Ruse, Williams is narrowing the narrative by specifying certain population genetics principles that apply within it. Romer, as we have seen, did not need to specify, nor did he want to specify, the exact nature of the evolutionary theory underpinning the transition from one stage of the narrative to the next. He only needs to state the compatibility of the latter with the former principles.  For Williams, such principles are multiply applied in the course of the narrative explanation: “To explain the fixation of the multitude of genes which together generate efficient land limbs would require a multitude of similar D-N explanations” (p. 517). Williams’s generic explanation provides a D-N pattern that gets instantiated whenever a certain trait is explained as the result of a selection process: “the explanation of each 	   88	  actual fixation of a mutation increasing efficiency as land limbs is an instantiation” of a generic pattern (p. 518). She writes: Usually, a narrative explanation will have two or more generic explanations, one for each or a suite of complementary traits; for example, the land-limb generic explanation would be completed by an air-breathing generic explanation. The narrative explanation would then be sets of instantiations, by different mutations, of the different generic explanations. (p. 518)  Just as Hempel above, Williams’s generic (D-N) explanations would occur at successive events or stages of a narrative. She makes it clear that this is a description of the “underlying structure of the narrative explanation” (ibid); biologists provide explanatory sketches. The question now is how the multiple generic explanations are integrated into a single narrative explanation. It is worth quoting Williams in full: How are these separate generic explanations integrated to form a single narrative explanation? Note that the selective value of a mutation depends on which other mutations have already been fixed (e.g., the selective value of a muscle strengthening mutation is dependent on what bone strengthening mutations have already been fixed); because of this, the narrative explanation is not merely a set of instantiations of the generic explanations, it is a set of sequences of instantiations of the generic explanations. (ibid)  Narrative explanation is reduced to D-N explanation: narrative explanation is a set of sequences of instantiations of generic (D-N) explanations. Again, narrative structure collapses into D-N structure. But the no-collapse thesis generalizes to sets of sequences of D-N explanations, and the end event of the narrative – the explanandum event does not deductively follow from the beginning event.   Williams attempted reduction further illustrates a point that I made regarding narratives and D-N derivations in the previous section. Narratives allow imprecision as to the exact nature of specific genetic events that shape the evolution of limbs. It could be 	   89	  that the muscle strengthening mutations happens and fixes first, even though its selective advantage is smaller than if it happened later, after the bones changed.  Similarly, the narrative need not specify whether the genetic change had a large or small effect or whether the fish was iteroparous or semelparous, all details that would have to be specified in an actual model. The narrative qualitatively specifies determinate values for the determinable variables of the system; and this is compatible with alternative formal specifications via D-N derivations. The insights of a narrative explanation come from the order of events and the scenario it depicts via the qualitative specification of determinate values; as we saw in the case of Romer’s narrative, such qualitative specification shows where in the causal structure the mutations actually fixed need to be formally specified via the principles of population genetics. This is why Romer’s narrative-based explanation leaves wide open what the exact order and nature of the underlying genetic transitions is.  The explanatory role of narratives is not parasitic upon D-N structure, and narrative structure is compatible with different possible deductive chains. I will say more about this in the next section.   3.7 Narratives and the Problem of Explanation Explanation is a multifaceted and context-dependent enterprise. As Arthur Fine has put it, “what counts as an explanation can be expected to depend on particular features of the context of inquiry” (Fine 1989, p. 180). In this spirit, my approach has not been to argue for a specific account of explanation; the most general lesson to be learned from the 	   90	  preceding discussion is that what counts as an explanation involves both narrative and D-N elements.  A more specific lesson is that in some contexts, D-N explanation can be embedded in the order of a narrative that gives us the overall causal structure of a process. Explanations that employ narrative representations of the world I call narrative-based explanations. Now, I have argued that a narrative represents a sequence of causally connected events without specifying what I mean by “causally connected.” This, I suggest, varies from context to content. In characterizing a narrative as a sequence of causally connected event-types, no particular account of causation was presupposed. Causal relations between the events can be construed using for instance, Woodward’s interventionist approach (Woodward 2005), Salmon mark transmission approach (Salmon 1984), or the conserved quantity theories of causation (Dowe 2000), depending on the scientific context at hand.    So, although I am insisting that the events are causally connected, I am not offering an account of causal explanation.  Rather, I have used my account of narrative structure to characterize explanations as they are actually presented by scientists. In many situations, an explanation is offered in terms of a certain order in which things happen in the world.   Such explanations have a narrative structure. The order postulated involves certain processes acting at the beginning stage of the narrative, and other processes acting at the next stage. The stages are “causally connected” in the sense that something that happens in the beginning stage leads to the middle stage, and the happenings in the middle stage lead to the end stage. I take it that we can this at face value without having 	   91	  to determine with philosophical theory of causal explanation applies best to the case at hand.   This chapter has shown that narrative explanations can have D-N elements embedded in them. James Cushing has aptly termed D-N explanations “formal explanations,” i.e., the derivation of Kepler laws from Newton’s laws of motion and gravitation, of Boyle’s law from the principles of statistical mechanics, explanations in terms of conservation principles, and the existence of a polymorphic equilibrium under heterozygote advantage, are cases in point.63 These examples remind us that there are stand alone formal explanations; not all formal explanations are presented as part of a larger narrative, although they can be become so as science develops. Hempel, Ruse, and Williams only succeeded in reducing narratives to an irreducibly narrative sequence of D-N arguments. Narrative explanation can have D-N elements in it, but the overall narrative structure does not collapse into a D-N argument.  And a major outcome of the discussion is that there is a lot more to narrative-based explanation than historical explanation.64 Up to now, it has been taken for granted 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  63According to Cushing, “formal explanation” in the form of deductive arguments gives us “no understanding of what physical processes causes the planet to follow an elliptical orbit” (Cushing 1994, p. 13). Indeed, in the case of Newton’s theory, its success did not depend on determining which processes produced gravitational attraction. I add that if we want to understand what physical processes cause the planets to orbit we need narrative theorizing. Although understanding has not been prominent in the present discussion, in Chapter 1 and especially in Chapter 2, we saw how narratives were connected to the production of understanding or insight. I will return to this topic in the concluding chapter, to argue that narrative-based explanation yields causal understanding of phenomena.   64 A discussion of narratives in historical explanation, including historical explanation in evolutionary biology, is beyond the scope of this dissertation. On the historical nature of evolutionary biology, the interested reader should consult History and Evolution, edited by Mathew and Doris Nitecki (Nitecki and Nitecki, eds., 1982), and Gould (1989). Of relevance for the present discussion are the chapters by Robert Richards, David Hull, and Mark Ereshefsky. For a recent discussion of narrative explanation in history, see Carr (2008). Indeed, Carr’s paper is a contribution to a Forum on historical explanation in the February 2008 issue of History and Theory, that focuses on narrative explanation. A useful anthology of essays can be found in Fay, and Pomper, and Vann (1998). Contingency in historical explanation has acquired prominence in the literature. Indeed, the contrast between historical (or narrative) explanation and D-N explanation can be also seen in Stephen Gould’s view that the distinctive feature of history is 	   92	  that narratives are important only in historical explanation, and that the narratives in question are particularized. This chapter has shown that there are no grounds for this assumption.65  I argue that Romer’s narrative plays an explanatory role in virtue of representing a sequence of events that plausibly led to the emergence of land-life. A historical narrative (Hull 1992), such as Romer’s, represents a sequence of particular events (or event-tokens), in the duration of a particular system, at a specific period of time; in this sense it is a particularized narrative.66  In contrast, a generalized narrative, such as the one at the core of Wright’s shifting balance theory, represents a causally connected sequence of event-types or states undergone by a kind of system. At each event type, the system is in a particular kind of state at an unspecified time. Narratives play an explanatory role by showing a causal order of events in which the action of processes produces certain changes of state in a system.  Defenders of narrative explanation were at pains in characterizing what makes a narrative explanatory. Gallie’s view of a “developmental whole,” and Goudge’s view that 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  “contingency;” “A historical explanation does not rest on direct deductions from laws of nature, but on an unpredictable sequence of antecedent states, where any major change in any step of the sequence would have altered the final result” (Gould 1989, p. 283). A narrative exhibits such an unpredictable sequence of states, and the end state depends, i.e., is contingent upon, the antecedent states. Clearly, this is the case of Romer’s story when he says that the land invasion was a “happy accident,” i.e., it depended – it was contingent – on a particular sequence of events. Had the order of these events been different, it would have been another story. Gould’s “replaying the life tape” thought experiment has been analyzed and further elaborated by John Beatty (2006). Derek Turner has discussed Beatty’s paper in Turner (2011). For narratives, history and Gould’s contingency, see Beatty and Carrera (2011), and the references therein.  65 For an account of historical explanation in evolutionary biology that pursues narrative explanation as how possibly explanation, see O’Hara (1988). The topic of “how possibly” explanation in evolutionary biology continues to be debated, e.g., see Forber (2010), Reydon’s criticism of it (Reydon 2011), and Forber’s reply (Forber 2011).  66 It is important to keep in mind that the period to which Romer’s narrative is “particularized” goes from 416 to 359 millions years form our era; the events that it describes take place in the late Devonian, between 385 and 359 millions years. So, the duration of the system is very long indeed. Romer’s explanation is particularized in the sense that it is spatiotemporally restricted. 	   93	  a narrative formed an “intelligible whole,” are cases in point.67 In either case, what was needed was an account of narrative structure, or so I suggest. Whether Romer’s narrative can be considered a developmental or an intelligible whole, it plays an explanatory role by exhibiting a plausible sequence of events for the evolution of land dwellers. In Chapter 2 I argued that narratives are not reducible to equations or if-then conditional statements. In this chapter, I have argued that they do not reduce to arguments. Indeed, the power of a narrative representation of a process is that it is not constrained by D-N derivations that involve equations, or if-then conditionals. Ruse’s and Williams’ discussions provided hints of how population genetics principles could be applied in Romer’s narrative; but the application of population genetics in determining specific mutational steps, is not what made the narrative explanatory.  For Romer, all that was required was that the transitions between states of the system were consistent with evolutionary theory, but which specific theory was immaterial. Romer’s story is explanatory precisely in virtue of the causal sequence of events it represents, not in virtue of the laws that might be involved in a given change of state.  Narrative-based explanation and D-N explanation are not at opposed ends in either historical or non-historical sciences. In both contexts, theoretical derivations can do their work embedded in the explanatory order of a narrative. In the next chapter, we will see examples of narrative-based explanations that embed D-N derivations.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  67 David Hull (1975) also argued for the unity of historical narratives in terms of the unity of their central subjects, historical entities.  	   94	  All along in this chapter, I have kept in mind that narratives continue to be distinguished from D-N explanation in terms of their particularity. In his Basic Elements of Narrative, David Herman (2009) distinguishes narrative from D-N explanation, and writes:  Classical accounts of the CLM [Covering Law Model] do not address explanation might relate to narrative. Can there even be such a thing as a narrative explanation – given that narrative concerns itself with the particular and the contingent, with how specific things were, are or will be … versus how in general they have to be? (Herman 2009, p. 98).   This chapter shows that there is indeed such a thing: narrative explanations of how in general things have to be.  Another passage in Herman’s book deserves to be quoted: The previous examples raise general question about the status that narrative, as a radically particularized, non-quantitative mode of accounting-for, might have in fields of inquiry that traditionally rely on quantitative methods, such as evolutionary biology, physics, and neuroscience. But further research in this area should also explore whether stories shape (overtly or covertly) what might at first blush appear to be non-narrative modes of explanation. (Herman 2009, p. 103)   The case studies in this and in the next chapter, illustrate how particularized and generalized stories can shape a non-narrative mode of explanation, i.e., the D-N model.  After contrasting covering-law explanations with stories, Herman closed with a “coda” on the role of stories in science:  A key question is whether scientists use narrative as a vehicle for what remains at heart a descriptive and explanatory enterprise, or whether stories in fact play a fundamental, even constitutive, role in the work of science. (op. cit., p. 104)    I have addressed that key question, and have argued that narratives are not mere instrumental vehicles in scientific theorizing; narratives do play a constitutive role in scientific theorizing. Some narratives lead to mathematical theories, but they don’t drop 	   95	  out once the theory is in place; they are constitutive of the structure of theories. This chapter has shown how narratives are constitutive of scientific explanation.  Arguments cannot capture causal order; they only establish what conclusions follow from a set of assumptions. Where a narrative shows how a sequence of events in the Devonic period could have plausibly led to land faunas, the use of laws, e.g., those of population genetics, in a D-N argument narrows down the conditions under which such outcome could be obtained, e.g., the mutational steps involved in the evolution of limbs.  In closing I suggest a connection between the heuristic and explanatory role of narratives. By means of narrative theorizing, scientists explore a space of outcomes before (D-N) mathematical deductions are in place; they explore the structure of processes without being wed to a particular D-N formulation. The narrative suggests where deductions would be worth pursuing. In this sense, the heuristic role contributes to the explanatory role, which emerges when the exploration of the space of possibilities has yielded a particularly plausible account in the view of the theorizer.  Hempel’s examples of explanation were in narrative form, and this is no mere pedagogical strategy. It reflects that narratives are usually our starting point in our efforts to understand the world. The narrative structure of explanations leaves open how features of natural processes are connected in specific D-N arguments. And D-N arguments can play an explanatory role as elements of a larger narrative.  3.8 Concluding Remarks Narratives are constitutive of scientific explanation; in many contexts (but not all), explaining involves setting a generic order of events. Explanation involves both 	   96	  narratives and arguments. Narratives represent an overall causal structure that is investigated through D-N arguments. Their relation is mediated by the no-collapse thesis: narrative structure does not collapse into the D-N structure. In this way, D-N arguments can do their job in an irreducibly narrative order.  Arguing for narrative explanation as a form of explanation that does not employ laws, as Dray and Goudge did, set the wrong agenda for a philosophical understanding of narratives in scientific explanation and in theorizing in general.  Paul Ricoeur has aptly diagnosed the situation: “If we limit ourselves to saying that no explanation satisfies the covering law model and that there are causal analyses that are not explanations in terms of a law, we are in error” (Ricoeur 1983/1984, p. 127).  I share his preference: “This is why, for my part, I would prefer to emphasize the fact that laws are interpolated into the narrative fabric instead of insisting upon their inappropriateness” (ibid.). We have seen how laws, as premises of D-N arguments, are indeed “interpolated into the narrative fabric.”  In this chapter, I have revisited the first discussion on narratives within philosophy of science, as an initial chapter in the philosophy of biology. Bringing that discussion back to life teaches us that narrative-based explanation is not at odds with D-N explanation. Subsequent work on narratives in the philosophy of science appeared in 1999, this time on a case study from the history of physics. Narratives are no longer the province of historical sciences such as paleontology; they can be found as central elements of theoretical physics as well. To that I know turn.  	  	  	   97	   Chapter 4: Narratives in Physical Theorizing  4.1. Introduction So far I have given examples of a narrative theory, and of narrative-based explanation in evolutionary biology. Subsequent developments, however, have shown that narratives are also integral to theories in theoretical physics and economics, i.e., Stephan Hartmann’s “Models and Stories in Hadron Physics” (Hartmann 1999), Mary Morgan’s “Models, Stories, and the Economic World” (Morgan 2001), RIG Hughes’s “Theoretical Practice: the Bohm-Pines Quartet” (Hughes 2006), and Norton Wise’s “Science as (Historical) Narrative,” (Wise 2011).  In this chapter, I focus only on Hartmann’s and Hughes’s work, not only to simplify the discussion, but also as a way to forestall the view that narratives may play a role in less mathematical or less mature or in some other respect second-rate sciences like evolutionary biology, but not in physical theorizing.  Thus, in section 4.2, I discuss and further elaborate Hartmann’s and Hughes’s case studies, to argue that narrative theorizing is pervasive in physics.68 In section 4.3, I discuss the lessons to be learned more generally from narratives in physical theorizing, regarding the lessons from previous chapters.  Some concluding remarks follow in section 4.4. 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  68 Hartman (1999), Hughes (2006) and (2010). In “Models, Stories, and The Economic World,” Mary Morgan has also argued that stories are integral to models, and has discussed their role. Her work on narratives in economic models occupies two full chapter of her recent book The World in the Model: How Economists Work and Think (Morgan 2012, Chapters 6 and 9). Although I do not discuss her case studies in any detail here, I will compare her ideas to those of Hartmann and Hughes. 	   98	  Hartmann’s case study comes from the history of hadron physics, or the physics of the strong nuclear force. Hughes’s comes from the physics of plasmas and many body systems. In each case, an overarching fundamental theory was involved, namely, quantum chromodynamics (the theory of strong interactions) and quantum mechanics.  Despite the difference in contexts, Hartmann and Hughes reach some common conclusions from their analyses. First, in both cases narratives depict the structure of processes as sequences of event-types in certain kind of systems; secondly, the narratives are consistent with the fundamental theory, but are not derivable from then. The narratives involved are generalized narratives that are consistent with a theoretical framework, as the narratives of the previous chapters. Thirdly, narratives contribute to the understanding of the systems involved. In Hartmann’s case study, narratives provide a plausible mechanism for quark confinement; in Hughes’s, narratives provide a “physical picture” of the behavior of a physical system in terms of both its individual and collective aspects.    4.2 Narratives of Quarks and of Electron Gases. 4.2.1 Narratives in Models of Quarks Hartmann’s piece was his contribution to the volume Models as Mediators (Hartmann 1999), edited by Morgan and Margaret Morrison (Morgan and Morrison, eds. 1999). His case study is of “phenomenological models” that were used to investigate the consequences of quantum chromodynamics; by a “phenomenological model,” Hartmann means a simplified representation of a system, where the consequences of a fundamental 	   99	  theory can be explored.69 That said, I will not be making a distinction between theory and model in what follows. When I speak for myself, I will refer mainly to theorizing.  In “Models and Stories in Hadron Physics” Hartmann claims that “There is no good model without a story that goes with it” (Hartmann 1999, p. 344). He analyses a phenomenological model of strongly interacting sub-nuclear particles, or “hadrons” (“heavy particles,” i.e., protons, neutrons, pions) known as the MIT-bag model.70 Hadrons are made of quarks (and quarks are made of “gluons”), and the MIT bag model investigates a peculiar type of behavior known as “quark confinement.”71  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  69 The guiding idea in the Morgan and Morrison volume was that models provide knowledge that is independent from theory. Hartmann argues that one way in which models provide such kind of knowledge  is via stories that are not derivable from formalisms. Hartmann’s interest in stories/narratives is derivative from his interests in models. My emphasis is on narratives. For discussions o the notion of model, see Da Costa and French (2003), Morrison (2007), Bailer-Jones (2009), and Frigg and Hartmann (2012). Material models are discussed in de Charadevian and Hopwood (eds.) (2004). Giere (1999) provides an insightful discussion of the different notions of model and how they have been used in the philosophy of science. Hartmann’s notion of model corresponds to Giere’s “representational model.”  70 The MIT model was originally formulated in 1974 by five authors, all from the Laboratory for Nuclear Science, at the Department of Physics at MIT (Chodos, et al. 1974). It is part of a family of models of quark confinement which represent hadrons as bound states of quarks (Yndurain 1999). For a retrospective account of the MIT bag model, see Jaffee (1977). Hartmann has also discussed the MIT bag model as a case study of idealization in quantum field theory in Hartmann (1998). In short, proton and neutrons are "baryons" - "heavy" particles; electrons are light particles or "leptons" - which together with "mesons" form the hadrons. As atoms and molecules are held together by the electromagnetic force, protons and neutrons are held together by the "strong force." Once thought to be "elementary" particles, hadrons are now known to be made up of quarks, and the strong force involves interactions between quarks and also between the gluons that compose quarks. Just as electromagnetic interactions involve the exchange of particles called photons, the strong interaction involves an exchange of "gluons." And just as  a particle carries an electric charge, quarks carry what physicists call "color charge" to differentiate it from charge in electromagnetic interactions. The theory of strong interactions is then a theory of the dynamics of “color charge,” which is why it was baptized "quantum chromodynamics," or QCD. Quantum chromodynamics is the fundamental theory of the “strong interaction force” between quarks and gluons that binds them together in protons and neutrons and also holds protons and neutrons together in atomic nuclei. It belongs to the class of theories that result from the marriage between quantum mechanics and Einstein’s special theory of relativity, namely, “quantum field theories” (‘t Hooft 2007, Zee 2010). QCD is one of the pillars of the so-called “standard model” of particle physics.  71Asymptotic freedom, confinement, and "chiral symmetry" were part of the "experimental world" to which Quantum Chromodynamics was born. They were part of the "phenomena" of QCD  (Wilczek 1983, 2000b, 2004). Asymptotic freedom occurs in the high energy regime (short distances), and confinement and chiral symmetry occur in the low energy regime (long distances). By the time the MIT bag model was formulated, there wasn't a derivation of confinement from the principles of QCD, since the approximation techniques of QCD fail at long distances, where interactions get stronger and stronger. For historico-philosophical discussions of the significance of confinement for QCD see Pickering (1984) and Cao (2011).  	   100	  R.L. Jaffe, one of the authors of the MIT Bag Model, describes the phenomenon of confinement:  Quarks, however, have not been found free in nature; and if present theories are correct they will never be: they are thought to be permanently confined to the interior of the particles they compose" (Jaffe 1977, p. 201).   Quarks have never been observed in isolation, as “free quarks;” they come in triplets (baryons) or duplets (mesons). Despite the recalcitrant empirical evidence for it, confinement has not been obtained (has not been proven from) from the principles of Quantum Chromodynamics (QCD), the fundamental theory of strong interactions.72  In the MIT bag model, “the quarks making up a hadron are imprisoned in what may be called a bag …” (Johnson 1979, p. 112). Bags are regions of space that satisfy certain boundary conditions (e.g., energy conditions) to the effect that “no quark leaves the bag.”   The mathematical formalism of the model establishes such boundary conditions, but, as Hartmann emphasizes, some important questions are left open, such as: “How does a bag result physically?” Hartmann’s point is that the answer to this question is a story that represents a process of bag formation. Let us first look at the story, and then take a cursory look at the formal side of the model. Here is Hartmann’s description of the story:  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  72 This was particularly true by the time the MIT bag model was formulated. Quantum field theories are applied by means of approximation (perturbation) techniques that, in the case of QCD, fail at long distances (low energies regime) where interactions (and the coupling constant) get stronger and stronger. Thus the need for phenomenological models. DeTar and Donogue have expressed the situation: “In anticipation of further progress in understanding the large-distance behavior of QCD, various phenomenological models have been proposed that incorporate guesses at this behavior [confinement]. The MIT bag model is an example of such a model. It is elegant and simple" (DeTar and Donoghue 1983, p. 232). For differing views on whether confinement has been or not deduced from QCD see Zee (2010), and Wilczek (2000). A clear textbook discussion can be found in Yndurain (1999), Chapter 6. For historico-philosophical discussions of the significance of confinement for QCD see Pickering (1984) and Cao (2011). 	   101	  The story starts with a description of the initial state: In the beginning, there was only a highly complicated (‘non-perturbative’) vacuum with strongly interacting gluons. This is plausible from QCD. In the next step, a single quark is put in this messy environment. What will happen? Well, the quark will ‘dig a hole’ (to use the metaphoric language of physicists) in the vacuum by pushing the gluons away due to the repulsive color-interaction. (Hartmann 1999, 337)  A remarkable feature of QCD is that not only quarks have charge (color), but gluons also have charge (color) and then can interact. The state with lowest possible energy in QCD (vacuum) is filled with strongly interacting gluons. As Francisco Ynduráin has put it,  quarks move in a vacuum that is “in fact, a soup of gluons” (Ynduráin 2001, p. 158).  Or as Ulrich Mosel has described it: “This vacuum is not empty space but a very complicated state with an infinite number of strongly interacting virtual quarks, antiquarks, and gluons” (Mosel 1989, p. 217). In this state, the approximation (perturbation) techniques of QCD break down and this is why it is called “nor-perturbative” vacuum (Mosel, ibid.).  Assigning determinate values to the determinable properties of the system, physicists specify the beginning of the story of bag formation, e.g., there is an infinite number of strongly interacting gluons. In the second stage, a quark is put in that “messy environment.” Since like charges (color) repel, the quark will form a “hole” by expelling the gluons in the space around it and a “bag” is formed (Mosel, op. cit.).  The story represents a sequence of two events or stages whose specification of determinate values is consistent with what QCD says about hadron behavior; in particular about its vacuum structure. But the order of events itself is not fixed by QCD; the second stage does not follow from the first by QCD principles, but as an event in a narrative. Such sequence of event-types occurs in any hadron system.   	   102	  The story allows the theorizer to visualize hadrons as “bags” of quarks in the QCD vacuum (Mosel, op. cit.). This allows for a mathematical study of the properties of hadrons. As already stated, the qualitative specification of states can have mathematical specifications.  The formation of the bag leaves the system with two kinds of vacuum states: one “inside” the bag where QCD calculations can be performed (second stage); and the so-called true (non-perturbative) QCD vacuum of the first stage. The theorist can, for example, determine the relation between the pressure “ouside” the bag and “inside” it. The external pressure limits quark movement to the region “inside” the bag where they are confined. The difference between the energies inside and outside the bag is the “bag constant” B	  (DeTar and Donogue 1983, p. 237; Mosel op. cit.). Let us see how a formal specification of the bag’s properties would go, e.g., its total energy.73 The bag is a region from where no quark can leave; formally speaking this amounts to establishing appropriate boundary conditions on the bag surface, e.g., the flux of the quarks through the surface is zero. Inside the bag, quarks move “quasi-free,” i.e., interactions with other quarks are negligible.74  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  73 I adopt Hartmann’s exposition of the MIT bag model (Hartmann 1999, p. 335-336). Formaly speaking, “bag models” are a class of models which have in common that hadron are represented as bound states of quarks. DeTar and Donoghue list the MIT bag model, the Stanford Linear Accelerator Center (SLAC) bag model, and the soliton bag model (op. cit., p. 236). Se also Yndurain (op. cit.). My exposition reduces to the bare basics of the mathematical formulation.  74 This is a fascinating fact. Inside the bag (short-distance, interactions get weak) quarks move as “free particles;” they enjoy asymptotic freedom. See note 14 above. Hartmann describes this when he points out that the radius of the bag “reflects an equilibrium constellation: The pressure from the outside due to the non-perturbative gluonic interactions [the interactions in the low energy, short distance regime] balances the pressure from the motion of the quarks in the bag interior. Since there are no real gluons present in the inside of the bag, quarks move almost freely in this region” (Hartmann 1999, p. 337)   	   103	  Let  be the radius of the bag, and  the numbers that characterize the physical state of a single particle;75 the condition imposed on the bag yield the following energy values:    This considers a single quark. But hadrons are collections of  “valence quarks,” i.e., mesons that are made of a quark-antiquark pairs and baryons that are made of three quarks. Let us denote the collection ; ignoring interactions we write the total kinetic energy of the bag:   There is a potential energy coming from the external pressure that keeps the bag stable with no quarks out. Let B be the bag pressure, then the potential energy is:   The total energy of the bag -  - is the sum of the kinetic and the potential energies:  From here further relevant quantities are calculated, such as the equilibrium radius of the system and the total energy at the equilibrium radius.76 What is important for me is to highlight how the mathematical specification of the determinable properties of the system 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  75 Those are the “quantum numbers” that characterize the quantities that are conserved in a system: energy, angular momentum, spin, etc.  76 , the bag pressure is the only parameter of the theory, and has to be adjusted to obtain the values of the observables (mass, charge, etc). For details, see Hartmann (1999), DeTar and Donogue (1983), Yndurain (1989), and Mosel (1989).   	   104	  makes sense given the narrative that represents the stages of a mechanism of bag formation as states in the duration of a system.   At each stage, the story provides a qualitative specification of determinate values of the determinable properties of the system that can be mathematically investigated. Otherwise, how could the physicist think in terms of an external pressure that stabilizes the bag? The formation of the bag is a consequence of neither the equations of QCD nor the equations of the model, but of a sequence of events in a narrative.  So far I have analyzed the MIT story using the framework presented in Chapter 1. As a genuine story, it has a beginning fixed by a certain specification of determinate values of the determinable properties of the system; the initial stage leads to the next where a bag is formed. What about Hartmann’s account?  Hartmann described the story in terms of two steps, and I have spelled out the narrative structure involved. Here is how he further characterizes narratives:  A story is a narrative told around the formalism of the model. It is neither a deductive consequence of the model nor of the underlying theory. It is however inspired by the underlying theory (if there is one). This is because the story takes advantage of the vocabulary of the theory (such as ‘gluon’) and refers to some of its features (such as its complicated vacuum structure). Using more general terms, the story fits the model in a larger framework (a 'word picture') in a non-deductive way. (Hartmann 1999, p. 344)  By saying that a story is told around the formalism of a model, Hartmann has in mind physicists supplementing an already existing formalism with a story. Indeed, he motivates his paper with the following opening paragraph:  Working in various physics departments for a couple of years, I had the chance to attend several PhD examinations. Usually, after the candidate derived a wanted result formally, on the blackboard, one of the members of the committee would 	   105	  stand up and ask: “‘But what does it mean? How can we understand that x is so large, that y does not contribute, or that z happens at all?’” Students who are not able to tell a ‘handwaving story’ in this situation are not considered to be good physicists. (Hartmann 1999, p. 326)   The story is important “when it comes to finding out if some examination candidate ‘really understands’ what he calculated” (ibid.). Scientists resort to stories when they want to explain what their formalisms really mean. Hartmann argues that telling “a plausible story is also an often used strategy to legitimate a proposed model” (ibid.).  The MIT bag model didn’t have better empirical support than other competing models of the time, e.g., the Nambu-Jona-Laisinio model. Despite this, Hartmann argues, it gained acceptance because of the story that went with it. This is important, and suggests a more is important role for narratives than that of explaining what a mathematical formalism means. Indeed, it suggests the structural role that, I have argued, narratives play.  Not only can the doctoral candidate – or theoretical physicists in general – tell a story when asked what their mathematical results mean; sometimes, their mathematical results are embedded in a narrative that guides the development of the model. This is the case of the MIT model.  The story that goes with it is not told only to explain the model’s formalism; it constitutes the model. It represents the very system whose mathematical properties are going to be investigated.  In the MIT bag model, mathematical representation does it job embedded in a narrative representation of the physical (hadron) world. The narrative does not only play a heuristic role in motivating and guding the model’s formalism. Structurally, the system is represented by both narrative and mathematical structures.  	   106	  Hartmann has expressed his view in slogan form: “A story is therefore, an integral part of the model; it complements the formalism. To put it in a slogan: a model is an (interpreted) formalism + a story” (Hartmann, op.cit. Italics in the original).  This slogan is quite compatible with the threefold role I propose, with the following proviso: if the “+” sign is interpreted in terms of the structural role of narratives, the latter do not merely complement the formalism.  The MIT model is a “remarkably good one” (Hartmann op. cit., p. 336). What are the characteristics of a good story? What criteria do we have to assess the quality of a story? It goes without saying that the story in question should not contradict the relevant theory. This is a necessary formal criterion. All other non-formal criteria are of course, much weaker. Here are two of them: (1) The story should be plausible. It should naturally fit in the framework that the theory provides. (2) The story should help us gain understanding of the physical mechanisms. (op. cit., p. 344)  The MIT-bag story represents a mechanism of bag formation that is consistent with QCD, and this is what makes it plausible. Regarding understanding, Hartmann remarks: “It is very difficult to explicate how a model and its story exactly provide understanding” (ibid.) This calls for more than a complementary role for narratives, and begs the sort of constitutive role I have been proposing.   Through narrative theorizing, physicists could conceive a mechanism of quark confinement that was consistent with QCD; in this sense it was also a plausible mechanism. Such mechanism can occur inside a hadron. The structure of the mechanism was represented as a sequence of two event-types; one event leading to the next.  Through narrative theorizing, physicists envisage a way in which confinement can be produced in hadron systems: this provides understanding. Henk De Regt and Dennis 	   107	  Dieks have developed a “contextual approach” to scientific understanding that they use to address Hartmann’s question above (De Regt and Dieks 2005, p. 155-156).  Among the criteria for undertanding they include is visualisability. In their response to Hartmann’s question, De Regt and Dieks suggest a relation between stories and visualizability in the MIT bag model. This seems plausible, since narratives depict happenings in the temporal unfolding of processes or mechanisms in the world. I leave this connection for future work.  For the time being, let us ask whether narratives play an explanatory role in the MIT-bag case. Well, it will depend on whether one thinks that explanation is understanding, or wants to keep them as separate virtues.77 It would seem that the physicists that formulated the MIT- bag model did not explain confinement; through a narrative they represented a physically possible process that produces confinement, and this allowed a mathematical investigation of the properties of hadrons. Be that as it may, the MIT narrative allowed physicists to investigate the hadron world, given that at low energies and long distances the QCD machinery breaks down. In the next case study, narratives are used to provide a “physical picture,” of the behavior of a physical system, and will also produce understanding.     	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  77 On one side of the spectrum, Hempel thought that explanation produced understanding in the form of “deductive systematization,” and Michael Friedman and Philip Kitcher elaborated that in terms of unification (Friedman 1974, Kitcher 1981; for a review see Salmon 1989). Wesley Salmon thought that unification and fitting phenomena in a causal nexus with causal processes and interactions both contribute to understanding (Salmon 1998).  On the other side, a number of authors have argued that explanation and understanding are distinct (De Regt and Dieks 2005; see the essays in de Regt, Leonelli, Eingner eds. 2009). De Regt and Dieks motivation is that the kind of insight that produces understanding is not captured by extant philosophical accounts of explanation.  	   108	  4.2.2 Narratives and the Behavior of Electrons in Metals  This section will follow the same pattern of the previous section. First I will briefly explain the problem situation in which the story arises. Then I will analyze the story involved. After that, I will describe the formalisms associated with the story and provide a discussion.   The example at hand comes from R.I.G Hughes’s analysis of a series of papers by David Bohm and David Pines’s in the early 1950s, which he elegantly calls the “Bohm-Pines quartet” (Hughes 2010, p. 26).78 During the 1920s and 1930s, physicists studied gases containing a very large number of electrons and ions that exhibited a kind of organized behavior that was believed to be a new state of matter. It wasn’t solid, liquid, or gas; it was called “plasma” (Hughes op. cit., p. 30).   Bohm and Pines studied such plasma systems as they offered “a clue to a fundamental understanding of the behavior of electron in metals” (Pines 1987, p. 67).79 Thus Bohm and Pines developed a plasma theory of the collective behavior of electrons in metals, and their theoretical account provided a novel approach to many-body problems in physics.  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  78 The references to the Bohm and Pines papers can be found in Hughes (2010), Chapter 2. Hughes frames his analysis with the notion of a “theoretical practice:” shared assumptions (methodological, theoretical, etc) that “provide a normative framework for theoretical discourse” (op. cit., p. 26). Hughes’s primary aim is to identify and describe the different elements of a theoretical practice, e.g., the use of models, the use of theories, modes of descriptions (which include narratives), and the use of approximations. 79 This quote is from Pines contribution (Chapter 4) to a festschrift in honour to Bohm, Quantum Implications (Hiley and Peat eds., 1987). Pines provides a rich historical perspective on his work with his former PhD supervisor. Pines observes that a “plasma for the physicist is not a jelly-like substance. It is a gas containing a very high density of electrons and ions” (op.cit. p. 66). Plasmas became convenient systems to study “many-body” problems. As Pines indicates, interest in plasmas “grew because theoretical physicists came to recognize that an idealized model for a plasma represents a particularly simple, and often soluble, example of a many-body problem” (op cit., p. 67).   	   109	  The organized behavior of the plasma systems manifests itself in coherent high frequency oscillations known as plasma oscillations. Bohm and Pines starting point was that in such systems, with a density of 100 billions electrons per cubic centimeters, the electrons interactions produced the plasma oscillations.  Theoretical treatments of metals, in the late 1930s, assumed that electrons moved “independently” of each other, i.e., their interactions were completely ignored. In describing metals as plasmas, Bohm and Pines wanted to correct the previous “one-electron” model of metals and take account of the electrons interactions that gave rise to the collective behavior.80 Alexei Kojevnikov provides a concise and instructive summary of the significance of he Bohm and Pines papers: The results include the first mathematical account of many-body interactions of electron in metals, a demonstration of the limitations of existing individual electron theories; the conditions under which the individual-electron theory held, and an exploration why, despite its seemingly unnatural assumptions (disregarding the interaction between electrons, etc.) the agreement between the calculations of the old theory and experimental measurements was in many cases quite good. (Kojevnikov 2002, p. 186).   And Bohm and Pines’ conclusion to one of their papers gives us the flavor of their undertaking: Our main conclusion is that neither the collective description nor the individual particle description of the electron gas is by itself entirely accurate. For not only is each description needed in its appropriate region, but also the interaction between the collective and the individual aspects determines many important properties of the system. It is just this synthesis of individual and collective aspects that makes the electron gas such an exceptionally interesting medium (Bohm and Pines 1952, p. 339. Italics added).   	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  80 They also wanted to show why, despite its theoretical inadequacy, the one-electron model enjoyed empirical success. I am following Pines (1987) account; Hughes also gives the background to the Bohm-Pines quartet (Hughes 2010, Chapter 2, p. 29-31).  Alexei Kojevnikov (2002) discusses the historico-sociological context of Bohm’s approach to modeling collective behavior and the theoretical background to the Bohm and Pines papers.  	   110	  The synthesis of individual and collective aspects of behavior is at the center of their work. Indeed, such synthesis will not only have a mathematical description, but also a “narrative description” as Hughes terms it.81 Hughes finds such narrative description in a “physical picture” that Bohm and Pines offer as an explicit goal of their work; their aim is to “develop a detailed physical picture of the behavior of electrons in a dense electron gas” (Bohm and Pines 1952, p. 358).  For Bohm and Pines, a “physical picture is important “[…] because it is essential for the proper development and understanding of the necessary mathematical formulation” (ibid.). In my terms, Bohm and Pines provide a narrative representation of the physical process they mathematically investigate. As we shall see, it is a narrative that exhibits the “synthesis” of collective and individual behavior: how the electron gas system goes from individual to collective behaviour.  Here is the physical picture that Bohm and Pines provide: On the basis of the above results [the mathematical description of the collective and the individual aspects of the system] we are led to the following physical picture of the screening process. As any electron moves through the assembly, the other electrons are pushed away from it by the Coulomb repulsion. Each particle is thus surrounded by a cloud of extent  [the Debye length], in which there is a deficiency of electrons, which is responsible for screening the field of the particle in question. As a result of this screening, the cross section of the interparticle collision is so greatly reduced that the mean-free path of an electron is considerably greater than the interparticle spacing. Thus for many purposes, the electron plus its associated cloud may be regarded as an effective free particle (Bohm and Pines 1951, p. 339).82 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  81 According to Hughes, the narratives that depict the physical picture comprise one of three “modes of description,” along with the physical and the mathematical descriptions. The physical descriptions are in English, augmented by the vocabulary of physics, and couched in terms of “electrons,” “fields,” and so on” (Hughes, op. cit., p. 56-57).  The Hamiltonian of the system being modeled provides the mathematical description. I will discuss the Hamiltonian below.  82 In physical terms, the “Debye length” determines the transition from individual to collective behavior. That is the radius at which electric fields produced by individual electrons can be "screened out." Outside of this region, the collective aspects of the system become significant. At distances greater than the Debye length, electron-electron interactions screen out the fields produced by individual particles, making the 	   111	   As in the hadrons case, the story represents a causally connected sequence of event-types of a kind of system (an electron gas). It fixes a beginning kind of event by specifying a certain set of determinate values of determinable properties (electron density, energy, forces).  The system begins at a state with many electrons (high electron density) moving through the gas, and pushing away other electrons by Coulomb repulsion (like charges repel).  A cloud is formed that surrounds each electron and co-moves with them and screens off the influence of the fields produced by the other electrons. This leads to a state with a low density of electrons in the neighborhood of the individual particles. Inside the cloud an electron moves freely (interactions are negligible). Outside the range delimited by the radius of the cloud, collective behavior in the form of organized oscillations is brought about by the long-range part of the Coloumb force. The onset of the oscillations is the last event-type of the story.  Here is Hughes’s description of Bohm and Pines’s physical picture:   It provides, in a vocabulary markedly different from the one used in descriptions obtained from the system’s Hamiltonian, a summary of results already achieved. Organized oscillations are brought about by the long range part of the Coulomb interaction. Each individual particle suffers small perturbations arising from the combined potential of the other particles. Comoving clouds screen the field of 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  latter's effects negligible. This marks the onset of collective behavior that manifests itself in the form of plasma oscillations that propagate unperturbed by the Coulomb fields of individual electrons. In contrast, at distances shorter that the Debye length, electrons move as "free particles" due to the repulsion effect of the Coulomb force on the neighboring electrons. This neighboring region forms a "cloud" that "co-moves" with an electron and has a uniformly distributed positive charge, according to the model of plasma that Bohm and Pines adopted. The clouds screen the particles' fields inside the Debye radius. As Bohm and Pines explain it, in this region, "an assembly of effectively free particles" interact "only through the short range part of the Coulomb force. The screening of the field of a given particle is actually brought about by the Coulomb repulsion which leads to a deficiency of electrons in the immediate neighborhood of the particle [the "cloud"]" (Bohm and Pines 1952, p. 351).     	   112	  each particle. This screening is brought about by the Coulomb repulsion, which leads to a deficiency of electrons in the neighbourhood of the particle. The same process also leads to a large reduction in the random fluctuations of the density in the gas at large wavelengths. (Hughes 2010, p. 60)  Hughes emphasizes the description of causal processes: “Though it appears late in the second paragraph, the key word here is “process.” The behaviour of the electron gas is described in terms of causal processes, whereby one thing brings about, or leads to another” (ibid. Italics in the original).  In emphasizing the descriptive aspects, he can tell the story backwards, beginning with the end i.e., the bringing about of organized oscillations. But Hughes is clearly referring to the narrative structure of Bohm and Pines’s picture.  As described above, the narrative depicts the processes that bring about collective behavior in a sequence of stages that correspond to event-types that the system undergoes. It characterizes particular beginning, middle, and end states by specifying determinate values of determinable properties: high or low density of electrons, short or long range of the Coulomb force, small perturbations on individual particles, etc.  The narrative begins with a combination of determinate values of the determinable variables: high density of electrons where each particle is slightly perturbed by other particles and ends with the manifestation of collective behavior with another specification of determinate values: sustained oscillations as distances larger that the radii of the clouds. Since the whole processes is represented as a sequence of event-types,  the narrative exhibits the synthesis – so important for Bohm and Pines – of collective and individual aspects of electron behavior as changes in the states of the system. This is 	   113	  important, since, as Bohm and Pines knew well, the mathematical descriptions of the process do not represent such synthesis.    Let us now take a look at two basic aspects of the formalism, namely, the equation representing the collective and individual behavior, and the Hamiltonian representation of the system. The basic notion in the mathematical description of the system is electron density (number of electrons per unit volume).  Bohm and Pines study the variations in electron density due to the repulsive nature of the Coulomb interaction between electrons, which "act like variations of pressure on air, and can be transmitted through the electron gas as plasma oscillations" (Hughes 2010, p. 34). As Pines explained, it was necessary to find the collective variables, and then "to devise a mathematical formulation in which both collective and individual particle variables appeared" (Pines 1987, p. 74).  So, one aspect of the mathematical representation involves electron density as a collective variable; the authors investigate density fluctuations at different wavelengths (Hughes 2010, p. 34-35). The main result is an expression that is the sum of two factors that represent the contributions of the collective aspects of electron movement (oscillations) and the movement of electrons as individual, “free” particles. The latter contribution is understood as the random thermal motion of the electrons: The behavior of electrons in a dense electron gas is analyzed in terms of the density fluctuations. These density fluctuations may be split into two components. One component is associated with the organized oscillation of the system as a whole, the so called "plasma" oscillation. The other is associated with the random thermal motion of the individual electrons and shows no collective behavior (Bohm and Pines op. cit., p. 338).   	   114	  Thus, each component  of the electron density is expressed as the sum of two parts: the collective coordinate, and  the individual coordinate. The first oscillates harmonically; the second represents fluctuations resulting from the random thermal motion of individual electrons:  ( = Constant). As Hughes explains, at a more fundamental level, the mathematical description of the system is provided by its Hamiltonian, which represents its total energy, i.e., the sum of kinetic plus potential energy. A Hamiltonian H can be written as the sum of terms, each representing a different source of energy in the system, e.g., kinetic, electrostatic potential energy (Hughes 2010, p. 51; Kible and Berkshire 2004). Bohm and Pines specific problem is to write a Hamiltonian in terms of the individual and collective behavior of the system that will have different energy levels. As an example, here is one of the Hamiltonians they obtain:83  The first term represents individual electrons; the second the collective oscillations; the third, a very weak residual electron-electron interaction (at short lengths electrons are screened off from each other). This equation is used to calculate certain quantities, e.g., the energy of the system at the ground state.  The mathematical descriptions in the Bohm-Pines quartet represent the system as a sum of individual and collective terms, and track the corresponding density fluctuations. The narrative in contrast, fixes a beginning by means of a qualitative specification of determinate values of the determinable variables that leads to a second 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  83 I simplify the notation for the sake of discussion. Bohm and Pines use  (Hughes 2010, p. 42) 	   115	  stage that ends with the onset of collective behavior. The mathematical formalism provides us with the energy values corresponding to individual motion and collective motion.  We can see how the narrative “is essential for the proper development and understanding of the necessary mathematical formulation.” (ibid.). The mathematical formulation provides the energy values that correspond to individual or collective behavior, but remains silent on how the system undergoes change from individual to collective behavior.   The narrative guides the development of the formalism; it shows the structure of the processes whose mathematical properties are being investigated. For Bohm and Pines, the formalism is understood insofar as they have a “picture” of the structure of the processes they are investigated. Such picture is provided by a narrative.  The equations are used to tell the story of the synthesis of individual and collective behavior. But the equations themselves do not tell that story: they do not fix a beginning that leads to a middle that leads to an ending kind of event.  In terms of my threefold approach, the Bohm-Pines case study involves heuristic and structural roles for the narrative. Bohm and Pines’s picture of physical behavior guided the development of their formalism. As in the MIT bag model case, the narrative that provides the picture does not drop out when the formalism is in place, and Bohm and Pines offer it as an integral part of their theoretical framework. Their theorizing requires both the narrative and the mathematical framework; the former is part of the structure of their theory.  	   116	  In depicting the “synthesis” of individual and collective behavior, the narrative provides understanding of what process the formalism is about. In this case, this kind of understanding does not seem to be related to explanation. Be that as it may, narratives are constitutive of the Bohm and Pines’s theoretical framework.  More generally, Hughes writes on narratives:   Descriptions of this kind - 'narrative descriptions', as I will call them - are used throughout physics. Although their closest affiliation is with the theoretical manifolds of classical physics, within theoretical practice they are effectively independent of 'high theory', and as in the present case, can coexist alongside theoretical manifolds of many different persuasions. And for obvious reasons, they are the lingua franca of experimental practice. (Hughes 2010, p. 61)  Hughes last remark refers to the side of scientific practice I don’t discuss in this work. I take it that the “obvious reasons” have to do with a narrative’s capacity for representing processes. Indeed, tracking processes is one central task of experimental practices (Griesemer 2010).  In closing, it is interesting to quote a footnote to the text just quoted: The importance of narrative descriptions has been emphasized by several authors. Stephan Hartmann (1999) has drawn attention to the contribution they make to hadron physics. He calls them simply ‘stories”. The narrative mode also undergirds a different account of physical science. Peter Machamer, Lindley Darden, and Carl Craver (2000) have shown that our best account of neuroscience is in terms of mechanisms, and the descriptions they provide of mechanisms are narrative descriptions. (Hughes 2010, p. 61, n. 53)   Just in the spirit of this dissertation, Hughes sees a broad role for narratives in natural science. In Chapter 2 I argued that, in effect, theories of mechanisms are generalized narratives.  In sum, the picture arising from the Bohm and Pines case study is as follows: the mathematical theory establishes the properties of the system, e.g., energy values for the 	   117	  collective and individual aspects of the behavior, and the narrative provides the overall causal structure of such behavior.  Let us now take stock on what we have discussed so far.   4.3 Taking Stock As it was observed in Chapter 1, within analytic philosophy, narratives have been the province of the philosophy of history and the philosophy of biology. But as the examples discussed in this chapter help to illustrate, narratives have played a role in theoretical physics as well. Theoretical physicists are not only interested in calculating and predicting; they are also interested in representing the causal structure of the processes underlying their formalisms, and this is where narrative theorizing becomes important. The MIT bag model, and the Bohm-Pines quartet are two cases in point.  As Hughes remarks, narratives and formalism coexist; and I argue that theorizing involves and interplay between narrative and mathematical representation. In the examples studied, the narratives guide and motivate the development of the formalisms and form an integral part of the theoretical frameworks.  However, their role doesn’t terminate once the formalism is in place, as it is customarily supposed. They don’t only play a heuristic role. As an integral part of the structure of models and more complex theoretical frameworks, such as Bohm and Pines’s, narratives are crucial tools in the theoretical representation of processes.  That narratives play a structural role gives further philosophical significance to Hartmann’s observation that they are not derived from the formalism of models or 	   118	  theories. If they were, they wouldn’t constitute a way of theorizing of their own. This is reinforced by my claim, in Chapter 2, that narratives are not reduced to equations.  Equations and narratives are different kinds of representations and produce different kinds of insights. Both are needed in research. Explanations, it was argued in the previous chapter, often involve both narrative and formal (D-N) elements. Equations are used in telling stories, but they don’t tell stories, nor stories are derived from them.  I have emphasized that narratives do not play a role only by complementing formalism; they influence their development and become and integral part of the structure of the theoretical frameworks.  We see have seen two examples from theoretical physics, where narratives coexist with formalisms of many sorts, and the formalisms are understood in the light of the narrative structure. And sometimes, stories drop out once the mathematical framework is in place.  For Hartmann and Hughes, stories are integral to the MIT bag model and to the Bohm-Pines framework. I have used my threefold role approach in order to further articulate their views, and provide support to my thesis about the centrality of narratives in scientific theorizing. Stories are not auxiliary devices that one can dispense with once we have mathematized theories, or use just to explain what formalisms mean.  There is, however, an important difference in Hartmann’s and Hughes’s approaches to their case studies, that should not be obscured by my discussion in this chapter.  Hartmann’s analysis shows narratives as essential to what Mary Morgan calls model creation and model usage. The story told with the MIT bag model, provided 	   119	  understanding of how confinement could be produced in a way that was consistent with QCD. This, according to Hartmann, was crucial to the acceptance of the MIT bag model even with little empirical support over other competing models.  Hughes’s approach, in contrast, is to analyze the Bohm and Pine series as a “theoretical practice,” and identify its elements.84 As we have seen, he identifies a form of narrative description as an element of the Bohm and Pine’s theoretical practice. This, I have suggested, can be read as establishing a structural role for narratives. That said, Hughes does not claim that narratives are essential for theoretical practices in the same way in which Hartmann, and Morgan, claim that narratives are essential to models. In this sense, the structural role of narratives only means that narratives are elements of theoretical practices, in Hughes sense.  In order to argue for a more essential role of narratives in the Bohm and Pines case study, I have provided an interpretation of their claim that physical pictures are needed to understand the development of formalisms. Hughes is silent on this aspect of the Bohm and Pines’s quartet.  Despite those differences between Hartmann and Morgan, and Hughes, it is clear that both formalisms and narratives provide representations of phenomena. The equations of the MIT bag model represent confinement insofar as they specify properties of an object (the bag) depicted by a story.  In the Bohm-Pines case, the equations define properties of the system as sums of the individual and the collective aspects, but solving them does not yield physical behavior as a synthesis of individual and collective movement. The process depicted by the story exhibits such synthesis. 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  84 See note 80 above. 	   120	  In sum, both cases of physical theorizing crucially involve interplay of generalized narrative structure and mathematical structure. In such interplay, narratives play a heuristic and structural roles, and I leave it open whether understanding is to be related to explanation or not. Both cases seem to be instances of understanding and not explanation, and they suggest a relation between narratives and visualizability that remains to be explored.  I emphasize situations in theoretical physics where narratives drop out after their heuristic role is fulfilled, and what we have is an interpreted formalism doing its job. Bag models are standard content in textbook presentations of QCD; from the point of view of the fundamental theory, the “MIT bag model may be described a ordinary QCD plus the boundary condition that no quark current or energy-momentum may leave a prescribed bag …” (Ynduráin 1999, p. 263). There is no reference to a story. It was Hartmann who draw our attention to the importance of narratives in hadron physics.  Bohm and Pines emphasized the importance of a physical picture, and Hughes   identified the narrative character of such description. The usual mathematical format of theoretical physics should not be understood as evidence for the dispensability of narratives that play only at most a heuristic role.   4.4 Concluding Remarks The main conclusion of this chapter is that narrative theorizing is present in theoretical physics. Through narrative theorizing, physicists represent the causal structure of processes as a sequence of causally connected beginning, middle, and end event-types of a system, i.e., by means of generalized narratives.  	   121	  This provides a kind of understanding that does not come from mathematical deductions. Theorizing in physics exhibits a subtle interplay between narrative and mathematical thinking. Thus the common view that narratives are important only for our historical, or less mathematized sciences, turns out to be wrong.  	   122	   Chapter 5: Narratives in Biological Theorizing  5.1. Introduction In Chapter 4 I further elaborated previous work on narrative theorizing in theoretical physics. That dispels the very entrenched view that narratives belong in the more historical, and less mathematized sciences. And further supports my proposal in Chapters 2 and 3, that the formal components of theories or explanations are often embedded in narrative structure. In relation to Chapter 3, the present chapter offers examples of generalized narratives that serve as basis for biological explanations that are not historical in any special sense.  The first case is Darwin’s theory of natural selection, as it was formulated in the Origin of Species. The structure of the theory has three aspects; a generalized narrative of the origin of species, an abstract if-then conditional formulation of the process of natural selection, and exemplary narratives (also generalized) that provided “imaginary illustrations” of the action of natural selection.85   I revisit an episode in the immediate reception of Darwin’s theory, namely, Flemming Jenkin’s criticism of Darwin’s theory. In brief, Jenkin’s criticism was that in 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  85 I am indebted to Paul Bartha for suggesting a connection between Darwin’s imaginary illustrations and Kuhn’s “exemplars.” In a series of papers, James Lennox has argued that such imaginary illustrations represent a cognitive strategy used by Darwin to test the explanatory potential of Darwin’s theory of natural selection which he calls “Darwinian Thought Experiments” (Lennox 1991, 2005, 2008a,b). Lennox argues that such thought experiments are in effect narratives. Nancy Nersessian has argued for the role of “thought-experimental narratives” in theorizing (Nersessian 2008). I leave the interesting connection between narratives and thought experiments for future work. The notion of an “exemplary narrative” is introduced  and discussed in Creager, Lunbeck, and Wise (2007). In this volume, exemplary narratives are understood as a particularized descriptions of specific situations; see especially the contributions by Mary Morgan (p. 157-185, 264-274).  	   123	  one of the illustrations presented by Darwin, natural selection could not have preserved a beneficial variation, due to Darwin’s assumption of blending inheritance.  I address the question of whether Darwin’s theory was affected or not by Jenkin’s criticism (Lennox 1991, Gayon 1992/1998, Bulmer 2004). The answer requires that we realize that the exemplary narratives are constitutive of Darwin’s theory. In response to Jenkin’s criticism, Darwin modified his theory by eliminating one of the exemplary narratives, while leaving the generalized narrative of speciation, and if-then conditional formulation untouched. Section 5.2 is devoted to Darwin’s case.  The second problem pertains to the R.A. Fisher - Sewall Wright controversy in population genetics that William Provine has made prominent. What was the nature of the controversy? Provine’s answer is that the Fisher and Wright debate was about their “qualitative” theories of evolution, i.e., their “mass selection” and “shifting balance” theories, and not about their mathematical theories. However, this only provides the locus of the controversy but does not tell us what it was about. I discuss how the controversy derives from differences in Fisher’s ad Wright’s narratives of evolution.86 In section 5.3, I analyze the structure of Fisher’s and Wright’s “qualitative” theories and show that they are narrative theories of evolutionary processes. I consequently argue that the Fisher-Wright controversy was about the causal structure of the evolutionary process, as represented by their narrative theories.  In section 5.4, I revisit the actual debates that Provine identified, in the light of the 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  86 A major producer of Fisher and Wright’s disagreement was the importance of interactions between genetic loci in evolution, i.e., “epistasis.” They approached such interactions in radically different ways. For Fisher the effect of a gene could be studied averaging it across genetic backgrounds. For Wright, epistatic interaction are what produce adaptive peaks of different heights in the surface of selective values (Phillips, Otto, and Whitlock 2000, p. 2). For the importance of epistasis in evolution, see Wolf, Brodie III, and Wade eds., (2000). Brodie III’s excellent introduction to the latter volume has an insightful discussion of Fisher and Wright. Although I don’t discuss this aspect here in detail, in section 5.3.3 I note that Fisher’s and Wright’s approaches to epistatic interactions are quite consistent with their narratives.  	   124	  differences between their narratives. What prompted the controversy were ultimately irreconcilable differences over their stories of how evolutionary processes brought about adaptive change in nature.  In 5.4.4, I discuss Robert Skipper’s proposal that the Fisher-Wright controversy is a relative significance controversy in the sense of Beatty (1997), and make a brief excursion into some work on scientific controversies, to indicate a potential lesson from the present case study. Concluding remarks follow in section 5.5.  Both of these cases show a subtle interplay between the heuristic, explanatory, and structural roles of narratives. Such interplay, I claim, is not typical only of evolutionary biology, but of scientific theorizing in general.   5.2. Darwin’s Theory of the Origin of Species by Means of Natural Selection  5.2.1 The Narrative Theory of Speciation In this section I discuss the structure of Darwin's theory of evolution and divergence by natural selection. As Darwin suggested by the title of his book, I argue that, at its core, Darwin’s theory was about the process of adaptive divergence driven by natural selection that leads over time to the formation of new species.87 That this is the core of his narrative is also clear from the section headings in Chapter 4 of the Origin, which connect all of the components of Darwin’s thesis: “Natural Selection - its power compared with man's selection - its power on characters of trifling importance - its power at all ages and on both sexes - Sexual Selection - On the generality of intercrosses between individuals of the same species - Circumstances favourable and unfavourable to Natural Selection, 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  87 This is in the same spirit and further supports a recent by Juan Bouzat (2014).   	   125	  namely, intercrossing, isolation, number of individuals - Slow action - Extinction caused by Natural Selection - Divergence of Character, related to the diversity of inhabitants of any small area, and to naturalisation - Action of Natural Selection, through Divergence of Character and Extinction, on the descendants from a common parent - Explains the Grouping of all organic beings” (Darwin 1859/1964)   Darwin presents his theory of speciation aided by the only diagram in the Origin,88 that applies the basic narrative structure repeatedly over time, in intervals of a thousand of generations (Darwin 1859/1961, 117-126). The iteration of the narrative structure is embodied in Darwin’s “principle of divergence:” “…from the simple circumstance that the more diversified the descendants from any one species become in structure, constitution and habits, by so much they will be better enabled to seize on many and widely diversified places in the polity of nature, and so be enabled to increase in numbers” (Darwin, op. cit., p. 112).  The narrative starts out with a population of a certain species evolving by natural selection in a given environment. Descendants are produced that differ among them in different degrees, and natural selection will favor those individuals whose traits increase their survival and reproductive success.  Organisms “having nearly the same structure, constitution, and habits, generally come into the severest competition with each other” (Darwin 1859/1964, p. 110). Those descendants that differ most in their phenotypes, i.e., which are more divergent in character, do not face competition for the same resources, and continue to evolve by natural selection. This is where “the importance of the principle of benefit being derived from divergence of character comes in; for this will generally lead to the most different or divergent variations … being preserved and accumulated by natural selection” (Darwin 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  88 See the discussion of Darwin’s diagram in Bouzat (2012).  	   126	  op. cit., p. 117). The divergent forms keep evolving by natural selection until they become and are recognized as new species.  As we see, the process has two stages. In the first stage descendants are produced and natural selection accumulates beneficial variations. In the second stage, those variations which, as the result of local adaptive differentiation diverge most in their structures and behaviors, will face less severe competition and will be more successful at surviving and reproducing, i.e., will be favored by natural selection. Repeated over time, these stages lead to the formation of new species. Adaptive differentiation within populations leads over time to adaptive branching and this leads to speciation. Along the way, extinction has taken place: For it should be remembered that the competition will generally be most severe between those forms which are more nearly related to each other in habits, constitution, and structure. Hence all the intermediate forms between the earlier and later states, that is between the less and more improved state of a species, as well as the original parent-species itself, will generally tend to become extinct. (Darwin1859/1964, p. 121)   Darwin’s narrative theory involves the action of natural selection, the principle of divergence, and extinction.  Let's take a brief look at how the diagram illustrates Darwin’s narrative. Its x axis represents a hypothetical ecological variable, and the y axis represents time. It depicts 11 initial species denoted by upper case A-L, clustered in two distinct groups. Lower case letters with superscripts represent their descendants.  Evolution proceeds from a species “A”: “… species (A) is supposed to have produced two fairly well-marked varieties, namely  and ” (op.cit., p. 117).  After “the next thousand generations” variety  produces variety  “which will, owing to the 	   127	  principle of divergence, differ more from (A) than did variety . Variety  produces two other varieties that are different from each other and “more considerably from their common parent (A)” (ibid). The process goes on and on until a new variety (species) is produced. At each time unit, a lineage is a modified descendant of the previous one  (Reznick 2011, p. 177). As Reznick and Robert Ricklefs remark: “Thus  is not just  1,000 generations later; it is a daughter lineage that outcompeted ” (Reznick and Ricklefs 2009, p. 839).  Darwin’s theory represents speciation as a sequence of causally connected event-types that have beginning, middle and end: variability and natural selection, divergent forms face less severe competition for the same resources, and new species are formed over long periods of time. I arguer that this is Darwin’s narrative theory, which causally connects, through two stages, natural selection and speciation via the principle of divergence. Previous interpretations have broken apart Darwin’s theory in the Origin into two components: a theory of natural selection and a theory of speciation ("divergence of character") (Mayr 1991, 1992). The separation of Darwin’s theories was historically motivated to allow the theory of evolution by natural selection to be embraced while arguing that Darwin had an incomplete theory of speciation (Mayr 1942/1999, 1947, 1977, 1982, 1992, 1994; Coyne 1984, Coyne and Orr 2007).89  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  89 Whether Darwin’s theory of speciation turns out to be right or wrong according to our current lights is not something that concerns me here. Mayr, for instance, takes Darwin’s to be a theory of sympatric speciation.  In contrast, Grant and Grant argue that Darwin’s theory of speciation was largely allopatric (or at least parapatric), in keeping with Mayr’s view, (Grant and Grant 2010). For a discussion of Mayr’s claims on Darwin’s theory of speciation, and Darwin’s theory of speciation in relation to contemporary evolutionary biology, see Mallet (2008), and Reznick (2010). David Kohn discusses Darwin’s principle of divergence in Kohn (2009). David Reznick and Robert Ricklefs discuss the principle of divergence in relation to evolutionary ecology, and offer the interesting suggestion that it provides a connection between microevolution and macroevolution (Reznick and Ricklefs 2009).  	   128	  But I insist that Darwin did not formulate a theory of natural selection and a theory of speciation; he formulated a narrative theory of the origin of species by means of natural selection, as it can be read in the title of his book. We lose an appreciation for the depth and breadth of Darwin’s theory if we separate out natural selection and reduce it to a logical argument expressed in terms of an "if-then" conditional isolating natural selection from the narrative about divergence and the origin of species.    I now move to the literature where Darwin’s theory is more narrowly construed as a statement that establishes certain generic conditions for evolution by natural selection to occur. I show that even so construed, Darwin’s theory of natural selection has a narrative structure. I argue that the logical core of the theory of natural selection has to be understood in conjunction with exemplary narratives that Darwin used to illustrate the action of natural selection in nature.  To clarify the nature of the exemplary narratives, as well as how they are embedded within his broader narrative, I analyze Darwin’s response to the criticism posed by Flemming Jenkin in the next section. I suggest that Darwin’s “general conditions” formulation of natural selection should be viewed as the logical core of his larger narrative theory of the origin of species. As a crucial supporting element of the latter, the “conditions” formulation of natural selection fleshes out the primary mechanism that Darwin thought would lead to divergence. As we shall see below, this mechanism operates as long as there is variation, heredity, and an ecological “struggle for life.”   My claim is that the  “if-then” conditional characterization of natural selection is embedded in Darwin’s narrative theory of speciation.  To reiterate, there is not a separate 	   129	  theory of natural selection and a theory of speciation in the Origin, but a theory of the origin of species by natural selection. My perspective on Darwin’s theory is in complete accord with the one that has very recently been offered by Juan Bouzat: It is natural selection, when presented as a creative force leading to adaptive divergence, which provides causal efficacy in Darwin’s theory of the origin of species. In a way, the Origin was written as one long argument to provide a mechanistic explanation (natural selection) as the vera causa for the origin of species. (Bouzat 2014, p. 24-25)  The “if-then” formulation of natural selection, which I will discuss next, constitutes the logical core for the larger theory that presents natural selection as the creative force that Bouzat emphasizes. It is a core that dictates the conditions required for the mechanism that drives divergence to operate in nature.  To establish these conditions, Darwin employs a further narrative component, this time in the form of exemplary narratives that illustrate the action of natural selection, as a general mechanism for evolution. In summary, Darwin’s theory of the origin of species by natural selection comprises a generalized narrative, which is supported by an if-then conditional statement and the exemplary narratives that go with it.   5.2.2 Fleming Jenkin and the If-Then Formulation    James Lennox (1991) has emphasized that in Chapter 1 of the Origin (“Variation under Domestication”) Darwin “supplied us with a general selection theory abstracted from Darwin’s reflections on the literature devoted to the production of varieties of domesticated organisms” (p. 227).  Indeed, in his closing paragraph, Darwin highlights the “accumulative action of selection, whether applied methodically and more quickly, or 	   130	  unconscious and more slowly, but more efficiently…” (1859/1961, p. 43).  In Chapter 2 (“Variation under Nature”), Darwin makes the case that a process analogous to domestication is at play in nature; and in Chapter 3 (“The Struggle for Existence”) he argues that in a world with limited resources, there is an ecological struggle for existence, and the chances of survival of an individual depend not only on interactions with the physical environment, but also with other organisms. It is in Chapter 3 that Darwin formally introduces the process of natural selection: Owing to this struggle for life, any variation, however light and from whatever cause proceeding, if it be in any degree profitably for the individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring. The offspring also, will thus have a better chance of surviving, for, of the many individuals of any species that are periodically born, but a small number can survive. I have called this principle, by which each slight variation, if useful if preserved, by the term Natural Selection, in order to mask its relation to man’s power of selection. (Darwin 1859/1964, p. 61)  In the ecological struggle for life, some variations will increase the chances of survival of their bearers, and will be passed on to their offspring. The offspring in turn will also have a greater chance of survival.  Natural selection preserves variations that are “useful,” i.e., increase the chances of survival. Chapter 4 opens with two questions and an optimistic claim: “How will the struggle for existence, discussed too briefly in the last chapter, act in regard to variation? Can the principle of selection, which we have seen is so potent in the hands of man, apply to nature? I think we shall see it can act most effectually (p. 80). He starts his answer by further characterizing natural selection, synthesizing the previous results:  Let it be borne in mind in what an endless number of strange peculiarities our domestic productions, and in a lesser degree, those under nature, vary; and how strong the hereditary tendency is … Let it be borne in mind how infinitely 	   131	  complex and close-fitting are the mutual relations of all organic beings to each other and to their physical conditions of life. Can it, then, be thought improbable, seeing that variations useful to man have undoubtedly occurred, that other variations useful in some way to each being in the great and complex battle for life, should sometimes occur in the course of thousands of generations? If such do occur, can we doubt (remembering that many more individuals are born than can possibly survive) that individuals having any advantage, however light, over others, would have the best chance of surviving and of procreating their kind? On the other hand, we may feel sure that any variation in the least degree injurious would be rigidly destroyed. This preservation of favourable variations, and the rejection of injurious variations, I call natural selection. (ibid.)  The basic content of this second passage is the same. Lennox has provided an apt characterization of what Darwin has done: Darwin has provided an abstract description of an elaborate causal mechanism here. He identifies a number of universal (or nearly universal) features of living nature – reproductive superfecundity, character variability, the active struggle for self-maintenance and the constant search (among sexual organisms) for reproductive partners. (Lennox 1991, p. 228).  Darwin treatment is “abstract” in the sense that his description of natural selection does not refer to any concrete system or organism; he is characterizing natural selection in terms of certain generic processes that ought to operative if such process is to occur in nature. As Lennox puts it, Darwin singles out certain “nearly universal” properties that living systems ought to posses if they evolve by natural selection.  Darwin has provided a general formulation of his theory as an if-then conditional statement: If there is heritable variation, and if some variants are useful in the struggle for life (i.e., they increase the chances of survival of their bearers), then, these variants are passed on to the next generation, and will supplant less beneficial ones over time (e.g., will be preserved by natural selection).  The theory of natural selection is standardly presented in this form within textbooks and 	   132	  research literature. To look at some recent textbook examples: “…if some individuals tend to leave more offspring than others because they carry certain inherited traits, then those traits will tend to increase” (Barton, et al., 2007); and an example from the philosophical literature: “Darwin argued that if a population of organisms vary in some respect, and if some variants leave more offspring than others, and if parents tend to resemble their offspring, then the composition of the population will change over time – the fittest variants will tend to supplant the less fit” (Okasha 2006, p. 10).   One can interpret Darwin’s strategy as one of providing necessary and sufficient conditions for the process of natural selection to occur.90 Darwin’s abstract formulation inspires the influential formulation by Richard Lewontin of the logical structure of the theory of natural selection as encompassing three “principles;” “phenotypic variation,” “differential fitness,” and “heritability of fitness” (Lewontin 1970, p. 1). My goal is not to discuss Lewontin’s or other if-then formulations of the principle of natural selection;91 rather, it is to argue that the if-then conditional formulation involves a narrative part and that it is embedded within a larger narrative structure accounting for the origin of species.  Here, I highlight the narrative structure surrounding Darwin’s ideas about natural selection by analyzing an episode in the reception of the Origin of Species that involved the “illustrations” of the action of natural selection that Darwin presented in Chapter 4, 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  90 For penetrating, insightful, and interestingly different analyses of this strategy of presenting the theory of natural selection, and a comparison of variant versions, see James Griesemer (2000, 2005), and Peter Godfrey-Smith (2009). For how Darwin came to the abstract formulation see Jean Gayon 1992/1998, Chapter 1, p. 36-59, and M. J. S. Hodge 1987/2008, Chapter XIV, p. 248-250.  91 John Maynard Smith’s version, for example, was variation, multiplication, and heredity (Maynard Smith 1987). Griesemer (2000) discusses the differences between Lewontin’s and Maynard Smith versions. Lewontin’s formulation is motivated by the units of selection problem. He argues that the principles of natural selection apply to the whole biological hierarchy (op. cit.). Darwin’s motivation, as I se it, is to provide the structure of a causal process. Hodge (op. cit.) has emphasized that Darwin’s theory of natural selection is a causal theory. For an review and a discussion of the different formulations, in the context of the problem of the levels of selection, see Chapter 1, “Natural Selection in the Abstract,” of Okasha (2006). 	   133	  after discussing natural selection in the abstract.  I argue that such illustrations are narratives that are constitutive of Darwin’s theory. By Darwin’s “theory” I mean the if-then statement embedded in the broader narrative theory of the origin of species via divergence driven by natural selection. The episode concerns a criticism by the Scottish engineer Fleeming Jenkin to Darwin’s theory. The argument went right to the heart of Darwin’s views on variation and his assumption of blending inheritance. According to this assumption, when different traits are inherited, they blend and form an intermediate one.  Jenkin argued that if traits do blend, one of Darwin’s illustrations of the action of natural selection does not work, because novel variants are inevitably blended away. Historians of evolutionary theory have expressed differing views on the impact of Jenkin’s analysis on Darwin’s theory.92 As Jean Gayon has put it: “The real problem is whether the theory of natural selection was substantially affected by Jenkin’s attack” (Gayon 1992/1998, p. 85-86).  Or as expressed eloquently in the title of a more recent paper by biologist Michael Bulmer: “Did Jenkin’s swamping argument invalidate Darwin’s theory of natural selection?” (Bulmer 2004, p. 281). I argue that Jenkin’s criticism substantially affected Darwin’s theory, but only at the level of the exemplary narratives.  Let’s consider Jenkin’s argument in more detail. In June 1867, Jenkin published a review of the Origin in the North British 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  92 Note that I am analyzing Darwin’s theory of natural selection, and not Darwin’s argument. Jonathan Hodge has convincingly argued, I think, that Darwin’s argument for natural selection comprises a case for its existence as a causal process operating nature, a case for its competence to produce such change, and a case for its responsibility in producing extant and extinct species. He interprets Darwin as following the Hershellian vera causa ideal, and thus the three cases contribute to demonstrate that natural selection is a real, effective causal process in nature (Hodge 1977, 1987, 1989, 1992; reprinted in Hodge 2008). My suggestion would be that the exemplary narratives are crucial for the cases of existence and competence.  	   134	  Review.93 The argument is presented in a section entitled “Efficiency of Natural Selection.” Here is Darwin on the review, in a letter to J.D. Hooker, in 1869: It is only about two years since the last edition of the Origin, and I am fairly disgusted to find how much I have to modify, and how much I ought to add. Fleeming Jenkin has given me much trouble, but has been of more real use to me than any other essay or review. (Darwin to Hooker, January 16, 1869)  The review questioned the causal efficacy of natural selection in one of Darwin’s illustrations. Such illustrations, depict specific kinds of ecological interactions, e.g., predators and their prey, or plants and their insect pollinators. I claim that the illustrations exhibit the action of natural selection as a sequence of event-types in a system that undergoes change, i.e., they are examples of a more generalized narrative. Correlatively, I argue that they function as Kuhnian “exemplars.”  According to Kuhn, science students come to understand physical laws – which Kuhn called “symbolic generalizations” – through handling them in exemplary problem situations (force law; simple pendulum).94 Such exemplary problem situations are among the shared elements of a community of practitioners.95  In a like manner, Darwin hoped that the readers of the Origin would learn about his theory from seeing how natural selection works in certain kinds of scenarios, which I call exemplary narratives.96 He starts the section “Illustrations of the action of Natural 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  93 Reprinted in Hull, ed., (1973).  94 As opposed to understanding physical laws, or in this case, Darwin’s if-then conditional from certain deductive rules for their application. 95 Kuhn discussion of “exemplars” is in the postscript to the second edition of The Structure of Scientific Revolutions (Kuhn 1970, p. 187-191). For a penetrating and insightful discussion of Kuhn’s exemplars, see Nickles (2012).  96 As indicated in note 1 above, James Lennox has argued that in providing his illustrations, Darwin is performing thought experiments that test the explanatory potential of Darwin’t theory. Although I remain silent on the relation between narratives and thought experiments, my account is consistent with Lennox’s; as I will argue below, by being constitutive of the structure of the theory, exemplary narratives show how 	   135	  Selection,” by saying: “In order to make it clear how, as I believe, natural selection acts, I must beg permission to give one or two imaginary illustrations” (p. 90).    The narrative character of Darwin’s imaginary illustrations was first highlighted by Lennox in his 1991 paper, “Darwinian Thought Experiments: A Function for Just-So Stories,” and furher elaborated in Lennox (2005):97   By a “Darwinian thought experiment” I refer to imaginative narratives that serve as tests of natural selection’s explanatory potential. They posit hypothetical or imaginary test conditions specifying particular instantiations of the causal processes identified by the theory and displays a concrete state of affairs needing explanation as the end result of repeated iteration of these processes. (Lennox 2005, p. 90).   I now read Lennox using the framework presented. The narratives display a specific kind of system as a sequence of events-types that lead to an end event over time. The events of the narratives are supposed to always happen in the same order in nature, and the end event results from a “repeated iteration” of the processes at play at each stage or event of the narrative.  Although I am not emphasizing their role as thought experiments, Darwin’s imaginary illustrations can exhibit the explanatory potential of the theory, and in this sense they can function as shared examples of how natural selection works.  What hat matters for their role in Darwin’s theorizing (as thought experiments or exemplary narratives) is their narrative structure. Let us first consider the first exemplary narrative. It involves a population of wolves with slower and faster members. Darwin sets up the scenario: Let us take the case of a wolf, which preys on various animals, securing some by 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  Darwin’s theory would explain the specified scenarios, and in this sense they exhibit the explanatory potential of the theory. 97 See note 85 above. 	   136	  craft, some by strength, and some by fleetness; and let us suppose that the fleetest prey, a deer for instance, had from any change in the country increased in numbers, or that the other prey had decreased in numbers, during the season of the year when the wolf is hardest pressed for food (Darwin 1859/1964, p. 90).   Fast and slow, strong and weak wolves live in a population (i.e., variation is present). The beginning event is an environmental change that makes the number of fastest prey increase, e.g., deers. With the fastest prey more abundant, “[…] the swiftest and slimmest wolves would have the best chances of survival, and so be preserved or selected (...)” (ibid). In the second event of the narrative, the faster wolves out-survive and out-reproduce the slower (i.e., variants differ in fitness) and pass along their fitness-enhancing trait to their offspring (i.e., variants are heritable), so that, the advantageous trait increases in frequency.  The second narrative also involves a population of wolves. But in this case the beginning event is different: evolution commences not with a change in the environment, but with the origin of a favorable variation – in this case a new dietary preference – that was not previously present: “Even without any change in the proportional numbers of the animals on which our wolf preyed, a cub might be born with an innate tendency to pursue certain kinds of prey” (Darwin, 1859/1964, p. 91). The new variation confers greater survival ability and subsequently increases in frequency due to natural selection. Darwin is “illustrating” the action of natural selection with narratives that represent the same kind of system but differ in their sequences of events. In the first narrative, evolution commences with an environmental change. In the second, it begins with the appearance of a new favorable variation.  Jenkin contested the second sequence of events. If evolution begins with a new 	   137	  favorable variation, such variation could not be preserved by natural selection, given Darwin’s assumption of blending inheritance.  On the model of blending inheritance the offspring is a blend of contributions from both parents; parents differing in height, for example, would give rise to offspring with intermediate height. As David Reznick has described it “Inheritance was thought to be like the blending of black and white paint to produce gray” (Reznick 2010, p. 47). Here is Jenkin’s argument. With blending inheritance, if a single, new advantageous variant arose in a population, such a variant could not be passed unchanged to the next generation, since the individual possessing it would mate with an organism possessing the previously prevailing type, and the trait and the advantage it confers would be diluted, each generation, until disappearing.  As a result, the advantageous variant could not be preserved and accumulated by natural selection. Jenkin’s point is that natural selection was not causally efficacious in the case in which evolution starts with a new, single variant, given that blending inheritance is true.98 What was Darwin’s reaction to Jenkin’s criticism? How did it affect Darwin’s theory? What did Darwin modify in reaction to it?  Darwin accepted Jenkin’s criticism, and as John Beatty observes, in “subsequent editions of the Origin, Darwin deleted the second illustrative narrative concerning wolf evolution (…)” (2010, p. 29). Instead, in the 6th edition we find the following paragraph: In former editions of this work I sometimes spoke as if this latter alternative [the alternative depicted in the second scenario] had frequently occurred. . . . Nevertheless, until reading an able and valuable article in the “North British Review” (1867), I did not appreciate how rarely single variations, whether slight or strongly-marked, could be perpetuated. (Darwin1872, p. 71) 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  98 Blending inheritance was overturned by Mendelian inheritance. The significance of this for Darwin’s theory are brilliantly discussed by R. A. Fisher in Chapter 1 of The Genetical Theory of Natural Selection (Fisher 1930/1999).  	   138	   As the result of Jenkin’s criticism, Darwin now thinks that natural selection does not lead to the perpetuation of single, newly appearing variant. Gayon (op. cit.) and Bulmer (op.cit.) argue that Jenkin’s criticism did not make Darwin abandon his theory, nor did it invalidate it, but they do not discuss whether it affected the structure of the theory or not.99 So, what was the significance of Darwin’s deleting one of the narratives in subsequent editions of the Origin, for the structure of his theory?  My answer is that Darwin did substantially modify his theory, but only at the level of the exemplary narratives. He did not abandon his broader narrative theory about the origin of species by means of divergence driven by natural selection, nor did he alter the if-then formulation of natural selection.  Rather, he refocused his attention on preexisting variation – which was clearly present in natural populations  – and deemphasized novel variants, eliminating the one problematic exemplar. Thus, Darwin adjusted his narrative theory to avoid Jenkin’s criticism by trimming out scenarios that involved the preservation of single, new variants. I maintain that by affirming the first narrative and rejecting the second, Darwin both elaborated and restricted the scope of his theory.  In essence, Darwin retreated from stories that described how variation arose and grounded subsequent arguments on the empirically justified assumption that such variation would be present. Darwin could shift the boundaries of his theory without having to rebuild its core; he could delimit the scope of his if-then conditional by 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  99 I am omitting the interesting biological discussions in Gayon’s chapter and in Bulmer’s paper. For Gayon, Jenkin’s criticism reveals ambiguities with Darwin’s use of the terms, “individual variation,” “individual differences,” and “single variation.” Bulmer, identifies three senses in which “swamping argument” was being used. In particular, Bulmer argues that Jenkin’s arguments was based on Darwin’s assumption of blending inheritance, but his conclusion was based on the assumption that each pair of animals with separate sexes would have a single surviving offspring; in this case the population size would be reduced in half each generation.  	   139	  eliminating one of the scenarios he initially thought could be used as an instance of evolution by natural selection. As it turned out, it was a scenario with a sequence of events in which favorable variations are not preserved over time, based on a blending inheritance view of inheritance. And consequently, it was a sequence of events that would not be conducive to the divergence of species.  The present discussion does not diminish the importance of the if-then conditional formulation of natural selection. It has played an enormous role in shaping our modern understanding of evolution by natural selection, as well as debates regarding the units and levels of selection (Okasha 2006). My point has been that Darwin’s theory in the Origin does not reduce to these conditionals alone. To imitate Hartman’s formula in Chapter 4, Darwin’s theory = generalized narrative of speciation, supported by if-then conditional, supported by exemplary narratives.  In retrospect, the problem that Jenkin posed for Darwin was indeed a serious one. Darwin’s generalized narrative and the exemplary narratives that constituted his theory did not have the theoretical and genetic framework they required. More precisely, they were narratives whose background framework was yet to be constructed, i.e., the discovery of Mendelian genetics and theoretical population genetics.100  Thus, Jenkin’s problem wasn’t solved until R.A Fisher showed, in his 1918 seminal paper, “The Correlation Between Relatives on the Supposition of Mendelian Inheritance,” that quantitative characters, such as height or size, could be determined by 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  100 Population genetics broadly considered to include quantitative genetics. In population genetics, the basic unit of analysis is a “Mendelian factor” or gene at a chromosomal locus, or at several loci, the simple example of which is a single locus with two alleles. Quantitative genetics studies “continuous traits,” such as height, or weight as the result of many independent Mendelian factors of small effect.  	   140	  many Mendelian factors of small effect.101 In a Mendelian system of inheritance, genes do not blend but segregate intact and independently, and novel variants are passed unchanged to offspring. As Fisher puts it, in such system, “there is no tendency of variability to diminish, except in so far as by the gradual action of selection certain genes tend to disappear” (…) (Fisher 1922b, p. 26). Fisher essentially struck down the model of blending inheritance in one blow. Fisher devoted much attention to highlighting the differences between blending and the particulate-Mendelian scheme of heredity. In the first chapter of The Genetical Theory of Natural Selection, “The Nature of Inheritance,” he writes: “It has not been so clearly recognized that the particulate inheritance differs from the blending theory in an even more important fact. There is no inherent tendency for the variability to diminish” (Fisher 1930/1999, p. 9).  It took Fisher’s demonstration of the compatibility of Mendelism with Darwin’s natural selection to restore Darwin’s second exemplary narrative as a scenario for natural selection (Fisher 1918, 1922).102 Although Darwin was not alive to resurrect his 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  101 Fisher (1918) is the founding document of quantitative genetics.   102 Fisher (1918) ends the battles between the “biometricians” and “Mendelians” (Provine 1971; Gayon 19892/1998)  on whether results obtained by Galton’s work on the statistical correlation of quantitative traits between relatives could be obtained under the assumption of Mendelian inheritance. In this sense it is the founding document of mathematical quantitative genetics. Fisher (1922), is the founding document of theoretical population genetics. First, it poses the problem of finding the statistical distribution of gene frequencies given certain factors that can change the genetic composition of a Mendelian population, e.g., natural selection, which as we shall see below, exerted an decisive influence on Sewall Wright’s work. Among other results, Fisher predicts a polymorphic equilibrium under selection; the solution that will be crucial in the late 1970s debates over the maintenance of genetic variability (Lewontin 1974). Second, and quite remarkably, it provides the first application of stochastic methods to evolution. Beginning with Section 2 of the 1922 paper, “The Survival of Individual Genes,” and through Sections 3, 4, and 5, Fisher inaugurates the stochastic theory of evolution; a) Fisher formulates the first model of genetic drift (“Hagedoorn effect”) as a Markov (in Fisher’s terms a Poisson process) process, which has come to be called the “Wright-Fisher” model of genetic drift. It should be called the Fisher-Wright model (refer to Edwards). It was Fisher’s 1922 paper that got Wright going on evolution in Mendelian systems; b) Fisher formulates stochastic diffusion-like equations; the sort of equations that later Kolmogorov developed (refer to Feller), and which form the core of the diffusion models that Wright, and more prominently Motto Kimura, made the core of the stochastic theory of evolution that we have (refer to Edwards and Ewens). In 	   141	  illustration, the view of evolution that Fisher pioneered highlights the appearance and subsequent spread of “single variations.”  Evolution can commence with a new variant that will not be diluted and lost over time but will be preserved under the Mendelian mechanism. Such scenario is, for example, described by population geneticists Nicholas Barton and Michael Whitlock: “The establishment of a new and favorable allele involves two stages: first, the increase of a single mutant copy to appreciable frequency around its original location, and second, its spread through the whole population” (Barton and Whitlock 1997).  Such a view results from the “synthesis” of Mendelism and Darwinism that Fisher started in the foundation of population genetics. My next case study is situated in the heyday of that synthesis.   5.3 Fisher’s and Wright’s Theories.  William Provine has characterized the period after the Origin as one of “persistent controversies” (Provine 1988). During the synthesis of Mendelism and Darwinism, two different narrative theories of evolution were formulated which constitute the target of this section, i.e., R. A. Fisher’s “mass selection” theory and Sewall Wright’s “shifting balance” theory. The post-Origin controversies took the form of a debate between Fisher and Wright over their narrative theories that began in print in 1929.103   	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  order to see how Fisher 1918 and 1922 relate as a foundation for the mathematical theory of evolution, see Edwards (2013). Edwards paper does this in the context of clarifying Fisher’s theorizing in formulating his Fundamental Theory of Natural Selection. I will return to this below.  103 For the history of the synthesis between Mendelism and Darwinism that led to the development of population genetics, see Provine (1971), and Gayon (1992/1998). This synthesis was followed by a broader “modern synthesis” in which the results of population genetics were made consistent with other evolutionary disciplines, e.g., experimental population genetics (Dobzhansky 1937); systematics (Mayr 1942); and paleontology (Simpson 1944). For the synthesis in general, see Mayr and Provine (eds.) (1980).   	   142	  Provine has analysed and amply documented the R.A Fisher-Sewall Wright controversy (Provine 1985/1992, 1986). Provine’s main thesis is that Fisher and Wright’s disagreements were not over their mathematical/quantitative theories but over what he called their “qualitative” theories of evolution: “Qualitative evolutionary theory was the subject on which Fisher and Wright disagreed so strongly and to such great effect” (Provine 1986, 266). Provine never articulated his sense of qualitative theory beyond meaning “non-mathematical.” I claim that without an analysis of the kind of theory involved, one cannot fully appreciate what it is that Fisher and Wright were disagreeing about and what kind of controversy they engaged in. Fisher’s mass selection and Wright’s shifting balance are theories in a narrative sense, and it was their narratives that were in theoretical conflict.  As we shall see, the narrative structure of each theory depicted radically different causal structures, i.e., different sequences of causally connected event-types. Let’s begin with Fisher.   5.3.1 Fisher’s Mass Selection Theory.  Fisher’s training in mathematics and theoretical physics, as well as his prodigious gifts in these areas, are usually highlighted when his name is introduced. His strategy of comparing “the whole investigation” on biological populations to “the analytical treatment of the Theory of Gases” (Fisher 1922) is well known and has been widely discussed (Provine 1971/2000, Gayon 1992/1998, Morrison 2000, 2004, Skipper 2009). Less emphasis has been placed on his early biological interests, and his expressed opinion on the limitations of mathematics in theorizing. I highlight those two aspects of Fisher’s 	   143	  scientific personality, to motivate the importance of narratives in his published work.   His daughter and biographer Joan Fisher Box writes: “The choice of mathematics never detracted from Ron’s biological pursuits” (1978, p. 17). Fisher Box refers to the choice of mathematics as a subject for a scholarship to enter Cambridge, over a scholarship in biology. Fisher wrote to a former teacher “a mathematical technique with biological interests is a rather firmer ground [as a subject for a scholarship] than a biological technique with mathematical interests (…)” (cited in Fisher Box, ibid.) Fisher remarked that had he chosen biology, it “would have worked out much the same (…)” (Fisher Box, ibid). He would have still used mathematics to explore biological problems. Indeed, in his last year at Harrow school, he was awarded two prizes, and he chose the Collected Works of Charles Darwin as one of them. Fisher, writes Fisher Box, “went up to Cambridge in possession of volumes he was to read and reread with loving care throughout his life” (Fisher Box, ibid.).  The choice of mathematics had a deep biological motivation: to lay the theoretical foundations of Darwin’s theory of natural selection (Fisher Box, op.cit). And his thinking was framed and guided by Darwin’s narrative. In this sense, I suggest that Darwin’s generalized narrative played a huge heuristic role in Fisher’s theoretical enterprise.  As Fisher’s student, A.W.F Edwards has put it: “Fisher was from the outset influenced by Darwin’s writings to a much greater extent than any of his contemporaries; he was a “successor” in the truest sense” (2012, p. 423). As we shall see, Fisher’s narrative theory refines the causal structure posited in Darwin’s narrative, whose theoretical tensions Fisher sorted out through his mathematical work. Importantly, Fisher 	   144	  stated the limitations of mathematics in grasping the causal structure of evolutionary processes.  In 1932, in his contribution at the 6th International Congress of Genetics, he writes: As a mathematician by trade perhaps I should explain that I shall use no mathematics, partly because I recognize that the first duty of a mathematician, rather like that of a lion tamer, is to keep his mathematics in their place, but chiefly because I think mathematics, though well fitted to elucidate detailed points of special intricacy, are after all only a special means of carrying out reasoning processes common to all scientific work, and are out of place in a theory covering a wide range of disparate phenomena. I believe that no one who is familiar, either with mathematical advances in other fields, or with the range of special biological conditions to be considered, would ever conceive that everything could be summed up in a single mathematical formula, however complex. (Fisher 1932, p. 165-166) The general theory of evolution covers such a “wide range of disparate phenomena,” and so many causal influences that expressing them in a single mathematical formula is not possible. As a consequence, Fisher’s major treatise, The Genetical Theory of Natural Selection (Fisher 1930/1998), was primarily narrative in structure, with only occasional mathematical details and proofs. In correspondence with Wright on discrepancies over mathematical results, he adds the following related remarks: Mathematicians always tend to assume that the hardest mathematics will be the most important, and this is perhaps true enough in the well worn topics. It is certainly not true of my book [The Genetical Theory of Natural Selection], where the apparently non-mathematical parts, where I have left the mathematics undone, are often of the greatest ultimate interest. (Fisher to Wright, October 25, 1930. Quoted in Provine (1986), p. 266. Italics in original) According to Fisher, mathematics plays a supporting role in scientific reasoning, to “elucidate points of special intricacy.” But a theory of evolution ought to integrate multiple causal influences and apply to a wide range of “disparate phenomena.” Fisher’s 	   145	  central concern was to understand the causal structure of the evolutionary process and in this, guided by Darwin’s narrative, he engaged in narrative theorizing.  Quite in keeping with his remarks on mathematics and with Darwin’s narrative style of theorizing, Fisher formulated a generalized narrative that lied at the core of what came to be known as Fisher’s “mass selection” theory. However, in contrast to Wright, who re-formulated his narrative in a number of papers, Fisher makes his narrative explicit in very few places, even if it guides and shapes the thinking that culminates in “The Genetical Theory of Natural Selection.”  Most explicitly, Fisher formulated his narrative in “Darwinian Evolution of Mutations” (Fisher 1922b). As was Darwin’s, Fisher’s is a generalized narrative. It represents a sequence of causally connected event-types that occur over and over again, at every locus of every population. It represents a kind of system - a large biological population - undergoing certain changes of state that correspond to the different stages of the process. The narrative fixes a beginning and an end by specifying certain determinate values of the determinable variables that characterize the process, e.g., population size, gene frequencies. Thus, Fisher’s narrative begins with an event of a certain kind, a mutation, and ends with an event of another kind, the fixation (or loss) of an initially rare mutant. Accidents of sampling are the primary agents of gene frequency change in the beginning, with selection slightly tilting the balance from extinction to fixation; natural selection predominates in the middle stage: If we suppose then that a mutation has occurred, and an entirely new gene is present in a single individual of a population consisting of some thousands of millions, the history of its survival may be broadly divided into two periods. In the first period its survival or extinction is due mainly to chance; in the second 	   146	  period mainly to the general advantage or disadvantage in the struggle for existence, which the new allelomorph confers, on the average and in combination with the existing currency of genetic types, as compared with the alternative allelomorph which it displaces (Fisher 1922b, 33).  Let’s pause and take a closer look at the structure of the narrative and Fisher’s background assumptions. Fisher envisages evolution occurring in large, undivided populations: “abundant species will, ceteris paribus, make the most rapid evolutionary progress …” (Fisher 1930/1999, 98). Evolutionary changes in such a system are tracked as changes in gene frequencies.  In the first stage, rare alleles either accumulate or go extinct largely due to chance – for example, when a mutation that would on average be slightly advantageous happens to arise in an individual carrying traits that make it disadvantageous or in an individual that by chance happens to die before reproducing. In the second stage, alleles that are slightly advantageous on average and have reached a certain frequency continue to accumulate steadily by natural selection until the most advantageous allele at each locus has nearly swept through the species. It is a story of how natural selection, acting on variation added only by mutation, drives a single type of gene (allele) to near fixation (near 100% frequency) at each genetic locus.  As with the other narratives discussed in previous chapters, the second stage in Fisher’s narrative does not deductively follow from the first. The initially rare allele may become extinct and there is no allele that natural selection drives to fixation; or natural selection might fail to drive it to fixation in the second stage due to an environmental change. In addition different mathematics (and different D-N derivations) are involved at 	   147	  each stage. In the first stage, Fisher treats the “survival of individual genes” as a stochastic (branching) process; the second stage brings the equations of natural selection with Fisher’s Fundamental Theorem of Natural Selection as the theoretical principle underlying it. The end-event in the second stage is not a necessary consequence of the initial conditions and the equations of the first stage.     A consequence of this is that calling Fisher’s theory “mass selection” does not do justice to the causal structure it exhibits. For “mass selection” refers only to the second stage of Fisher’s narrative. The first stage is also critical. It concerns the accumulation of variation upon which selection acts, precisely the problem left open in Darwin’s theory.  As we have seen, the first stage involves the “fortuitous survival” (vs. the “extinction”) of new – initially rare – mutations. Those mutations that survive the “first period,” and increase in frequency to levels where sampling error has little impact on their fate, then experience the second stage of "mass selection." In Fisher’s words, “beneficial mutations are initially subject to the full forces of random survival (…)” (1930/1999, 117). This leads to the second phase where they are subject to the full force of natural selection, and they further increase in frequency until becoming fixed in the population. Fisher’s theory would be better called the “fortuitous survival-mass selection” theory; this would reflect its irreducible narrative structure.   How does Fisher’s narrative compare to Darwin’s? Darwin’s narrative theory delineated a space of possibilities well before Fisher’s mathematical framework of evolution was in place. I suggest that in exhibiting the causal structure of the process of natural selection, Darwin’s narrative allowed Fisher to explore a space of outcomes and see what needed to be proved. In particular, it made clear in Fisher’s mind that the 	   148	  compatibility of the Mendelian system of inheritance and Darwin’s natural selection had to be proved.   In this sense, Darwin’s narrative exerted a powerful heuristic role in motivating and shaping Fisher’s theoretical project. It motivated Fisher into applying mathematical methods to solving biological problems; in particular those posed by Darwin’s theory. This is a theoretical enterprise for which he happened to be particularly well equipped. As Anthony Edwards has put it: “Studying for the mathematical tripos wile relaxing with Darwin and Mendel could not have been a better preparation for the work that was to follow” (Edwards 2001, p. 77).  Critically, the mathematical questions emerged from, and gained shape and meaning from the narrative, not from previous mathematical theory. The theoretical challenge required establishing a robust connection between natural selection and the particulate Mendelian basis of inheritance. By solving this challenge, Fisher placed Darwin’s narrative on a firmer and broader basis. This, I submit, was expressed in Fisher’s own narrative.   5.3.2 Wright’s Shifting Balance Theory.  Wright’s theory was presented in Chapter 3, as an example of a narrative theory. Here I place it within the development of Wright’s work and discuss it in comparison with Fisher’s theory. Whereas Fisher provided a general story about changes in frequency of genes, Wright’s story was more about changes in frequency of gene combinations.  His initial interests were in understanding gene action. This led him to study experimental organisms as multi-factorial systems. Such interaction systems produced 	   149	  multiple, unpredictable configurations, and Wright imagined evolution as movement across a “field” of gene combinations, with peaks at combinations of higher fitness, and valleys at combinations of lower fitness.  The “problem of evolution,” as Wright saw it,  is that of a mechanism by which the species may continually find its way from lower to higher peaks in such a field. In order that this may occur, there must be some trial and error mechanism on a grand scale by which the species may explore the region surrounding the small portion of the field which it occupies. To evolve, the species must not be under the strict control of natural selection. Is there such a trial and error mechanism? (Wright 1932, 163-164).  This passage already reflects a crucial difference between Wright’s and Fisher’s narrative theories of evolution, on how natural selection “controls” evolution. For Wright, selection alone was not sufficient for evolution to proceed as a continuous exploration of the field of gene combinations. Another mechanism was needed; and it was random processes to which Wright turned. As Michael Wade has put it: “In Wright’s theory, random genetic drift and local individual selection in combination can achieve results unattainable by selection alone” (Wade 1992, p. 37).  Under the sole influence of natural selection, evolution would get stuck at a single equilibrium configuration, where mutations are all deleterious. Wright understood evolution as involving a combination of evolutionary factors, which included not only selection and drift but also migration. This multi-factorial view was motivated by his experimental work on gene action. I suggest that Wright’s narrative thinking allowed him to discern a single kind of causal structure from what were in fact “four rather unrelated lines of research that led me [Wright] to a viewpoint on evolution very different from those propounded by Haldane 	   150	  and Fisher at about the same time, the 1920’s” (Wright 1978, p. 1197).104  The lines of research that inspired Wright’s shifting balance theory were:  1) his work as an assistant to W. E. Castle’s selection experiments in hooded rats (1912-1915); 2) his PhD research on interaction effects in color characters in guinea pigs; 3) inbreeding, outbreeding, and selection in Guinea pigs and 4) his analysis of the breeding history of the Shorthorn cattle.  From (1) Wright learned the efficacy of mass selection and its inherent limitations in producing deleterious effects such as a loss in fecundity. From (2) Wright “recognized that an organism must never be looked upon as a mere mosaic of “unit characters,” each determined by a single gene, but rather as a vast network of interaction systems” (Wright 1978, p. 1198). Genes are expressed differently in different combinations.  This led to a pictorial representation of evolution as a “surface of selective values” with peaks of different heights separated by valleys. Natural selection, according to Wright, “must somehow operate on combinations of interacting genes as wholes to be most effective” (ibid). The problem was how such combinations could be seized upon by natural selection. As Provine has aptly put it, “in a large random breeding population, distinctive interaction systems of genes are rarely clearly expressed and therefore cannot be seized upon by the selection process” (Provine 1986, p. 235).105 The solution to this came from (3), where inbred lines of Guinea pigs showed 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  104 Wright arrived at his theory “while in the Animal Husbandry Division of the US Bureau of Animal Industry in Washington (…)” (Wright, op. cit., p. 1194). The difference with Haldane and Fisher lay precisely in Wright’s idea that “adaptation involved a shifting balance between evolutionary forces (…)” (Coyne et al., 1997). Regarding the role of stochastic factors, Haldane wrote that Wright “holds that this random survival has played a part in evolution much more important than assigned to it by Fisher and myself. Only a very thorough discussion, which has not yet even begun, can decide which of us is correct” (Haldane 1932/1990).   105 On this very point see also the excellent discussion in Wade (1992).  	   151	  strong differentiation due to sampling effects. This suggested to Wright that random fluctuations could make different genetic combinations available for the scrutiny of natural selection, in species that were subdivided into local, small subgroups.  Finally, from the breeding history of Shorthorn castle Wright learned how superior herds “successively made over the whole breed by being principal sources of sires” (Wright 1978, p. 1119). The composition of a group in a higher peak could be diffused to the whole species.  Provine then writes: Reasoning from his theory of animal breeding to his theory of evolution in nature, Wright proceeded upon the plausible but wholly unproved assumption that evolution in nature proceeded primarily by the three-level process utilized by the best animal breeders: (1) local mass selection and inbreeding, (2) dispersion from the most successful populations, and (3) transformation of the whole species or breed. (Provine 1986, p. 236)   The critical point for this thesis is that the reasoning employed by Wright is not logico-deductive, but narrative. He didn’t reach conclusions from a set of premises, or a set of models but conceived the structure of a process as a sequence of three events or stages in a narrative, which Provine calls “levels.”  Wright goes from his theory of animal breeding to his theory of evolution in nature, through a narrative in which the processes involved figure in a sequence of events or “phases” that constitute a larger process. He connects them not as steps in a deductive sequence, but as generic events in a story: evolution commences with a mixture of random and selective differentiation in subgroups, and ends with the spread of a better adaptive interaction system to the rest of the species. In the middle, sub-populations further differentiate and natural selection allows new, fitter combinations, to rise in 	   152	  frequency. Wright’s narrative depicts a causally connected sequence of event-types or states that species undergo in nature.  As in Fisher’s narrative, a given stage in Wright’s narrative does not necessarily follow from the previous stage. A new mutation allowing a sub-population to reach a new peak may be lost by chance. Even if the mutation succeeds in establishing within a population, that population may then be kicked off of the new peak by immigration. The environment may change so that a previous fitness peak is no longer one.  The heuristic role of Wright’s narrative can be seen already. During his early experimental work, Wright imaginatively constructed narrative scenarios, where different processes in animal breeding were synthesized into a single causal process in nature having a beginning, middle and end. Wright’s narrative started as a mental sketch of the evolutionary process.   Wright did not present it in print until 1932, in his talk at the Second International Congress of Genetics; and he did not explicitly formulate this process as a “three-phase shifting balance theory” until 1965, in a paper entitled “Factor Interaction and Linkage in Evolution” (Wright 1965).  Let’s look at the 1965 formulation, and its narrative structure:  Phase 1 consists of the differentiation of innumerable small local populations by more or less random processes that lead, here and there, to the crossing of shallow saddles in the surface of selective values that separate lower from higher peaks. Phase 2 is the occupation of the higher peaks by local mass selection and involves much greater changes of gene frequency than phase 1. Phase 3 is the diffusion [via migration] of the significant aspects of the genetic constitution of these successful populations throughout as a result of excess population growth and excess emigration, followed by the appearance of still more successful centres of diffusion at points of contact. Evolution on this view, is not a frontal advance, but the result of continual minor readjustments within the virtually infinite field of gene combinations expected where the conditions are favourable for these three phases. (Wright 1965, p. 86. Italics in the original.)   	   153	  Biologists Michael Whitlock and Patrick Phillips provide a somewhat similar description of the phases, and emphasize its story-like character:  The shifting balance process, in its strict interpretation, imagined that species were subdivided into many demes weakly connected by migration. Demes might be small enough that genetic drift can sometimes overwhelm the effects of natural selection and take the population to the domain of attraction of a new peak (i.e. the allele frequencies can drift to a point where the deterministic effects of selection would be expected to take the population to a new peak; this is referred to as Phase I). Individual selection could then take that population near to the height of the new peak (Phase II), at which time Wright envisioned intergroup selection would act to pull the whole species toward the new peak (Phase III). This story has served as a significant theory of adaptive evolution for the greater part of the 20th century. (Whitlock and Phillips 2000, 347. Italics added.)106  What started as a mental model of an evolutionary process became a full-fledged narrative theory, in which a certain specification of determinate values of the determinable variables fixed a beginning, and an end (as we saw in Chapter 2). Besides its heuristic role, Wright’s generalized narrative played a structural role underlying his mathematical framework.  Notice how, in the quote above Wright italicizes the dominant process at each phase. The alternation of causal influences Wright called a shifting balance. Wright thought that such shifting balance of processes over time enhanced the power of selection to produce adaptive improvement.  Evolution, in Wright’s view, is a “continual readiness to shift to a superior state of balance which is the essence of the shifting balance theory of evolution” (Wright 1978, p. 1119). Wright’s theory solves his “problem of evolution;” to find “a mechanism by which 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  106 For discussions of the phases of the shifting balance see also Wade (1992) and (2012), Coyne, Barton, and Turelli (1997), and Wade and Goodnight (1998). The latter two papers were the first two of a discussion pro and con on the shifting balance theory which is the target of the Whitlock and Philips paper from which this quotation comes, Whitlock and Philips (2000).  	   154	  the species may continually find its way from lower to higher peaks” in the field of gene combinations, as depicted in Wright’s “surface of selective values.”  I argued above that Wright conceived this process through narrative thinking. We see how Wright’s narrative exploration of evolution led him to the formulation of a general theory of evolution that – we now see – differed radically from Darwin’s and Fisher’s.  Indeed, Darwinian selection, which Wright baptized “mass selection,” is the dominant force of evolution in the second phase of Wright’s generalized narrative. While, random processes were important for Fisher in the first stage of his narrative, they were not creative, simply hindering selection by causing the loss of beneficial mutations. Darwin, as far as I can tell, and definitely Fisher, didn’t think the action of natural selection needed to be boosted by random processes.   Wright in contrast, not only postulated a different beginning for the evolutionary process with drift carrying more causal weight, but also a different end with a different type of selection – selection acting not just within, but also between groups. He did this by specifying different combinations of determinate values to the relevant determinable properties that characterized the state of the system at each stage.   5.3.3 A Comparison  In its heuristic role, Wright’s narrative broadened the space of possibilities for evolution by natural selection. And it also framed and motivated Wright’s mathematical work on how drift, migration and selection jointly shaped the genetic configuration of natural populations. This is in stark contrast with Fisher’s narrative, which motivated the search 	   155	  for a theoretical foundation of natural selection as the principal, single factor driving evolution. Their narratives motivated their different approaches to mathematical work.  Wright made his approach explicit, making a tacit contrast with Fisher’s. According to Wright, science aims at synthesis:    Science has largely been advanced by the analytic procedure of isolating the effects of single factors in carefully controlled experiments. The task of science is not complete, however, without synthesis: the attempt to interpret natural phenomena in which numerous factors are varying simultaneously. Studies of the genetics of populations, including their evolution, present problems of this sort of the greatest complexity. (Wright 1948, p. 279. Italics added.)   The tacit contrast with Fisher’s approach runs in the passage that immediately follows:  Many writers on evolution have been inclined to ignore this and discuss the subject as if were merely a matter of choosing between single factors. My own studies of population genetics have been guided primarily by the belief that a mathematical model must be sought which permits simultaneous consideration of all possible factors. Such a model must be sufficiently simple to permit a rough grasp of the system of interactions as a whole and sufficiently flexible to permit elaboration of aspects of which a more complete account is desired. (ibid. Italics added.)  As we have seen, Wright’s narrative depicts the simultaneous action of the different factors, at the different stages of the shifting balance process. Wright then refers to his 1931 paper, “Evolution in Mendelian Populations,” as an example:  On attempting to make such a formulation (Wright, 1931) it was at once apparent that any one of the factors might play the dominant role, at least for a time, under specifiable conditions … (ibid).   Indeed, in his 1931 paper, Wright combines all factors in a single remarkable formula for the equilibrium distribution of gene frequencies:    	   156	   This is a general one-locus, two-allele case:  is the allele frequency in the subpopulation; is the mean fitness as a function of genotypic fitnesses and allele frequency; is the effective population number;  is the proportion of the subpopulation replaced by migrants;  and  are forward and reverse mutation rates;  is a constant that makes all  add to one;  is the probability that the frequency in the subpopulation is .  As James Crow has stressed it: “This equation is basic to Wright’s discussion of his shifting balance theory of evolution …” (Crow 1990, p. 71-72). Indeed, it underlies the first phase of the shifting balance process. And Crow has also observed: “It is in the context of phase 1 that Wright did most of his theoretical work” (op. cit., p. 78).  Wright did not have to develop the mathematics of “mass,” Darwinian selection for the second phase, which was developed by Fisher and Haldane.107 And Wright never mathematized phase 3. Crow has described the situation thus: Wright was very mathematical in his treatment of phase 1. Phase 2 requires no complex mathematics; it simply is mass selection. Surprisingly, Wright’s treatment of phase 3 was entirely descriptive. (Crow, op. cit., p. 79)  By “descriptive,” Crow really means narrative. The mathematical investigation of phase 3 began with Crow et al. (1990), which was followed up by Nicholas Barton (1992), which was followed up by Kondrashov (1992), Phillips (1993), and Gavrilets (1996). As Barton and Whitlock diagnosed in 1997: “The theory underlying the first two phases of the 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  107 In Fisher (1922). Haldane published a series of ten papers with the eloquent title, “A Mathematical Theory of Natural and Artificial Selection,” from 1924 to 1934. Haldane summarized his series in an appendix to his book, The Causes of Evolution (Haldane 1932). The interested reader should consult the Princeton Science Library edition, edited by Egbert G, Leigh Jr. Besides an instructive introduction, Leigh Jr. writes a superb commentary to Haldane’s appendix, where he explains Haldane’s mathematical theory of selection and discusses its significance in contemporary notation (Haldane 1932/1990).   	   157	  “shifting balance” is well established, while the third phase has only recently received detailed attention” (Barton and Whitlock 1997, p. 201).108 Wright’s narrative theory of a shifting balance of factors evolution influenced his mathematical approach to evolutionary problems.  For Fisher in contrast, natural selection was the sole driving force of evolution. But this does not mean that he thought evolution was the result of a single factor. Drift and selection are at play in both events of his narrative. But he attributes different combinations of values to the determinable properties that characterize the state of the system at the first stage: population size , and gene frequencies.  Whereas for Fisher  is very large, for Wright the population is of intermediate size are subdivided into smaller groups. Fisher tracks a single gene throughout the process, whereas Wright contemplates different combinations of genes whose interactions (“epistatic interactions”) generate different adaptive peaks in the surface of selective values. These values fix different beginnings, middle, and ends in their respective narratives; the different values of  allow for a different significance of random drift vs. selection.   Patrick Phillips, Sarah Otto, and Michael Whitlock have expressed Fisher’s and Wright’s approaches to genetic configurations:109 Fisher believed that the interactions of alleles at different loci are relatively unimportant and that the evolutionary future of an allele could be well summarized by its effect averages across all genetic backgrounds. Consequently, Fisher believed that the force of natural selection, rather than idiosyncratic interactions among genes, is paramount in determining the evolutionary trajectory 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  108 Barton and Whitlock (1997) provide a review of the theoretical results regarding phases 1 and 2; for reviews and discussion of the shifting balance that takes into account the three phases, see Wade (1992), Coyne et al. (1997) and Wade and Goodnight (1998).  109 On this very subject Steven Frank’s contribution to Svensson and Calbeck eds. (2012) should be consulted (Frank 2012, p. 49-50). 	   158	  of the population. Wright on the other hand, believed that these epistatic interactions are central, as they define the valleys and peaks of the fitness landscape [surface of selective values] within which organisms evolve. (Phillip and Otto and Whitlock 2000, p. 20)  Fisher wanted then to give further theoretical consistency to his narrative theory. In the Preface, he characterizes The Genetical Theory of Natural Selection as a first attempt “to consider the theory of Natural Selection in its own merits” (Fisher 1930/1990). This involved establishing a theoretical principled that expressed the causal connection between the structure of genetic variability at a given time in a population and the adaptive improvement produced by natural selection as a theoretical principle.  Such a principle was formulated as Fisher’s Fundamental Theorem of Natural Selection, in chapter 2 of Fisher (1930/1999): “The rate of increase in fitness [adaptive improvement] of any organism at any time is equal to its genetic variance of fitness at that time [structure of genetic variability]” (p. 35).  Interpretations of Fisher’s Theorem, which began with Price (1972), have shown that the theorem singles out the increase in fitness ascribable exclusively to natural selection acting through changes in gene frequencies (Edwards 1994, 2014). Fisher’s theoretical principle expresses a fundamental causal link between changes in adaptation and changes in gene frequencies by natural selection. As Alan Grafen has aptly put it, Fisher thought that his fundamental theorem isolated what we might call the adaptive engine of natural selection” (Grafen 2003).  We see how Fisher’s and Wright’s mathematical frameworks were in keeping with their generalized narratives of the evolutionary process. They developed alternative frameworks for evolution, which, in broad retrospective strokes can be respectively 	   159	  characterized as a theory of evolution in large, homogeneous populations, and a theory of evolution in structured (subdivided) populations.110  The heuristic and structural roles of Fisher’s and Wright’s narratives go a long way in shaping the kind of mathematical framework they developed. Heuristically speaking, their narratives provided them with spaces of possibilities where certain fundamental causal structures were laid out and their outcomes explored. Structurally speaking, their narrative theories played a constitutive role in their mathematical frameworks.  In the next section, the explanatory role of Fisher’s and Wright’s narratives becomes prominent, when I revisit William Provine’s work on the Fisher-Wright controversy over the causes of variability. As Provine highlights it, Fisher and Wright could reach agreement over mathematical differences, but never over their narrative theories. Furthermore, mathematical agreement did not settle their narrative differences over the causal structure of the evolutionary process. I start with Provine’s example of mathematical agreement, and, in my terms, narrative disagreement.   5.4 The Debate 5.4.1 The Rate of Decay of Genetic Variability.  According to Provine, Fisher and Wright could reach agreement over a quantitative discrepancy and still disagree over their “qualitative” (narrative) theories. As a preamble to discussing Provine’s account of the Fisher-Wright controversy, I describe how the 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  110 For a paper-length particularly lucid and insightful exposition and comparative discussion of the main results of both frameworks, see Barton and Whitlock (1997). Masterful textbooks discussion can be found in Felsenstein (1978), and Charlesworth and Charlesworth (2010). 	   160	  interaction between Fisher and Wright was crucial to establishing the theoretical framework of population genetics. Some episodes of the controversy took place in the context of that interaction.  The crucial initial step towards establishing the mathematical framework of population genetics was taken by Fisher in his 1922 paper “On the Dominance Ratio.” Fisher states its goal as follows: “The present note is designed to discuss the distribution of the frequency ratio of the allelomorphs [alleles] of dimorphic factors, and the condition under which the variance of the population may be maintained” (Fisher 1922/1990, p. 298). Evolution consisted in changes in the frequencies of genes. Fisher’s insight was to consider the population as a statistical aggregate of gene frequencies (“frequency ratios”) and to determine their equilibrium distribution, just as Maxwell had done regarding the velocities of molecules in a gas; instead of the velocity of a single molecule Maxwell obtained a statistical distribution of velocities at equilibrium.111  In a note to his 1922 paper, Fisher writes that in order to fully elucidate the  “genetical situation” of populations; “It was first necessary to form an opinion on the distribution of the gene ratios of factors exposed to different selective conditions, and then to ascertain their respective contributions to the genetic variance, and to selective progress” (Author’s Note to Fisher 1930, paper 86 of the Collected Papers). Provine has aptly characterized Fisher’s approach:  Fisher’s conception [in “On the Dominance Ratio”] was that an evolving population could be characterized at any time by the statistical distribution of genes in the population. The evolutionary history of the population became simply the history of the changes in this statistical distribution of genes (Provine 1990, p. 202).   	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  111 An insightful exposition of Maxwell’s approach and his derivation can be found in Torretti (1999).  	   161	   In his 1930 review of Fisher’s masterpiece, The Genetical Theory of Natural Selection (Fisher 1930), Wright gave a clear and succinct statement of the approach: The central problem in the analysis of statistical consequences of Mendelian heredity is that of determining the distribution of gene frequencies under the pressures of mutation, selection, migration, etc., and not less important, as affected by size of population. Under given conditions, what proportion of the genes will be fixed? How many will have frequencies in the neighbourhood of 50%? How many 99%? How rapidly will new mutations attain fixation under favourable selection? (Wright 1930, p. 350)  Wright’s adoption of Fisher’s approach, upon reading Fisher (1922) can be seen as an initial mathematical agreement that was to have far reaching consequences. Between 1922 and 1931, Fisher, Wright, and J.B.S. Haldane had laid down the mathematical framework upon which population genetics was to develop.112 The state of a population was characterized as a distribution of gene frequencies, and the shape of this distribution was mathematically investigated under the influence of random and deterministic factors. It is remarkable that while converging to a common mathematical framework, Fisher and Wright developed radically different narrative theories of evolution.  Let us now return to Fisher’s letter to Wright where he emphasized that “little discrepancies” with Wright were clearing up, and that the non-mathematical parts of The Genetical Theory of Natural Selection, where the mathematics had been left undone, were for him the most important parts. Provine follows with a comment worth quoting in full: Fisher’s insight here is accurate for Wright’s work as well as for his own work. Without a clear understanding of Fisher’s point here, one cannot appreciate the 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  112 See Provine (1971/2001), for historical account of the early years of population genetics from the background debates between “Biometricians” and “Mendelians,” up to Fisher, Wright, and Haldane. For a paper length account of  those crucial years, there is no better place than Edwards (2001).  	   162	  tension between the evolutionary views of Wright and Fisher. With this letter, both Wright and Fisher knew that their most quantitative results agreed in all significant particulars. What divided them was decidedly not the differences in their quantitative analyses but their qualitative views about the process of evolution, on which they differed greatly. (Provine 1986, 266)  The main elements of Provine’s interpretation are present in this passage. First, Fisher and Wright’s differences were over their “qualitative” theories, and not over their quantitative ones. And Provine further remarks that their mathematical theory was insufficient “to encompass their qualitative ideas of evolution in nature” (ibid).  Provine did not say much about the nature of Fisher’s and Wright’s “qualitative” theories, nor why they were the source of controversy despite mathematical agreement. When Provine argues that Fisher and Wright’s differences are over their qualitative theories, I argue that it is their narrative theories that are at stake. This will lead us to see why their mathematical theories did not encompass their narrative theories.    In effect, Provine writes: “On all occasions, when Fisher and Wright appeared to disagree on quantitative questions, they were able to settle the differences and reach near total agreement” (Provine 1985/1992, p. 202). Provine’s example of this is the calculation of the rate of decay of genetic variation that was mentioned above. Without selection, random drift depletes genetic variability. Fisher had calculated the rate of decay of variability to be 1/4N (Fisher 1922). Wright calculated it to be 1/2N (Wright 1931). In a letter in 1929, Wright reported the discrepancy to Fisher. Later, Wright sent Fisher his 1931 paper in manuscript. In a letter in October 1929, Fisher writes: (…) I have now fully convinced myself that your solution is the right one (…)” (cited in Provine 1986, p. 259).  Fisher writes: “With this correction I find myself in entire agreement with your 	   163	  value 2N for the time of relaxation and with your corrected distribution of factors in the absence of selection” (ibid.). In 1930, he published “The Distribution of Gene Ratios for Rare Mutations,” where he acknowledged the error, and obtained the correct result using more elegant and sophisticated mathematics. In the author’s note to this paper, Fisher summarizes:  Among other results [of the 1922 paper], the conclusion was drawn that in the total absence of mutations and of selective survival, the quantity of variation, the variance, of an interbreeding population group would decrease by reason of random survival, at a rate such that “the time of relaxation” was 4n generations, where n is the number breeding each generation. (Fisher 1930, p. 205)  And tells the reader that During last year [1929] Professor Sewall Wright of Chicago has been good enough to send me in MS. an investigation in which, while confirming may other conclusions of my paper, he arrives at a time of relaxation of only 2n generations. (Fisher 1930, p. 205)  Fisher is to “eradicate the error by giving a more rigorous and comprehensive treatment of the whole subject” (ibid.).  In his review of Fisher’s The Genetical Theory of Natural Selection already cited above, Wright discusses the details of the quantitative discrepancy, and expresses their agreement:   Summing up, our mathematical results on the distribution of genes frequencies are now in complete agreement as far as comparable, although based on very different methods of attack. (Wright 1930/1986, p. 352)   The expressions of agreement are eloquent. Equally eloquent are expressions of “Differences in Interpretation,” which is the title of a whole section in Wright’s review of Fisher’s book.  Let’s quote Wright: Dr. Fisher is interested in the figure 1/2N, measuring decrease in variance, only 	   164	  because of its extreme smallness, from which he argues that the effects of random sampling are negligible in evolution (except as bearing on the chances of loss of a recently originated gene). (Wright 1930/1986, p. 83)  Wright is in effect saying that for Fisher the effects of random sampling are negligible in evolution except during the first stage of Fisher’s process. This is a minor role for drift, in Wright’s view.  As it has been stated already, for Wright, drift is crucial to how new genetic combinations eventually move towards a region of higher adaptation (adaptive peaks) through natural selection. For Fisher, natural selection needs no such aid. Without random sampling, Wright posits, evolution would get stuck at a single adaptive equilibrium. As Michael Whitlock has stated it:  Wright, in his shifting balance theory (SBT) of evolution, posited that a species becomes stuck on the local equilibrium of an adaptive peak, and can only move to the domain of attraction of a higher peak by the action of genetic drift followed by subsequent selection (Wright 1931a, 1932; Simpson 1953; Barton and Rouhani 1987, 1993). (Whitlock 1997, p. 1044)   Wright stresses his difference with Fisher: I on the contrary, have attributed to the inbreeding effect [effects of random sampling] measured by this coefficient, an essential role in the theory of evolution, arguing that the effective breeding population, represented by N of the formula, may after all be relatively small compared to the actual size of the population. (Wright 1930, p. 83)  Wright highlights the role of drift by emphasizing that he considers a smaller population size as the “effective breeding population,” which is an important parameter in his mathematical framework of evolution, the effective population number.  For Fisher, in contrast:  Both periods [4N and 2N] are in most species so enormous that they lead to the 	   165	  same conclusion, namely that random survival while of great importance in conditioning the fate of an individual mutant gene, is a totally unimportant factor in the balance of forces by which the actual variability of the species is determined. (Fisher 1930, p. 205. Italics added.)  Fisher is in effect saying that drift is important in the first event-type of his narrative. Other than that, drift is not important in shaping the “balance of forces” that shape the genetic structure of populations.  In his review of The Genetical Theory of Natural Selection, Wright proceeds by making explicit, for the first time (Provine 1986), his alternative view of evolution in a way that gives the flavor of his narrative in the making. Due to the reduced size of the population, there is “random drifting of the gene frequencies about their mean positions of equilibrium. In such a population we can not speak of single equilibrium values [as in Fisher’s large population scenario] but of probability arrays for each gene, even under constant external conditions” (Wright 1930/1986, p. 85).  If populations are too small, random drifting leads to extinction. But in populations of intermediate size it would not:  At a certain intermediate size of population, however, (relative to prevailing mutation and selection rates), there will be a continuous kaleidoscopic shifting of the prevailing gene combinations, not adaptive itself, but providing an opportunity for the occasional appearance of new adaptive combinations of types which would never be reached by a direct selection process [i.e., Fisher’s mass selection]. (Wright 1930/1986, p. 85. Italics added)   The contrast with Fisher cannot be stronger. That new adaptive combinations would never be reached by selection alone motivates the three-phases of Wright’s process, which just begins to be adumbrated in these lines. Wright’s colorful description of the process in terms of a “kaleidoscopic shifting” of combinations was used in several papers 	   166	  (1932, 1935, 1942, 1949, 1951). Wright describes the kind of evolutionary process that follows: There would follow thorough-going changes in the system of selection coefficients, changes in the probability arrays themselves of the various genes and in the long run and essentially irreversible adaptive advance of the species. It has seemed to me that the conditions for evolution would be more favorable here than in the indefinitely large population of Dr. Fisher’s scheme. It would, however be very slow, even in terms of geologic time, since it can be shown limited by mutation rate. (Wright 1930/1986, p. 86).   And here is Fisher’s view in full:  A population of a thousand million or a billion individuals can thus only exhibit the most insignificant fraction of the possible combinations, even if no two individuals are genetically alike. Although the combinations which occur are in all only a minute fraction of those which might with equal probability have occurred, and which may occur, for example, in the next generation, there is beyond these a great unexplored region of combinations none of which can be expected to occur unless the system of gene ratios is continuously modified in the right direction. There are moreover, millions of different directions in which such modification may take place, so that without the occurrence of further mutations all ordinary species must already possess within themselves the potentialities of the most varied evolutionary modifications. It has often been remarked, and truly, that without mutation evolutionary progress, whatever direction it may take, will ultimately come to a standstill for lack of further possible improvements. It has not often been realized how very far most existing species must be from such a state of stagnation, or how easily with no more than one hundred factors a species may be modified to a condition considerably outside the range of its previous variation, and this in a large number of different characteristics. (Fisher 1930/ 1999, p. 96)  For Fisher, species are very far from the state of stagnation from which, according to Wright, species can only escape through drift. No factors other than selection and mutation and a changing environment are required for the adaptive progress of species according to Fisher.  For Wright, drift boosts the possibility of adaptive evolution by allowing the appearance of new adaptive combinations. In this sense, drift increases the possibilities of 	   167	  natural selection, which is present in all three phases of the shifting balance process.  We see that the value 1/2N is viewed fundamentally different in Fisher’s and Wright’s different narrative representations of evolution, with N representing a large population size to Fisher vs. a smaller local population size to Wright (Wade 1992). Fisher’s and Wright’s agreement over a mathematical result does necessitate agreement over their narratives. This is why “the level of quantitative analysis available was insufficient to encompass their qualitative ideas of evolution in nature,” as Provine remarked above. In disagreeing about their narratives, Fisher and Wright were disagreeing about the causal structure of the evolutionary process. Right from the beginning, their shared mathematical framework was motivated by and embedded in radically different narrative representations. Such representations, which started as mental sketches, later became explicit theories, and were the source of their persistent debates.  A second form of the debate, concerns the evolution of dominance, which takes place roughly at the same time as the discrepancy over the rate of decay in genetic variability and conforms to the same pattern of quantitative agreement vs. narrative disagreement. This example also illustrates how narrative theories play a heuristic role before they have been formulated as full-fledged mathematical theories. As we shall see, it was Fisher’s account of the evolution of dominance that made Wright realize that he had a radically different understanding of the evolutionary process. 	   168	   5.4.2 The Evolution of Dominance.  New theories usually face challenges to their explanatory power. Darwin’s theory of natural selection was no exception in this respect. Indeed, around the 1900s, there was a period that Julian Huxley described as the “eclipse of Darwinism” (Bowler 1983).  In the years that followed, biologists sought out evolutionary explanations for phenomena that initially appeared puzzling, asking how natural selection might underlie these features. For example, one phenomenon that appeared to defy explanation by natural selection was dominance. For dominance, the puzzle was why individuals carrying both wildtype and mutant alleles were often similar to the wildtype, even for mutants that had just appeared. To undestand the puzzle further, it is worth briefly delving into the details. Genes come in different combinations of alleles. The pea color gene examined by Gregor Mendel, for example, had two alleles coding for yellow and green. Upon crossing, some alleles are expressed in the resulting phenotypes, while the other alleles present remain “hidden,” unexpressed at the phenotypic level. An allele A of the former type is called “dominant,” while an allele a of the latter type is called “recessive.” Pea plants carrying both yellow and green alleles bear yellow peas, that is, the yellow allele is dominant, while the green allele is recessive.  With complete dominance, the heterozygote Aa looks exactly like the homozygote AA. In nature, traits that are most frequently found in natural populations, i.e., “wildtype alleles,” exhibit dominance, while mutant alleles tend to be recessive. For Fisher, the prevalence of dominance in wildtype alleles called for an evolutionary explanation, in 	   169	  terms of their selective advantage over alternative wildtype alleles that were less dominant.   In a series of papers, Fisher applied his theoretical framework to provide a selective explanation for the phenomenon of dominance (1928, 1929, 1930/1999).  Fisher noted the problematic nature of dominance for natural selection:  This feature in the behavior of multiple allelomorphs [dominance of the wild type] appears to offer a serious difficulty to the theory that the evolutionary adaptation of specific forms has taken place by the occasional and gradual replacement by mutant genes of the allelomorphic wild type genes from which they arose. For, in their dominance the wild type genes appear to be clearly of a different nature from the mutant genes which arise from them. (Fisher 1928, p. 116)  In other words, the wildtype alleles of today were mutant alleles when they first arose. So, how can there be a difference in kind between the dominance property of wild-type and mutant alleles? Fisher outlines his answer:  This difficulty will lose its force if it appears that there is a tendency always at work in nature which modifies the response of the organism to each mutant gene in such a way that the wild type tends to become dominant. It is the purpose of the present paper to examine this possibility. (ibid. Emphasis in the original)  In his theoretical models, Fisher explores whether dominance is an evolved tendency that results of natural selection gradually accumulating beneficial substitutions that modify (“modifier genes”) and increase dominance levels of the wild-type over long periods of time. Under this view, dominance was the result of the action of genes that caused heterozygotes to resemble homozygotes.  Fisher’s account of dominance follows the order of events in his narrative with new modifiers alleles appearing and then rising in frequencies. The action of modifiers, in making the heterozygotes resemble homozygotes, counters the deleterious effects of the 	   170	  recessive mutants (Otto and Bourguet 1999). In that way, such modifiers would be beneficial to their bearers and would be preserved and increased in numbers by natural selection. Dominance would evolve as a consequence of selection for modifiers of dominance.  In contrast, Wright’s account of dominance was not based on his narrative. He took a physiological approach. According to Wright, genes produced enzymes, and dominance and recessivity were associated with high or low gene activity; they were the result of the workings of genes in metabolic networks.  Fisher published his first paper on the evolution of dominance in 1928 in The American Naturalist, and Wright immediately wrote a response in 1929 in the same journal. What motivated Wright’s rapid response? Wright explained the reason of his interest in Fisher’s account of dominance some years later:  My interest in his [Fisher’s] theory of dominance was based in part on the fact that I had reached a very different conception of evolution (1931) [“Evolution in Mendelian Populations”] and one to which his theory of dominance seemed fatal if correct. As I saw it, selection could exercise only a loose control over the momentary evolutionary trend of populations [phase 2]. A large part of the differentiation of local races and even of species was held to be due to the cumulative effects of accidents of sampling in populations of limited size [Phase 1]. Adaptive advance was attributed more to intergroup than intragroup selection” [Phase 3] (Wright 1934/, p. 200).   The reading of Fisher’s 1929 paper on dominance made Wright aware of Fisher’s different narrative representation of evolution. But Wright, as Provine notes, nowhere refers to his theory in his first response to Fisher: “Thus in the first published interchange between Wright and Fisher it was impossible to detect that what was really at issue was two basically different theories of evolution in nature” (Provine 1985, p. 214). What was 	   171	  explicit were their differences in their views on the efficacy of very weak selection.  Fisher’s and Wright’s narratives framed their thinking about evolution well before they were explicitly formulated as theories. The debate over dominance is initially about their narratives as mental sketches of generic scenarios – mental models – of evolutionary change (1985, 1986). Wright’s reading of Fisher’s first paper on dominance produced a clash of narrative mentalities over the causal structure of evolution. They had opposed views on the efficacy of very weak selection. As in the case of the decay of genetic variation, for Provine, in the debate over dominance Fisher and Wright agree over their mathematics while disagreeing over their qualitative (narrative) theories. Indeed, in his response to Fisher, Wright presented a model where he calculated the selective strength of Fisher’s modifiers, to conclude that they were very low, of the order of the mutation rate.  Fisher agreed with this, and states that Wright’s “primary formulas differ in no essential respects from my own and the selective intensity which inclines Professor Wright to reject the theory is in fact the same that originally led me to adopt it” (Fisher 1929, p. 553). Provine emphatically declares: “No statement could be more true or accurate, or revealing of the qualitative, as opposed to quantitative differences in the fundamental views of evolution of Wright and Fisher” (1986, p. 249). Or, as I shall put it, revealing of the narrative differences between Wright and Fisher.   Fisher thought that, relative to other evolutionary forces, such minute selective intensities were effective acting over long enough periods of time, whereas Wright thought that drift, or other evolutionary forces would wipe them out.  Wright thought that if something like Fisher’s account of dominance was correct, this 	   172	  would be fatal to his view of evolution because drift would be incapable of opposing even the weakest selection pressures and bring subpopulations in the vicinity of other adaptive peaks: “If either was correct on the evolution of dominance, it was perceived by the other as fatal to his entire conception of evolution. No wonder each defended his theory of the evolution of dominance with such vigor” (Provine 1986, p. 302).  Provine highlights that the main point of contention was the “population number” N. Wright argues: Unfortunately, it is difficult to estimate N in animal and plant populations. In the calculations, it refers to a population breeding at random, a condition not realized in natural species as wholes. In most cases, random interbreeding is more or less restricted to small localities [local sub-group size]. These and other conditions such as violent seasonal oscillation in numbers may well reduce N to moderate size, which for the present purpose may be taking as anything less than a million. If mutation rate [mutation can also overwhelm the small selection strengths] is of the order of one in a million per locus, an interbreeding group of less than a million can show little effect of selection of the type which Dr. Fisher postulates even though there be no more important selection process and time be unlimited. (Wright 1929b, p. 560)   Wright’s narrative scenario for evolution is in the background. Populations in nature are not randomly breeding except in small, restricted localities; this and other factors greatly reduced the effective population size to much less than the actual number of breeding individuals in a species.113 Recall that in the first phase of the shifting balance process populations of intermediate size are subdivided into smaller subgroups or demes.  Provine reproduces Fisher’s reply to Wright: I am not sure I agree with you as to the magnitude of the population number N. To reduce it to the number in a district requires that there shall be no diffusions [no migration] even over the number of generations considered. For the relevant purpose I believe N must be usually the total population on the planet, enumerated at sexual maturity, and at the minimum of the annual or other periodic fluctuation. For birds, twice the number of nests would be good. I am glad, however, that you 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  113 For an insightful discussion of the concept of effective population size see Chapter 4 of Rice (2004).  	   173	  stress the importance of this number. (Fisher to Wright, 13 August 1929; in Provine 1985/1992, p. 215)   The difference is acute indeed. Fisher holds N to be as large as the total population of the planet! Provine argues that at this point of their exchanges over dominance, “both Fisher and Wright knew that the real issue between them was not merely a disagreement about the evolution of dominance, but a deep disagreement about the evolutionary process in general” (Provine 1985/1992, p. 215-216).  But, exactly what is this deep disagreement about? Why is the truth of one theory fatal to the “entire conception of evolution” of the other? How, for instance, do their discussions over N reflect such a deeper disagreement? I have argued that Fisher’s and Wright’s theories are generalized narratives that represent the causal structure of the evolutionary process, as a sequence of causally connected event-types. Consequently, Fisher and Wright’s deep disagreement is about the causal structure of evolution.  Provine highlights that Fisher’s mathematical framework harmonizes with his account of dominance. In fact, this happened only because Fisher focused on the part of the result that fits with his narrative (the sign of selection for dominance), and not the part that did not (the size of the selected effect), which he dismissed.  Wright’s reaction to Fisher’s 1929 paper speaks of the theoretical force of their narratives. The kind of power that Fisher’s account of dominance attributed to natural selection was extremely unlikely given the causal structure postulated by Wright’s narrative, where natural selection exercised control of the evolutionary process only when more powerful than other forces, particularly drift (in the second phase).  	   174	  If Fisher’s narrative represented the true causal structure of the evolutionary process and dominance could be brought about by natural selection acting on modifiers of such minute selective strengths, given the other evolutionary forces at play, Wright’s narrative would postulate the wrong causal structure. Fisher and Wright’s narratives represented incompatible causal structures in nature.  The heuristic role of narratives is crucial in the debate over dominance, as Fisher and Wright never referred to explicitly formulated theories. As frames for exploring a space of possibilities in which causal structure is discerned, narratives can suggest or rule out certain kind of explanations and certain kinds of mathematical models. Let’s see this in more detail.  As hinted above, Fisher’s explanation of dominance follows the two-stage pattern of his generalized narrative: (recessive) mutations are introduced together with genes that modify other genes and survive or become extinct due to random processes, modifiers that make heterozygotes resemble the dominant homozygote wild-type increase in frequency.  Fisher’s narrative provides the framework in which he conceives his explanation of dominance. In thinking about why new mutations tend to be recessive and masked by the wild-type alleles already present within a population, Fisher expanded the scope of his narrative to understanding how genetic systems could evolve.  That is, he applied his narrative (mutations arising, surviving the vagaries of chance loss, and rising by selection to fixation) to mutations that "modify" the genetic system, altering the dominance of wildtype alleles. In this sense, the heuristic role gives rise to the explanatory role.    	   175	  And, by expanding the scope of his narrative to the evolution of genetic systems, Fisher's narrative suggested the type of mathematical model that he needed to develop: a model with at least two genes, one gene bearing wildtype and mutant alleles, and a second one bearing alleles that would alter the dominance properties of the first.  Fisher's narrative – his attempt to see the world in terms of the selective spread of mutations – led him to create a certain type of model, modifying the dominance properties of a gene.  The narrative played a heuristic role for Fisher, specifying what model, out of the world of possible models, needed to be developed.  In Wright’s case, his narrative rules out the Fisherian form of explanation, and reinforces his physiological approach. That dominance evolves by the Fisherian process is very unlikely for Wright. This illustrates how, playing a heuristic role, narratives constrain the form and the kind of explanation worth pursuing, and also the kind of mathematical model worth formulating.  Fisher and Wright agreed over their derivations of the selective strength of modifiers for dominance, but these selective values were placed in different causal structures, which led to different interpretations of dominance evolution: modifiers increasing in frequency and making heterozygotes resemble the wild type vs. drift swamping those minute selection coefficients and maintaining the genetic composition of populations fluctuating around their equilibria. A quotation from Daniel Hartl nicely summarizes the points at hand: There, precisely is the rub: Fisher implicitly invoking a population so large that even tiny forces would in the end win out, Wright believing that accidents of sampling in populations of limited size would swamp out such small selective effects. When he was asked about Fisher’s theory at a group discussion at the University of Wisconsin in 1967, I recall Wright saying that Fisher’s theory was all right, but, considering the magnitude of the forces, he thought it about as likely 	   176	  that dominance would evolve by Fisher’s mechanisms as the chance that a sustained gentle wind might blow a loaded freight car along a railroad track. (Hartl 1989, p. 184)  Sarah Otto and Denis Bourguet have aptly characterized the Fisher-Wright debate: The debate had deep philosophical roots reaching beyond the evolution of dominance: Fisher and Wright were essentially arguing over the power of selection (Fisher 1929; Wright 1934a; Provine 1986). Fisher claimed that given sufficient time, even extremely weak selection would result in a large cumulative impact on evolution. Wright countered that extremely weak selection would be overwhelmed by mutation (1929b), pleiotropic effects (1929b), and drift (1929a). (Otto and Bourguet 1999, p. 561-562)  The “deep philosophical roots” lie, in the fact that the debate is about the causal structure of evolution. The power of natural selection is different in each narrative. Fisher and Wright’s differences over dominance derive from their narrative differences over the causal role and limitations of selection in the evolutionary process.  In this episode narratives play predominantly heuristic and explanatory roles. As Fisher and Wright continued to develop their theoretical frameworks, they became constitutive of them, and thus played a structural role. Let’s now consider one further episode in the controversy.   5.4.3 Panaxia dominula.  The next debate between Fisher and Wright has an organism occupying center stage; a moth known as tyger moth which lived in Oxford, England. In contrast to the dominance case, when the Panaxia dominula debate took place in the late 1940s, mass selection and the shifting balance have been explicitly formulated as theories, and they were structurally integral to Fisher’s and Wright’s theoretical frameworks.  	   177	  Based on their narrative theories, Fisher and Wright are going to give radically different explanations for why distinct morphs of the same species exist in a given area (“polymorphisms”). The maintenance of such “conspicuous polymorphisms” became a target for evolutionary explanation. In the early 1940s, the prevailing view among evolutionists, e.g., Ernst Mayr and Theodosius Dobzhansky, was that such polymorphisms were the result of chance processes, i.e., random genetic drift, and thus were selectively neutral (non-adaptive) largely influenced by Sewall Wright’s shifting balance theory (Provine 1985, 1986; Beatty 1987).  Fisher and E. B. Ford defended natural selection as an explanation for polymorphisms in their paper “The Spread of a Gene in Natural Conditions in a Colony of the moth Panaxia Domiluna L” (Fisher and Ford 1947).  As Provine described it: “It was precisely the view that conspicuous polymorphisms were selectively neutral, with their distributions determined by random drift, that so stimulated Fisher and Ford (1986, p. 420). A colony of Panaxia in Oxford, was ideally suited for Fisher and Ford study. The most common form was the heterozygote, or medionigra; and the rare one was one of the homozygotes, kown as  bimacula. The frequency of medionigra fluctuated markedly over the years, and the particular characteristics of the colony (limited geographic area, small size) permitted the estimation of population size using mark-recapture techniques. The question then was: “How much fluctuation of the medionigra gene occurred from year to year, and could this fluctuation be explained by random drift in a population of the size calculated?” (Provine 1986, p. 412). The frequency of a gene can increase in one generation, and decrease in the next, 	   178	  just as a result of chance variation in reproductive output. That kind of chance fluctuation in the frequencies of genes over time is called random genetic drift.114 But gene frequencies can also fluctuate randomly because the effects of natural selection vary in space and time; outcomes that appear to be random can instead be the result of fluctuating selection. Fisher and Ford argued that the fluctuations of the medionigra gene were produced by varying natural selection and not by random genetic drift. This they claim undermined Wright’s theory of evolution in sub-divided populations.   As we know, Wright attributed an important role for drift in the first phase of his theory: this served as the basis for the claims that polymorphisms were adaptively neutral.115 In section 6 of their paper, “The Significance of Changes in Gene-Ratio,” Fisher and Ford start by emphasizing that on Wright’s view, evolutionary progress proceeds most effectively in sub-divided populations through random, non-adaptive changes due to reduced population size.  The possibility in which they are interested is one which, “if established, would cut at the root of the whole theory, namely, that populations, large and small, are subjected from generation to generation to selective intensities capable of producing greater fluctuations in gene-ratios than could be ascribed to random sampling” (p. 168). Their paper then is devoted to establish this possibility. Indeed, in the summary of their findings they report: 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  114 Wonderful expositions and discussion of theory of genetic drift can be found in Felsenstein (1978), Barton, et al. 2007, and Charlesworth and Charlesworth (2011).  115 Provine has documented the changes in Wright’s attitude towards the importance of drift in evolution, whose time frame coincides with what S.J. Gould has called the “hardening of the Modern Synthesis;” the transition from a pluralistic approach regarding the causes of evolution, to a more selectionist approach (Gould 1983). Wright insisted that he never thought of random drift as an alternative to natural selection, c.f. (1948, 1970, 1977), and regretted that he was understood to have done so (Provine 1986, p. 420).  	   179	  It is, in fact, found that the observed fluctuations in gene-ratio are much greater than could be ascribed to random survival only. Fluctuations in natural selection (affecting large and small populations equally) must therefore be responsible for them. (p. 173)  Their closing remark goes:  Thus our analysis, the first in which the relative parts played by random survival and selection in a wild population can be tested, does not support the view that chance fluctuations in gene-ratios, such as may occur in very small isolated populations, can be of any significance in evolution. (ibid.)   In their summary of Wright’s view, Fisher and Ford wrote: “Wright believes that such non-adaptive changes in gene-ratio may serve an evolutionary purpose by permitting the occurrence of genotypes harmoniously adapted to their environment in ways not yet explored, and so of opening up new evolutionary possibilities” (p. 167).  In opposition to this, Fisher and Ford agued that even in large populations, evolution would explore different genetic combinations, due to fluctuating natural selection. In other words, they argue that a chance exploration of novel combinations is also possible within the causal structure of Fisher’s narrative, e.g., if fluctuations in gene frequencies are due to variable selection across space or time in large populations.  Variable natural selection in nature is well confirmed. The pattern  that “natural populations in general, like that to which this study is devoted, are affected by selective action varying from time to time in direction and intensity, and of sufficient magnitude to cause sufficient variation in all gene ratios, is in good accordance with other studies of observable frequencies in wild populations” (p. 171).  This fact, they emphasize, is fatal for Wright’s theory: “Evidently, however large a population might be, its gene ratios will fluctuate in the same manner and to approximately the same extent as those of the smallest isolated population which can be 	   180	  expected to persist in nature” (ibid). This is best understood in terms of narrative structure. Small isolates are not necessary for gene frequencies to fluctuate by chance; thus, evolution does not require the kind of beginning that Wright postulates. If the beginning of the process is undermined the whole narrative structure is undermined: there is no middle, and no end.   Wright’s responded in 1948, Fisher and Ford replied in 1950, and then Wright again in 1951. Wright’s main line of defense was to insist that his claim that evolution was not under the sole control of selection did not mean that drift was an alternative to natural selection; evolution requires both.  In 1970, Wright clarifies misunderstandings regarding his shifting balance theory and refers to the whole exchange between Fisher and Ford and himself: “The most frequent criticism has been by those [Fisher and Ford] who have maintained that random drift was being presented as an alternative to natural selection in the transformation of population” (Fisher and Ford, 1947, 1950; Wright, 1948, 1951a)” (Wright 1970, p. 24).  Wright clarifies his position: This sort of criticism ignores the point that no evolutionary significance has ever been attributed to random drift except as a trigger which occasionally causes selection to be directed toward a new and superior selective peak in the surface of selective values.  To ascribe an effect brought about in this way to either random drift by itself or selection by itself obscures the fact that both have played indispensable roles. (Wright 1970, p. 25)  Wright’s clarification is not going to have much of an impact since Fisher’s narrative selection requires no such trigger. In Wright (1948), he also clarifies that he considered subgroups as partially isolated. The sort of small, fully isolated groups that Fisher and Ford refer to are doomed to extinction. And he insists that he has never given the 	   181	  importance to non-adaptive differentiation that Fisher and Ford attribute to him, along the same lines of the 1970 paper quoted above. He insists that evolution results from a combination of different factors, and that “any one of the factors might play the dominant role, at least for a time, under specifiable conditions (…)” (Wright 1948/1986, p. 499).  Again, this is best understood relative to narrative structure. The role of the different factors, e.g., selection or drift, depends on the stage of the narrative they are in. We can recast Wright as saying that any one of the factors might play a dominant role at a given stage of the narrative, under specifiable conditions.  Wright reiterates his general view, formulated in Wright (1931) that in the long run, “evolution as a process of cumulative change depends on a proper balance of the conditions which at each level of organization – gene, chromosome, cell, individual, local race – make for genetic homogeneity or genetic heterogeneity of the species” (Wright 1948/1986, p. 499).  In their reply, Fisher and Ford (1949) are unimpressed with Wright’s “balance of many factors” defense of his theory. They find it irreconcilable with earlier writings, and quote from Wright (1931) “where he says of non-adaptive radiation [through random movement of subgroups] (p. 208): “In short, this [the shifting balance process] seems from statistical considerations the only mechanism which offers an adequate basis for a continuous and progressive evolutionary process” (Fisher and Ford 1949, p. 118).  Wright’s second reply (Wright 1951), reiterates the same line of defense, and insists that his central theme has always been the “interplay of directed and random processes in populations of suitable structure (…)” (Wright 1951/1986, p. 521). But he also acknowledges that his views on evolution have changed since the early papers that 	   182	  Fisher and Wright cite, and that his early formulations may have been too extreme.116 Be that as it may, it wouldn’t matter much to Fisher and Ford, since what they are contesting is precisely that interplay. In Fisher’s narrative, evolution by natural selection does not need the kind of contribution from drift that Wright postulates in his narrative. In Wright’s narrative as we have seen, drift opens up wider possibilities for selection. For Fisher, the evolutionary process does not require a drift-enhanced exploration of evolutionary possibilities. He has another story to tell. At that point in time, 20 years after the dominance episode, it is clear that the persistence of their controversies is due to irreconcilable differences in how they understand the causal structure of the evolutionary process. All along, the source of the “debates” was a clash of narrative mentalities that grasped the causal complexities of the evolutionary process in radically different ways.    5.4.4. Interpreting the Fisher-Wright Debate  In the previous chapters we have seen how scientific theorizing involves interplay between the narrative and the formal, logico-mathematical aspects of theorizing. I have argued that the narrative is not fully reducible to the formal, e.g., equations, D-N arguments, or if-then conditionals. This is why Fisher and Wright’s agreement over mathematical results never settled their narrative differences.  In “Patterns of Scientific Controversies,” Philip Kitcher (2000) characterizes a “rationalist” view of controversies, according to which the latter are to be settled by mathematical or experimental proof. He makes an observation that can be fruitfully 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  116 Provine has discussed Wright’s shifting attitude on the role of drift in evolution (Provine 1986, 420-435). John Beatty has also discussed it, and the larger influence of Wright’s theory through the work of Theodosious Dobzhansky, in Beatty (1987).  	   183	  applied to my analysis of the Fisher and Wright case: Rationalist accounts face the problem of accounting for the persistence of controversy. If there are rational grounds for favoring one point over another relatively early in the controversy, then some explanation of why apparently intelligent people continue to resist. (Kitcher 2000, p. 25)  Indeed, if mathematical deductions (in D-N arguments) alone could settle scientific debate, then the Fisher-Wright debate would have perhaps ended after the first round of disagreement over the decay of genetic variability. But, as Provine (1985, 1986) has emphasized, and Robert Skipper (2002, 2009) after him, the Fisher-Wright controversy was a persistent one. Provine documented its persistence sisted from 1928 until 1962, the year Fisher died. Skipper has studied debates over Fisher’s and Wright’s general evolutionary theories well beyond Fisher and Wright.  In 2002, Skipper analyses what he calls “the reignited Fisher-Wright controversy,” an exchange that took place between 1997-2000 between Jerry Coyne, Nicholas Barton, and Michael Turelli on one side criticizing Wright’s shifting balance theory, and Michael Wade and Charles Goodnight defending it.117 He concluded that the new Fisher-Wright debate is a “relative significance controversy” sensu John Beatty (1995, 1997). According to Beatty, evolutionary biologists typically argue about the proportion of evolutionary phenomena that their theories correctly explain (Beatty 1997), and not about which is the true, correct theory of the phenomena. In 2009, Skipper extends his analysis and brings up to date the debate over the evolution of dominance and the polymorphism in Panaxia up by reviewing 20 years of the relevant biological literature after Provine (1995). He argues that subsequent 	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  117 Coyne et al., 1997; Wade and Goodnight 1998; Coyne et al., 2000; Goodnight and Wade 2000. Plutynski (2005) provided a different philosophical perspective on this debate. For a biologist’s perspective, see Whitlock and Phillips (2000).   	   184	  developments further support his relative significance controversy interpretation:  The three debates considered in detail in this essay show, among other things, that there is ample room in the domain of evolutionary genetics for both Fisher’s and Wright’s evolutionary views. Differently put, each of the debates considered here is what Beatty (1995) calls a relative significance controversy. Such controversy reflects a theoretical pluralism, or the notion that that the domain under scrutiny is fundamentally heterogeneous, so there can be no expectation that a single theory will explain the entire domain. Thus in such a controversy, the aim is to establish the applicability of some theory or set of theories as opposed to determining the one theory that explains the entire domain. That is, the aim is to determine the significance of a theory relative to another (or others) in the domain. (Skipper 2009, p. 317).  I think that Skipper has convincingly argued that the controversies pro and con Fisher’s and Wright’s theories can be considered relative significance debates in the sense of Beatty (1995), and that this contributes to explain its persistence (Skipper 2002, 2009). My analysis has been limited to Fisher and Wright. I have argued that Fisher and Wright disagreed over their narrative theories of evolution, and that this is crucial to explaining their continued disagreements despite their mathematical agreements. What does this add to Skipper interpretation of the “reignited” Fisher and Wright debate?  It shows how the narrative dimension of theorizing will maintain plenty of room for disagreement insofar as narratives are not reducible to equations or if-then conditionals, and narrative-based explanations do not collapse into the D-N derivations contained in them. As Kitcher indicated, an account of scientific controversies based on paradigmatic reason alone, to use Bruner’s term, would have a hard time explaining why they persist.  So, I argue that the narrative nature of Fisher’s and Wright’s theories matters for Skipper’s interpretation of the post Fisher-Wright debates; they represent different beginning and endings of the evolutionary process, with the factors involved playing 	   185	  different causal roles. The problem is how much of evolution each narrative represents; not which one explains all of evolution.  The reigniting of the Fisher-Wright debate that Skipper documents indicates that Fisher’s and Wright’s narrative theories can be considered foundational for evolutionary biology.  Traditionally, scientific controversies have been thought to be about arguments. Recent work has begun to broaden this picture and include elements other than arguments and logic. It has been argued, for example, that scientists disagree over “shared background assumptions” (Baltas 2000), or their disagreement is produced by rhetorical elements in scientific discourse (Pera 2000), or by conflicting ideals of unification (Kitcher 2000). The debate between Fisher and Wright provides us with an example of the kind of controversy that arises when narratives are involved.   It might be that a relative significance controversy is not the kind of controversy that gets settled. Be that as it may, we have seen why the narrative disagreements between Fisher and Wright could not be settled by their agreements over shared mathematical results. As Skipper observes, “there is ample room in the domain of evolutionary genetics for both Fisher’s and Wright’s evolutionary views” (op.cit., p. 317). Whether the room is a quiet one, is another matter.   5.5. Concluding Remarks.  In this chapter, I have presented historical case studies of narrative theories in evolutionary biology: Darwin’s theory of the origins of species by means of natural selection, and Fisher’s and Wright’s mass selection and shifting balance theories. These theories represent the action of processes and mechanisms in nature by means of 	   186	  generalized narratives. Processes are depicted as a sequence of causally connected event-types, with beginning, middle, and end. The event-types correspond to the stages or phases of the processes involved. The first episode was Darwin’s formulation of the theory of the origin of species by natural selection in the Origin. By showing that Darwin’s theory has a narrative structure, I could provide an answer to the question of how Fleeming Jenkin’s criticism impacted Darwin’s theory. We saw that Jenkin’s criticism led Darwin to modify the theory at the level of the exemplary narratives that provided illustrations of the action of natural selection, while leaving the if-then conditional formulation, and the generalized narrative of speciation untouched.  The second episode came from the history of population genetics, in the form of the Fisher-Wright debate made prominent by William Provine. I re-examined the debate in the light of my analysis of the narrative structure of Fisher’s and Wright’s theories. I argued that being about their narratives, their debate is about the causal structure of the evolutionary process. This, combined with my claim that narratives are not reducible to if-then conditionals, equations, or D-N arguments, explains why Fisher and Wright never reached agreement over their theories of evolution, even if the could sort out mathematical differences. And it also accounts for the persistence of the controversy.  I have also argued that narratives play a heuristic, a structural, and an explanatory role in research. This threefold role is at play in Darwin, Fisher, and Wright.  Their narratives a) shaped and framed their thinking about evolution, and defined a space of possibilities which guided and motivated the kind of mathematical theory that Fisher and Wright developed; b) formed an integral part – were constitutive – of their 	   187	  theoretical frameworks; in Darwin’s case it was the theoretical framework c) Postulated an order of relevant causal factors which provided the basis for explanations of evolutionary phenomena.  This chapter has continued my exploration of narrative theorizing in natural science, and how narratives interact with equations, D-N arguments, and if-then conditionals as components of theoretical frameworks. Recent perspectives on scientific controversies have urged that elements other than logic or arguments play a prominent role, and that controversies are not always about settling arguments. My Fisher-Wright case provides suggests that narratives should make it to the list. Let us know move to some final remarks.   	   188	   	  Chapter 6: Concluding Remarks  In the first chapter of this dissertation, I claimed that a narrative turn in the philosophy of science would contribute to a better understanding of theory. This contrasted with the narrative turn in the humanities, which was a movement away from theory.  Having arrived at my final chapter, I hope the reader has a more or less definite picture of what my initial claim involves. Narratives are constitutive of theory construction, theory structure, and explanation. There lies their threefold role. This goes against the widely held view that narratives play only a heuristic role and drop out once mathematical or otherwise formal theories are in place. Through narrative theorizing, scientists represent scenarios where a certain order of events leads to certain outcomes; the specification of the determinate values of the determinable variables that characterize the states of system allows the theorizer to depict the action of multiple causal factors at a given event that bring about the next. Narratives allow theorizers to represent happenings in the successive states of a system. Through a narrative, a scientist can represent generic beginnings, middles, and ends of a process, and the phenomena to be explained are the end events of that order. This, I claim, is a crucial aspect of how scientists theoretically grasp and explain nature.  The main tenets of this thesis are bound to encounter resistance from narratologists and scientists alike: we have already seen that narratologists distinguish narratives from theories and explanations, and it has been mentioned that scientists 	   189	  consider story telling as bad science. The marginalization of narratives as instances of bad science has made it difficult to explore their role.   In this concluding chapter, I discuss an example of scientists’ critique of narratives. My example is Steven J. Gould and Richard C. Lewontin’s critique of the “adaptationist programme,” epitomized in their paper “The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme” (Gould and Lewontin 1979).  Section 3 of the paper is entitled “Telling Stories.” Gould and Lewontin’s main target is a the explanation of the presence of a given trait in natural populations in terms of their of selective/adaptive advantage. This is done, they argue, through story telling that is often immune to criticism and does not leave room for the consideration of alternative explanations. If an “adaptationist story” could be dismissed because it has failed a test, alternatives could be considered. But this is not what happens: Unfortunately, a common procedure among evolutionists does not allow such definable rejection for two reasons. First, the rejection of one adaptive story usually leads to its replacement by another, rather than to a suspicion that a different kind of explanation might be required. Since the range of adaptive stories is as wide as our minds are fertile, new stories can always be postulated. And if a story is not immediately available, one can always plead ignorance and trust that it will be forthcoming … Secondly, the criteria for acceptance of a story are so loose that many pass without proper confirmation. Often, evolutionists use consistency with natural selection as the sole criterion and consider their work done when they concoct a plausible story. But plausible stories can always be told. (Gould and Lewontin 1979, p. 153. Emphasis added.)  The stories in question explain the evolution of a trait as the “best” adaptive response to a certain environmental factor. I take Gould and Lewontin’s as a typical statement of story telling as bad science: one can always imagine another story and add it ad hoc to explain 	   190	  a certain phenomenon. There are stories as one can imagine them: “just so stories.” No doubt, this is not good science.  In contrast, I have been arguing that narratives are part of good science. Gould and Lewontin’s complaint is that scientists are quick to jump to obvious scenarios, often invoking optimality reasoning, without exploring possible alternatives. What Gould and Lewontin did not highlight is that a proper exploration of alternatives also occurs via narrative reasoning. I suggest that Gould and Lewontin would not be against rigorous narrative theorizing.  In the picture I am proposing, we want narratives whose beginnings are not easy ad-hoc stipulations. In the case of the explanation of traits as adaptations to environmental challenges, for example, the space of outcomes is constrained by energy considerations and developmental processes.   A story about the evolution of a trait has to specify a beginning in terms of determinate values of determinable variables of the system in question: certain energy trade-offs, a set of possible phenotypes, a kind of environment. A beginning so specified will lead to middle and end events of a story that is not the mere result of a biologist’s fertile imagination. In contrast, the beginning of the adaptive stories that Gould and Lewontin are attacking is the very environmental problem for which the trait is an adaptation: they are just so stories.  On the other hand, we have seen that narrative-based explanations can embed D-N elements that further constrain the space of possible outcomes given the specification of a state in the narrative.  Narratives of the evolution of adaptive traits are tested via the development of mathematical models. Summing up: the kind of story-telling that Gould 	   191	  and Lewontin rightly criticize is a story-telling that is not involved in narrative theorizing, as I have characterized it. The stories that were analyzed in the physics case studies do not seem to have been considered “just so stories.” Their beginnings were specified within very clear theoretical constraints. Gould and Lewontin’s critique of story-telling in evolutionary biology reminds us that not all story-telling amounts to narrative theorizing.  I will return to the Gould and Lewontin critique towards the end of this chapter. Before doing that, I would like to sketch the broader picture of science that results once the narrative and mathematical elements have been integrated.   At a given time, there is a diversity of narratives and mathematical formalisms that do not map one-to-one in scientific practice. As I have argued, narrative structure cannot be reduced to mathematical structure. Different narratives can embed the same mathematical formalisms.  In their heuristic role, narratives draw the attention of the theorizer to certain mathematical problems, e.g., the fate of a single gene; the statistical distribution of genes; the relation between fitness and genetic variability; the probability of peak shifts, the stability of a predicted optima.  In this way, narratives can change as the result of novel mathematical results, or mathematical/formal theories can change as the result of novel narratives. This interplay is crucial in shaping the attainment of scientific agreement, as well as the generation of scientific controversy. There can be agreement on how to mathematically characterize a certain system, but disagreement over narrative structure. This leads to conflicting 	   192	  explanations of phenomena. We have seen an example of this in the Fisher-Wright controversy.   A challenge for research on narratives in science is that narratives may not be explicit in scientific papers or textbooks, or they may be buried in the larger text of a paper or in mathematical formalism. This I suggest, is a prime motive for an integration of history and philosophy of science.   Wright is particularly explicit in formulating his narrative, but this might not be the general case. Unfortunately, it is ad-hoc, poorly tested narratives that are more visible and attract criticism. The impact of the Gould and Lewontin type of criticism has been to associate narratives with bad science. What results is a seriously impaired understanding of the role of narratives in research, one that reinforces the view that narrative and good science are at odds.  As I read Gould and Lewontin’s paper, their attack was not on stories per se, but on a certain sloppy use of stories within evolutionary biology. Indeed, later on, Gould and Lewontin independently expressed positive views on the use of narratives but only for historical sciences. That may explain the widespread negative reading of their paper, regarding narratives in natural science.  Gould developed a narrative-based account of the significance of history within evolutionary biology, which I have summarized in Chapter 3, footnote 17.  Lewontin has succinctly expressed his view: “A great deal of the body of biological research and knowledge consists of narrative statements” (Lewontin 1991, 143).  He continues: “Evolutionary biology, like historical geology, soil science, and cosmology, is a historical 	   193	  science. It is the purpose of all of these sciences to provide a correct narrative of the sequence of past events and an account of the causal forces and antecedent conditions that led to that sequence” (ibid.).  As William Wimsatt has put it, referring to Lewontin’s remarks just cited, “[his] account seems right here not only for the obvious historical sciences, but more broadly, for any of those that study complex mechanisms” (Wimsatt 2007, 154). As a first step toward a philosophy of narratives in natural science, the present dissertation supports Wimsatt’s claim.  I end by emphasizing the beginning of another story. 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