UBC Theses and Dissertations

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UBC Theses and Dissertations

Probabilistic causal processes Katz, Jonathan Richard 1982

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PROBABILISTIC CAUSAL PROCESSES by JONATHAN RICHARD KATZ M.A., The U n i v e r s i t y of Manitoba, 1973 A THESIS SUBMITTED IN PARTIAL FULFILMENT THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OP PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Philosophy) We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1982 © Jonathan Richard Katz, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Jonathan Katz _ . , Philosophy Department o f The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 ^ January 21, 1983 Date DE-6 (3/81) i i ABSTRACT Many t h e o r i s t s take c a u s a l i t y to be the heart of s c i e n t i f i c e x p l a n a t i o n . I f we couple t h i s view with the i d e a , again common enough, t h a t causes are something l i k e s u f f i c i e n t c o n d i t i o n s f o r t h e i r e f f e c t s , then we have r a i s e d a d i f f i c u l t y f o r any theory of s c i e n t i f i c e x p l a n a t i o n that admits " f i n a l " (genuine) s t a t i s t i c a l e x p l a n a t i o n s , f o r a s t a t i s t i c a l e x p l a n a t i o n must a l l o w t h a t f a c t o r s r e l e v a n t to an event to be e x p l a i n e d need not determine t h a t event, but only make i t probable to some degree (other than zero or one). I f we do not wish to give up the p o s s i b i l i t y of genuine s t a t i s t i c a l e x p l a n a t i o n s we must e i t h e r (1) give up t h i s c e n t r a l c a u s a l i n t u i t i o n i n e x p l a n a t i o n , or (2) admit that causes act as something other than s u f f i c i e n t c o n d i t i o n s — say i n a p r o b a b i l i s t i c manner. This i s , of course, l i t t l e h e l p unless we can c l e a r l y e x p l i c a t e the n o t i o n of a p r o b a b i l i s t i c cause, one of the tasks I have attempted to accomplish i n t h i s t h e s i s . The g e n e r a l s t r u c t u r e of t h i s e f f o r t i s i n three p a r t s . In the f i r s t chapter I generate the b a s i c concepts u n d e r l y i n g the n o t i o n of a p r o b a b i l i s t i c cause. In t h i s I f o l l o w c l o s e l y the development of t h i s idea as c o n s t r u c t e d by Wesley Salmon. W i t h i n t h i s view s c i e n t i f i c e x p l a n a t i o n c o n s i s t s i n the t r a c i n g of c a u s a l i n f l u e n c e v i a causes as processes, and i n p r o v i d i n g the p r o b a b i l i t y r e l a t i o n s among events which are the product of c a u s a l i n t e r a c t i o n s . In the second chapter I f u r t h e r develop the idea of c a u s a l processes by comparing t h i s n o t i o n w i t h the more t r a d i t i o n a l analyses of c a u s a t i o n , the r e g u l a r i t y and c o u n t e r f a c t u a l t h e o r i e s . There I show how the process ontology very n a t u r a l l y overcomes problems i n both of these views. I a l s o note the advantages t h i s conception of causes holds over these i i i received views with respect to the problem of determinism. In the third and f i n a l chapter I discuss, and attempt to overcome, d i f f i c u l t i e s that are specific to the notion of a probabilistic causal process. iv TABLE OF CONTENTS ABSTRACT i i ACKNOWLEDGEMENTS v i INTRODUCTION 1 Notes - I n t r o d u c t i o n 16 I STATISTICAL EXPLANATION 18 1. N o n - i n f e r e n t i a l E x p l a n a t i o n 18 a) S t a t i s t i c a l Relevance 20 b) Homogeneity 21 c) Screening Off 26 2. R e c a p i t u l a t i o n and Objections 28 3. The Causal-Relevance Model 33 a) Causal Processes 35 b) Causal Forks: Conjunctive and I n t e r a c t i v e 37 4. Objections 44 a) Indeterminism 44 b) The Paradox of P r o b a b i l i s t i c E xplanation 49 c) Other Problems 54 Notes - Chapter I 59 I I CAUSALITY AND PROCESSES 63 1. I n t r o d u c t i o n 63 2. Mackie I: Causes as INUS Conditions 67 3. Mackie I I : Counterfactuals and Causal Processes 73 4. Lewis' Counter-proposal 88 5. C a u s a l i t y and Indeterminism: A Reprise 97 6. P r o b a b i l i s t i c C a u s a l i t y 103 Notes - Chapter I I 112 V TABLE OF CONTENTS - continued I I I PRODUCTION AND PROPAGATION 1 1 9 1. Doing i t the Hard Way 119 a) P o s i t i v e Relevance 119 b) C u t t i n g the Chain 130 2 . Transmission Lines 137 a) P r o b a b i l i t i e s and Processes 137 b) Causal Influence 148 Notes - Chapter I I I 163 BIBLIOGRAPHY 168 ACKNOWLEDGEMENTS V I would l i k e to thank the U n i v e r s i t y of B r i t i s h Columbia and the Department of Philosophy f o r t h e i r generous support while t h i s work was w r i t t e n . I would a l s o l i k e to thank the members of my committee, E l Rand, Steven S a v i t t , and e s p e c i a l l y Edwin Levy, whose encouragement, tempered w i t h patience and c o n s t r u c t i v e c r i t i c i s m , provided the necessary c o n d i t i o n s f o r i t s completion. To my colle a g u e s , comrades, and f r i e n d s I need only say 'thanks'. This work i s dedicated to my mother and f a t h e r . 1 INTRODUCTION Many t h e o r i s t s take c a u s a l i t y to be the heart of s c i e n t i f i c e x p l a n a t i o n . I f we couple t h i s view with the id e a , again common enough, that causes are something l i k e s u f f i c i e n t c o n d i t i o n s f o r t h e i r e f f e c t s , then we have r a i s e d a d i f f i c u l t y f o r any theory of s c i e n t i f i c e xplanation that admits " f i n a l " (genuine) s t a t i s t i c a l e x p l a n a t i o n s , f o r a s t a t i s t i c a l e x p l a n a t i o n must al l o w that f a c t o r s r e l e v a n t to an event to be explained need not determine that event, but only make i t probable to some degree (other than zero or one). I f we do not wish to give up the p o s s i b i l i t y of genuine s t a t i s t i c a l explanations we must e i t h e r (1) give up t h i s c e n t r a l c a u s a l i n t u i t i o n i n ex p l a n a t i o n , or (2) admit that causes act as something other than s u f f i c i e n t c o n d i t i o n s — say i n a p r o b a b i l i s t i c manner. This i s , of course, l i t t l e help unless we can c l e a r l y e x p l i c a t e the notion of a p r o b a b i l i s t i c cause, one of the tasks I have attempted to accomplish i n t h i s t h e s i s . The general s t r u c t u r e of t h i s e f f o r t i s i n three p a r t s . In the f i r s t chapter I generate the bas i c concepts underlying the notion of a p r o b a b i l i s t i c cause. In t h i s I f o l l o w c l o s e l y the development of t h i s idea 1 as constructed by Wesley Salmon. Wi t h i n t h i s view s c i e n t i f i c explanation c o n s i s t s i n the t r a c i n g of causal i n f l u e n c e v i a causes as processes, and i n p r o v i d i n g the p r o b a b i l i t y r e l a t i o n s among events which are the product of causa l i n t e r a c t i o n s . In the second chapter I f u r t h e r develop the idea of cau s a l processes by comparing t h i s notion with the more t r a d i t i o n a l analyses of c a u s a t i o n , the r e g u l a r i t y and c o u n t e r f a c t u a l t h e o r i e s . There I show how the process ontology very n a t u r a l l y overcomes problems i n both of these views. I a l s o note the advantages t h i s conception of causes holds over these 2 r e c e i v e d views with respect to the problem of determinism. In the t h i r d and f i n a l chapter I d i s c u s s , and attempt to overcome, d i f f i c u l t i e s that are s p e c i f i c to the notio n of a p r o b a b i l i s t i c causal process. In the remainder of these p r e f a t o r y remarks I would l i k e to sketch some of the 'generating' ideas and arguments that l ed to the a n a l y s i s presented i n each of these three chapters. Although not i n t e g r a l to the arguments presented l a t e r , t h e i r e x p o s i t i o n here w i l l help to frame the context f o r these arguments, and therefore a s s i s t the reader i n l o c a t i n g h i m s e l f / h e r s e l f w i t h i n the rather large p h i l o s o p h i c a l landscape of causation and e x p l a n a t i o n . (a) Chapter I presupposes a n o n - i n f e r e n t i a l conception of explanation and, w i t h i n such a conception, the p l a u s i b i l i t y of s t a t i s t i c a l g e n e r a l i z a t i o n s which are not e p i s t e m i c a l l y r e l a t i v i z e d . Let us begin with t h i s l a t t e r c l a i m . S t a t i s t i c a l explanations are e s s e n t i a l l y ambiguous. This i s seen most c l e a r l y when we consider s t a t i s t i c a l e x p l a n ation as (Hempelian) arguments from s t a t i s t i c a l g e n e r a l i z a t i o n s or laws, v i a a set of i n i t i a l c o n d i t i o n s , to a co n c l u s i o n which describes the explanandum event. Hempel w r i t e s , I f a given o b j e c t or set of objects has an a t t r i b u t e A which with high s t a t i s t i c a l p r o b a b i l i t y i s a s s o c i a t e d w i t h another a t t r i b u t e C, then the same object or set of objects w i l l , i n gene r a l , a l s o have an a t t r i b u t e B which, w i t h high s t a t i s t i c a l p r o b a b i l i t y , i s associated w i t h non-C. Thus, with each g e n e r a l i z a t i o n we can c o n s t r u c t an argument to each 3 c o n c l u s i o n , C and non-C, f o r any p a r t i c u l a r case. 3 The response to t h i s ambiguity was i n two p a r t s : f i r s t to d i s t i n g u i s h the l o g i c a l , or i n d u c t i v e p r o b a b i l i t y conferred on the conclusion by the premises, from the s t a t i s t i c a l p r o b a b i l i t y mentioned i n the s t a t i s t i c a l g e n e r a l i z a t i o n s e r v i n g as a premise i n the argument; second, to e s t a b l i s h a requirement of " t o t a l evidence" to guide the a p p l i c a t i o n of such i n d u c t i v e s t a t i s t i c a l e x p l a n a t i o n s . We are concerned only with t h i s second p a r t , the requirement of t o t a l evidence. What t h i s requirement means, f o r our purposes, i s that any explanatory argument c o n t a i n i n g a s t a t i s t i c a l g e n e r a l i z a t i o n w i l l be r e l a t i v i z e d to the evidence a v a i l a b l e . A f t e r a l l , i n d u c t i v e arguments ( u n l i k e deductive arguments) are j u s t those which are s e n s i t i v e to f u r t h e r i n q u i r y — t h e i r soundness i s r e l a t i v e to the evidence a v a i l a b l e . Since a l l the evidence i s never i n , such epistemic r e l a t i v i z a t i o n would r u l e out the p o s s i b i l i t y of an i n d u c t i v e - s t a t i s t i c a l argument which was, i n some sense, " f i n a l " , i . e . , one which d i d not respond to the c o l l e c t i o n of any f u r t h e r evidence. However, i f the world i s i n d e t e r m i n i s t i c , then n o n - r e l a t i v i z e d s t a t i s t i c a l g e n e r a l i z a t i o n s would seem to be necessary f o r explanation of phenomena. Salmon describes Hempel's p o s s i b l e responses to the concept of n o n - r e l a t i v i z e d s t a t i s t i c a l g e n e r a l i z a t i o n s : that i t i s e i t h e r vacuous, or meaningless. The f i r s t i s a v e r s i o n of determinism: the only cases where a s t a t i s t i c a l g e n e r a l i z a t i o n i s n o n - r e l a t i v i z e d are t r i v i a l ones, where a l l (or no) A's are B. Hempel denies, however, that he i s a d e t e r m i n i s t i n t h i s sense. Rather, h i s r e j o i n d e r i s that epistemic r e l a t i v i z a t i o n i s e s s e n t i a l to s t a t i s t i c a l g e n e r a l i z a t i o n s , and, t h e r e f o r e , the concept of a s t a t i s t i c a l g e n e r a l i z a t i o n c o n t a i n i n g a reference c l a s s that i s not r e l a t i v e to our 4 s t a t e of knowledge, i . e . , o b j e c t i v e l y homogeneous, i s meaningless. This 4 response, as Salmon p o i n t s out, i s too strong. The idea of an o b j e c t i v e l y inhomogeneous reference c l a s s seems s t r a i g h t f o r w a r d — i t simply describes the s i t u a t i o n where we have knowledge of the existence of some f a c t o r s which w i l l p a r t i t i o n the reference c l a s s i n question i n a s t a t i s t i c a l l y r e l e v a n t manner (but we are u n w i l l i n g or t e c h n i c a l l y unable to a s c e r t a i n which members of the c l a s s have t h i s f a c t o r . ) In a d d i t i o n , there are t r i v i a l cases of o b j e c t i v e homogeneity, i . e . , u n i v e r s a l g e n e r a l i z a t i o n s . In sum, then, i f we have a Hempelian i n d u c t i v e - s t a t i s t i c a l (I-S) e x p l a n a t i o n c o n t a i n i n g a s t a t i s t i c a l g e n e r a l i z a t i o n , and i f we can a s s e r t that the reference c l a s s of that s t a t i s t i c a l g e n e r a l i z a t i o n i s o b j e c t i v e l y homogeneous, then we have an I-S explanation s i m p l i c i t e r , one that i s not e p i s t e m i c a l l y r e l a t i v i z e d . I f the world i s , at bottom, i n d e t e r m i n i s t i c , then we must al l o w f o r these types of e x p l a n a t i o n . Does t h i s r e s u l t re-open the p o s s i b i l i t y of s t a t i s t i c a l ambiguities i n e x p l a n a t i o n of j u s t the kind that Hempel's epistemic r e l a t i v i z a t i o n , and requirement of t o t a l evidence, were invoked to avoid? Only i f we s t i l l c onsider explanations as arguments, f o r i t i s the deduction of c o n t r a d i c t o r y conclusions t h a t presents the d i f f i c u l t y . Hempelian explanatory arguments must conta i n at l e a s t one law, e i t h e r u n i v e r s a l or s t a t i s t i c a l i n c haracter, a s e t of i n i t i a l c o n d i t i o n s , d e s c r i b i n g the s p e c i f i c circumstances i n q u e s t i o n , and, as the c o n c l u s i o n an explanandum statement d e s c r i b i n g the r e s u l t to be e x p l a i n e d . To show that the explanandum event "occurred 'by v i r t u s o f the circumstances i n question, and ' i n accordance with' those laws, i s then to show that the statement d e s c r i b i n g the r e s u l t can be v a l i d l y 5 i n f e r r e d from the s p e c i f i e d s e t of premises." I f we can overturn the 5 i n t u i t i o n behind t h i s i n f e r e n t i a l conception, we can disarm the force of t h i s ambiguity. According to t h i s conception i t i s v a l i d i n f e r e n c e , i n the manner p r e s c r i b e d , which provides a necessary c o n d i t i o n f o r e x p l a n a t i o n . However, we know that v a l i d i n ference has nothing to do with the content of an argument — i t i s p u r e l y a formal c o n s i d e r a t i o n . Therefore, i t can't be i n v i r t u e of anything the premises say, or what they are about, that such an argument i s necessary f o r e x p l a n a t i o n . But then i n what sense i s i t required f o r the explanation of the explanandum event? V a l i d arguments can be s u c c e s s f u l l y employed to do a v a r i e t y of t h i n g s : they can demonstrate p r o p o s i t i o n s to be c o n d i t i o n a l l y t r u e , they can convince others of t h e i r t r u t h , they can uncover t r u t h s not r e a d i l y apparent. But I f a i l to see t h a t the "deduction r e l a t i o n " c a r r i e s any explanatory weight. But of course i t i s not the deduction which e x p l a i n s — i t only serves to provide a framework w i t h i n which we may l o c a t e the laws and i n i t i a l c o n d i t i o n s which are appropriate to the event i n q u e s t i o n . Their appropriateness i s guaranteed because they provide an inference to the explanandum event. And we must a l s o note that not j u s t any v a l i d argument (with the explanandum as conclusion) w i l l do here. I t must contain as premises a general law statement and a d e s c r i p t i o n of the p a r t i c u l a r circumstances or i n i t i a l c o n d i t i o n s surrounding the event i n q u e s t i o n . And not j u s t any g e n e r a l i z a t i o n w i l l do — i t must be a well-confirmed (true) g e n e r a l i z a t i o n l i n k i n g these i n i t i a l c o n d i t i o n s to the explanandum event. Yet none of t h i s seems to depend on the p o s s i b i l i t y of c o n s t r u c t i n g an argument with these appropriate laws and i n i t i a l c o n d i t i o n s . Subsumption under a covering law does not have to be deductive subsumption. What 6 c h a r a c t e r i z e s t h i s a l t e r n a t i v e p a t t e r n of covering-law explanation i s e q u a l l y based on the c a u s a l and s t a t i s t i c a l r e l a t i o n s between events. The task set f o r the f i r s t chapter i s , then, to e x p l i c a t e t h i s explanatory p a t t e r n . (b) The t h r u s t of the second chapter i s to compare f u r t h e r the causal conception o u t l i n e d i n the f i r s t chapter w i t h two of the more t r a d i t i o n a l accounts of c a u s a l i t y , along w i t h the t r a d i t i o n a l d i f f i c u l t i e s these accounts must f a c e . Although the development of t h i s s e c t i o n i s r e l a t i v e l y uncomplicated (see below), a p r e l i m i n a r y remark with respect to the d i v i s i o n of labor seems appropriate here. Salmon's approach to s c i e n t i f i c e x p l a n a t i o n proceeds on two f r o n t s : an account of explanation based on s t a t i s t i c a l relevance r e l a t i o n s and causal r e l a t i o n s ; and an account of c a u s a l i t y which i s compatible with explanations i n t h i s mode. This l a t t e r e f f o r t (the causal account), as I s h a l l argue i n Chapter I I I , i s the c r u c i a l one, f o r i t allows Salmon's causal explanatory schema to be amenable to the indeterminism of twentieth century p h y s i c s . I t a l s o provides a deep metaphysical c o n s t r u c t i o n which can cut across many p h i l o s o p h i c a l boundaries, independent of i t s r o l e i n Salmon's account of e x p l a n a t i o n . Or so we s h a l l discover i n my examination i n t h i s chapter of the two t r a d i t i o n a l accounts o f f e r e d by J.L. Mackie and David Lewis. Mackie defends a r e g u l a r i t y view of c a u s a t i o n . C r i t i c s of t h i s view p o i n t to a d i s t i n c t i o n among r e g u l a r i t i e s that i s u n a v a i l a b l e to Mackie, t h a t i s , that r e g u l a r i t i e s which are an i n d i c a t i o n of causal r e l a t i o n s support, u n l i k e non-causal r e g u l a r i t i e s , t h e i r corresponding c o u n t e r f a c t u a l c o n d i t i o n a l a s s e r t i o n s . Mackie's defense, i n l i g h t of t h i s c o u n t e r f a c t u a l d i f f e r e n c e between c a u s a l and non-causal r e g u l a r i t i e s , leads him to conclude t h a t the d i f f e r e n c e i s s t i l l there, but wrongly based i n c o u n t e r f a c t u a l c l a i m s . What there i s , f o r Mackie, which generates t h i s d i s t i n c t i o n i s some form of "mechanism". He then sets about c o n s t r u c t i n g t h i s mechanism from w i t h i n h i s r e g u l a r i t y theory by assembling various threads from J.S. M i l l , K. Popper and W. Kneale. David Lewis defends a c o u n t e r f a c t u a l a n a l y s i s of c a u s a t i o n . His c r i t i c i s J . Kim, who p o i n t s out t h a t Lewis' c o u n t e r f a c t u a l theory i s too broad: i t c l a s s i f i e s some non-causal c o u n t e r f a c t u a l s i t u a t i o n s as c a u s a l . What I attempt to show i n t h i s chapter i s t h a t the "mechanism" f o r which Mackie searches, and the addendum to Lewis' theory which would d i s t i n g u i s h c a u s a l from non-causal c o u n t e r f a c t u a l s , i s j u s t the 'process' ontology t h a t Salmon proposes w i t h i n h i s causal-relevance model of e x p l a n a t i o n . In a d d i t i o n , I show th a t t h i s ontology of processes a l s o answers Kim's i n i t i a l c r i t i c i s m of o n t o l o g i c a l confusion i n Mackie's e a r l i e r views on c a u s a t i o n . I t should be noted t h a t I make no attempt to a d j u d i c a t e between these two t h e o r i e s of c a u s a l i t y , but simply i n d i c a t e some of the p o s i t i v e consequences of adopting t h i s powerful o n t o l o g i c a l n o t i o n . In t h i s I hope to lend some l e g i t i m a c y and impetus to the idea of a process ontology, f o r w i t h i n Salmon's theory of e x p l a n a t i o n i t must r i s e to meet s e v e r a l c r i t i c i s m s — the t o p i c of Chapter I I I . (c) The t h i r d chapter takes as i t s p o i n t of departure the idea of a p r o b a b i l i t s t i c c a u s a l process and proceeds by c o n f r o n t i n g two d i s t i n c t l i n e s of c r i t i c i s m . The f i r s t c r i t i c a l l i n e concerns the nature of a ' s t a t i s t i c a l ' cause —; the problems that revolve around the relevance r e l a t i o n s among c a u s a l l y connected events where these relevance values are low or even n e g a t i v e . The second c r i t i c a l l i n e ponders the nature of the causal l i n e s or processes themselves from two aspects: how p r o b a b i l i t i e s , u s u a l l y considered 8 a f u n c t i o n of the r e l a t i o n s between set s of events, can be a s s o c i a t e d with an ontology of processes; and, i f so a s s o c i a t e d , how the transmission of t h i s p r o b a b i l i s t i c property can be e x p l i c a t e d , i . e . , the e x p l i c a t i o n of the t r a n s m i s s i o n of p r o b a b i l i s t i c causal i n f l u e n c e w i t h i n t h i s model of p r o b a b i l i s t i c causal processes. Simply put, the attempt i s to c o n s t r u c t a concept of a p r o b a b i l i s t i c causal process from three d i s t i n c t and deep ' f a c t s ' about the world: ( i ) t h a t the world may w e l l be i n d e t e r m i n i s t i c a t bottom, and thus any theory of c a u s a l i t y or e x planation should allow f o r t h i s p o s s i b i l i t y ; ( i i ) t h a t s c i e n t i f i c i n q u i r y i n t o the s t r u c t u r e of the world _is_ the search f o r causes; and ( i i i ) t h at t h i s causal s t r u c t u r e , whether d e t e r m i n i s t i c or i n d e t e r m i n i s t i c , may p r o f i t a b l y be o n t o l o g i c a l l y viewed as continua,. or p r o c e s s - l i k e . The two l i n e s of c r i t i c i s m explored i n t h i s chapter can be seen as questions concerning the c o m p a t i b i l i t y of ( i ) w i t h ( i i ) , and of ( i i ) w i t h ( i i i ) . A few remarks, then, are i n order here, on the c o m p a t i b i l i t y of ( i ) and ( i i i ) , t h at i s , on the c o m p a t i b i l i t y of continuous causal processes i n an i n d e t e r m i n i s t i c world. Levy, i n a recent a r t i c l e , r a i s e s a serious 1 8 d i f f i c u l t y f o r j u s t such a c o m p a t i b i l i t y . The main elements which give r i s e to Levy's c r i t i c i s m can be simply s t a t e d . The c e n t r a l feature of Salmon's model of explanation i s s p a t i o - t e m p o r a l l y continuous causal processes. One of the major advantages claimed f o r t h i s model i s i t s c o m p a t i b i l i t y with the indeterminacy of quantum mechanics. Indeed, Salmon says, I do not b e l i e v e quantum indeterminacy poses any p a r t i c u l a r problems f o r a p r o b a b i l i s t i c theory of c a u s a l i t y , or f o r the not i o n of continuous causal processes.^ 9' The problem a r i s e s when we consider Reichenbach's notion of the m a t e r i a l g e n i d e n i t y of quantum p a r t i c l e s . 1 0 Three necessary, but not s u f f i c i e n t , c o n d i t i o n s f o r the m a t e r i a l g e n i d e n t i t y , or " d i s t i n g u i s h a b i l i t y " , of o b j e c t s are: (a) spatio-temporal c o n t i n u i t y , (b) s p a t i a l e x c l u s i o n , and (c) the v e r i f i a b i l i t y of (inter-)changes of s p a t i a l p o s i t i o n s . B r i e f l y , what Reichenbach demonstrates i s that any attempt to s a t i s f y these three requirements i n the quantum domain (and thus regain d i s t i n g u i s h a b i l i t y ) would r e s u l t i n the a s s e r t i o n of causal anomalies (e.g., a c t i o n - a t - a - d i s t a n c e ) . As a r e s u l t both Reichenbach and Salmon give up m a t e r i a l g e n i d e n t i t y i n favor of 11 a system without cau s a l anomalies. Levy cl a i m s , however, that Salmon cannot give up t h i s p r i n c i p l e and s t i l l "employ s p a t i o - t e m p o r a l l y continuous causal processes as explanatory devices i n the quantum domain." He bases t h i s c l a i m on the l i n k between the lack of c o n t i n u i t y i n that domain, which e n t a i l s the f a i l u r e of m a t e r i a l g e n i d e n t i t y , and on the indeterminacy r e l a t i o n s . The indeterminacy r e l a t i o n s render the question of c o n t i n u i t y undecidable by o b s e r v a t i o n , and s t a t i s t i c a l evidence plus p h i l o s o p h i c a l argument support the lack of c o n t i n u i t y . 1 ^ . However, what " s t a t i s t i c a l evidence plus p h i l o s o p h i c a l argument support" i s not the lack of c o n t i n u i t y s i m p l i c i t e r , but lack of m a t e r i a l g e n i d e n t i t y . As Reichenbach's d i s c u s s i o n shows, the necessary p r o p e r t i e s of m a t e r i a l g e n i d e n t i t y that lead to anomalous r e s u l t s are the p h y s i c a l e x c l u s i o n 14 p r i n c i p l e ( i n the case of fermions ), or the r e - i d e n t i f i c a t i o n p r i n c i p l e 1 5 ( i n the case of bosons ), and not the c o n t i n u i t y p r i n c i p a l . That i s , i n these cases g e n i d e n t i t y , or d i s t i n g u i s h a b i l i t y , f a i l s , but not 10 ( n e c e s s a r i l y ) because of a f a i l u r e of c o n t i n u i t y . Nor does the causal anomaly ( a c t i o n - a t - a - d i s t a n c e ) which would r e s u l t were we to attempt to maintain m a t e r i a l g e n i d e n t i t y , a f f e c t the p r i n c i p l e of c o n t i n u i t y . For Salmon, caus a l processes have two c h a r a c t e r i s t i c s : they are sp a t i o - t e m p o r a l l y continuous, and they are "markable" — they have the 1 6 c a p a c i t y to transmit " m o d i f i c a t i o n s " or " i n f o r m a t i o n " . What Levy suggests, but does not c l a i m to have demonstrated, i s that the f a i l u r e of m a t e r i a l g e n i d e n t i t y i s im p l i e d by the f a i l u r e (or non-existence) of both necessary c r i t e r i a f o r causal processes. Maintaining c o n t i n u i t y , as I have suggested above, w i l l be of no help unless we can ensure that continuous caus a l processes can be "marked". A n t i c i p a t i n g t h i s p o s s i b l e response, Levy claims t h a t the la c k of m a t e r i a l g e n i d e n t i t y i n the atomic domain i n v o l v e s both a lack of S-T c o n t i n u i t y and the i n a b i l i t y to v e r i f y ( i n t e r - ) changes of s p a t i a l p o s i t i o n . I t should be noted that , f o r Reichenbach, the v e r i f i c a t i o n of ( i n t e r - ) changes of p o s i t i o n i s u s u a l l y accomplished by the "mark" method. Thus, the f a i l u r e of m a t e r i a l g e n i d e n t i t y i n the quantum domain e n t a i l s the f a i l u r e of the "mark" method there. What I wish to argue i n response i s that the " m a r k a b i l i t y " needed to v e r i f y ( i n t e r - ) changes of s p a t i a l p o s i t i o n i s a much more s t r i n g e n t requirement than the " m a r k a b i l i t y " r e q u i r e d of Salmonian causal processes. Thus a process can be e s t a b l i s h e d as c a u s a l , even though we are unable to v e r i f y 18 ( i n t e r - ) change of s p a t i a l p o s i t i o n . F i r s t we must note t h a t , f o r Salmon, 'marks' are not used to d i s t i n g u i s h between caus a l processes, but rather serve only to demonstrate c a u s a l c a p a c i t y . Let us c a l l t h i s f i r s t a p p l i c a t i o n of 'marks' (those 1 9 necessary f o r r e - i d e n t i f i c a t i o n ) "ear-marks", and the Salmonian 1 1 m o d i f i c a t i o n s (necessary to show c e r t a i n p e r s i s t a n c e s of s t r u c t u r e as causal) 20 "marks" s i m p l i c i t e r . Can a process be causal even though i t lacks the property of m a t e r i a l g e n i d e n t i t y ? Can a process be 'markable' even though i t i s not 'ear-markable'? C e r t a i n processes which lack m a t e r i a l g e n i d e n t i t y may yet be f u n c t i o n a l l y g e n i d e n t i c a l . Reichenbach d i s t i n g u i s h e s f u n c t i o n a l g e n i d e n t i t y from m a t e r i a l g e n i d e n t i t y : f u n c t i o n a l g e n i d e n t i t y may v i o l a t e p r i n c i p l e s (b) and ( c ) , yet c o n t i n u i t y i s preserved. For example, when two b i l l i a r d b a l l s c o l l i d e , and rebound at equal speeds, we cannot say whether the k i n e t i c energies of the two b a l l s were exchanged, or merely that t h e i r v e l o c i t i e s were reversed. On e i t h e r i n t e r p r e t a t i o n the world l i n e of the energy i n v o l v e d remains continuous. For Reichenbach and.thus, Levy argues, f o r Salmon as w e l l , m a t e r i a l g e n i d e n t i t y turns out to be an i d e a l i z a t i o n of the behaviour of macroscopic o b j e c t s . "There i s no m a t e r i a l g e n i d e n t i t y at a l l 2 1 i n the world; there i s only f u n c t i o n a l g e n i d e n t i t y . " Therefore, I s h a l l suggest that the c o n t i n u i t y i m p l i c i t i n f u n c t i o n a l g e n i d e n t i t y must be the l o c a l e of the c o n t i n u i t y of causal processes. K i n e t i c energy, as i n the above b i l l i a r d b a l l example, i s Reichenbach's paradigm here. "Energy", 2 2 however, "cannot be ear marked." Nevertheless, energy can be "marked", i n j u s t the manner necessary to demonstrate i t s causal c a p a c i t y , without assuming r e - i d e n t i f i a b i l i t y , v e r i f i a b i l i t y of ( i n t e r - ) change of s p a t i a l p o s i t i o n , or d i s t i n g u i s h a b i l i t y . Consider any electro-magnetic wave phenomena,"e.g., r a d i o , l i g h t , e t c . Any of these can be modified at t h e i r source, and these m o d i f i c a t i o n s w i l l be maintained without f u r t h e r i n t e r a c t i o n . L i g h t may be reduced to a s i n g l e wavelength by i n t e r p o s i n g a colored f i l t e r , r a d i o waves may be marked by 12 modulation of c a r r i e r waves by an audio-frequency c u r r e n t . Neither phenomenom obeys the p r i n c i p l e of s p a t i a l e x c l u s i o n , nor can e i t h e r be ear marked such that an i n d i v i d u a l photon or s i n g l e r a d i o wave could be r e - i d e n t i f i e d over time from among i d e n t i c a l l y prepared sets of such e n t i t i e s . Yet, as Reichenbach himself maintains, c o n t i n u i t y i s preserved. Now, what of atomic phenomena? With the acceptance of the quantum indeterminacy r e l a t i o n s we lose any p o s s i b i l i t y of as s i g n i n g a d e f i n i t e t r a j e c t o r y to any i n d i v i d u a l p a r t i c l e , mainly because these p a r t i c l e s lack the property of m a t e r i a l g e n i d e n t i t y . Is there a sense i n which we can speak of the " c o n t i n u i t y " of these p a r t i c l e s over time despite t h e i r lack of a w e l l - d e f i n e d t r a j e c t o r y ? ( I might emphasize here that t h i s i s not a problem generated by indeterminism per se. I t seems p o s s i b l e that a system might be genuinely i n d e t e r m i n i s t i c i n that no s t a t e of that system at time t ^ w i l l determine an outcome of that system at time t j , t ^ < t j , yet the system may e x h i b i t c o n t i n u i t y i n that the s t a t e f u n c t i o n that describes i t i s a continuous 23 v f u n c t i o n of t . Lack of c o n t i n u i t y i s , i n t h i s sense, a stronger claim than a f a i l u r e of determinism.) The sense, I b e l i e v e , i n which we can speak of the continuous nature of these p a r t i c l e s i s much the same sense we employ i n speaking of f u n c t i o n a l l y g e n i d e n t i c a l o b j e c t s . The motion that gets t r a n s f e r r e d when two b i l l i a r d b a l l s c o l l i d e i s continuous i n t h i s f a s h i o n , as i s the electro-magnetic energy of l i g h t and r a d i o waves. And although not ear-markable, t h i s continuous process i s markable. I f we i n i t i a l l y a c c e l e r a t e i d e n t i c a l l y prepared hydrogen ions (protons) we can observe t h i s increase i n energy at some l a t e r time, say upon impact with some t a r g e t 13 m a t e r i a l . That we can do t h i s t e s t i f i e s to t h e i r c a p a c i t y t o ' t r a n s m i t t h i s m o d i f i c a t i o n (the increase i n k i n e t i c energy) through space-time. That t h e i r t r a j e c t o r y i s not determinable a t each p o i n t seems to be an a d d i t i o n a l f e a t u r e of t h i s process. Thus I t h i n k that f u n c t i o n a l g e n i d e n t i t y i s compatible w i t h Salmonian causal processes, and that we do not los e c o n t i n u i t y of t h i s f u n c t i o n a l g e n i d e n t i t y s o l e l y because of the lack of a w e l l - d e f i n e d t r a j e c t o r y . I am not at a l l sure whether t h i s response i s s a t i s f a c t o r y . I agree w i t h Salmon that the t r u l y anomalous r e s u l t s that a r i s e from a lack of c o n t i n u i t y — e.g., a c t i o n - a t - a - d i s t a n c e — s t i l l remain. In t h i s regard I would l i k e to make a f i n a l comment on another of Levy's examples which r e s t s on an absence of c o n t i n u i t y . Levy supposes a set of arrows f i r e d from a p o i n t S i n an e a s t e r l y d i r e c t i o n , a l l of which a r r i v e at a t a r g e t W, even though there i s a "causal gap", a break i n the spatio-temporal c o n t i n u i t y , i n reg i o n R, as shown i n the f i g u r e below: s» j ( > w R The s t a s t i c a l relevance of S f o r W i s strong, indeed i t i s determined that arrows from S w i l l a r r i v e a t W. Levy imagines that t h i s knowledge provides an explanation here, even though we are prevented from accounting c a u s a l l y f o r t h i s phenomena by way of a s p a t i o - t e m p o r a l l y continuous process. (Or, a t l e a s t , that we are i n no more explanatory trouble here than we are i n e x p l a i n i n g genuinely i n d e t e r m i n i s t i c yet causal phenomena.) Why should spatio-temporal gaps ( t h a t cannot, i n p r i n c i p l e , be f i l l e d by fu t u r e study) defeat e x p l a n a t i o n any more than indeterminism does? 14 I haven't a d e f i n i t i v e argument here. I would suggest, however, t h a t these two explanatory lacunae are not on a par. This i n t u i t i o n ( f or i t i s no more than that) r e s t s on three p o i n t s . (1) The "gap" e x h i b i t e d i n t h i s example seems analogous to the gap i n the knowledge of ancient mariners who could p r e d i c t with p e r f e c t accuracy the r i s e and f a l l of the t i d e s from t h e i r knowledge of the motion of the moon. However, the explanation of t h i s c o r r e l a t i o n had to wait f o r Newton, and a causal account. Causal e x p l a n a t i o n s , when they can be given, w i l l supercede merely s t a t i s t i c a l c o r r e l a t i o n s . And Levy might agree that we would have a b e t t e r explanation should t h i s gap be f i l l e d . But again we may be asked, why shouldn't spatio-temporal gaps be an u l t i m a t e ( i . e . , i r r e d u c i b l e ) f e a t u r e of the world, as i s indeterminism? (2) As I have suggested above, p h y s i c a l c o n t i n u i t y i s a weaker assumption than that of determinism. Therefore, v i o l a t i o n s of c o n t i n u i t y would be l e s s acceptable, e x p l a n a t o r i l y , than i n d e t e r m i n i s t i c c o r r e l a t i o n s . I f there are l e v e l s of anomaly, then a p h y s i c a l l y disconnected world of r e g u l a r i t i e s seems more anomalous to me than an i n d e t e r m i n i s t i c one. Why t h i s i s so seems to be a r e s u l t of contemplating the "gap" i n Levy's example. Suppose we were to carve our i n i t i a l s on an arrow shot from S. What are we to say of i t s ' c o n t i n u i t y ' when that same arrow a r r i v e s at W? But t h i s i d e n t i t y i s d i s a l l o w e d due to the f a i l u r e of m a t e r i a l g e n i d e n t i t y here. And i f spatio-temporal c o n t i n u i t y goes, then even f u n c t i o n a l g e n i d e n t i t y f a i l s . That i s , due to R even the assumption of the continuous existence of the k i n e t i c energy associated with the arrow from S to W i s questionable. Part of the reason, no doubt, f o r i n c r e d u l i t y here i s a product of t h i s example. Arrows are n o t o r i o u s l y causal — the t i m e - l i k e separation of S and W allows 15 f o r c a u s a l i t y . More c l e a r l y anomalous are the c o r r e l a t i o n s of two events which are separated by a s p a c e - l i k e i n t e r v a l . I t would be a more j u s t comparison to match a d e t e r m i n i s t i c a l l y c o r r e l a t e d p a i r of events which are separated by a s p a c e - l i k e i n t e r v a l , with an i n d e t e r m i n i s t i c a l l y c o r r e l a t e d p a i r of events separated by a t i m e - l i k e i n t e r v a l . I f i n d the former more mysterious than the l a t t e r . (3) I agree with Salmon that s c i e n t i f i c e x p l a n a t i o n should provide "knowledge of the mechanisms of production and propagation of s t r u c t u r e s i n the world." These concepts are dependent on c o n t i n u i t y , and not on determinism. The e x p l o r a t i o n , and perhaps expansion, of" h i s ideas on the productive c a p a c i t i e s of causal i n t e r a c t i o n s , and the propagative c a p a c i t i e s of i n d e t e r m i n i s t i c yet continuous causal processes, i s the subject of what f o l l o w s . 16 I n t r o d u c t i o n - Notes 1. The two seminal works are h i s (1971) and (1978). 2. Hempel (1962), p. 133. 3. This problem i s a l s o r e f e r r e d to as the "ambiguity of the reference c l a s s . " Any o b j e c t or event i s a member of an i n f i n i t e number of c l a s s e s defined by t h e i r a s s o c i a t i o n with d i f f e r e n t a t t r i b u t e s . The p r o b a b i l i t y of the occurrence of the a t t r i b u t e we wish to e x p l a i n w i l l , i n g eneral, vary w i t h i n these c l a s s e s . For any given a t t r i b u t e of an o b j e c t i n a c l a s s there w i l l always be a d i f f e r e n t c l a s s , which contains the object i n question, and which has the p r o b a b i l i t i e s r eversed. 4. Salmon (1977b). 5. Hempel (1962), p. 100. 6. Salmon (1978), p. 408. 7. Mackie (1974) a l s o responds to Kim's c r i t i q u e of Mackie (1965). 8. Levy (1982); a l s o J . Hanna (1981) discusses t h i s problem but from w i t h i n a context q u i t e d i f f e r e n t from Salmon's explanatory model — one that i n c l u d e s a n o n - r e l a t i o n a l ( o b j e c t i v e ) i n t e r p r e t a t i o n of p r o b a b i l i t y and one that construes explanations as arguments. Both of these p o i n t s f i g u r e e s s e n t i a l l y i n Hanna's argument, therefore i t i s of l e s s i n t e r e s t to us here. 9. Salmon (1980a), p. 73. 10. Reichenbach (1971), Section 26. 11. Levy (1982), p. 437. 12. Loc. c i t . 13. Loc. c i t . 14. Reichenbach (1971), p. 235. 15. Op. c i t . , p. 234. 16. " M a r k a b i l i t y " i s another Reichenbachian n o t i o n , op. c i t . , Section 23. 17. Levy (1982), p. 444, f n . 10. I should p o i n t out t h a t Levy's o b j e c t i o n s are w e l l - t a k e n , and p o i n t to a serious flaw i n Salmon's attempt to hold both a Reichenbachian account of quantum mechanics and the c o n t i n u i t y of causal processes. What I attempt to render here i s a modified account of these continuous causal processes that i s c o n s i s t e n t both w i t h the lack of m a t e r i a l g e n i d e n t i t y and w i t h Salmon's intended c o n s t r u c t i o n . 17 18. I f s u c c e s s f u l then t h i s response w i l l defuse Levy's r e b u t t a l to h i s second a n t i c i p a t e d o b j e c t i o n — see Levy, l o c . c i t . 19. F o l l o w i n g Reichenbach (1971), p. 226. 20. Salmon admits that he i s not using the mark method as i t was o r i g i n a l l y intended (as a c r i t e r i o n f o r temporal d i r e c t i o n . ) Reichenbach, Salmon c l a i m s , noted i t s inadequacy f o r that purpose. Salmon (1978), f n . 11. 21. Reichenbach (1971), p. 236. 22. Op. c i t . , p. 226. 23. See Hanna (1981), f n . 29. 18 CHAPTER I STATISTICAL EXPLANATION "A theory which agonizes e n d l e s s l y about c e r t a i n knowledge and neglects the probable, represents a somewhat a r t i f i c i a l i n t e r e s t . " C.I. Lewis, Mind and  the World Order In the f i r s t two se c t i o n s of t h i s chapter I s h a l l describe i n some d e t a i l the machinery of Wesley Salmon's model of s t a t i s t i c a l e xplanation i n order to acquaint the reader w i t h the f u l l network of the terms with which f u r t h e r issues w i l l be framed. This network i s a conceptual background for s e c t i o n 3 where I s h a l l examine Salmon's move from the S t a t i s t i c a l - R e l e v a n c e model to the Causal-Relevance model of s t a t i s t i c a l e x p l a n a t i o n . In the 4th and f i n a l s e c t i o n I s h a l l be concerned with l o c a t i n g those areas of t h i s l a t e r model which w i l l be the focus of i n t e r e s t to us i n Chapters I I and I I I . 1. N o n - i n f e r e n t i a l E x p l a n a t i o n The r e c e i v e d opinion was that to e x p l a i n an event was to produce a set of statements, d e s c r i b i n g general u n i f o r m i t i e s as w e l l as p a r t i c u l a r f a c t s , from which a statement d e s c r i b i n g the event to be explained (the explanandum) could be d e r i v e d . These explanations came i n two v a r i e t i e s : a deductive (D-N) ex p l a n a t i o n provided a set of statements from which the explanandum would ( l o g i c a l l y ) f o l l o w ; i n d u c t i v e (I-S) explanations provided something l e s s than deductive grounds towards the explanandum as c o n c l u s i o n . The s t r e n g t h of an explanation was l o g i c a l s t r e n g t h . Given the premises of 1 9 an explanation/argument we understand why the event was to be expected. Given these premises we are i n a p o s i t i o n to p r e d i c t the occurrence of the explanandum event. With arguments as explanations there i s a symmetry between ex p l a n a t i o n and p r e d i c t i o n . Likewise, i n the i n d u c t i v e s i t u a t i o n , the degree to which the event to be explained was to be expected, given the explanatory premises, i . e . , the i n d u c t i v e strength of the argument, given the evidence, becomes the strength of the e x p l a n a t i o n . I t i s here, with i n d u c t i v e arguments as explanations, that Salmon's i n s i g h t takes h o l d . A c e n t r a l feature of Salmon's view of explanation i s the cl a i m that explanations are not arguments. He c l e a r l y saw that the r e l a t i v e frequency of the occurrence of an event, given the explanatory f a c t s , was not a measure of explanatory success; a low p r o b a b i l i t y d i d not hinder our under-standing of why that event had occurred. 1 2 Richard J e f f r e y presents the c l e a r e s t example: i n n f l i p s of a f a i r c o i n the p r o b a b i l i t y of at l e a s t one head i s [ l - Q / 2 ) 1 ] . In a sequence of 10 f l i p s we have both good reason to expect a head ( p r o b a b i l i t y of 1023/ 1024), and thus, according to the received view, a good i n d u c t i v e argument to the conc l u s i o n that there w i l l be at l e a s t one head. But suppose we f l i p the c o i n only once, and i t lands heads. The p r o b a b i l i t y of 1/2 provides no 'expectation', and gives the l e a s t p o s s i b l e support to an i n d u c t i v e argument to t h i s c o n c l u s i o n . Yet we don't wish to deny that we' can e x p l a i n (or that we understand) why that c o i n came up heads. We may g e n e r a l i z e t h i s c o n c l u s i o n : take any event that occurs r e g u l a r l y but i n f r e q u e n t l y . I f we know the c o n d i t i o n s (C) f o r i t s p o s s i b l e occurrence, and the s t o c h a s t i c law which describes t h i s r e g u l a r i t y by, among other t h i n g s , a s s i g n i n g the p r o b a b i l i t y P, then although we may p r e d i c t under c o n d i t i o n C, given p r o b a b i l i t y P, that i t w i l l not occur, we have explained i t s behavior whether i t occurs or not. I f i t does occur our s u r p r i s e at i t s occurrence i s 3 due to i t s r a r i t y , not to i t s i n e x p l i c a b i l i t y . Broadly speaking, the view to be adopted here i s that to e x p l a i n the occurrence of a p a r t i c u l a r event i s to describe i t s place i n a p a t t e r n of of other f a c t s , c o n d i t i o n s or events. To analyze explanation would then be to d escribe the k i n d of r e l a t i o n s among events that would r e s u l t i n such a p a t t e r n . We have seen that l o g i c a l , or i n f e r e n t i a l , grounds are too narrow, t h a t i n c e r t a i n s t a t i s t i c a l c a s e s . t h i s l o g i c a l p a t t e r n i s inadequate for Hempel-style e x p l a n a t i o n s , yet these cases seem c l e a r l y e x p l a i n a b l e . They are a l s o too broad: there are many counter-examples i n which there are arguments s a t i s f y i n g Hempel's requirements, yet these arguments f a i l to 4 e x p l a i n . Salmon denies t h a t the explanatory p a t t e r n i s a p a t t e r n of i n f e r e n c e . His a l t e r n a t i v e i s the r e l a t i o n of s t a t i s t i c a l relevance, and the concept of homogeneity. (a) S t a t i s t i c a l Relevance Suppose that some of the b a l l s i n an urn are red. Let D be the sequence of draws of b a l l s from the urn, each b a l l being returned a f t e r being drawn and i t s c o l o r recorded. Let R be the c l a s s of red t h i n g s . The l i m i t of the frequency w i t h which red b a l l s are drawn r e l a t i v e to the t o t a l number of draws, as t h i s number increases without bound, w i l l express the p r o b a b i l i t y , P(R/D), of a red draw from t h i s urn. D i s c a l l e d the reference c l a s s , R the a t t r i b u t e c l a s s . Suppose t h a t , i n t h i s case, P(R/D)=l/2. The choice of an a t t r i b u t e c l a s s presents no problem. The question we ask, e.g., "What i s the p r o b a b i l i t y of red on the next draw?" determines the a t t r i b u t e c l a s s . The choice of the proper reference c l a s s i s l e s s s t r a i g h t f o r w a r d , however. Suppose that i n our example, as a matter of f a c t , 21 every odd-numbered draw, beginning with the f i r s t , turns out red. I f we take the sequence of a l l draws as our reference c l a s s , then P(R/D)=l/2. However, i f we p a r t i t i o n the c l a s s D i n t o odd- (0) and even- (E) numbered draws, then P(R/D&0)=1. I t i s now c r u c i a l f o r our p r e d i c t i o n of the outcome on the next draw whether i t i s a member of 0 or not. Being a member of 0 i s s t a t i s t i c a l l y r e l e v a n t to whether the next draw w i l l be a member of R. To e f f e c t a p a r t i t i o n ^ of t h i s reference c l a s s i s to f i n d an a t t r i b u t e 6 (e.g., 0) such t h a t p(R/D&0) ^(P(R/D); that i s , such that having t h a t a t t r i b u t e makes a d i f f e r e n c e to the p r o b a b i l i t y of the event i n q u e s t i o n . At l e a s t three p o i n t s should be noted. (1) We have shown how s t a t i s t i c a l l y r e l e v a n t f a c t o r s c o n t r i b u t e to our p r e d i c t i v e c a p a c i t i e s -7 t h e i r adequacy as explanatory f a c t o r s w i l l be taken up below, i n s e c t i o n 2. (2) In our example the p e r f e c t c o r r e l a t i o n (or constant conjunction) between red and odd-numbered draws suggests a p o s s i b l e causal connection. This suggestion could have been avoided by c o n s i d e r i n g a case i n which p(R/DSO) i s lowered to somewhat l e s s than one (but other than 1/2). Yet, as we s h a l l see l a t e r , we hope to undermine the c l o s e connection between s t r i c t l y determined events (where P(a/b) = 1 or 0) and c a u s a l l y connected ones. (3) Whether or not i t i s a r e l a t i o n of explanatory value, whether or not i t i s a r e l a t i o n which points to (or d i r e c t s us to) causal r e l a t i o n s , the r e l a t i o n of s t a t i s t i c a l relevance, as i n the above example, at l e a s t captures the f a c t that c e r t a i n sets of f a c t o r s make a d i f f e r e n c e to the occurrence of a given event. (b) Homogeneity Since every event belongs to an innumerable number of reference c l a s s e s , we need some g u i d e l i n e s i n choosing an appropriate one. Salmon i n s t r u c t s us to "choose the broadest homogeneous reference c l a s s to which the s i n g l e event belongs." The requirement of being the "broadest" c l a s s i s to i n sure the r e l i a b i l i t y of our s t a t i s t i c s - the l a r g e r the sample the more c l o s e l y the r e s u l t s correspond to the l i m i t i n g frequency. As w e l l , i t insures a g a i n s t i r r e l e v a n t place s e l e c t i o n s , or p a r t i t i o n s , of the reference c l a s s . For example, suppose that some of the odd-numbered draws i n our example were drawn with the l e f t hand ( L ) , and some with the r i g h t . I t would be an a r t i f i c i a l narrowing of the reference c l a s s i f we were to take t h i s property of the draws i n t o c o n s i d e r a t i o n i f P(R/DSOSL) = P(R/D&0). We have gained no r e l e v a n t i n f o r m a t i o n and have decreased the s i z e of our sample. Being a left-handed draw i s s t a t i s t i c a l l y i r r e l e v a n t to the outcome. Now i f every p a r t i t i o n i n g property i s s t a t i s t i c a l l y i r r e l e v a n t to the occurrence of R i n D&O, then we may say t h a t D&O i s a homogeneous reference c l a s s w i t h respect to the a t t r i b u t e R. In g eneral, i f there i s no property which p a r t i t i o n s a reference c l a s s i n a manner s t a t i s t i c a l l y r e l e v a n t to a given a t t r i b u t e , then we may c l a i m t h i s c l a s s to be homogeneous with respect to that a t t r i b u t e . And we may d i s t i n g u i s h three v a r i e t i e s of homogeneity: p r a c t i c a l , epistemic, and o b j e c t i v e . We say that a reference c l a s s i s a p r a c t i c a l l y homogeneous when we know the c l a s s to be inhomogeneous, and, as w e l l , know what a t t r i b u t e s would provide a s t a t i s t i c a l l y r e l e v a n t p a r t i t i o n , yet i t would, f o r example, be more tr o u b l e than i t i s worth to determine which elements of the reference c l a s s belong to which place s e l e c t i o n s . We know, for i n s t a n c e , that there are f a c t o r s which, i f known i n s u f f i c i e n t d e t a i l , would p a r t i t i o n the reference c l a s s of throws of a die such that we could reduce or increase the odds f o r any one r o l l . I t i s only a p r a c t i c a l matter that we do not, thus 23 t h i s reference c l a s s i s p r a c t i c a l l y homogeneous. In other cases we b e l i e v e or suspect that a reference c l a s s i s inhomogeneous, yet we do not know what f a c t o r s might e f f e c t a s t a t i s t i c a l l y r e l e v a n t p a r t i t i o n . For example, we know that exposure to r a d i a t i o n i s s t a t i s t i c a l l y r e l e v a n t to the incidence of leukemia i n those so exposed, although not a l l i r r a d i a t e d subjects c o n t r a c t leukemia. And we b e l i e v e that there are a t t r i b u t e s which would d i s t i n g u i s h those members of the reference c l a s s which c o n t r a c t the disease from those that do not. As yet we do not know what these f a c t o r s are, t h i s c l a s s i s e p i s t e m i c a l l y homogeneous. We know of no f a c t o r s which p a r t i t i o n t h i s c l a s s i n a r e l e v a n t manner. Now i t may be the case that one has more than p r a c t i c a l or epistemic reasons to consider a reference c l a s s homogeneous. Salmon speaks 9 of reference c l a s s e s that are " s t r i c t l y " or " u n q u a l i f i e d l y " homogeneous. That i s , there are i n p r i n c i p l e no f u r t h e r f a c t o r s which would r e l e v a n t l y d i v i d e the reference c l a s s i n q u e s t i o n . These are what Salmon l a t e r r e f e r r e d to as o b j e c t i v e l y homogeneous reference c l a s s e s . The homogeneity of the reference c l a s s here i s not a f u n c t i o n of p r a c t i c a l d i f f i c u l t i e s , nor i s i t r e l a t i v i z e d to our s t a t e of knowledge; rather i t i s traceable to, and d e r i v a b l e from, the c u r r e n t l y accepted t h e o r i e s which apply to the phenomena i n q u e s t i o n . At the moment the only p l a u s i b l e candidates f o r sets of events t h a t form such a c l a s s (and that d i s p l a y p r o b a b i l i t y values l e s s than the extreme) are found i n the mi c r o p h y s i c a l domain. For example, a c o l l e c t i o n of r a d i o a c t i v e atoms of a given element e x h i b i t s a c h a r a c t e r i s t i c decay r a t e , expressed as that element's h a l f - l i f e , and a f f e c t e d by the "spontaneous" 24 emission of energy, sometimes i n the form of an alpha p a r t i c l e . Given the h a l f - l i f e , we may determine the p r o b a b i l i t y of a given atom's d i s i n t e g r a t i o n or energy emission. Furthermore, the theory claims that the set of atoms of a s i n g l e element are o b j e c t i v l e y homogeneous with respect to the a t t r i b u t e of d i s i n t e g r a t i o n . There i s no property which would determine a r e l e v a n t place s e l e c t i o n of these atoms, i . e . a property which would p i c k out, from among the o r i g i n a l reference c l a s s , a subclass of atoms that would be more (or l e s s ) l i k e l y to d i s i n t e g r a t e . U n l i k e epistemic or p r a c t i c a l homogeneity, the concept of o b j e c t i v e homogeneity seems problematic. Although the f u l l s c a l e d i s c u s s i o n of some of the issues that w i l l be r a i s e d here s h a l l be postponed u n t i l l a t e r i n t h i s chapter (and again i n the next chapter) we note the f o l l o w i n g queries here. Some people maintain, Salmon says, that A i s o b j e c t i v e l y homogeneous f o r B only i f a l l A's are B or no A's are B; such people are deter-m i n i s t s . They hold that causal f a c t o r s always determine which A's are B and which A's are not B; these causal f a c t o r s can, i n p r i n c i p l e , be discovered and used to c o n s t r u c t a place s e l e c t i o n f o r making a s t a t i s t i c a l l y r e l e v a n t p a r t i t i o n of A. 1 0 There are r e a l l y two issues here: what c o n s t i t u t e s a complete e x p l a n a t i o n , and what r o l e causes p l a y i n i n t r i n s i c a l l y s t a t i s t i c a l s i t u a t i o n s . When o f f e r i n g an e xplanation by means of a p r a c t i c a l l y or e p i s t e m i c a l l y homogeneous reference c l a s s we e i t h e r know or suspect that there could be f u r t h e r f a c t o r s which would improve the p u r i t y of these c l a s s e s . In t h i s way our e x p l a n a t i o n i s admittedly incomplete. When o f f e r i n g an o b j e c t i v e l y homogeneous c l a s s we are making the very strong c l a i m that according to our t h e o r i e s we have assembled a l l the r e l e v a n t f a c t o r s , that our explanation i s complete. What Salmon denies i s that t h i s assemblage of f a c t o r s w i l l 25 a u t o m a t i c a l l y y i e l d p r o b a b i l i t i e s of 1 or 0. 1 1 What he allows f o r , then, i s the existence of i n t r i n s i c a l l y s t a t i s t i c a l s i t u a t i o n s , and traces the sense of incompleteness generated by these s t a t i s t i c a l s i t u a t i o n s to a d e t e r m i n i s t i c b i a s . C l e a r l y , the question of whether the world i s 1 2 d e t e r m i n i s t i c should not be s e t t l e d w i t h i n a theory of e x p l a n a t i o n . The second concern expressed i n the above passage i s again about completeness, but from a d i f f e r e n t tack. Our explanatory task i s not f u l f i l l e d by mere c o r r e l a t i o n — even i f these c o r r e l a t i o n s are p e r f e c t . The f a c t o r s we are l o o k i n g for enjoy a more proximate r e l a t i o n to the explanandum event than s t a t i s t i c a l relevance; they are causes of t h a t event. I f a s t a t i s t i c a l r e l a t i o n represents a mere symptomatic and not causal connection, then an explanation based on that r e l a t i o n i s incomplete, for i t w i l l be superseded by the r e s p e c t i v e causal account. And, t h i s o b j e c t i o n continues, i f the s t a t i s t i c a l r e l a t i o n does represent a causal connection, and, i f t h i s reference c l a s s of causal events i s homogeneous, then they w i l l n e c e s s i t a t e t h e i r e f f e c t s , i . e . , give p r o b a b i l i t i e s of 1 or 0. Thus any e x p l a n a t i o n with p r o b a b i l i t y values less than the extremes w i l l be incomplete. Salmon's response i s to admit t h a t , when they can be given, causal explanations supersede symptomatic e x p l a n a t i o n s . But he goes on to c l a i m t h a t the value of a causal response i s j u s t that of an increase i n homogeneity; and that p r o v i d i n g t h i s concept, as w e l l as b l o c k i n g unwanted symptomatic accounts i n favor of causal ones, can be done without recourse to 1 3 "an independent concept of causal r e l a t i o n . " B r i e f l y , what Salmon n o t i c e s here i s that the explanatory advantage provided by causal r e l a t i o n s i s due to t h e i r a b i l i t y to "screen-off" non-causal, or symptomatic, 26 c o r r e l a t i o n s , and that t h i s screening o f f c a p a c i t y can be described i n p u r e l y s t a t i s t i c a l terms. We s h a l l s p e l l out t h i s s t a t i s t i c a l analogue of c a u s a t i o n , f o r i t w i l l perform a c r u c i a l r o l e i n Salmon's new account of e x p l a n a t i o n . (c) Screening Off S t a t i s t i c a l l y r e l a t e d events may or may not be c a u s a l l y r e l a t e d . I f they are not, then, i n the presence of the cause of one of the r e l a t a , the other w i l l be rendered s t a t i s t i c a l l y i r r e l e v a n t , and, t h e r e f o r e , e x p l a n a t o r i l y i r r e l e v a n t . We say that the cause "screens o f f " these merely s t a t i s t i c a l l y r e l a t e d f a c t o r s . Suppose, f o r example, that event B i s s t a t i s t i c a l l y r e l e v a n t f o r event A. That i s , P(A/B) ^ p(A). I f B i s not a cause of A, then the presence of B w i l l be screened o f f by the presence of any c a u s a l l y r e l a t e d f a c t o r C. Formally, C screens o f f B from A i f : (1) P(A/C) = P(A/BSC) and (2) P(A/B&C) f P(A/B) Clause (2) ensures that the screening o f f r e l a t i o n i s non-symmetrical: i f C screens o f f B from A, B does not screen o f f C from A. Salmon then formulates the "screening-off r u l e " : When one property i n terms of which a s t a t i s t i c a l l y r e l e v a n t p a r t i t i o n i n a reference c l a s s can be e f f e c t e d screens o f f another property i n terms of which another s t a t i s t i c a l l y r e l e v a n t p a r t i t i o n of the same reference c l a s s can be e f f e c t e d , then the screened-off property must give way to the property which screens i t o f f . This r u l e , o b v i o u s l y , a l s o a p p l i e s to cases where a c a s u a l l y r e l a t e d f a c t o r i s screened o f f by a more proximate cause. With t h i s screening o f f r e l a t i o n , and the screening o f f r u l e , Salmon has attempted to give an account of c a u s a l i 27 r e l a t i o n s i n terms of s t a t i s t i c a l r e l a t i o n s alone. i n a d d i t i o n , he has provided an e x p l i c a t i o n of our causal i n t u i t i o n s (our demand f o r causes i n explanation) by noting the increase i n homogeneity e f f e c t e d by the presence of causes. However, he i s a l s o " w i l l i n g to admit that symptomatic e x p l a n a t i o n seem to have genuine explanatory value i n the absence of knowledge of causal r e l a t i o n s , that i s , as long as we do not know that we are 15 d e a l i n g o n l y with symptoms." I t i s t h i s l a t t e r c l a i m which i s d i r e c t l y repudiated i n Salmon's new account of e x p l a n a t i o n . As w e l l , an independent c h a r a c t e r i z a t i o n of c a u s a l r e l a t i o n s i s introduced. These t o p i c s w i l l , of course, be discussed below. Here we s h a l l only o f f e r a few remarks concerning the p o s i t i o n described i n the above q u o t a t i o n . P a r t i t i o n i n g a reference c l a s s by means of a f a c t o r which i s c a u s a l l y r e l a t e d to the explanandum event w i l l always increase the homogeneity of the p a r t i t i o n e d c l a s s . That i s , causes are always s t a t i s t i c a l l y r e l e v a n t to t h e i r e f f e c t s . I f explanation c o n s i s t s i n p r o v i d i n g s a t i s t i c a l l y r e l e v a n t f a c t o r s , then explanation demands, when they can be given, f a c t o r s which are c a u s a l l y , and not merely s t a t i s t i c a l l y , r e l a t e d to the event to be e x p l a i n e d . Since not a l l s t a t i s t i c a l l y r e l a t e d f a c t o r s are causes, Salmon o f f e r s the screening o f f concept i n order to p i c k out those s t a t i s t i c a l l y r e l e v a n t f a c t o r s which are causes from those which are not. And, Salmon c l a i m s , i n the absence of knowledge of c a u s a l l y r e l a t e d f a c t o r s , we should be prepared to o f f e r s t a t i s t i c a l c o r r e l a t i o n s alone as e x p l a n a t i o n s . Suppose, then, that "we don't know th a t we are d e a l i n g only with symptoms." Does t h i s imply that we know, or b e l i e v e , that we are not 28 d e a l i n g only w i t h symptoms? But t h i s could be the case only i f these f a c t o r s e x h i b i t screening o f f . Does t h i s imply that we do not know what (or whether) causes might be operating here? But then these merely symptomatic f a c t o r s w i l l never provide more than epistemic homegeneity of the reference c l a s s they p a r t i t i o n . Since i t i s only the p o s s i b i l i t y of o b j e c t i v e l y homogeneous reference c l a s s e s that allows f o r genuine indeterminism, we seem, on t h i s view, to be fo r c e d to c l a i m that i t i s only w i t h c a u s a l l y r e l a t e d f a c t o r s that we can a r r i v e at f i n a l , or genuine s t a t i s t i c a l e x p l a n a t i o n s . A l t e r n a t i v e l y , we may c l a i m t h a t a reference c l a s s i s o b j e c t i v e l y homogeneous des p i t e mere symptomatic c o r r e l a t i o n s i f we know there to be no a p p l i c a b l e c a u s a l f a c t o r s . But then i t seems an open question whether much i n the way of e x p l a n a t i o n i s being o f f e r e d , i n l i g h t of t h i s knowledge, by c i t i n g these c o r r e l a t i o n s . I t i s not c l e a r whether these general c o n s i d e r a t i o n s about the adequacy of t h i s s t a t i s t i c a l analogue of c a u s a l i t y , i n terms of screening o f f , provides the h i s t o r i c a l motivation f o r Salmon's l a t e r , more robust, view of c a u s a t i o n . In the next s e c t i o n we w i l l r a i s e more s p e c i f i c d i f f i c u l t i e s w i t h t h i s concept, which w i l l complete our look at t h i s e a r l i e r theory of e x p l a n a t i o n , and s e t the stage f o r Salmon's new account. 2. R e c a p i t u l a t i o n and O b j e c t i o n s . Before c o n s i d e r i n g o b j e c t i o n s to S a l m o n ' s . s t a t i s t i c a l approach l e t us b r i e f l y summarize h i s p o s i t i o n c i r c a 1970. To give an explanation of the occurrence of a p a r t i c u l a r event i s to provide a set of f a c t o r s ( p r o p e r t i e s , a t t r i b u t e s ) s t a t i s t i c a l l y r e l e v a n t to that event. This set w i l l p a r t i t i o n the o r i g i n a l reference c l a s s of the event i n question i n t o a set of subclasses or c e l l s . ( I f the set of r e l e v a n t f a c t o r s are C 1/..,C n, then there are 2 n such c e l l s . ) Each p a r t i t i o n e d c e l l should be as broad as p o s s i b l e , yet each should remain homogeneous with respect to the event i n q u e s t i o n . P r o b a b i l i t y values are then assigned to each c e l l , r e l a t i n g the occurrence of the explanandum event to the co n d i t i o n s represented by t h a t c e l l , the event to be explained now lo c a t e d i n one of these s u b c l a s s e s . Explanation progresses by i n c r e a s i n g the homogeneity of the p a r t i t i o n e d c e l l s . We might b r i e f l y i l l u s t r a t e t h i s as f o l l o w s : we wish to know why S performed as w e l l as she d i d on her philosophy f i n a l exam. Suppose that we determine that there are only three r e l e v a n t f a c t o r s : hours of study per week (H), l e v e l of m o t i v i a t i o n during those hours (M), and an e a r l y s t a r t i n preparing f o r the exam (E). The o r i g i n a l reference c l a s s C of students i n the course can now be p a r t i t i o n e d , and p r o b a b i l i t y values assigned. I f we s t a r t our p a r t i t i o n i n g w i t h f a c t o r H alone, we see that the homogeneity can be i n c r e a s e d , f o r some students' long hours (H) achieve the same r e s u l t s as others' s h o r t hours (H). The a d d i t i o n of f a c t o r s M and E f u r t h e r d i v i d e s and ' p u r i f i e s ' each s u b c l a s s . Given t h a t 95% of the members of (C&H&M&E) do w e l l on t h e i r exams, and that S i s a member of t h i s subclass ( and (C&H&M&E) i s 1 6 homogeneous), we have thus explained her performance. 1 7 Kruger draws our a t t e n t i o n to s e v e r a l d i f f i c u l t i e s i n Salmon's approach, some of which we w i l l f i n d i n s t r u c t i v e . Salmon, Kruger 1 8 c l a i m s , takes C to be an explanatory f a c t o r f o r E even through P(E/C&A)<P(E/A), i . e . , C is s t a t i s t i c a l l y r e l e v a n t to E, and lowers the p r o b a b i l i t y of E, given A. C does not e x p l a i n E, f o r Kruger, but rather "points to a d i f f i c u l t y f o r the attempt to e x p l a i n E, which c o n s i s t s i n the 19 presence of C." In terms of the above example, the p r o b a b i l i t y of 30 S's f a i l i n g her exam c e r t a i n l y decreases i f she i s a member of the subclass of students who study long, hard, and d i l i g e n t l y . (Suppose, as before, that these are a l l the r e l e v a n t f a c t o r s . ) Suppose she f a i l s her exam. How can we e x p l a i n t h i s event by f a c t o r s which decrease i t s p r o b a b i l i t y ? This o b j e c t i o n contains s e v e r a l threads of misunderstanding. Let us attempt to untangle them. F i r s t , however, to answer the above question, what other f a c t o r s might one use here? These are, by hypothesis, a l l and only those f a c t o r s which make a d i f f e r e n c e . Kruger seems to have missed the V p o i n t that the values of p r i o r and p o s t e r i o r weights have l i t t l e to do with 20 explanatory power — they are, at best, a "fortunate dividend." Salmon gives s e v e r a l examples where homogeneity i s increased, yet p o s t e r i o r 21 weights i n c r e a s e , decrease, or even remain the same. I t i s homogeneity, we r e c a l l , which gives explanatory f o r c e . A second theme can be discerned here — c a l l i t the "supra-explanatory" c a p a c i t y of s t a t i s t i c a l e x p l a n a t i o n s . Having assembled the r e l e v a n t f a c t o r s and a s s o c i a t e d p r o b a b i l i t y values which are s t a t i s t i c a l l y r e l e v a n t f o r , and thus e x p l a i n the occurrence of E, we have, i n f a c t , assembled j u s t those f a c t o r s r e l e v a n t f o r the non-occurrence of E. I f the r e l a t i o n s h i p between E and i t s environment i s indeed s t a t i s t i c a l , then no set of f a c t o r s can guarantee i t s occurrence (or non-occurrence). Although the te n s i o n f e l t here can be traced d i r e c t l y to the idea of explanation as arguments — that from the same premises (explanans) we cannot derive c o n t r a d i c t o r y conclusions (explananda) — that tension may s t i l l e x i s t i n some form even w i t h i n a n o n - i n f e r e n t i a l view of e x p l a n a t i o n . In any case, 31 t h i s d i f f i c u l t y can be r a i s e d i n Salmon's more recent account, and we s h a l l postpone our d i s c u s s i o n of i t u n t i l then (Section 4b). There i s another, stronger thread which runs through t h i s and othe 22 o b j e c t i o n s that Kruger r a i s e s . Suppose we assemble a l l the r e l e v a n t f a c t o r s and, regardless of whether p o s t e r i o r weight i s increased or decreased, the improbable happens. S f a i l s her exam even though she i s a member of that subclass who study long, hard and d i l i g e n t l y . How do we e x p l a i n such an event? What i s i t that i s u n s a t i s f y i n g about the f o l l o w i n g Salmonian attempt: here are a l l the r e l e v a n t f a c t o r s and the p r o b a b i l i t y values ( a l l we could know of the event's r e l a t i o n to other events that make d i f f e r e n c e ) and, as we can see, the u n l i k e l y has occurred? One thing that i not u n s a t i s f y i n g i s the low p r o b a b i l i t y value s i n c e , as i n the c l a s s i c p a r e s i s example the p r o b a b i l i t y i s again low, but we are s a t i s f i e d by the s t a t i s t i c a l l y r e l e v a n t f a c t o r of l a t e n t untreated s y p h i l l i s . The d i f f e r e n c e i s that i n t h i s l a t t e r case we are aware1 of a causal connection, here betwee s y p h i l l i s and paresis-. And although there may w e l l be a causal connection between d i l i g e n t study and exam success, we can hardly claim a c a u s a l 23 connection between d i l i g e n t study and f a i l u r e . As we described i n Section 3a, Salmon admits that c a u s a l connections supersede s t a t i s t i c a l r e l a t i o n s , and that i t i s j u s t these relevance r e l a t i o n s which i n d i c a t e the presence of c a u s a l i t y (screening o f f occurs.) And he admits, though r e l u c t a n t l y i t seems, " t h a t symptomatic explanations seem to have genuine explanatory value i n the absence of knowledge of caus a l r e l a t i o n s ."^ B u t c a n h e e x p l a i n , even symptomatically, what happened to our student above? Kruger maintains that 25 symptoms never e x p l a i n anything — even te m p o r a r i l y . Salmon attempts 32 to pass over our strong causal i n t u i t i o n s i n explanation by accommodating them w i t h i n the s t a t i s t i c a l property of screening o f f . Is t h i s "accommodation" g e n e r a l l y s u c c e s s f u l ? We have already r a i s e d some general doubts — here we s h a l l mention a more s p e c i f i c counter-example. In an e l e c t r o n - p o s i t r o n p a i r production by gamma r a d i a t i o n we have a case of " c o l l a t e r a l " c a u s a t i o n . The presence of the e l e c t r o n i s c e r t a i n l y s t a t i s t i c a l l y r e l e v a n t to the presence of the p o s i t r o n , and we know there not to be a cau s a l connection between the two, t h e i r s t a t i s t i c a l relevance being only symptomatic. Yet any causal connection we might provide f o r the production of one w i l l not screen o f f the other — without the e l e c t r o n , say, there would be no p o s i t r o n . Here i s a case of a non-causal r e l a t i o n s h i p of s t a t i s t i c a l relevance whose true cause does not screen o f f . Thus the s t a t i s t i c a l concept of c a u s a t i o n , by means of the screening o f f r e l a t i o n , i s not adequate to capture c e r t a i n causal c o n t e x t s . However, the l a r g e r d i f f i c u l t y i s not simply that of an inadequate s t a t i s t i c a l analogue of causal contexts i n ex p l a n a t i o n , but rather that of a deep conceptual c o n f l i c t w i t h i n any genuine s t a t i s t i c a l model of explanation 27 t h a t i n c l u d e s a r e p r e s e n t a t i o n of our causal i n t u i t i o n s i n e x p l a n a t i o n . One side of t h i s c o n f l i c t can be presented i n what can be c a l l e d "the 28 argument from s u f f i c i e n t c o n d i t i o n s . " Any genuine explanation would seem to r e q u i r e some reference to causes (and any theory of explanation to the r o l e causes play.) A cause, whatever e l s e i t may be, i s always something which, c e t e r i s p a r i b u s , i n v a r i a b l y produces i t s e f f e c t . Thus i f a genuine e x p l a n a t i o n i n c l u d e s a reference to causes, then i t cannot be a s t a t i s t i c a l e x p l a n a t i o n . I f we are not to abandon t o t a l l y the p o s s i b i l i t y of genuine s t a t i s t i c a l e x p l a n a t i o n , and i f we f e e l the p u l l of the causal concept i n 33 e x p l a n a t i o n , then we must r e j e c t the idea of causes as s u f f i c i e n t c o n d i t i o n s f o r t h e i r e f f e c t s . Salmon, rec o g n i z i n g the import of the causal concept i n h i s recent m o d i f i c a t i o n of s t a t i s t i c a l e x p l a n a t i o n , adopts j u s t such a c o n c l u s i o n . I t i s to t h i s new Causal-Relevance model that we now t u r n . 29 3. The Causal-Relevance Model. In March, 1978, at the s p r i n g meeting of the American P h i l o s o p h i c a l A s s o c i a t i o n ( P a c i f i c D i v i s i o n ) , Salmon presented a model of s c i e n t i f i c e x p l a n a t i o n that both r e t a i n e d many features of h i s S-R model and added a new, fundamental, aspect. This new aspect i s the r o l e of causes i n e x p l a n a t i o n . Compare Salmon (1971): The unwanted "symptomatic ex p l a n a t i o n " can be blocked by use of the scr e e n i n g - o f f concept, which i s defined i n terms of s t a t i s t i c a l i r r e l e v a n c e alone. We have not found i t necessary to introduce an independent concept of c a u s a l r e l a t i o n i n order to handle t h i s problem. w i t h Salmon (1978): This a t t i t u d e [which allows non-causal as w e l l as causal laws to f u n c t i o n as covering laws i n s c i e n t i f i c explanations] i s s u r e l y too t o l e r a n t . ...At t h i s p o i n t , i t seems to me, we experience v i v i d l y the force of the i n t u i t i o n s u n d e r l y i n g the c a u s a l conception of s c i e n t i f i c explanation ... we must give the causal conception i t s due. Salmon does not e n l i g h t e n us as to the arguments which moved him from the former p o s i t i o n to the l a t t e r . Since the p u b l i c a t i o n of (1971) there have been not a few t h e o r i s t s who have pointed out the inadequacies of rendering c a u s a l r e l a t i o n s s o l e l y v i a the screening o f f r e l a t i o n (by " s t a t i s t i c a l 32 i r r e l e v a n c e alone.") We have touched upon some of these arguments i n the previous s e c t i o n . 3 4 By now defending a causal v e r s i o n of s t a t i s t i c a l explanation Salmon places himself squarely i n the middle of the problematic described at the end of the previous s e c t i o n . However, Salmon denies that there i s a c o n f l i c t here: Developments i n twentieth-century science should prepare us f o r the e v e n t u a l i t y that some of our s c i e n t i f i c e x p l a n a t i o n s w i l l have to be s t a t i s t i c a l — not merely because our know-ledge i s incomplete (as Laplace would have maintained) but ra t h e r because nature i t s e l f i s i n h e r e n t l y s t a t i s t i c a l . Some of the laws used i n e x p l a i n i n g p a r t i c u l a r events w i l l be s t a t i s t i c a l , and some of the r e g u l a r i t i e s we wish to e x p l a i n w i l l a l s o be s t a t i s t i c a l . I have been urging that causal c o n s i d e r a t i o n s p l a y a c r u c i a l r o l e i n explanation; indeed, I have j u s t s a i d that r e g u l a r i t i e s — and t h i s c e r t a i n l y includes s t a t i s t i c a l r e g u l a r i t i e s — r e q u i r e causal e x p l a n a t i o n . I do not b e l i e v e there i s any c o n f l i c t here. I t seems to me that, by employing a s t a t i s t i c a l conception of causation ... i t i s p o s s i b l e to f i t toqether harmoniously the caus a l and s t a t i s t i c a l f a c t o r s i n 33 e x p l a n a t o r y c o n t e x t s . Whether there i s such a coherent " s t a t i s t i c a l conception of c a u s a l i t y " w i l l occupy us i n Chapters I I and I I I . Our task f o r the remainder of t h i s chapter w i l l be to e x p l i c a t e and defend Salmon's newer model of s c i e n t i f i c e x p l a n a t i o n t a k i n g f o r granted, f o r the moment, an harmonious f i t between c a u s a l and s t a t i s t i c a l f a c t o r s . In Salmon's new account, which we s h a l l c a l l the Causal-Relevance (C-R) view, an explanation of a p a r t i c u l a r event has three components, the f i r s t two of which are the f o l l o w i n g : 1) A s e t , RF, of f a c t o r s s t a t i s t i c a l l y r e l e v a n t to that event. 2) The p r o b a b i l i t y values a s s o c i a t e d with the relevance r e l a t i o n s . These two f a c t o r s mark no departure from Salmon's e a r l i e r approach. What the C-R view re q u i r e s i n a d d i t i o n i s 35 3) A c a u s a l account of the relevance r e l a t i o n s , i . e . , of the r e l a t i o n s between members of RF and the event to be e x p l a i n e d . We have s t a t e d these three c o n d i t i o n s i n our own terms because we b e l i e v e t h a t Salmon's fo r m u l a t i o n contains some minor problems which could cloud the is s u e s we wish to r a i s e . Salmon says: We do, I b e l i e v e , have a bona f i d e explanation of an event i f we have a complete s e t of s t a t i s t i c a l l y r e l e v a n t f a c t o r s , the p e r t i n e n t p r o b a b i l i t y values, and a causal explanation of the relevance r e l a t i o n s . ^ There are a l e a s t two p o s s i b l e d i f f i c u l t i e s with t h i s f o r m u l a t i o n , ( i ) I t may appear c i r c u l a r f o r one of the d e f i n i n g c o n d i t i o n s on explanation i s to re q u i r e causal explanations of the relevance r e l a t i o n s . ( i i ) I t i s unclear what c o n s t i t u t e s a complete set of s t a t i s t i c a l l y r e l e v a n t f a c t o r s . In f a c t , as we s h a l l see below, i n one of Salmon's main i l l u s t r a t i o n s of a s u c c e s s f u l C-R e x p l a n a t i o n , there are good grounds f o r saying that the set of r e l e v a n t f a c t o r s i s , i n a sense, incomplete. In order to f a c i l i t a t e e x p o s i t i o n we w i l l d i v i d e the d i s c u s s i o n of Salmon's caus a l account i n t o two p a r t s , roughly corresponding to the meta-p h y s i c a l and epistemic aspects of t h i s account. F i r s t we s h a l l look a t the nature of causes as processes, and then to the r o l e these processes p l a y i n our explanatory e f f o r t as common causes, a notion f i r s t suggested by Reichenbach. (a) Causal Processes The s a l i e n t feature of Salmon's causal account i s to deny that there i s a c a u s e - e f f e c t r e l a t i o n , that causation i s a r e l a t i o n a t a l l . The mysterious "hidden power" that Hume searched f o r i n v a i n , to connect events c a u s a l l y , i s dispensed with i n favor of the concept of a process, or c a u s a l 36 35 l i n e , the t e r m i n i of which are causal i n t e r a c t i o n s . Causal processes as continua avoid the problem of the connection between one event and another, f o r continua are everywhere 'dense'. Events, on t h i s account, are s t r u c t u r e s analyzed i n terms of these two p r i m i t i v e concepts of process and i n t e r a c t i o n . The r e l a t i v e frequency of events provides the s t a t i s t i c a l component of C-R explanations; the explanation i s completed when we place these events i n c e r t a i n patterns of causal processes. In the f o l l o w i n g s e c t i o n we w i l l d e s cribe these p a t t e r n s ; here we w i l l d e t a i l these Salmonian p r i m i t i v e s . Processes are s p a t i o - t e m p o r a l l y continuous phenomena. Two d i s t i n c t i o n s are of importance here: between causal and non-causal, or pseudo-, processes; and between causal processes and causal i n t e r a c t i o n s . Causal processes are processes that are capable of t r a n s m i t t i n g c a u s a l i n f l u e n c e or i n f o r m a t i o n , pseudo processes are not. That i s , a causal process t h a t has been modified or "marked" as a r e s u l t of an i n t e r a c t i o n w i l l remain so modified wihtout f u r t h e r i n t e r a c t i o n . A beam of (white) l i g h t i s a cau s a l process and may be modified, or marked, by i t s passage through a monochromatic f i l t e r . I t then transmits t h i s i n f o r m a t i o n , a red s i g n a l say, without f u r t h e r a s s i s t a n c e . The shadow cast by an o b j e c t placed i n t h i s beam of l i g h t i s a pseudo-process. I f i t i s 'marked' by a deformation of e i t h e r the o b j e c t which casts i t , or the surface upon which i t i s cas t , i t w i l l not maintain that m o d i f i c a t i o n once the deformations are removed. A minor d i f f i c u l t y i s the dearth of such non-causal pseudo-processes. Shadows, p e r f e c t vacuums, and the l i k e (?) are candidates which are indeed non-causal, but, as w e l l , seem ha r d l y p r o c e s s - l i k e . However, a more serious d i f f i c u l t y can be seen. Processes can be d i s t i n g u i s h e d as causal only i f they are capable of t r a n s m i t t i n g a "mark", yet t h i s mark i s c l e a r l y the r e s u l t of_ a 37 c a u s a l i n t e r a c t i o n . Unless we have a second d i s t i n c t i o n , where caus a l i n t e r a c t i o n s are c h a r a c t e r i z e d independently of causal processes, we s h a l l f i n d ourselves i n a v i c i o u s c i r c l e . In the above instance the f i l t e r i s a causal process, and i t s i n t e r s e c t i o n with the beam of l i g h t i s a causal i n t e r a c t i o n . Salmon w r i t e s : I n t e r a c t i o n s are the s o r t s of things we are i n c l i n e d to i d e n t i f y as events. R e l a t i v e to a p a r t i c u l a r context, an event i s comparativley small i n i t s s p a t i a l and temporal dimensions; processes t y p i c a l l y have much longer d u r a t i o n s , and they may be more extended i n space as w e l l . " * 6 Obviously, the simple spatio-temporal dimensions w i l l not d i s t i n g u i s h processes from i n t e r a c t i o n s . C e r t a i n m i c r o - p h y s i c a l e n t i t i e s have e x t r a -o r d i n a r i l y b r i e f l i v e s as processes, while c e r t a i n chemical r e a c t i o n s are rat h e r l o n g - l i v e d i n t e r a c t i o n s . What i s needed i s a c h a r a c t e r i z a t i o n , of i n t e r a c t i o n s e s p e c i a l l y , which w i l l provide a more s t r u c t u r a l d i f f e r e n c e . Salmon recognizes t h i s d i f f i c u l t y ; h i s response i s to c h a r a c t e r i z e c a u s a l i n t e r a c t i o n s i n terms of i n t e r a c t i v e f o r k s . Since t h i s approach i s an extension of Reichenbach's notion of conjunctive causal f o r k s , we w i l l t u rn to i t s a n a l y s i s f i r s t , and r e t u r n to t h i s problem at the end of the f o l l o w i n g s e c t i o n . (b) Causal Forks: Conjunctive and I n t e r a c t i v e . The con j u n c t i v e c a u s a l fork may be f o r m a l l y described i n the f o l l o w i n g manner. Suppose we have noticed a s t a t i s t i c a l c o r r e l a t i o n between events (or event-types) A and B such t h a t 1) P(A&B) > P(A)P(B). That i s , the p r o b a b i l i t y of t h e i r co-occurrence i s higher than the product of t h e i r independent p r o b a b i l i t i e s . I f the two events are not d i r e c t l y 38 connected c a u s a l l y , we may hypothesize a common cause, C, such that C forms a con j u n c t i v e f o r k w i t h A and B. That i s , C i s r e l a t e d to A and B as f o l l o w s : 2) P(A&B/C) = P(A/C)P(B/C) 3) P(A&B/C) = P(A/C)P(B/C) 4) P(A/C) > P(A/C) 5) P(B/C) > P ( B / C ) 3 7 (1) then f o l l o w s l o g i c a l l y from (2) - ( 5 ) . Roughly, (4) and (5) a s s e r t that f a c t o r C i s p o s i t i v e l y r e l e v a n t to the occurrence of A, and to the occurrence of B. Statements (2) and (3) show t h a t , r e l a t i v e to C (and C) A and B are s t a t i s t i c a l l y independent. Since A and B are independent r e l a t i v e to C we 38 see that the f o l l o w i n g a l s o holds: 6) P(A/C) = P(A/BSC) f P(A/B). (6) i s the c l a i m t h a t c o n j u n c t i v e f o r k s e x h i b i t screening o f f . That i s , the presence of f a c t o r C absorbs the s t a t i s t i c a l dependence between A and B; given C, the occurrence of B becomes i r r e l e v e n t f o r the occurrence of A, and v i c e v e r s a . For conjunctive f o r k s the concept of screening o f f t r a v e l s 39 i n t a c t from Salmon's e a r l i e r view. An example should be of help here. Let us d i s p l a y the ( a l l too) f a m i l i a r r e l a t i o n between the f a l l i n g barometer and the coming storm i n l i g h t of the above c o n d i t i o n a l p r o b a b i l i t i e s . We f i r s t note the p o s i t i v e s t a t i s t i c a l dependence between the approaching storm (A) and the f a l l i n g barometer (B). We hypothesize t h e i r common cause to be the atmospheric c o n d i t i o n s ( C ). The presence of C c e r t a i n l y r a i s e s the p r o b a b i l i t y of both A and B. And w i t h i n t h i s narrower reference c l a s s , i . e . , under c o n d i t i o n C, we f i n d t h a t the p r o b a b i l i t y of the j o i n t occurrence of the f a l l i n g barometer and storm i s j u s t that of the product of t h e i r independent p r o b a b i l i t i e s 39 under those c o n d i t i o n s . We a l s o note t h a t , with the knowledge that c o n d i t i o n C o b t a i n s , the occurrence of A i s i r r e l e v a n t to our assignment of a p r o b a b i l i t y to B, and v i c e v e r s a . Screening o f f occurs. 40 Bas van Fraassen, i n a recent manuscript, o f f e r s what he takes to be an i n c o m p a t i b i l i t y between the concept of a conjunctive c a u s a l f o r k and contemporary t h e o r i z i n g i n p h y s i c s . His example i s very schematic, and r e l i e s on only two assumptions: that the occurrence of the phenomena under c o n s i d e r a t i o n i s genuinely i n d e t e r m i n i s t i c , and that these phenomena e x h i b i t a p a r t i c u l a r l y strong p a i r - w i s e c o r r e l a t i o n — s i m i l a r to that found i n Compton s c a t t e r i n g and photon p a i r p r o d u c t i o n . I f the causal p r i n c i p l e s as described i n terms of conjunctive forks does i n f a c t d i s a l l o w these kinds of examples, then i t w i l l have to be modified i f i t i s to be amenable to c u r r e n t p h y s i c a l theory. The d e t a i l s of the counter-example are as f o l l o w s . Suppose that from the complete d e s c r i p t i o n of some i n i t i a l s t a t e S a system always goes i n t o another s t a t e c h a r a c t e r i z e d by a set of a t t r i b u t e s {F^} or {G^}, and that t h i s s t a t e t r a n s i t i o n i s i n d e t e r m i n i s t i c , the p r o b a b i l i t y of change to some F^ or i s l e s s than the extreme. That i s , (a) P(F i/S) = J_» P(G ±/S) = J_ n n In a d d i t i o n , the two end states are s t r o n g l y c o r r e l a t e d such t h a t (b) P(F i&G i/S) = 1. "In other words, i t i s pure chance whether the s t a t e to which S t r a n s i t s i s c h a r a c t e r i z e d by a given one of the F - a t t r i b u t e s , and s i m i l a r l y f o r the G - a t t r i b u t e s , but c e r t a i n that i t i s c h a r a c t e r i z e d by F 1 i f i t i s 41 c h a r a c t e r i z e d by G 1, by F2 i f by G2/ and so on." But i f S i s a complete s t a t e d e s c r i p t i o n , then (c) P ( F i & G I / S ) = P ^ / S ) = 1 and n (d) P(F i/S) P(G ±/S) = ( i ) 2 Now, only i f the p r o b a b i l i t y (1) i s zero or one (the d e t e r m i n i s t i c case) n are(c) and (d) equal, as required by c r i t e r i o n (2) above. "In a l l other cases. S does not q u a l i f y as the common cause of the new states being F^ 42 or G^, and i f S i s complete, nothing e l s e can q u a l i f y e i t h e r . " R e c a l l that p r e v i o u s l y , i n the barometer example, knowledge of the i n i t i a l C onditions completely absorbed the dependency between the c o r r e l a t e d events, the approaching storm and the barometer readings. Here the s t a t e d e s c r i p t i o n S can screen o f f from only i f i t i s completely determined to which f i n a l s t a t e the system evolves. I f the p r o b a b i l i t y of t h i s t r a n s i t i o n i s le s s than one, then the knowledge of the one f i n a l s t a t e s t i l l depends on knowledge of the other, and thus S cannot screen o f f F-states from G-states, and thus cannot q u a l i f y as a causal antecedent i n the conjunctive f a s h i o n . Since an attack on van Fraassen's assumptions of these strong p a i r - w i s e c o r r e l a t i o n s , or on indeterminism, would f l y i n the face of j u s t those s i t u a t i o n s "twentieth-century physics should prepare us f o r " , Salmon's response i s to modify c o n d i t i o n (2) and thus expand the notion of common cause to include i n t e r a c t i v e f o r k s . C e r t a i n p a i r s of events, although not d i r e c t l y c a u s a l l y connected, demonstrate a more intima t e r e l a t i o n s h i p than t h a t which i s allowed f o r by t h e i r s t a t i s t i c a l dependence v i a a conjunctive causal f o r k . These events are connected by a perhaps more ' a c t i v e ' causal connection, the i n t e r a c t i v e f o r k . This s t r u c t u r e i s defined by r e p l a c i n g (2) wi t h (2*) P(A&B/C) > P(A/C)P(B/C) 41 i n which case S, i n the van Fraassen example, would s t i l l q u a l i f y as a common cause of F^ and . The i n t e r a c t i v e f o r k covers more than j u s t i n d e t e r m i n i s t i c , quantum-mechanical s i t u a t i o n s . Consider the c o l l i s i o n of two b i l l i a r d b a l l s : whatever the p r o b a b i l i t i e s f o r t h e i r emergence from t h e i r c o l l i s i o n w i t h momenta of c e r t a i n values, they w i l l yet be r e l a t e d by the conservation of momentum — the sum of the r e s u l t a n t momenta w i l l be equal that of the i n c i d e n t b a l l . The common cause — the i n c i d e n t b i l l i a r d b a l l — does not screen o f f the s t a t i s t i c a l relevance between the r e s u l t i n g momenta. However, i f the sta t e d e s c r i p t i o n of the b i l l i a r d b a l l system completely determines the momentum of the object b a l l , then screening o f f does occur, and i n t h i s 43 s p e c i a l case the i n t e r a c t i v e f o r k reduces to the conjunctive f o r k . With the device of the i n t e r a c t i v e fork Salmon expects to accomplish at l e a s t two o b j e c t i v e s : to provide a s a t i s f a c t o r y explanatory account of a very pervasive v a r i e t y of common causes which are not covered by fo r k s of the conjunctive v a r i e t y ; and to c h a r a c t e r i z e causal i n t e r a c t i o n s , v i a the 'marks' described above (p.36), i n a n o n - c i r c u l a r f a s h i o n . Let us examine t h i s l a t t e r o b j e c t i v e f i r s t . The problem i s how we are to c h a r a c t e r i z e 'marks' without recourse to causes or causal processes. To t h i s end Salmon o f f e r s , with l i t t l e f u r t h e r enlightenment, the concept of an i n t e r a c t i v e f o r k . He says: ...very roughly...that when two processes i n t e r a c t , and both are modified i n such ways that the changes i n one are c o r r e -l a t e d with changes i n the other — i n the manner of i n t e r -a c t i v e f o r k — we have a causal i n t e r a c t i o n . 4 4 But now, i f we review the above formal c h a r a c t e r i z a t i o n to determine "the manner of an i n t e r a c t i v e f o r k " we see only that causal forks of t h i s v a r i e t y 42 are j u s t those whose e f f e c t s are c o r r e l a t e d with one another. To des c r i b e c a u s a l i n t e r a c t i o n s by means of i n t e r a c t i v e forks i n t h i s way serves only to re-name them. Nevertheless, something seems to be o f f e r e d here which we might attempt to unravel as f o l l o w s . When a causal process, such as the atmospheric c o n d i t i o n i n the barometer example, i s promoted as a common cause of s t a t i s t i c a l l y r e l a t e d e f f e c t s (the approaching storm and the f a l l i n g barometer readings), we see these e f f e c t s as separate r e s u l t s , whose only ( r e a l ) connection i s a common ca u s a l ancestor. The causal l i n e s which terminate i n these r e s u l t s can be ret r a c e d to t h e i r i n t e r s e c t i o n , or perhaps genesis, i n c o n d i t i o n C, but there i s no i n t e r a c t i o n here. This kind of account n i c e l y provides the causal s t o r y of i d e a l measuring instruments, where the phenomena measured and the measurement r e s u l t do not modify one another. But when the c o r r e l a t e d e f f e c t s are brought about not as a r e s u l t of mere common o r i g i n but rat h e r from the i n t e r f e r e n c e , or i n t e r a c t i o n , of one process with another we have a d i f f e r e n t c a u s a l s t o r y to t e l l . The i n f l u e n c e of the causal l i n e ( s ) which produce(s) these e f f e c t s does not then d i v i d e i n t o completely independent caus a l l i n e s , i t s e f f e c t s remain c o r r e l a t e d . These c o r r e l a t e d m o d i f i c a t i o n s are a t the heart of both the concept of a causal i n t e r a c t i o n and an i n t e r a c t i v e causal f o r k . How are we to understand them? C e r t a i n l y one cannot be used to e x p l i c a t e the other. We see then that the c o r r e l a t i o n of completely independent events, as i n the conj u n c t i v e f o r k , i s explained by t h e i r common causa l ancestor, the presence of which renders t h e i r co-occurrence mutually i r r e l e v a n t , at l e a s t f o r purposes of ex p l a n a t i o n . An i n t e r a c t i v e f o r k , however, boasts of more than j u s t common ancestry — i t shows the c o r r e l a t i o n and (apparent) mutual i n f l u e n c e between two e f f e c t 43 events to be a product of a previous mutual m o d i f i c a t i o n or i n t e r a c t i o n . This mutual i n f l u e n c e i s not d i r e c t , but rather i n d i r e c t through t h i s previous i n t e r a c t i o n . Thus i t w i l l not do to attempt an e x p l i c a t i o n of t h i s previous i n t e r a c t i o n v i a "the manner of an i n t e r a c t i v e f o r k " , f o r i t i s j u s t t h i s "manner" we are attempting to e x p l a i n . 45 A s i m i l a r p o i n t i s , I b e l i e v e , made by van Fraassen i n h i s c r i t i c i s m of the concept of an i n t e r a c t i v e f o r k . R e c a l l that a common cause i s demanded whenever (1) P(A&B) > P(A)P(B), and that an i n t e r a c t i v e fork i s defined by (2*) P(A&B/C) > P(A/C)P(B/C). I f we define the f u n c t i o n 1 P c ' ( p r o b a b i l i t y r e l a t i v e to C) as (7) P C(X) = P(X/C), P C(X/Y) = P(X/Y&C) then we may ' d e - c o n d i t i o n a l i z e ' the p r o b a b i l i t i e s i n (2*) which y i e l d s (1*) P C(A&B) > P C ( A ) P C ( B ) . (1*) i s , of course, an instance of (1) and thus demands explanation by way of a common cause . This regress stops only when some s a t i s f i e s the o r i g i n a l equation (2). Van Fraassen's complaint i s t h i s : an i n t e r a c t i v e causal fork leaves a s t a t i s t i c a l 'residue' — events connected by such a fork are more s t r o n g l y c o r r e l a t e d than the product of t h e i r independent p r o b a b i l i t i e s — and are thus subjects f o r f u r t h e r e x p l a n a t i o n . This regress stops only when a conjunctive causal f o r k which screens o f f the c o r r e l a t e d e f f e c t s can be adduced. As Salmon himself notes, the only s i t u a t i o n i n which a co n j u n c t i v e f o r k can e x p l a i n a c o r r e l a t i o n of the i n t e r a c t i v e type i s when the p r o b a b i l i t i e s are 1 or 0, that i s , i n the d e t e r m i n i s t i c case. 44 I t i s of i n t e r e s t to note that one of the motivations i n p r o v i d i n g a c a u s a l account i s that such an account screens o f f p u r e l y symptomatic, e.g., storm-barometer, c o r r e l a t i o n s . Now we f i n d c e r t a i n non-screening o f f c a u s a l connections, and, i f we are to remain true to our i n i t i a l d e s i r e s , these r e s i d u a l c o r r e l a t i o n s must a l s o be e x p l a i n e d . This explanatory r e i t e r a t i o n i s a c e n t r a l feature of s c i e n t i f i c i n q u i r y ( n e a t l y captured i n the t i t l e "Why ask 'why?'?") and, given the p o s s i b i l i t y of always being able to reach a c o n j u n c t i v e causal f o r k , we might s u c c e s s f u l l y complete such an i n v e s t i g a t i o n . To do t h i s , however, as the argument of t h i s s e c t i o n suggests, i s to demand of the world that i t be, u l t i m a t e l y , d e t e r m i n i s t i c . Current p h y s i c a l theory suggests that t h i s may very w e l l not be the case. Is there a c o n f l i c t then, between c a u s a l i t y , or causal e x p l a n a t i o n , and indeterminism, as van Fraassen's c r i t i c i s m suggests? 4. Objections 46 (a) Indeterminism. Whether the world i s d e t e r m i n i s t i c or i n d e t e r m i n i s t i c i s not to be s e t t l e d a p r i o r i (and thus not to be s e t t l e d w i t h i n a theory of explanation.) Any account of s c i e n t i f i c e xplanation should remain n e u t r a l on t h i s i s s u e , a v i r t u e Salmon claims f o r h i s theory. However, a complete C-R e x p l a n a t i o n c a l l s f o r an account of causes, or causal processes, and thus, i t i s claimed, begs the d e t e r m i n i s t i c / i n d e t e r m i n i s t i c q u e s t i o n . In t h i s s e c t i o n we w i l l present t h i s apparent c o n f l i c t by a s l i g h t m o d i f i c a t i o n of one of Salmon's examples. (The consequences of t h i s counterexample f o r the defense of Salmon's theory w i l l be a r e c o n s i d e r a t i o n of what Salmon takes to be a c a u s a l account of events; s p e c i f i c a l l y what he takes to be a p r o b a b i l i s t i c 45 c a u s a l process, and what place the l a t t e r concept has i n our p r e - t h e o r e t i c network of causal concepts. This task w i l l be the focus of Chapter I I . ) The example with which Salmon chooses to i l l u s t r a t e h i s C-R model i s that of the high incidence of leukemia among s o l d i e r s who witnessed, a t clo s e range, the atomic bomb t e s t code-named "Smokey" i n 1957. Although the incidence of t h i s cancer among these observers was s m a l l , i t was s i g n i f i c a n t l y higher than the incidence among the general p o p u l a t i o n . Suppose we wish to e x p l a i n why a p a r t i c u l a r s o l d i e r , GI Joe, contracted leukemia. According to our sketch of the C-R model i n S e c t i o n 3, there are three c o n d i t i o n s to be met i n order to provide such an e x p l a n a t i o n . (1) We assemble a l l those f a c t o r s s t a t i s t i c a l l y r e l e v a n t to the event to be ex p l a i n e d . Here the s p e c i f i c s of GI Joe's p a r t i c i p a t i o n i n Smokey are f a c t o r s s t a t i s t i c a l l y r e l e v a n t to h i s c o n t r a c t i o n of leukemia. For ease of e x p o s i t i o n l e t us c o l l e c t these d e t a i l s i n t o a s i n g l e f a c t o r , F, which i n c l u d e s GI Joe's being s i t u a t e d two kilometers from the b l a s t . (2) We e s t a b l i s h the p e r t i n e n t p r o b a b i l i t y v a l u e s . For GI Joe these are the p r o b a b i l i t y of the occurrence of leukemia among those i n d i v i d u a l s under c o n d i t i o n F. (3) We give a causal account of the r e l a t i o n between the r e l e v a n t f a c t o r F and the event to be e x p l a i n e d . Salmon w r i t e s : There i s a causa l process which connects the occurrence of the bomb b l a s t with the p h y s i o l o g i c a l harm done to people a t some distance from the e x p l o s i o n . . . At each end of the causal process ... there i s a ca u s a l i n t e r a c t i o n ... Each of these i n t e r a c t i o n s may w e l l be i r r e d u c i b l y s t a t i s t i c a l and i n d e t e r m i n i s t i c . Thus to e x p l a i n GI Joe's leukemia we f i r s t e s t a b l i s h h i s exposure to r a d i a t i o n i n 1957, describe the r e l e v a n t p r o b a b i l i t y values, and p o i n t to the 46 " w e l l - e s t a b l i s h e d f a c t that such r a d i a t i o n does i n t e r a c t with c e l l s i n a way 48 which makes them s u s c e p t i b l e to leukemia at some l a t e r time." Now although Salmon e n t e r t a i n s the p o s s i b i l i t y that the i n t e r a c t i o n s at both ends of the above causal process - may by i r r e d u c i b l y s t a t i s t i c a l , v i r t u a l l y everyone ( i n c l u d i n g Salmon we b e l i e v e ) suspects t h a t the r a d i a t i o n - c e l l i n t e r a c t i o n w i l l be b e t t e r understood as research on r a d i a t i o n and on c e l l s t r u c t u r e and f u n c t i o n proceeds. In other words, we do not have a w e l l - e s t a b l i s h e d theory according to which the present p r o b a b i l i t i e s are i n p r i n c i p l e i r r e d u c i b l e . I f we now ask why a p a r t i c u l a r member of the reference c l a s s picked out by a t t r i b u t e F got leukemia, we know of no s t a t i s t i c a l l y r e l e v a n t f a c t o r which w i l l p a r t i t i o n t h i s c l a s s , but we suspect that there are such f a c t o r s . I f we grant that t h i s reference c l a s s i s merely e p i s t e m i c a l l y homogeneous, then the C-R explanation o f f e r e d above i s not complete i n the sense that our t h e o r i e s do not r u l e out the assumption th a t there are a d d i t i o n a l f a c t o r s which are s t a t i s t i c a l l y r e l e v a n t to GI Joe's c o n t r a c t i n g leukemia; we j u s t don't know what these f a c t o r s are. However, suppose we reach a p o i n t i n our i n q u i r y which, f o r a v a r i e t y of t h e o r e t i c a l reasons, allows us to conclude that there are no such f a c t o r s . That i s , the c l a s s F', picked out by a t t r i b u t e F, i s o b j e c t i v e l y homogeneous with respect to the a t t r i b u t e of the c o n t r a c t i o n of leukemia: the c o n t r a c t i o n of leukemia by a member of F' i s an u t t e r l y random, but s t a t i s t i c a l l y r e g u l a r , event i n the world. Furthermore, f o r Salmon, genuine indeterminism i s defined i n terms of o b j e c t i v e homogeneity: an event e i s genuinely i n d e t e r m i n i s t i c i f and only i f there i s a reference c l a s s R which 49 i s o b j e c t i v e l y homogeneous with respect to e and 0 < P(e/R) < 1 . Thus 47 concern i s now focused on whether a C-R explanation can be o f f e r e d f o r the occurrence of GI Joe's- leukemia, given the genuine indeterminacy i n F 1. Is there a C-R explanation here? As i n the o r i g i n a l case, we s e t out to f i n d "some f a c t o r s s t a t i s t i c a l l y r e l e v a n t to the occurrence of leukemia i n the general p o p u l a t i o n . Factor F, as we saw, r e l e v a n t l y p a r t i t i o n e d t h i s c l a s s . Now the f a c t o r s must be r e l e v a n t to the occurrence of leukemia among the members of F': among those persons present at the time of the bomb b l a s t , what f a c t o r or f a c t o r s s i n g l e out those who c o n t r a c t leukemia from those who do not? But the c l a i m that t h i s reference c l a s s i s o b j e c t i v e l y homogeneous i s the c l a i m that there are no such f a c t o r s to be found. And i f we deny the p o s s i b i l i t y of a C-R e x p l a n a t i o n i n these circumstances, then, a f o r t i o r i , we deny C-R explanations i n any i r r e d u c i b l y s t a t i s t i c a l s i t u a t i o n , since the c l a i m of i r r e d u c i b i l i t y i s the c l a i m of o b j e c t i v e homogeneity. As we r e c a l l , however, one of the motivations f o r , and c o n s t r a i n t s on, the C-R view i s to present an account i n which the presence of indeterminacy does not c o n f l i c t w i t h the p r o v i s i o n of a c a u s a l e x p l a n a t i o n . The f a c t that there are no r e l e v a n t f a c t o r s here r u l e s out the p o s s i b i l i t y of causal processes whose t e r m i n i are such f a c t o r s , and thus there can,be no C-R e x p l a n a t i o n . In a l i m i t e d sense, though, we do have an e x p l a n a t i o n . We have met the f i r s t c o n d i t i o n by assembling whatever r e l e v a n t f a c t o r s there are (none), and thus the assignment of p r o b a b i l i t y values and causal account i s accomplished as w e l l , but vacuously. But t h i s w i l l not do, of course. Consider our unfortunate v i c t i m , GI Joe, who asks, "Why me?" Don't we ( s c i e n t i f i c a l l y ) owe him an answer here? Salmon's C-R c o n d i t i o n s might be vacuously f i l l e d , and yet there i s obviously something more to be s a i d . 48 Salmon has remarked "What more could one ask of an explanation?" — a query answered by the l a t e r Salmon i n a word: causes. And i t seems Salmon's contention t h a t Joe's c u r i o s i t y / a n x i e t y i s a r e s u l t of h i s ignorance of the nature of p r o b a b i l i s t i c c a u s a l processes. One answer we might give Joe i s "That's the way the world i s . " We thus r e l i e v e o u r s e l v e s , by explanatory 'ascent', of f a c i n g Joe's s p e c i f i c concerns, r e p l a c i n g them w i t h t h e o r e t i c a l concerns such as demonstrating the completeness of the s u c c e s s f u l theory at hand. In other words, the d i s c o v e r y t h a t Joe i s a member of an o b j e c t i v e l y homogeneous group (with respect to the c o n t r a c t i o n of leukemia) renders i l l e g i t i m a t e the request for f u r t h e r e x p l a n a t i o n . But t h i s move w i l l not do. Claiming that F' i s o b j e c t i v e l y homogeneous i s j u s t to say that the occurrence of leukemia i n that p o p u l a t i o n i s i r r e d u c i b l y s t a t i s t i c a l . I f one were to ask, "Why i s F' o b j e c t i v e l y homogeneous?", that question a case of explanatory ascent to which the r e p l y i s , " t h a t ' s the way the world i s . " This l a s t response i s not the p u t a t i v e e x planation under c o n s i d e r a t i o n . The p u t a t i v e explanation c o n s i s t s of both the c l a i m that F' i s o b j e c t i v e l y homogeneous and the extremely complex grounds f o r such a c l a i m . The explanatory ascent described above reveals an important d i s t i n c t i o n between c e r t a i n requests f o r e x p l a n a t i o n . Joe, i t seems, remains l e g i t i m a t e l y d i s s a t i s f i e d when o f f e r e d the s t a t i s t i c a l explanation sketched above. The p u t a t i v e explanation may w e l l answer Joe's "Why me?" only when we consider t h i s query as "Why me at a l l ? " Joe's concern i s , however, best rendered by "Why me r a t h e r than her?", and t h i s , of course, i s a much d i f f e r e n t question — to which a l e g i t i m a t e , but perhaps u n s a t i s f a c t o r y from 49 Joe's p o i n t of view, answer, v i a explanatory ascent, i s that that's the way the world i s . A second, and more promising, attempt to d i s s o l v e the c o n f l i c t i s to say that the e n t i r e problem i s an a r t i f a c t of our p r e s e n t a t i o n . In our scen a r i o we imagined that a question was posed and then l a t e r we 'discovered' that the background reference c l a s s i n question was o b j e c t i v e l y homogeneous. Such a scenario d i s g u i s e s the f a c t , f o r example, that there are a number of s t a t i s t i c a l l y r e l e v a n t f a c t o r s i n v o l v e d i n the case, namely a l l those f a c t o r s which enabled us to chop a u n i v e r s a l c l a s s to F'. We agree t h a t there i s a sense i n which these f a c t o r s are present, but the questioner i s asking f o r something a d d i t i o n a l . We a l s o agree that we biased the scenario to b r i n g out the i s s u e s . Those issues could have been posed somwhat more d i r e c t l y by asking whether there can be a C-R e x p l a n a t i o n i n which the s e t , RF, of r e l e v a n t f a c t o r s i s empty. We have been suggesting that when the emptiness of RF i s due to the o b j e c t i v e homogeneity of the background reference c l a s s , the C-R advocate should agree that there i s a C-R explanation i n s p i t e of the emptiness of RF; to deny that there i s a C-R explanation i s to open the p o s s i b i l i t y that under c e r t a i n circumstances indeterminacy r u l e s out C-R e x p l a n a t i o n . (b) The Paradox of P r o b a b i l i s t i c E x p l a n a t i o n . Having agreed that the C-R advocate faces some d i f f i c u l t i e s i n denying that there i s a C-R e x p l a n a t i o n i n the case at hand, we now wish to p o i n t out that h i s acquiesence would r a i s e some problems as w e l l . We hope to conclude that an a f f i r m a t i v e approach by the C-R advocate w i l l prove to be l e s s problematic. 50 One problem, or set of problems, might be r a i s e d i n the f o l l o w i n g way: suppose our GI Joe does not c o n t r a c t leukemia. What explains t h i s event, given t h a t Joe s t i l l belongs to the o b j e c t i v e l y homogeneous reference c l a s s F'? The C-R response would, we b e l i e v e , c o n s i s t of j u s t those f a c t o r s o f f e r e d i n explanation of why Joe d i d c o n t r a c t t h i s d i s e a s e . This response, however, v i o l a t e s the f o l l o w i n g i n t u i t i v e p r i n c i p l e : (P) I f a given s et of f a c t o r s provides an adequate explana-t i o n of some event E, these same f a c t o r s cannot e x p l a i n not-E. Does the C-R advocate who admits i n d e t e r m i n i s t i c explanations have to give up t h i s p r i n c i p l e ? One might suggest two a l t e r n a t i v e s which would avoid t h i s r e s u l t , (a) The explanation of Joe's f a i l u r e to c o n t r a c t leukemia i s not r e a l l y the same as the explanation o f Joe's c o n t r a c t i o n of leukemia s i n c e the p r o b a b i l i t y values i n the former case are not the same as the p r o b a b i l i t y values i n the l a t t e r . Or (b) i f the two p r o b a b i l i t y values are the same, then the causal account provided would s u r e l y d i s t i n g u i s h the two C-R e x p l a n a t i o n s . That i s , the causal process which terminates i n the i n d u c t i o n of GI Joe's leukemia w i l l c e r t a i n l y be d i f f e r e n t i n kind from the causal process which f a i l s to i n t e r a c t and induce cancer. A l t e r n a t i v e (a) o b v i o u s l y cannot be g e n e r a l i z e d f o r i t works only when the p r o b a b i l i t y values i n q u e s tion are d i f f e r e n t . And a l t e r n a t i v e (b) r e s t s on i d e n t i t y c r i t e r i a f o r p r o b a b i l i s t i c causal processes: are there r e a l l y two d i f f e r e n t causal processes here? Or only one with a " p r o b a b i l i s t i c " or " i n d e t e r m i n i s t i c " r i d e r ? Before we attempt to reso l v e t h i s issue we should p o i n t out that there are some, i n c l u d i n g Salmon, who appear w i l l i n g to give up p r i n c i p l e P. One who does not so choose i s Wolfgang Stegmuller. From h i s v e r s i o n of p r i n c i p l e P he derive s what has been dubbed "The Paradox of the 51 E x p l a n a t i o n of the Improbable." 5 0 Stegmuller asks us to accept h i s own p r i n c i p l e of e x p l a n a t i o n , which he c a l l s the L e i b n i z c o n d i t i o n : (L) An explanation of why an event E occurred must give a j u s t i f i c a t i o n f o r expecting E ra t h e r than not-E. This p r i n c i p l e , however, t e l l s only against s t a t i s t i c a l e xplanation schemas which r e q u i r e that an expectation i s j u s t i f i e d only i f the p r o b a b i l i t y of the expected event i s h i g h . In Salmon's C-R model, as with h i s e a r l i e r s t a t i s t i c a l model, the requirement of high p r o b a b i l i t y has been dropped. Van Fraassen proposes an a l t e r n a t i v e to (L) which, he claims, t e l l s e q u a l l y a g a i n s t Salmon. This weaker p r i n c i p l e i s a c o n s t r a i n t on any explanation which purports to answer "Why E rather that F?", where F i s incompatible w i t h E. Van Fraassen p o s i t s the f o l l o w i n g : (R) An ex p l a n a t i o n of why E r a t h e r than F^must provide a reason why E occurred rather than F. (So f a r t h i s accords w e l l w i t h Joe's i n t u i t i o n s . ) Suppose now that from the t o t a l s i t u a t i o n A we can show that E f o l l o w s with an i r r e d u c i b l y greater p r o b a b i l i t y than F. That i s , P(E/A) > P(F/A). I f E does occur, then A i s the reason why E. I f F occurs, however, we have no e x p l a n a t i o n , f o r A i s the t o t a l amount of i n f o r m a t i o n , and "the information that A gave us a reason to 52 expect that E r a t h e r than F would occur." Thus the improbable has no e x p l a n a t i o n . However, the t o t a l i n f o r m a t i o n A i s no d i f f e r e n t the f i r s t time from the second, and i f A give s no reason why E occurred when F occurred r a t h e r than E, i t can give no reason why E occurred, when i t d i d . The most we have i s a j u s t i f i c a t i o n of b e l i e f that E w i l l occur, and not a reason why E d i d occur, when i t d i d . Our unwanted con c l u s i o n i s that i n the i r r e d u c i b l y s t a t i s t i c a l s i t u a t i o n n e i t h e r the improbable,,nor the probable are e x p l a i n a b l e . 52 Before we attempt to block t h i s p a r a d o x i c a l conclusion there are some p r e l i m i n a r y p o i n t s to be noted. F i r s t , demands such as (L) or (R) are what we i n t u i t i v e l y come to expect from an e x p l a n a t i o n . I t seems to me t h a t any attempt to d i s s o l v e t h i s paradox must leave at l e a s t the weaker c o n d i t i o n (R) i n t a c t . Second, i f we can provide a reason why E rather than F occurred, i . e . , s a t i s f y c o n d i t i o n (R), then we a l s o were j u s t i f i e d i n our b e l i e f that E rather than F would occur. But our j u s t i f i e d b e l i e f i n E's occurrence does not imply that we have adduced the reason why E r a t h e r than F occurred. This i s another aspect of the perhaps f a m i l i a r p o i n t of the 53 asymmetry between p r e d i c t i o n and e x p l a n a t i o n . And i t a l s o suggests a 54 way out of the paradox. A purely s t a t i s t i c a l a n a l y s i s of the r e l a t i o n between A and E (or F) w i l l enable us to p r e d i c t , or j u s t i f i a b l y expect, E (or F) to occur. In order to provide an e x p l a n a t i o n , however, that meets c o n d i t i o n (R), and which blocks the unwanted co n c l u s i o n , we must uncover a 55 r e l a t i o n , C, among A, E, and F such that (a) A provides a reason why E occurred rather than F i f E occurs and F does not and C(A,E,F). (b) I f C(A,E,F) then the information that A provides a reason f o r b e l i e v i n g that E occurs rather than F. (c) C(A,E,F) i m p l i e s n e i t h e r than A i s the case nor that E i s the case nor that F i s the case. The f i r s t c o n d i t i o n on C blocks the paradox by making only the probable e x p l a i n a b l e . The second c o n d i t i o n respects the i m p l i c a t i o n between ex p l a n a t i o n and j u s t i f i e d e x p e c t a t i o n , while the t h i r d c o n d i t i o n l i c e n s e s C to support c o n t r a r y - t o - f a c t c o n d i t i o n a l s . The obvious candidate for such a r e l a t i o n i s a c a u s a l one. The problem i s that any concept of causation t h a t answers to c o n d i t i o n (a) on C w i l l provide explanatory impetus only f o r the 53 probable outcome, the improbable w i l l remain unexplained. Kruger, i n h i s d i s c u s s i o n of t h i s paradox, r e a l i z e s the need f o r a causal adjunct i n e x p l a n a t i o n , as van Fraassen himself notes, y e t Kruger argues that the e x p l a n a t i o n of the probable and the improbable stand or f a l l together: The a n a l y s i s of the c o n d i t i o n s r e l e v a n t f o r the occurrence of e i t h e r E or non-E i s one and the same, whatever happens. But the question why E happens can only be understood as asking f o r something t h a t d i s t i n g u i s h e s the n a t u r a l process which brings E about from the n a t u r a l process which brings non-E about. Since the s t a t i s t i c a l a n a l y s i s ex hypothesis does not c o n t a i n any reference to a d i f f e r e n t i a t i n g charac-t e r i s t i c of t h i s k i n d , i t can only be an explanation of both E and non-E or_ of n e i t h e r of them. Whoever wants to assume that the improbable does not admit of an explanation has to opt f o r the second branch of t h i s a l t e r n a t i v e . This i s s u e now becomes can one opt f o r the f i r s t branch of t h i s a l t e r n a t i v e , admitting that both the probable and the improbable admit of e x p l a n a t i o n , yet avoid the consequences of denying i n t u i t i v e c o n d i t i o n s on explanation such as (L) or (R)? One way of avoiding the d e n i a l of (L) or (R) i s the p o s i t i n g of a causal account as argued above, but now a causal account t h a t e x p l a i n s both E and non-E, both the probable and the improbable. We would, t h e r e f o r e , change c o n d i t i o n (a) to a') I f C(A,E,F) then A provides a reason for E, and a reason f o r F, whichever occurs. I f c a u s a l i t y i s our game then, as J e f f r e y points out, t h i s i s not the "usual 57 s o r t of c a u s a l i t y . " We have already argued (p.32) t h a t Salmon i s f o r c e d , by adopting a causal account, to r e j e c t causes as s u f f i c i e n t c o n d i t i o n s f o r t h e i r e f f e c t s . What he has adopted i n i t s stead i s a s t a t i s t i c a l v a r i e t y of causation as described i n the previous pages, and one which accords with c o n d i t i o n ( a 1 ) . 54 What (a') does i s to make a b i t more e x p l i c i t the r e l a t i o n s h i p between a s t a t i s t i c a l e x p l a n ation and the range of events to be e x p l a i n e d . The causal concept we are adopting i s not dependent on the p r e s u p p o s i t i o n t h a t i t s e f f e c t ( s ) occur. Let me b r i e f l y r e - s t a t e van Fraassen's v e r s i o n of the p a r a d o x i c a l argument i n order to place my suggestion i n i t s proper p e r s p e c t i v e . 1. A e x p l a i n s E r a t h e r than not-E, i . e . , A provides a reason why E ra t h e r than not-E ( p r i n c i p l e R) which i m p l i e s : 2. A provides a j u s t i f i c a t i o n to expect E r a t h e r than not-E. 3. Suppose not-E occurs. 4. I f not-E occurs, then we could not have been j u s t i -f i e d i n expecting E. 5. Since (1) i m p l i e s ( 2 ) , (3) and (4) imply that A does not e x p l a i n E when not-E occurs, or, th a t A e x p l a i n s E only i f E oc c u r s . 6. But A i s no d i f f e r e n t when E occurs than when E does not occur t h e r e f o r e . . . But we have now i s o l a t e d the problem. (4) i s f a l s e . We may be p e r f e c t l y j u s t i f i e d i n expecting E, and remain so even i f not-E occurs. Nor does not-E's occurrence render our j u s t i f i c a t i o n to expect E, i . e . , the reasons adduced i n A f o r e x p l a i n i n g why E occurs r a t h e r than not-E, i n v a l i d . Thus we do not deny that (1) i m p l i e s ( 2 ) , rather we deny that i f we are j u s t i f i e d i n expecting E, then t h i s i m p l i e s t h a t E occurs. (That t h i s i s true i s demonstrated each time the f a v o r i t e does not run i n the money.) Thus a r e l a t i o n s h i p that meets c o n d i t i o n (a') rather than (a) i s r e q u i r e d . On t h i s view e x p l a n a t i o n , and j u s t i f i e d e x p e c t a t i o n , can be maintained i n the face of C O improbable occurrences. (c) Other Problems. What we hope to have shown, as a r e s u l t of the previous two s e c t i o n s , i s the need i n explanation f o r a concept of p r o b a b i l i s t i c or s t a t i s t i c a l c a u s a t i o n . Faced with the indeterminism of microphysics, and the more general paradox of s t a t i s t i c a l e x p l a n a t i o n , any theory of e x p l a n a t i o n which demands a ca u s a l adjunct w i l l have to adopt some such expanded notion of c a u s a l i t y . The question now becomes whether and to what extent t h i s conception can be brought to square with the f a m i l y of s t r u c t u r e s and r e l a t i o n s which surround our t r a d i t i o n a l causal concept. Does t h i s conception of s t a t i s t i c a l c ausal s t r u c t u r e deserve to be c a l l e d causal? T r a d i t i o n a l analyses w i t h respect to c o u n t e r f a c t u a l s , support of u n i v e r s a l g e n e r a l i z a t i o n s , r e g u l a r , or constant c o n j u n c t i o n , e t c . , w i l l be examined i n the next chapter, accompanied by, we hope, a more h i s t o r i c a l p e r s p e c t i v e . However, there are two p r e l i m i n a r y points we would l i k e to touch upon b r i e f l y i n t h i s s e c t i o n . The f i r s t concerns the conceptual p o s s i b i l i t y of modifying our c a u s a l concept. The second i s a few remarks concerning the r o l e of laws and t h e o r i e s w i t h i n t h i s p r o b a b i l i s t i c model. The c a u s a l t r a d i t i o n a l i s t faces the f o l l o w i n g rough-cut argument: (1) Explanation demands acknowledgement of our causal i n t u i t i o n s . (What t h i s acknowledgement amounts to w i l l , of course, vary.) (2) Experimental r e s u l t s i n microphysics show a fundamental i n c o m p a t i b i l i t y with the concept of c a u s a t i o n as we (a p r i o r i ) describe i t . Therefore, (3) e i t h e r (a) we give up causes at the m i c r o - l e v e l and, to some extent, as a necessary adjunct i n e x p l a n a t i o n , or (b) we re-assess our conception of causes i n l i g h t of experimental evidence. Now everyone accepts (2), and van Fraassen and Salmon each accept some v e r s i o n of (1) (depending on what they count as 'acknowledgement') 56 l e a d i n g van Frassen to (3a) and Salmon to (3b). The t r a d i t i o n a l i s t , however, takes exception to (3b). Simply put, h i s concern i s that causes, c a u s a t i o n , and r e l a t e d concepts comprise a c o n s t r u c t i o n , or 'family of p r a c t i c e s ' through which our experimental evidence i s assessed. Evidence ( i n quantum mechanics, say) which escapes t h i s c o n s t r u c t i o n w i l l have to be assessed i n some other f a s h i o n , and not by revamping our causal notions to f i t . We might c a l l the i n d e t e r m i n i s t i c micro-connections 'causal', but that i s c e r t a i n l y not what we mean (a p r i o r i ) by use of t h i s f a m i l y of p r a c t i c e s . We are not n o t i c i n g , i n quantum mechanics, a non-standard causal connection, but rat h e r a non-causal, standard (yet i n d e t e r m i n i s t i c ) connection. My response here w i l l presage some of what w i l l be argued i n the next chapter. B r i e f l y put, I o b j e c t to the t r a d i t i o n a l i s t s ' sacrosanct p o s i t i o n w i t h respect to the a n a l y s i s of concepts. I agree with Salmon t h a t s c i e n t i f i c e xplanation provides "knowledge of the mechanisms of production and propogation of s t r u c t u r e i n the world," and that these mechanisms do not merely approximate our p r e - t h e o r e t i c a l notions of causes and causation, but are the analysanda from which these concepts f l o w . I f , under the pressure of experimental m i c r o - s c r u t i n y , we are forced to change, or even abandon, our 17th and 18th century causal s t r u c t u r e s , then so be i t . The second p o i n t of i n t e r e s t might be r a i s e d i n the f o l l o w i n g way. We began by c l a i m i n g that simple p r o b a b i l i t y d i s t r i b u t i o n s do not e x p l a i n anything. For example, the r e l e v a n t p r o b a b i l i t i e s alone do not e x p l a i n the outcome of a s i n g l e f l i p of a c o i n . But can one not say that t h i s d i s t r i b u t i o n , based s o l e l y on the symmetry p r o p e r t i e s of the c o i n , does s a t i s f a c t o r i l y e x p l a i n the composite event which c o n s i s t s of the d i s t r i b u t i o n s as they are a c t u a l l y obtained i n experiments? Why need we 57 r e f e r to any temporal or. causal process, which we know l i t t l e enough about, to e x p l a i n adequately the d i s t r i b u t i o n , say, of heads i n one thousand f l i p s of a f a i r coin? Likewise, a p h y s i c i s t who balks at g i v i n g explanations of s i n g l e micro-events, w i l l yet f i n d the pur e l y s t a t i s t i c a l d i s t r i b u t i o n of lar g e aggregates to be e x p l a i n a b l e , based on the symmetry p r o p e r t i e s of the m i c r o - e n t i t i e s i n question alone. We would agree that t h i s composite event i s e x p l a i n a b l e , but only " i n the sense that there are dynamical laws which connect ensembles of systems c h a r a c t e r i z e d by c e r t a i n i n i t i a l c o n d i t i o n s with s t a t i s t i c a l 59 d i s t r i b u t i o n s of the f i n a l s t a t e s of these systems". The r o l e played by the symmetry p r o p e r t i e s i s the s a t i s f a c t i o n of the c o n d i t i o n of equal d i s t r i b u t i o n of i n i t i a l s t a t e s of the system, and even here these p r o p e r t i e s must be combined w i t h c e r t a i n c o n s t r a i n t s on the pr e p a r a t i o n of these i n i t i a l 60 s t a t e s . We might say, f o l l o w i n g Kruger, that these symmetry p r o p e r t i e s are our reasons f o r adopting the t h e o r e t i c a l basis w i t h i n which these dynamical laws operate. They then may be s a i d to e x p l a i n the laws which e x p l a i n events, and not the events themselves. To say t h i s however i s to say nothing more than that t h e o r e t i c a l concerns guide our assessment and assignment of p r o b a b i l i t i e s between sets of events; j u s t as i t i s t h e o r e t i c a l concerns which determine the p u r i t y , or o b j e c t i v e homogeneity, of the reference c l a s s i n c o n d i t i o n a l p r o b a b i l i t i e s . P r o b a b i l i t y functions then do represent a c e r t a i n t h e o r e t i c a l r e s u l t . And i t i s indeed t h e o r e t i c a l reasons which serve to e x p l a i n why p h y s i c a l laws are as good an approximation as they are. But t h i s t h e o r e t i c a l r o l e f or p r o b a b i l i t y f u n c t i o n s i s not what makes them explanatory. Their explanatory power (which, as a matter of f a c t , we have not denied) derives more from the f a c t that they reflect real contingencies in nature. In other words, statistics are truly explanatory, and not merely symptomatic, when and only when they have captured some real regularity in nature, when and only when they represent a feature of the causal process or processes at work in the system. 59 Notes: Chapter I 1. Salmon (1971). Most of what fo l l o w s i s based on t h i s seminal a r t i c l e . 2. J e f f r e y (1971) . 3. I t h i n k that t h i s a t t i t u d e towards h i g h l y improbable events defeats the 'argument from design' f o r the existence of God. For even though the chance set up which r e s u l t e d i n the complex arrangement taken as evidence f o r a designer i s given a minute p r o b a b i l i t y , t h i s a s t o n i s h i n g f a c t i s e x p l a i n a b l e sans deus. 4. For some of these see Salmon (1971), pp. 33-34. 5. This i s the "place s e l e c t i o n " of von Mises (1939), p.25. 6. Obviously we must choose an a t t r i b u t e that does not depend e s s e n t i a l l y on the a t t r i b u t e c l a s s i n q u e s t i o n . 7. The symmetry of p r e d i c t i o n and explanation i s a consequence of the conception of explanations as arguments. However, denying that explanations are inferences does not, a u t o m a t i c a l l y , destroy t h i s symmetry. 8. Salmon (1971), p. 43. 9. Op. c i t . , p. 64. 10. Op. c i t . , p. 45. 11. Nor i s i t the case that a p r o b a b i l i t y of 1 or 0 (P(a/b)=1 v 0) e n t a i l s that a i s homogeneous with respect to b. (Salmon (1971), p. 45). Further evidence may uncover a p a r t i t i o n i n g f a c t o r among the set of b's. 12. This t o p i c w i l l be taken up again, Section 4a. 13. Salmon (1971), p. 55. 14. Loc. c i t . 15. Op. c i t . , p. 54. 16. The high p r o b a b i l i t y assigned to (C&H&M&E) suggests i t as a s t a t i s t i c a l analogue to a set of s u f f i c i e n t c o n d i t i o n s f o r doing w e l l on the exam. The requirement that a l l subclasses of C be homogeneous, each subclass having a lower p r o b a b i l i t y than (C&H&M&E), suggests them as s t a t i s t i c a l analogues of necessary c o n d i t i o n s . See N. Koertge (1975), p. 274. 17. Kruger (1976). 18. Op. c i t . , p. 132. 60 19. Loc. c i t . 20. Salmon (1971), p. 46. "Fortunate" seems misleading here — l a t e r (p. 65) Salmon i s more p r e c i s e : "Whether the p o s t e r i o r weight i s higher than, or lower than the p r i o r weight i s r e a l l y beside the p o i n t . " 21. Salmon (1971), pp. 62-65. 22. I t should be noted here that although Kruger f i n d s the S t a t i s t i c a l - R e l e v a n c e model inadequate, he i s here assembling o b j e c t i o n s from others, notably Stegmuller. Whereas Stegmuller f i n d s the whole conception of S-R explanation untenable, Kruger's c r i t i c i s m seems to be r e p r e s e n t a t i v e of those which led to a r e v i s i o n of Salmon's view, t h a t i s , to the new Causal-Relevance model of s t a t i s t i c a l e x p l a n a t i o n . 23. Arthur C o l l i n s , i n (1966a), p. 496, o f f e r s t h i s explanation for the d i f f e r e n c e here: When someone co n t r a c t s p a r e s i s i t i s explained by h i s having s y p h i l l i s , even though only a small percentage of s y p h i l l i t i c s c o n t r a c t p a r e s i s . This i s a s t a t i s t i c about, not f o r the sake o f , e x p l a n a t i o n . "We might," claims C o l l i n s , "have reasons f o r accepting an explanation which are e x c e l l e n t , and which have nothing to do w i t h the c o r r e l a t i o n between the causal c o n d i t i o n s and event." (p. 497) This does seem to help our i n t u i t i o n s about causal s i t u a t i o n s with low p r o b a b i l i t y , but gives no a i d i n the 'counter-causal' i n s t a n c e . C o l l i n s ' whole t h r u s t i s to give the proper c h a r a c t e r i z a t i o n of causes as a necessary p a r t of e x p l a n a t i o n s , without the D-N model. For him, i n the counter-causal s i t u a t i o n , there would be no e x p l a n a t i o n . 24. Salmon (1971), p. 54. 25. Here (Kruger (1976), p. 132, " I do not think that symptoms ever e x p l a i n anything...") foreshadows Salmon almost p r e c i s e l y : " I no longer b e l i e v e that the assemblage of r e l e v a n t f a c t o r s provides a complete e x p l a n a t i o n — or much of anything i n the way of an e x p l a n a t i o n . " (1978), p. 419. 26. There are others, as we s h a l l see. Salmon's own example i s Compton s c a t t e r i n g — an i n c i d e n t photon producing an electron-photon p a i r . See Salmon (1978), p. 414. 27. In Salmon's l a t e r model t h i s requirement i s both e x p l i c i t and problematic; t h i s c o n f l i c t w i l l be the c e n t r a l concern of S e c t i o n 4b, below. 28. Arthur C o l l i n s argues i n t h i s f a s h i o n against Hempel's I-S model; however, nothing i n h i s argument turns on the deductive nature of Hempel's schema. See C o l l i n s (1966b) pp. 127-140, e s p e c i a l l y pp. 137, and h i s (1966a) p. 492. The f o r m u l a t i o n above i s due t o Kruger (1976), p. 142. 61 29. Most of what f o l l o w s has as i t s primary source Salmon (1978), h i s one pub l i s h e d account of t h i s new model. 30. Salmon (1971), p. 55. 31. Salmon (1978), pp. 408-409. 32. Douglas W. Shrader, J r . (1977), Arthur C o l l i n s (1966b) a n t i c i p a t e s Salmon, and Kruger (1976). 33. Salmon (1978), p. 409. 34. Op. c i t . , p. 419. 35. R u s s e l l ' s term i n h i s (1948), p. 460. 36. Salmon (1978), p. 410. 37. See Reichenbach (1971), p. 159. 38. When convenient ( i . e . , not confusing) we w i l l omit "the p r o b a b i l i t y of the occurrence of" preceding "events A and B". 39. See above, Section 3a. 40. Since p u b l i s h e d , van Fraassen (1980), p.29 41. Loc. c i t . 42. Loc. c i t . 43. Salmon (1978), f n . 20. 44. Op. c i t . , pp. 416-417. 45. van Fraassen (1980), p.30 46. Much of t h i s s e c t i o n i s indebted to my c o l l a b o r a t i o n with Edwin Levy. See Katz and Levy (1980). 47. Salmon (1978), p. 410. 48. Loc. c i t . 49. The p l a u s a b i l i t y of the hypothesis i s simply not an issue here. We, l i k e Salmon, are i n v e s t i g a t i n g t h e o r i e s of explanation which are supposed to be able to deal with s i t u a t i o n s i n v o l v i n g genuine i n d e t e r m i n a c i e s . Whether- there are such s i t u a t i o n s i s a separate q u e s t i o n . (Of course, the quantum domain i s the most l i k e l y place to look.) 62 50. This problem i s r a i s e d by Stegmuller and the above v e r s i o n f o l l o w s van Fraassen's e x p o s i t i o n i n h i s (1978). Stegmuller i s a l s o Kruger's (1976) t o p i c , pp. 134-138. 51. van Fraassen (1978), p. 162. 52. Loc. c i t . 53. Salmon traces the asymmetry between explanation and p r e d i c t i o n to the temporal asymmetry provided by causal analyses. Explanations demand causes and are the r e f o r e i n h i b i t e d temporally, u n l i k e p r e d i c t i o n . 54. This 'way out' i s suggested b r i e f l y by van Fraassen, and j u s t as b r i e f l y discounted. 55. van Fraassen's suggestions, (1978), p. 162. 56. Kruger (1976), p. 137. 57. J e f f r e y (1971), p. 23. 58. We s h a l l r e t u r n to the problem of the improbable i n Chapter I I I . 59. Kruger (1976), pp. 141-142. 60. Loc. c i t . 63 CHAPTER I I i CAUSALITY AND PROCESSES "Nothing happens without a reason why i t should happen ra t h e r than not happen." C h r i s t i a n Wolff (1679-1754) 1. I n t r o d u c t i o n In the preceeding chapter we have argued that causal accounts play an e s s e n t i a l r o l e i n e x p l a n a t i o n . We have shown that, i n l i g h t of c u r r e n t t h e o r i e s i n micro-physics, t h i s causal account must be compatible with the i n d e t e r m i n i s t i c , or s t a t i s t i c a l r e s u l t s i n that domain. The ca u s a l conception b r i e f l y o u t l i n e d there i n v i r t u e of processes and t h e i r i n t e r a c t i o n s c o n s t i t u t e s the general nature of t h i s conception, yet much remains to be s a i d . In t h i s chapter we s h a l l f i r s t look a t two t r a d i t i o n a l l i n e s of causa l a n a l y s i s , the " r e g u l a r i t y " and the " c o u n t e r f a c t u a l " t h e o r i e s . R e g u l a r i t y t h e o r i s t s attempt to analyze causes i n v i r t u e of the regular succession of objects or events, the regular precedence of objects as causes 1 2 being understood i n terms of t h e i r s u f f i c i e n c y or t h e i r n e c e s s i t y f o r 3 t h e i r e f f e c t s . C o u n t e r f a c t u a l t h e o r i s t s a s s i g n c r u c i a l weight to the p o s i t i o n of laws which are i n s t a n t i a t e d by, or presupposed by, causal c l a i m s . In examining both of these attempts we s h a l l focus on t h e i r c o m p a t i b i l i t y w i t h causes as processes, and t h e i r a b i l i t y to accommodate the i n d e t e r m i n i s t i c aspects of m i c r o - p h y s i c a l t h e o r i e s . Second, we s h a l l examine Anscombe's conclusions to, the e f f e c t t h a t c a u s a t i o n i s an unanalysable, p r i m i t i v e r e l a t i o n , and compare her r e s u l t s 64 w i t h respect to indeterminism with our own. Here we w i l l attempt to b u i l d our account of s t a t i s t i c a l causation from the foundation of causes as causal processes, as sketched i n the previous chapter. A few p r e l i m i n a r y remarks concerning the d i v i s i o n of labor e f f e c t e d here between the r e g u l a r i t y and c o u n t e r f a c t u a l accounts of causation are i n order. This d i v i s i o n stems from Hume's d e f i n i t i o n of cause. Hume wr i t e s i n the Enquiry: ...we may define a cause to be an o b j e c t , followed by  another, and where a l l the objects s i m i l a r to the f i r s t  are f ollowed by objects s i m i l a r to the second. Or i n other words where, i f the f i r s t o bject had not been, the second never had e x i s t e d . The f i r s t h a l f of t h i s d e f i n i t i o n , that which comes before "Or i n other words...", I take to be a statement of the r e g u l a r i t y t h e s i s of ca u s a t i o n . This f i r s t h a l f i s a l s o an a n a l y s i s of causation i n terms of the 4 " s u f f i c i e n c y " of the cause f o r i t s e f f e c t . L et us c a l l t h i s the 5 " s u f f i c i e n c y t h e s i s " , f o l l o w i n g Raymond M a r t i n . The second h a l f of t h i s d e f i n i t i o n , which Hume obviously thought e q u i v a l e n t to the f i r s t , suggests an a n a l y s i s of the ca u s a l r e l a t i o n i n terms of necessary c o n d i t i o n s . Lewis c o r r e c t l y sees t h i s second d e f i n i t i o n as. "no mere restatement of h i s f i r s t . . [ b u t ] something a l t o g e t h e r d i f f e r e n t " , and presents h i s c o u n t e r f a c t u a l a n a l y s i s as d i r e c t l y descended from t h i s " n e c e s s i t y t h e s i s . " Now whether, or why, Hume thought these two theses e q u i v a l e n t w i l l not be at issue here. Rather, t h e i r f u n c t i o n , f o r our purposes, i s to d i v i d e the responses to the a n a l y s i s of causation i n t o at l e a s t two camps. This w i l l not only f a c i l i t a t e e x p o s i t i o n and d i s c u s s i o n , but w i l l a l s o demonstrate how both of these d i s t i n c t outlooks r a i s e problems whose s o l u t i o n s may already be at hand. 65 To reach these problem areas we might begin by asking, as Hume d i d , what we mean when we cla i m of p a r t i c u l a r events c, e, that c causes e. Pa r t of what we might mean i s that c i s r e g u l a r l y followed by e. Our e x p l i c a t i v e task then s h i f t s to how we are to understand " r e g u l a r l y f o l l o w s " . That t h i s i s a s h i f t i s evidenced by the f a c t that "c causes e" i s a s i n g u l a r c a u s a l c l a i m , i t describes a connection between a p a r t i c u l a r instance of c and a p a r t i c u l a r instance of e. However, the r e g u l a r i t y involved here i s not found i n the p a r t i c u l a r i n s t a n c e , but rather i n the cla i m that t h i s s i n g u l a r instance of c followed by e i s an example of a r e g u l a r l y o c c u r r i n g p a t t e r n of events described by the general statement that things of kind C are followed (always, u s u a l l y , or i s some other s t a t i s t i c a l manner) by things of k i n d E. Two po i n t s are i n order here. This i s not an attempt to define c a u s a t i o n , nor to f i n d i t s l o g i c a l e q u i v a l e n t . We are only attempting to s o r t out the i m p l i c a t i o n s of the causal c l a i m , u l t i m a t e l y to discover whether these requirements r u l e out an ontology of processes as causes. The second p o i n t concerns the move from the p a r t i c u l a r to the general: from " t h i s p a r t i c u l a r c" to "things of k i n d C". "Kinds" of course can be determined i n an i n f i n i t e v a r i e t y of ways, and thus we are forced to q u a l i f y our s o r t i n g of causal c l a s s e s by demanding of i t s members that they be not only "of a k i n d " or " s i m i l a r " but " r e l e v a n t l y s i m i l a r " . But what could our c r i t e r i a of relevance amount to i n t h i s case but that the c l a s s i f y i n g property or p r o p e r t i e s be c a u s a l l y r e l e v a n t ? Hume's r e g u l a r i t y t h e s i s (the f i r s t h a l f of t h i s d e f i n i t i o n of cause) r e f l e c t s both of these p o i n t s . He cannot be s a i d to have defined "cause", f o r many objects f a l l i n g under the d e s c r i p t i o n provided i n the d e f i n i e n s are not inc l u d e d among those we would claim to f a l l under the 66 definiendum. (E.g., day i s r e g u l a r l y followed by n i g h t , yet does not cause i t . ) Furthermore, h i s q u a l i f i c a t i o n of these objects by the g e n e r a l i z e d c o n d i t i o n a l " a l l objects s i m i l a r to the f i r s t . . . " neglects to t e l l us how they are s i m i l a r . A p a r a l l e l d i f f i c u l t y i n f e c t s analyses that take Hume's q u a l i f y i n g clause as r e f e r r i n g to a n a t u r a l law, from which the r e l a t i o n s between the o b j e c t s mentioned i n i t i a l l y can be deduced. For t h i s a n a l y s i s to succeed there must be a d i s t i n c t i o n between a c c i d e n t a l and l a w - l i k e , or nomic, g e n e r a l i z a t i o n s , i . e . , between causal and non-causal laws. But t h i s , of course, presupposes an a n a l y s i s of c a u s a t i o n . To underscore the connection between these two camps we need only note that i n order to salvage the r e g u l a r i t y a n a l y s i s some have attempted to d i s t i n g u i s h nomic g e n e r a l i z a t i o n s v i a t h e i r support of the corresponding c o u n t e r f a c t u a l s . Therefore, i f , as a r e g u l a r i t y t h e o r i s t , one begins with the f i r s t h a l f of Hume's ' d e f i n i t i o n ' , then one faces the problem of d i s t i n g u i s h i n g those types of r e g u l a r i t i e s which support causal claims from those which do not. As we s h a l l see, Mackie denies that such a d i s t i n c t i o n can be drawn i n terms of c o u n t e r f a c t u a l s alone. His a l t e r n a t i v e i s to draw t h i s d i s t i n c t i o n by reference to a c o n s t r u c t i o n he c a l l s "pure laws of working". This c o n s t r u c t i o n i s not without i t s own d i f f i c u l t i e s , and, i n an attempt to overcome these d i f f i c u l t i e s , we s h a l l f i n d a place i n i t f o r an ontology of cau s a l processes. I f , as a c o u n t e r f a c t u a l t h e o r i s t , one begins with the l a t t e r h a l f of Hume's ' d e f i n i t i o n ' , then one has the problem of saying j u s t how such c o u n t e r f a c t u a l s serve as causal analysans: t h i s w i l l include what, i n gen e r a l , we take the t r u t h c o n d i t i o n s of c o u n t e r f a c t u a l s to be and, f u r t h e r -67 more, what d i s t i n g u i s h e s causal c o u n t e r f a c t u a l s from non-causal counter-f a c t u a l s . Although Lewis demonstrates that the use of c o u n t e r f a c t u a l s i s unproblematic, h i s account of causa t i o n , i n terms of c o u n t e r f a c t u a l s , runs a f o u l of Kim's o b j e c t i o n , that h i s a n a l y s i s must, but f a i l s t o , d i s t i n g u i s h between causal and non-causal c o u n t e r f a c t u a l s . Here again we s h a l l f i n d a r o l e f o r causal processes to p l a y . L e t us begin our i n q u i r y by examining a s o p h i s t i c a t e d v e r s i o n of the r e g u l a r i t y t h e s i s , that provided by J.L. Mackie. 2. Mackie I ; Causes as INUS Conditions Mackie claims that "at l e a s t p a r t " of what we mean when we a s s e r t t h a t c causes e i s that c i s "an i n s u f f i c i e n t but necessary p a r t of a 7 c o n d i t i o n which i s i t s e l f unnecessary but s u f f i c i e n t " f o r e. Mackie c a l l s t h i s c o n d i t i o n by i t s acronym: c i s an INUS c o n d i t i o n of e. The complex s u f f i c i e n t c o n d i t i o n of which c i s a necessary p a r t i s c a l l e d a "minimal s u f f i c i e n t c o n d i t i o n . " The d i s j u n c t i o n of a l l such minimal s u f f i c i e n t c o n d i t i o n s then forms a necessary and s u f f i c i e n t c o n d i t i o n f o r the event i n q u e s t i o n . To i l l u s t r a t e , consider the co n c l u s i o n of an auto ac c i d e n t i n v e s t i g a t i o n : the f a u l t y brakes caused the c r a s h . Since the crash might have occurred even had the brakes been p e r f e c t , and since the crash could have been avoided des p i t e the brakes by more j u d i c i o u s d r i v i n g , we cannot c l a i m the brakes to be e i t h e r a necessary or s u f f i c i e n t c o n d i t i o n of the a c c i d e n t . However, we can consider the brakes to be a necessary p a r t of a l a r g e r s et of c o n d i t i o n s , some p o s i t i v e (excess speed) and some negative (absence of a brake warning system) which, taken together, form a s u f f i c i e n t c o n d i t i o n of the a c c i d e n t . There may be many such sets of c o n d i t i o n s , each s u f f i c i e n t f o r the r e s u l t i n g accident; the d i s j u n c t i o n of these, then, w i l l 68 be both necessary (one of them must have occurred) and s u f f i c i e n t ( i t was a l l t h a t was necessary) f o r the r e s u l t on the occasion i n q u e s t i o n . Although Mackie both r e f i n e s and g e n e r a l i z e s h i s a n a l y s i s , the c e n t r a l feature of t h i s view remains as we have described i t above, and w i l l be adequate f o r our purposes. What we hope to show here and i n the f o l l o w i n g s e c t i o n i s , f i r s t l y , t h a t Mackie's a n a l y s i s i n terms of INUS c o n d i t i o n s i s not s i g n i f i c a n t l y d i f f e r e n t from an a n a l y s i s i n terms of s u f f i c i e n t c o n d i t i o n s alone, and as such w i l l be subject to our general c r i t i c i s m of such analyses f o r the understanding of s t a t i s t i c a l c a u s a t i o n . Secondly, we s h a l l see that an INUS a n a l y s i s presupposes a L e i b n i z - l i k e p r i n c i p l e of s i f f i c i e n t reason which, as w i l l be argued i n the f o l l o w i n g chapter, must be separated out of our causal reasoning i f we are to avoid a question-begging stance w i t h respect to indeterminism. T h i r d l y , but perhaps most i m p o r t a n t l y , we s h a l l i n d i c a t e how the concept of a causal 'process' can f i l l a c r u c i a l gap i n Mackie's a n a l y s i s . Mackie's a n a l y s i s lends i t s e l f most c l e a r l y to examples from everyday l i f e , examples i n which we p o i n t to a p a r t i c u l a r component of a s e t of c o n d i t i o n s which i t s e l f i s only one among many p o s s i b l e sets of condi-t i o n s , each s u f f i c i e n t f o r the r e s u l t . Our example of f a u l t y brakes causing an a c c i d e n t , or Mackie's of a short c i r c u i t causing a f i r e , are both "over-s p e c i f i e d " and " u n d e r - s p e c i f i e d " i n t h i s way. Since our o r d i n a r y t a l k about such everyday s i t u a t i o n s i s infused w i t h such causal claims, i t i s important to be able to say what these claims mean. However, w i t h i n the context of an i n d i v i d u a l science we t y p i c a l l y expect a great deal more of our claims to causal knowledge. P a r t i c u l a r , 9 i n d i v i d u a l r e s u l t s demand p a r t i c u l a r unique causes. In these contexts 69 Mackie's INUS c o n d i t i o n s reduce to c e t e r i s paribus s u f f i c i e n t c o n d i t i o n s . Let us see how t h i s would go. L e t X represent the set of c o n d i t i o n s which, i n conjunction with c o n d i t i o n A, forms a minimal s u f f i c i e n t c o n d i t i o n f o r the r e s u l t P. Then, Mackie suggests, "A caused p" i m p l i e s : ( i ) A i s at l e a s t an INUS c o n d i t i o n of P — t h a t i s , there i s a necessary and s u f f i c i e n t c o n d i t i o n of P which has one of these forms: (AX or Y ) , (A or Y ) , AX, A. ( i i ) A was present on the occasion i n q u e s t i o n . ( i i i ) The f a c t o r s represented by the 'X', i f any, i n the formula f o r the necessary and s u f f i c i e n t c o n d i t i o n s were present on the occasion i n q u e s t i o n . ( i v ) Every d i s j u n c t i n Y which does not c o n t a i n A as a conjunct was absent on the occasion i n q u e s t i o n . To c l a i m , then, that A caused P i s to imply that there are necessary and s u f f i c i e n t c o n d i t i o n s f o r P, that A was a non-redundant proper p a r t of these c o n d i t i o n s , and t h a t , on the occasion i n question, i t was the presence of A (along w i t h c o n d i t i o n s X) which was e f f i c a c i o u s . The a l t e r n a t i v e c o n d i t i o n s Y have t h e i r place i n ( i ) only to make p l a i n that A i s not, g e n e r a l l y , taken to be necessary f o r P (although a f t e r P has occurred we may take A to be 11 "necessary post factum" f o r P. ). And the p o s i t i o n of conditions represented by X serve to make c l e a r that A alone i s not s u f f i c i e n t f o r P. I would agree with the above a n a l y s i s i n that ( i ) - ( i v ) seem to be what i s minimally r e q u i r e d i n making a s i n g u l a r causal c l a i m . However, i t a l s o seems to be the case that i n c e r t a i n contexts, t y p i c a l l y s c i e n t i f i c ones, much more i s i m p l i e d by our causal a s s e r t i o n s . C e r t a i n l y t h a t a l t e r n a t i v e s u f f i c i e n t c o n d i t i o n s (Y) are absent i s i m p l i e d here, but a l s o that although our causal judgement i s r e l a t i v i z e d to f u l f i l l i n g c o n d i t i o n s X i n a set of minimal s u f f i c i e n t c o n d i t i o n s , these c o n d i t i o n s are not p a r t of 70 the a s s e r t i o n of the ca u s a l c l a i m i t s e l f , but are rather l i c e n s i n g c o n d i t i o n s f o r i t s a s s e r t i o n . When we cl a i m that the short c i r c u i t caused the f i r e , are we making any reference ( t a c i t or otherwise) to the existence of flammable material,- the presence of oxygen, etc.? Mackie l a t e r r e l a t i v i s e s h i s account to what he c a l l s a "causal f i e l d " of background c o n d i t i o n s and admits t h a t " i t i s i n general an a r b i t r a r y matter whether a p a r t i c u l a r feature i s regarded as a c o n d i t i o n (that i s , a p o s s i b l e causal f a c t o r ) or a p a r t of the 12 f i e l d . . . " What I am c l a i m i n g i s that p i c k i n g out a causal f a c t o r i s , i n an important sense, the 'bracketing o f f of j u s t such background c o n d i t i o n s , or f u l f i l l i n g c ausal f a c t o r s . I would agree that Mackie's a n a l y s i s i s programmatic toward such c l a i m s , and even e x p l i c i t l y allows f o r them (with the p o s s i b l e forms "(A or Y)" and "A"). I f we were to adopt Mackie's a n a l y s i s f o r our s c i e n t i f i c purposes, then i t would be i n terms of these more r e s t r i c t e d i m p l i c a t i o n s of our causal a s s e r t i o n s . Of course, i t i s i n j u s t these cases where our causal c l a i m i m p l i e s that A alone i s ' a s u f f i c i e n t c o n d i t i o n f o r P. 1 3 As noted above, t h i s r e s t r i c t e d sense of causation runs a f o u l of our program of a l l o w i n g a t l e a s t the p o s s i b i l i t y of s t a t i s t i c a l , yet c a u s a l , r e l a t i o n s . We might a l s o p o i n t out that even the u n r e s t r i c t e d causal c o n d i t i o n s , those that allow forms such as (AX or Y) or (AX) imply that there are some f a c t o r s , even i f we cannot s p e c i f y what they are, which taken together with the p u t a t i v e causal f a c t o r A, give s u f f i c i e n t c o n d i t i o n s f o r P; and t h a t t h i s i s , i n e f f e c t , the a s s e r t i o n of the existence of 'hidden v a r i a -b l e s . ' That i s , i f f o r something to be a cause i t must be p a r t of a set of s u f f i c i e n t c o n d i t i o n s , then t h i s alone would r u l e out, i n causal circum-14 stances, any pur e l y s t a t i s t i c a l s i t u a t i o n . We w i l l have more to say on 71 t h i s when we examine Mackie's d i f f i c u l t y i n c o n s t r u c t i n g what he c a l l s 1 5 " s t a t i s t i c a l laws of working." The obverse aspect of t h i s s i t u a t i o n i s the pres u p p o s i t i o n of a L e i b n i z i a n c o n d i t i o n w i t h i n t h i s a n a l y s i s . Mackie points out, i n reference to the c l a s s of s u f f i c i e n t c o n d i t i o n s f o r some r e s u l t P, that i f "there i s some necessary and s u f f i c i e n t c o n d i t i o n f o r t h i s r e s u l t [then] the d i s j u n c t i o n of a l l the minimal s u f f i c i e n t c o n d i t i o n s f o r i t c o n s t i t u t e s a necessary and s u f f i c i e n t c o n d i t i o n . " 1 * ' Marc-Wogau notes that t h i s i n f e r e n c e depends on the p r e s u p p o s i t i o n "that an a r b i t r a r y event C, i f i t 1 7 occurs, must have s u f f i c i e n t reason to occur." T h i s , of course, i s a L e i b n i z i a n " p r i n c i p l e of s u f f i c i e n t reason." Let us t r y to make t h i s c l e a r . Suppose K i s the s e t of minimal s u f f i c i e n t c o n d i t i o n s (a^,...,a ) f o r some r e s u l t R. Now form the d i s j u n c t i o n of K: ( a 1 v &2 v...v a n ) . This d i s j u n c t i o n , given the L e i b n i z c o n d i t i o n on R, i s then a necessary c o n d i t i o n of R. I f R occurs, then some a^, a member of K, must have occurred. (Marc-Wogau c a l l s t h i s a necessary post factum f o r R). Our conclusions from Chapter I (Section 4b) are d i r e c t l y a p p l i c a b l e here. R e c a l l t h a t p r e v i o u s l y we argued t h a t one may r e t a i n an analagous c o n d i t i o n on ex p l a n a t i o n even i n the face of p u r e l y s t a t i s t i c a l p r e - c o n d i t i o n s on R. That i s , we may have s u f f i c i e n t reason to expect R even i f R does not occur. Here we w i l l suppose that each a^ i n K i s again such a s t a t i s t i c a l p r e c o n d i t i o n . In other words, K i s made up of a set of co n d i t i o n s each of which i s on l y p r o b a b i l i s t i c a l l y r e l a t e d to the outcome R. On t h i s view the occurrence of R would demonstrate that some a^ occurred, but not th a t given the occurrence of a^, then R must f o l l o w . At l e a s t two points may be made here. (1) That a L e i b n i z - l i k e c o n d i t i o n on ex p l a n a t i o n , or here on causation, w i l l not present a threat to a causal conception of an i n d e t e r m i n i s t i c world only i f we are prepared to separate the ' s u f f i c i e n c y ' from the 'reason' i n such a p r i n c i p l e . At l e a s t p a r t of the s t a t i s t i c a l conception i s that one may have a l l the 'reasons' one may i n p r i n c i p l e have, and, t h e r e f o r e , e n t e r t a i n maximally r a t i o n a l expecta- t i o n s , yet f a l l short of a t t a i n i n g s u f f i c i e n c y — e i t h e r i n causal or r a t i o n a l terms. (2) From the above d i s c u s s i o n we see v i v i d l y why an account of causation which inc l u d e s some form of s u f f i c i e n c y must f a i l i n i n d e t e r -m i n i s t i c s i t u a t i o n s . (As an aside we might ask, "What motivates analyses of causation to in c l u d e some notion of s u f f i c i e n t c o n d i t i o n s ? " and speculate i n the f o l l o w i n g way: any r e g u l a r i t y theory descended from Hume must capture the concept of caus a l production, yet avoid reference to any 'hidden powers' which connect the cause with i t s e f f e c t . I b e l i e v e that such 'powers' are b u r i e d i n the c o n d i t i o n s we take to be s u f f i c i e n t . ) These conclusions do not a f f e c t any a n a l y s i s i n terms of necessary c o n d i t i o n s , nor the parts of Mackie's a n a l y s i s c a s t i n these terms. Of course Mackie's a n a l y s i s i s not complete u n t i l he has given an account of n e c e s s i t y and s u f f i c i e n c y . Athough I b e l i e v e that Mackie's a n a l y s i s , as i t stands, w i l l not be compatible with s t a t i s t i c a l or probabi-l i s t i c c a u s a t i o n , I think that a b r i e f excursion i n t o t h i s d i s c u s s i o n of c a u s a l n e c e s s i t y w i l l be i n s t r u c t i v e as to i t s p o s s i b l e r e h a b i l i t a t i o n . To a n t i c i p a t e our c o n c l u s i o n , I b e l i e v e we w i l l f i n d that causal processes w i l l bear the conceptual load which has been c a r r i e d by the s u f f i c i e n c y c o n d i t i o n s 1 8 on cau s a l r e l a t i o n s . 3. Mackie I I : Counterfactuals and Causal Processes 1 g In a rather long passage i n The Cement of the Universe Mackie attempts to overcome "the great d i f f i c u l t y f o r any r e g u l a r i t y theory of ca u s a t i o n " , that of d i s t i n g u i s h i n g between causal and a c c i d e n t a l r e g u l a r i -t i e s . In h i s c o n s t r u c t i o n of what he takes to be a d e f e n s i b l e p o s i t i o n w i t h respect to t h i s problem he moves s i g n i f i c a n t l y away from the i n i t i a l Humean ba s i s of the r e g u l a r i t y theory. Mackie's abandonment of Hume w i l l be of l e s s i n t e r e s t to us than what he i n f a c t c o n s t r u c t s : I take h i s f i n a l r e s o l u t i o n of t h i s problem to in c l u d e a t l e a s t an analogue of causes as processes. In t h i s s e c t i o n I w i l l sketch Mackie's argument and trace i t s development to t h i s p o i n t . From a Humean r e g u l a r i t y viewpoint laws of nature are u n r e s t r i c t e d but contingent u n i v e r s a l s . They are u n r e s t r i c t e d because they apply i n a l l space-time regions; they describe what always and everywhere a c t u a l l y o c c urs. However, there i s no n e c e s s i t y , " n a t u r a l " or otherwise, which connects antecendent to consequent, or any i n i t i a l impression with i t s successor. Hume saw the world as a succession of events, event stages, o r , anachronously, a succession of t i m e - s l i c e s . Since the world o f f e r e d no impression from which the idea of a "necessary connexion" between these s l i c e s could a r i s e , t h i s idea must have had i t s o r i g i n s elsewhere. In the world of impressions there were only contingent r e g u l a r i t i e s , patterns which h e l d more or l e s s u n i v e r s a l l y . The "great d i f f i c u l t y " f o r t h i s view i s the f o l l o w i n g : i n t u i t i v e l y we would l i k e to draw some d i s t i n c t i o n between those r e g u l a r i t i e s which are instances of "laws of nature" and those r e g u l a r i t i e s which hold u n i v e r s a l l y 74 yet a c c i d e n t a l l y . Within the Humean persp e c t i v e there seems no way to make such a d i s t i n c t i o n . The Humean conception i s too broad — i t includes merely a c c i d e n t a l c o r r e l a t i o n s along w i t h the t r u l y causal ones. Mackie confronts and, I t h i n k , resolves one such v e r s i o n of t h i s d i f f i c u l t y , a v e r s i o n which attempts to draw t h i s d i s t i n c t i o n i n terms of 20 c o u n t e r f a c t u a l s . A c a u s a l r e g u l a r i t y , or n a t u r a l law, w i l l support i t s corresponding c o u n t e r f a c t u a l c o n d i t i o n a l , an a c c i d e n t a l u n i v e r s a l w i l l not, a d i f f e r e n c e the Humean cannot recognize. For example, the a c c i d e n t a l l y true u n i v e r s a l " A l l the copper coins i n my pocket are shiny" does not e n t a i l , o r even support the c o u n t e r f a c t u a l " I f that other copper coin were i n my pocket, i t would be shiny"; whereas " A l l copper coins expand when heated" gives us reason to b e l i e v e the c o u n t e r f a c t u a l " I f that other copper coin were heated, 21 i t would expand." The Humean has two choices here. She may ' b i t e the b u l l e t ' and deny the d i s t i n c t i o n by defending the c l a i m that a l l u n i v e r s a l a s s e r t i o n s , a c c i d e n t a l or otherwise, hold as a consequence of n a t u r a l laws; t h a t a l l are e i t h e r examples of causal connections or can be derived from l a w - l i k e connections i n t h e i r causal h i s t o r y . ( A f t e r a l l , i t may be a n a t u r a l law t h a t 'pocketings' are always preceded by 'shinings'.) I f the world i s d e t e r m i n i s t i c , the Humean argues, then everything happens i n accordance with c a u s a l laws, and i t i s only an "unwarranted p r e j u d i c e that there should be 22 any such d i s t i n c t i o n " between a c c i d e n t a l and l a w - l i k e connections. 23 That i s , i n a d e t e r m i n i s t i c universe nothing i s merely a c c i d e n t a l . Now i f not prima f a c i e absurd, t h i s option a t l e a s t forces the Humean to counten-ance many 'laws' t h a t others would not, i n c l u d i n g the suggested l a w - l i k e connection, e i t h e r fundamental or derived , between 'pocketing' and ' s h i n i n e s s ' . 75 The second op t i o n f o r the Humean i s to draw the required d i s t i n c -t i o n , between a c c i d e n t a l and nomic u n i v e r s a l s , from w i t h i n her own theory. However, Mackie argues that a Humean cannot base t h i s d i s t i n c t i o n on c o u n t e r f a c t u a l grounds alone. In other words, Mackie agrees that a c c i d e n t a l u n i v e r s a l s do not support the r e l e v a n t c o u n t e r f a c t u a l s while nomic u n i v e r -s a l s do, but points out that the reasons f o r t h i s d i f f e r e n c e are not based i n a d i f f e r e n c e between these r e g u l a r i t i e s themselves. His argument i s i n two p a r t s : f i r s t e x p l a i n i n g why a c c i d e n t a l u n i v e r s a l s f a i l to support t h e i r c o u n t e r f a c t u a l a s s e r t i o n and, second, to e x p l a i n why l a w - l i k e u n i v e r s a l s do. Consider again the a c c i d e n t a l u n i v e r s a l (1) " A l l the copper coins i n my pocket are shiny", and the c o u n t e r f a c t u a l c l a i m (2) " I f t h i s were a copper c o i n i n my pocket, i t would be shiny." The evidence f o r the t r u t h of (1) i s based on a exhaustive enumeration of coins i n my pocket. And ( 2 ) , although s t r i c t l y true because of the f a l s i t y of the antecedent, i s nonetheless excluded from the 'scope' of ( 1 ) . I t does not seem reasonable, then, to argue from (3) "Suppose t h i s other c o i n were i n my pocket" and (1) to the conclusions "That other c o i n i s shiny" simply because the evidence f o r (1) completely undermines our evidence f o r ( 3 ) A s Mackie puts i t , "such a p a i r of c o n t r a d i c t o r y premises v a l i d l y e n t a i l s any conclusion at a l l , [but] 25 no one supposes f o r a moment that t h i s i s a s e n s i b l e way of arguing." The same k i n d of reasoning serves to show why nomic u n i v e r s a l s w i l l support t h e i r corresponding c o u n t e r f a c t u a l s . I f would seem, by the argument of the preceeding paragraph, that nomic u n i v e r s a l s a l s o f a l l outside the scope of t h e i r c o u n t e r f a c t u a l a s s e r t i o n : they r e f e r , as i t were, only to the a c t u a l world, while c o u n t e r f a c t u a l s are constructed out of p a t e n t l y non-a c t u a l s i t u a t i o n s . How, then, can we reasonably conjoin these a s s e r t i o n s , i f we could not c o n j o i n non-nomic r e g u l a r i t i e s with t h e i r c o u n t e r f a c t u a l s ? The answers are, as I have suggested, s i m i l a r . In the nomic case both a s s e r t i o n s w i l l be supported by the same evidence. That i s , our reasons f o r b e l i e v i n g the one w i l l not undermine, but r a t h e r s u s t a i n , our reasons f o r b e l i e v i n g the other. Consider, f o r example, the nomic u n i v e r s a l " A l l potassium exposed to oxygen i g n i t e s , " and the f o l l o w i n g cases: (a) This potassium w i l l be exposed to oxygen tomorrow, (b) This potassium was exposed to oxygen yesterday, but we are ignorant of the r e s u l t , (c) Some potassium i s now being exposed to oxygen, and (d) We suppose that t h i s b i t of potassium, which has not i n f a c t been exposed to oxygen, were so exposed. I f there i s evidence to support the proposed law, then that same evidence w i l l make i t reasonable to a s s e r t , with (a) t h a t t h i s b i t of potassium w i l l i g n i t e , with (b) that i t d i d i g n i t e , w i t h (c) that i t i s now i g n i t i n g , w i t h (d) that i t would have i g n i t e d . Whatever formal r e l a t i o n s h i p e x i s t s between purported laws and the evidence f o r them, t h i s r e l a t i o n s h i p seems to c h a r a c t e r i z e e q u a l l y a l l four cases. Thus Mackie concludes that the problem of co u n t e r f a c t u a l s can be reduced to (!) the general problem of i n d u c t i o n , and can be set aside i n t h i s i n s t a n c e . And now we have come to the heart of the matter. Mackie has explained the r e l a t i o n s h i p between c o u n t e r f a c t u a l s and causal laws, and exp l a i n e d t h i s using only those devices allowed him as a good Humean (along with some very general concept of confirmation.) And we might agree that the s p e c i a l d i f f i c u l t y of c o u n t e r f a c t u a l s has been resolved — t h a t the way i n which c a u s a l laws s u s t a i n them and non-causal r e g u l a r i t i e s do not does not e n t a i l any hidden powers i n the objects themselves. Rather, i t i s a product of the e v i d e n t i a l base f o r both causal a s s e r t i o n s and t h e i r corresponding 77 c o u n t e r f a c t u a l s . But we might go on to ask, why i s t h i s the case? Why are a l l forms of the c o n d i t i o n a l supported here i n the case of causal laws? In other words, the s p e c i a l d i f f i c u l t y presented by c o u n t e r f a c t u a l s may w e l l be overcome, yet the general problem remains: laws are d i f f e r e n t from merely a c c i d e n t a l u n i v e r s a l g e n e r a l i z a t i o n s and the d i f f e r e n c e i s unexplainable on Humean gounds alone. Mackie recognizes that i f t h i s d i f f e r e n c e could be made c l e a r , the success of the d i s t i n c t i o n "would compel us to r e j e c t a Humean r e g u l a r i t y theory of cuasation and admit that causal laws i n v o l v e 26 'connections' not r e d u c i b l e of concommitances and sequences." And he admits that "there s t i l l seems to be some l i n e to be drawn between such laws and those other contingent u n i v e r s a l s which we say are, i f they are t r u e , 27 o n l y a c c i d e n t a l l y t r u e . " By c a r e f u l l y assembling a v a r i e t y of suggestions (from J.S. M i l l , K. Popper, and W. Kneale) Mackie formulates a response to t h i s general d i f f i c u l t y . This response, I s h a l l attempt to show, c o n s i s t s i n p r o v i d i n g j u s t those non-reducible 'connections' Hume warns a g a i n s t — and thus Mackie's account i s decidedly non-Humean. In a d d i t i o n , as I b e l i e v e w i l l soon be obvious, Mackie's response i n c l u d e s a d i r e c t analogue of Salmon's process ontology. Mackie f i r s t c a l l s upon J.S. M i l l to deepen the problem. M i l l d i s -t i n g u i s h e s three forms of g e n e r a l i z a t i o n : a c c i d e n t a l u n i v e r s a l s , u n i f o r -m i t i e s of coexistence, and u n i f o r m i t i e s of succession. U n i f o r m i t i e s of co-e x i s t e n c e , even i f u n i v e r s a l , were rated as i n f e r i o r to those of succession, mainly because the l a t t e r have a basis i n the law of causation ( i . e . , the p r i n c i p l e of the u n i f o r m i t y of nature) while the former lack any such p r i n c i -28 29 p i e i n which they can be grounded. Yet as Mackie points out, 78 t h i s does not he l p . P a r t i a l support by the " u n i v e r s a l law of causation" marks an epistemic d i f f e r e n c e — ca u s a l laws are discovered by experiment and t e s t , laws of coexistence are found by enumeration — but no i n t r i n s i c d i f f e r e n c e seems to account f o r t h i s . From K a r l Popper Mackie gleans a suggestion as to the nature of the p h y s i c a l n e c e s s i t y i n n a t u r a l laws: a law "imposes s t r u c t u r a l p r i n c i p l e s on 30 the world" while l e a v i n g i n i t i a l c o n d i t i o n s f r e e . what are " s t r u c t u r a l p r i n c i p l e s " ? Both Mackie, who equates s t r u c t u r a l p r i n c i p l e s with h i s "pure 31 laws of working", and Popper proceed by example. B r i e f l y , Popper's example i s of a b i o l o g i c a l s t r u c t u r e , moas, a species of b i r d which, under fa v o r a b l e c o n d i t i o n s , w i l l reach a median age of 60 years. The a c t u a l c o n d i t i o n s , however, are not i d e a l and a l l such b i r d s die before they are 50. The u n i v e r s a l g e n e r a l i z a t i o n " A l l moas die before reaching 50" i s not, then, a n a t u r a l law, given i t s dependence of a c c i d e n t a l i n i t i a l c o n d i t i o n s . Yet, as Mackie points out, t h i s i s not a d i s t i n c t i o n based on the d i f f e r e n c e between s t r u c t u r a l and i n i t i a l c o n d i t i o n s , but based rather on what can stand i n the subje c t place i n a n a t u r a l law. Popper r e s t r i c t s the subject term to s t r u c t u r a l c o n d i t i o n s alone. We might add the r e l e v a n t unfavorable i n i t i a l c o n d i t i o n s to our account of the moa, and thus p r o j e c t the derived law " A l l moas under these c o n d i t i o n s die before reaching 50". This procedure of adding to the subject term i n a n a t u r a l law i s recommended by Mackie i n order to turn mixed laws i n t o pure laws of 32 working. Kepler's laws, f o r example, of the motions of the p l a n e t s , depend on the i n i t i a l c o n d i t i o n s , or c o l l o c a t i o n s of the p l a n e t s . I f we s u b s t i t u t e f o r these i n i t i a l c o n d i t i o n s d e s c r i p t i o n s of the re l e v a n t features alone ( v i z . , a sphere with such and such mass, r a d i u s , v e l o c i t y ) the r e s u l t i s d e r i v a b l e as a mathematical consequence of more basic and pure laws of 79 working ( i n t h i s case, Newton's law, of motion.) "Thus", Mackie concludes, "we can s o r t pure laws of working — some b a s i c , some derived — from both 33 mixed laws and c o l l o c a t i o n statements." The t h i r d (and f i n a l ) l i n e of thought Mackie c o l l a t e s with M i l l and Popper comes from K n e a l e . 3 4 Kneale's view i s that n a t u r a l laws are " p r i n c i p l e s of n e c e s s i t a t i o n " . C e r t a i n p r i n c i p l e s of t h i s k i n d are compre-h e n s i b l e (e.g., the necessary i n c o m p a t i b i i t y of redness and greenness), o t h e r s , l i k e c ausation, are not. N a t u r a l laws are incomprehensible, Kneale argues, because "our experience does not f u r n i s h us with the ideas which 35 would be required f o r an understanding of the connexions we a s s e r t . " The n e c e s s i t y i n n a t u r a l laws, Kneale c l a i m s , holds between the imp e r c e p t i b l e i n s i d e s of causal c o r r e l a t e s ; i f these were to be perceived the necessary connection would be something l i k e that of the i n c o m p a t i b i l i t y of redness and greenness. Now whatever the merits of t h i s analogy, or of Kneale's 36 conception of n e c e s s i t y here, Mackie expresses i n t e r e s t i n what Kneale goes on to say i n c h a r a c t e r i z a t i o n of our explanation of causal n e c e s s i t y by v i r t u e of the i n t e r n a l features of o b j e c t s . N a t u r a l laws, f o r Kneale, are c h a r a c t e r i z e d by t h e i r a s s o c i a t i o n w i t h transcendant hypotheses. These transcendant hypotheses are the basic t h e o r e t i c a l p o s t u l a t e s (and t h e i r mathematical representation) of large s c a l e t h e o r i e s , such as the wave or p a r t i c l e t h e o r i e s i n p h y s i c s . These the o r i e s do not concern observable o b j e c t s , but rather the mathematical s t r u c t u r e which represents the i n p r i n c i p l e unobservable features of the objects between which the causal r e l a t i o n s h o l d . Of course, however deeply buried or m y s t i c a l l y c lothed these connections might be, Mackie asks (as Hume would), 80 "What i s there i n i t except the succession of phases?" The answer, for Kneale, i s the inner s t r u c t u r e and the mathemati-c a l d e s c r i p t i o n of i t . The idea i s something l i k e the f o l l o w i n g : the unobservable i n s i d e s of a cause-event has a s t r u c t u r e , p o s t u l a t e d by the transcendant hypotheses.and mathematically d e s c r i b e d . This s t r u c t u r e develops with a logico-mathematical n e c e s s i t y i n t o a f u r t h e r s t r u c t u r e which we i d e n t i f y , v i a i t s observable f e a t u r e s , with an e f f e c t - e v e n t . What Mackie n o t i c e s i n Kneale 1s speculations i s the e v o l u t i o n of s t r u c t u r e . In any development c e r t a i n parameters w i l l change, perhaps as a f u n c t i o n of others, but c e r t a i n others w i l l remain the same. Mackie c a l l s 37 these s t a b l e s t r u c t u r a l features forms of p e r s i s t a n c e . I t i s these forms of p e r s i s t a n c e which make s t r u c t u r a l e v o l u t i o n or development both i n t e l l i g i b l e and necessary. Before we examine t h i s concept i n d e t a i l (the understanding of which w i l l be f a c i l i t a t e d by i t s s i m i l a r i t y to causal processes) l e t us r e c a p i t u l a t e the three suggestions Mackie c o l l a t e s i n t o t h i s n o t i o n . From M i l l we have the d i s t i n c t i o n s among c o l l o c a t i o n s , coexistences, and successions: the f i r s t e x e m p l i f i e d by pockets and c o i n s , the second by the gas laws, and the t h i r d by Newtonian laws of motion. I t i s the concept of a law of succession, a law which describes the development or temporal e v o l u t i o n of s t r u c t u r e , which i s adduced here. From Popper we have the d i s t i n c t i o n between i n i t i a l c o n d i t i o n s and l a w - l i k e s t r u c t u r e s or form. This allows f o r the se p a r t i o n of ' l o c a l i z e d ' or contingent matters from the pa t t e r n s i n t o which they f i t . And from Kneale we introduce "trancendancy", the idea that t h i s s t r u c t u r e i s i n t r i n s i c a l l y t h e o r e t i c a l , " i n t e r n a l " , unobservable — f o r Mackie t h i s provides the required idea of p h y s i c a l 81 n e c e s s i t y . The combination of these concepts comprise that Mackie terms "forms of p e r s i s t a n c e " and are what i s described by "basic laws of w o r k i n g " . 3 8 . Some remarks are i n order here as to how we might b e t t e r understand "forms of p e r s i s t a n c e " , f o r , on the face of i t , there seems to be some co n f u s i o n . The c o l l e c t i o n of ideas grounding Mackie's speculations are of qu i t e a d i s p a r a t e c h a r a c t e r . M i l l i s o f f e r i n g c ategories of r e g u l a r i t i e s , Popper i s d i s t i n g u i s h i n g ( i n some sense) content from form, while Kneale speaks of t h e o r e t i c a l (or transcendant) hypotheses. Yet Mackie i s s u r e l y t a l k i n g about p h y s i c a l events (forms of p e r s i s t a n c e ) . The d i f f i c u l t y seems to stem from the m a t e r i a l / f o r m a l ambiguity of "forms of p e r s i s t a n c e " . In the m a t e r i a l mode a form of p e r s i s t a n c e i s a p h y s i c a l s t r u c t u r e e x h i b i t i n g a c e r t a i n degree of coherence and order, or e v o l v i n g i n a continuous or o r d e r l y p a t t e r n . In t h i s sense Mackie i s r e f e r r i n g to m a t e r i a l events i n space-time: a p a r t i c l e at r e s t i n a p a r t i c u l a r frame; a p a r t i c l e moving with constant a c c e l e r a t i o n , i . e . , being acted on by a constant f o r c e , i t s change i n v e l o c i t y a f u n c t i o n of the square of the time; a beam of electro-magnetic r a d i a t i o n propagating through space. In the formal mode a "form of p e r s i s t a n c e " i s the "pure law of working" according to which the m a t e r i a l process evolves, the process being a " s i n g u l a r causal sequence which 39 i n s t a n t i a t e s some pure law of working...". By understanding Mackie i n t h i s way we then see that h i s "forms of p e r s i s t a n c e " correspond ( m a t e r i a l l y ) to Salmon's cau s a l processes. And speaking i n the formal mode, the establishment of pure laws of working are the explanatory goals which ipso f a c t o provide the explanatory desiderata of a causal " s t o r y " — they are d e s c r i p t i o n s of causal processes. 82 40 Having found a place w i t h i n Mackie's " r e g u l a r i t y " framework f o r t h i s Salmonian causal mechanism we can now formulate a response to a 41 general c r i t i c i s m of Mackie's program r a i s e d by Kim. Kim draws our a t t e n t i o n to the o n t o l o g i c a l issues i n v o l v e d i n making causal claims: the analysandum i s the c a u s a l r e l a t i o n between i n d i v i d u a l events and s t a t e s ; the analysans i s cast i n terms of n e c e s s i t y and s u f f i c i e n c y , and these ...seem best s u i t e d f o r p r o p e r t i e s and f o r p r o p e r t y - l i k e e n t i t i e s such as generic s t a t e s and events; and t h e i r a p p l i c a t i o n to i n d i v i d u a l events and s t a t e s seems best ex-p l a i n e d as being d e r i v a t i v e from t h e i r a p p l i c a t i o n to p r o p e r t i e s . . . s i n c e Mackie's c h i e f o b j e c t i v e i s to analyse s i n g u l a r causal statements, we must have a way of r e l a t i n g the t a l k of n e c e s s i t y and s u f f i c i e n c y to i n d i v i d u a l events that are s p a t i o - t e m p o r a l l y l o c a l i z e d . Thus we need e n t i t i e s t h a t possess both an element of g e n e r a l i t y and an element of p a r t i c u l a r i t y ; the former i s necessary f o r making sense of the r e l a t i o n s of n e c e s s i t y and s u f f i c i e n c y , and the l a t t e r 42 f o r making sense of s i n g u l a r causal judgements. But, of course, t h i s serves only to c h a r a c t e r i z e the problem i n g e n e r a l . The s p e c i f i c d i f f i c u l t i e s can be r a i s e d i n the f o l l o w i n g way: Mackie casts h i s a n a l y s i s i n terms of ' c o n d i t i o n s ' which are, i n the complex manner set out i n S e c t i o n ( 2 ) , conjoined or d i s j o i n e d to form an INUS c o n d i t i o n of an 'object' which i s t h e i r e f f e c t . The questions, r a i s e d by Kim, are f i r s t the l o g i c a l , and then the o n t o l o g i c a l , status of these c o n d i t i o n s . Consider the c o n d i t i o n s ABC, say one of the minimal s u f f i c i e n t c o n d i t i o n s f o r an event P, or an INUS c o n d i t i o n of the form (AX or Y ) . I f each of A,B,C,X, and Y are events, then these forms represent some s o r t of c o n j u n c t i v e or d i s j u n c t i v e compounding of events, and, i n the case of C, the -negation of one of these conjuncts. What are we to make, l o g i c a l l y , of the negation of an event? Sur e l y t h i s i s a non-standard use of t h i s operator. Consider, f o r example, the event of the death of Socrates. What sense are we to make of "not - the death of Socrates"? Or take the conjunction of events: 83 i f ABC i s minimally s u f f i c i e n t , then are we to construe t h i s (as we might t r u t h f u n c t i o n a l l y ) to mean A i s minimally s u f f i c i e n t , and B i s minimally s u f f i c i e n t , and C i s ...? But t h i s i s o b v i o u s l y not what i s intended here. Furthermore, consider the 'object' designated by a d i s j u n c t i o n such as (AX or Y). I f the i n d i v i d u a l names which make up t h i s d i s j u n c t i o n are taken as s i n g u l a r terms, as w e l l they might i n an a n a l y s i s of p a r t i c u l a r c a u s a l c l a i m s , then what does t h i s d i s j u n c t i o n designate? What obje c t corresponds to the complex event d e s c r i p t i o n "the cause of the f i r e or the death of Socrates"? Kim concludes that these and other d i f f i c u l t i e s are "symptomatic 43 of an underlying confusion of events with t h e i r d e s c r i p t i o n s . " Evidence of t h i s confusion appears a l s o i n Mackie's a n a l y s i s of necessary c o n d i t i o n : A i s a necessary c o n d i t i o n of P i f there are true u n i v e r s a l p r o p o s i t i o n s L and true s i n g u l a r statements S such that L and S together with the statement that A d i d not occur l o g i c a l l y imply the statement t h a t P 44 d i d not occur. The i m p l i c a t i o n suggested here (L.S.A ->P) depends on the "assumption that f o r a given event A there i s the statement that A o c c u r r e d . " 4 5 Since the i m p l i c a t i o n depends on the event d e s c r i p t i o n rather than the event per se, i f the events i n question are not uniquely d e s c r i b a b l e , then t h i s a n a l y s i s cannot be taken as c o n t a i n i n g bona f i d e s i n g u l a r terms whose r e f e r e n t s are p a r t i c u l a r i n d i v i d u a l events. What s o r t of e n t i t i e s w i l l f u l f i l l the requirements, stressed by Kim i n the passage quoted above (p.82),of g e n e r a l i t y and p a r t i c u l a r i t y ? Kim's p r e s c r i p t i o n i s f o r " r e a l i z a t i o n s of p r o p e r t i e s at p a r t i c u l a r space-time regions or by object s . " 4 * ' N e c e s s i t y and s u f f i c i e n c y can then be cashed i n terms of the c h a r a c t e r i s t i c s of p r o p e r t i e s as u n i v e r s a l s , while 84 p a r t i c u l a r causal connections can be seen as a r e l a t i o n between the i n s t a n t i a t i o n s of such p r o p e r t i e s a t p a r t i c u l a r places and times. What i s needed then i s some formal apparatus f o r representing t h i s " r e a l i z a t i o n of p r o p e r t i e s " and Kim i s ready a t hand with h i s proposal f o r event d e s c r i p t i o n : he takes the e x e m p l i f i c a t i o n of a property by an object a t a place/time as the paradigm of an event, and for m a l i z e s t h i s paradigm by the ordered t r i p l e 47 [x, P, t ] : o b j e c t x has property P a t time t . Kim then t r a n s l a t e s Mackie's a n a l y s i s , t a k i n g c o n d i t i o n s A,B,... e t c . , "as r e f e r r i n g to p r o p e r t i e s — or generic events, i . e . , p r o p e r t i e s 48 whose e x e m p l i f i c a t i o n by an object i s an event." And in s t e a d of conju n c t i v e or d i s j u n c t i v e p r o p e r t i e s , we simply speak of sets of p r o p e r t i e s . "ABC or CDF i s a necessary and s u f f i c i e n t c o n d i t i o n of P" then becomes "Whenever the set of p r o p e r t i e s {ABC} or {CDF} ; i s r e a l i z e d , P i s r e a l i z e d , and conversely." A l s o , A i s an INUS property f o r P i f and only i f A belongs to a t l e a s t one of a set of p r o p e r t i e s S^, each minimally s u f f i c i e n t f or P, and the f a m i l y of such sets (S^ e S) i s a necessary c o n d i t i o n f o r P ( i . e . , i f P i s r e a l i z e d , then one S^ i n S i s r e a l i z e d . ) An INUS c o n d i t i o n then 49 becomes a f u n c t i n of an INUS property: [x,A,t^] i s an INUS c o n d i t i o n of [y,P,t] i f f ( i ) [ X j A , ^ ] , [y,P,t] ; ( i i ) , A i s an INUS property of P; ( i i i ) Some set S^ i n S c o n t a i n i n g A and a t l e a s t one other property i s r e a l i z e d on the occasion of [x,A,t-^] ; ( i v ) S contains at l e a s t one set other than S^; (v) No set of p r o p e r t i e s i n S other than S^ i s r e a l i z e d on the occasion of [ y , P , t ] . 85 Mackie's causal a n a l y s i s i s then, that [x,A,t^] causes ty,P,t] i f [x,A,t^] i s at l e a s t an INUS c o n d i t i o n of [ y , P , t ] . Now Kim's i n t e n t i o n , i n the r e c a s t i n g of Mackie's theory i n the formal terms of event d e s c r i p t i o n s , i s to capture the import of t h i s a n a l y s i s without the o n t o l o g i c a l o b f u s c a t i o n inherent i n Mackie's approach. However, there are s t i l l some d e f i c i e n c i e s here. Consider c o n d i t i o n ( v ) . Kim emphasizes that the d e n i a l of any other member of S being r e a l i z e d does not mean that they are never r e a l i z e d , but only not r e a l i z e d on the occasion i n q u e s t i o n . L i k e w i s e , i n ( i ) we wish to i n sure that not only do [y,P,t] and [x,A,t^] occur, but a l s o that [y,P,t] occurs on the occasion of [ x , A , t ^ ] . This requirement, as Kim w e l l knows, i s more than j u s t the j o i n t r e a l i z a t i o n of these events. That i s , our i n t u i t i o n demands not only that these events be l o c a l i z e d i n some space-time r e g i o n , but more im p o r t a n t l y , that the occurrence of the one was the occasion  f o r the occurrence of the other. This l a t t e r c l a i m i s of great import, indeed, i t i s the heart of the matter. Mackie's i n i t i a l f o r m u l a t i o n s u f f e r e d from a f o r m a l / m a t e r i a l ambiguity — an ambiguity between the d e s c r i p t i o n of an event and the event i t s e l f . His l a t e r f o r m u l a t i o n 5 0 c l e a r e d away most, i f not a l l , of these d i f f i c u l t i e s . Yet Kim's formal devices only keep o n t o l o g i c a l order — what the c o n s t i t u e n t s of that order are remains open. Kim opts f o r some form of " o b j e c t " o n t o l o g y 5 1 w i t h events as the r e a l i z a t i o n of p r o p e r t i e s i n these o b j e c t s . But even i f we taken events as " p r o p e r t i e s r e a l i z e d at p a r t i c u l a r space-time regions", what we f a i l to capture, and what remains as a c r u c i a l gap i n our a n a l y s i s , i s the connection between the cause and i t s e f f e c t , i . e . , the connection i m p l i c i t i n the phrase "on the occasion o f " . What I would suggest, then, i s that an ontology of processes be considered here. Processes, as elaborated i n a Salmonian f a s h i o n , f i t n e a t l y i n t o the Mackie/Kim p i c t u r e : we need only 'extend' the element of time, t , i n Kim's ordered t r i p l e [x,A,t] to i n c l u d e the duration of the process, that i s , we need only ' t h i c k e n ' the t i m e - s l i c e to i n c l u d e space-time i n t e r v a l s . This accords w e l l w i t h our i n t u i t i o n s , since we do not u s u a l l y take the 'having of a property' to be a d u r a t i o n l e s s phenomenon. Or, a l t e r n a t i v e l y , we may adopt Kim's a n a l y s i s wholesale, and simply add to "[x,A,t-^] caused [y,P,t] i f [x,A,t.|] i s at l e a s t an INUS c o n d i t i o n of [ y , P , t ] " the f u r t h e r requirement that [x,A,t^] i s p a r t of a process whose l a t e r stage includes 52 t y , P , t ] . Kim's a n a l y s i s of event d e s c r i p t i o n s makes Mackie's INUS c o n d i t i o n on c a u s a t i o n , as a f u n c t i o n of INUS p r o p e r t i e s , l o g i c a l l y coherent; the i n s t a n t i a t i o n of these p r o p e r t i e s v i a causal processes provides o n t o l o g i c a l coherence. We w i l l conclude t h i s s e c t i o n with some remarks about Mackie's Humean program. Mackie's c e n t r a l concern i n the passages we have been examining i s to uncover the " n e c e s s i t y " i n c a u s a t i o n , a r e s u l t Hume thought e p i s t e m i c a l l y suspect, one which he u l t i m a t e l y relegated to a 'habit' of the mind to move from c o n s t a n t l y conjoined cause to i t s e f f e c t . Is the l o c a t i n g of n e c e s s i t y i n the p e r s i s t a n c e of s t r u c t u r e , or the q u a l i t a t i v e c o n t i n u i t y of a c a u s a l process, compatible with Mackie's avowed Humean i n t e n t ? To render i t compatible would be to expand Hume's theory of perception i n the f o l l o w i n g way. Roughly, f o r Hume, a l l ideas must have t h e i r ground i n t h e i r corresponding impressions. Furthermore, t h i s correspondence c o n s i s t s i n the resemblance of an idea w i t h the impression of which i t i s the i d e a . Since 87 a l l of our impressions are l o g i c a l l y d i s t i n c t ( i . e . , any one may be conceived without the conception of another) then the idea of a necessary connection cannot have come from any concatenation of impressions. In p a r t i c u l a r , the id e a of a cause i s l o g i c a l l y d i s t i n c t from the idea of i t s e f f e c t and thus, f o r Hume, the impressions which give r i s e to these ideas must have l o g i c a l l y d i s t i n c t e x i s t e n c e s . What Mackie sees, f o l l o w i n g Kneale, i s the inadequacy of resemblance as the c r i t e r i o n f o r the correspondence of impressions and i d e a s . Or r a t h e r , that the l o g i c a l d i s t i n c t n e s s of our impressions does not impair our a b i l i t y to see continuous (causal) processes, rather than a l o g i c a l l y d i s t i n c t s e r i e s of events. In Hume's disconnected world of c o n s t a n t l y conjoined images he could not but f a i l to see any image of the ( "productive q u a l i t y " i n events. Part of the reason f o r t h i s , of course, i s tha t the necessary connections he was loo k i n g f o r were not, as i t were, on the s u r f a c e . By admit t i n g Kneale's "transcendant hypotheses" Mackie provides t h i s connection by countenancing a 'deep s t r u c t u r e ' to a s e r i e s of events — a s e r i e s of events which are a c t u a l l y e a r l i e r and l a t e r stages of the same process. Salmon, as w e l l , has of t e n remarked on the e m p i r i c i s t s ' p r e j u d i c e of seeing the world i n s l i c e s or stages, as i f we were examining a s e r i e s of 53 s t i l l s l i f t e d from a movie f i l m . In the movie analogy ' r e a l i t y ' i s represented on the screen, objects w i t h i n t h i s r e a l i t y e x h i b i t i n g remarkable c o n t i n u i t y . "Remarkable" because on c l o s e r i n s p e c t i o n of the f i l m i t s e l f we see that we are being s y s t e m a t i c a l l y deceived, that what we are viewing i s a r a p i d f i r e sequence of i n d i v i d u a l (and thus l o g i c a l l y d i s t i n c t ) frames. Suddenly the 'continuous' existence of objects becomes problematic, an in f e r e n c e we are l i c e n s e d to draw only by resemblance and (here temporal) 88 c o n t i g u i t y . Both Salmon and Mackie r e j e c t t h i s analogy by t h e i r c a r e f u l c o n s t r u c t i o n of the concept of 'process' as fundamental — a concept whose c h a r a c t e r i s t i c s provide Mackie with an answer t o Hume's i n q u i r y , and Salmon w i t h a causal s t r u c t u r e which, he argues, can accommodate the p o s s i b i l i t y of 54 an i n d e t e r m i n i s t i c world. Is Mackie s t i l l to be considered a Humean? The answer to t h i s i s unimportant. What we have shown i n these l a s t few paragraphs i s j u s t how f a r Mackie has expanded the narrow confines of Hume's empiricism. Of more importance i s the c o m p a t i b i l i t y demonstrated between t h i s expanded empiricism and the notion of a causal process. Yet to be discussed i s the r e l a t i o n between t h i s concept and the p o s s i b i l i t y of i n t r i n s i c a l l y s t a t i s t i c a l "laws of working". Before we turn to t h i s task (where we s h a l l consider both Mackie's and Anscombe's approaches and compare them with Salmon's) we s h a l l consider another t r a d i t i o n a l l i n e of causal a n a l y s i s mentioned at the outset of t h i s chapter. This i s the c o u n t e r f a c t u a l theory, and i t s s o p h i s t i c a t e d proponent i s David Lewis. 55 4. Lewis' Counter-proposal Although Lewis o f f e r s an a l t e r n a t i v e to a Humean r e g u l a r i t y a n a l y s i s of causa t i o n , he begins w i t h Hume as w e l l . As we have noted above, Hume's d e f i n i t i o n of cause f e l l i n two p a r t s : the f i r s t suggesting causes as s u f f i c i e n t , the l a t t e r as necessary, f o r t h e i r e f f e c t s . Lewis begins w i t h t h i s l a t t e r h a l f , Hume's "other words": ...we may define a cause to be an ob j e c t , followed by  another, ... Or, i n other words, where, i f the f i r s t  o b j e c t had not been, the second never had e x i s t e d . This d e f i n i t i o n , Lewis suggests, i s a proposal f o r a c o u n t e r f a c t u a l a n a l y s i s of c a u s a t i o n . I f we but understood c o u n t e r f a c t u a l s , we could then understand 89 causal dependence, and thus causation, by it s light. To this end Lewis f i r s t offers an analysis of counterfactuals and counterfactual dependence. Lewis begins by defining propositions as sets of possible worlds, and by positing a primitive relationship of "overall similarity" among these worlds. Whatever value this semantic device (of possible worlds) might provide, I believe we can avoid i t s use here, and rather opt for the more natural Mackie-like suggestion regarding counterfactual propositions. That i s , counterfactuals are descriptions of our "supposings" in this world. I do not think this shift w i l l raise any great d i f f i c u l t y , nor wi l l i t be unfair to Lewis' main points. (Lewis himself offers alternative readings of his main definitions.) Consider the counterfactual, formed from any two propositions A and C, " i f A were true, then C would also be true." (In Lewis' symbols: ACZ1->C.) A O -»-C is vacuously true i f f A is not possibly realized. A P ^ C is non-vacuously true i f f " i t takes less of a departure from actuality to make the consequent true along with the antecedent than i t does to make the 57 antecedent true without the consequent." Suppose further that there is a family of possible suppositions A^, A 2 , . . . and a family (of equal cardinality) of results described by the propositions C1, C2,..., such that A^Ll -S-C.J , A2d->C^,,.. are a l l true. We say then that the C's depend counterfactually on the A's. For example, l e t R^  be the proposition specifying a particular reading of a barometer, and let be the proposition specifying the pressure of the surrounding a i r . Then "PJZ! ->R^ " is true i f f i t is less of a departure from actuality to suppose P^  and R^  then P^  and not-R^. And, i f the barometer is working properly, then this is true of a l l P^'s and R^'s — that i s , the readings depend counterfactually on the pressure. 90 For Lewis, c o u n t e r f a c t u a l dependence i m p l i e s causal dependence: I f a f a m i l y C j r C ^ r * * * depends c o u n t e r f a c t u a l l y on a f a m i l y A^,A2»... i n the sense j u s t e x p l a i n e d , we w i l l o r d i n a r i l y be w i l l i n g to speak a l s o of causal dependence A s i m i l a r r e l a t i o n s h i p f o r i n d i v i d u a l events i s then defined: i f c and e are d i s t i n c t p o s s i b l e events, then "e depends c a u s a l l y on c i f f the f a m i l y 0 ( e ) , 59 not-O(e) depends c o u n t e r f a c t u a l l y on the f a m i l y 0 ( c ) , not-O(c). That i s , the counterf a c t u a l s 0(c)C2 ->0(e) and not-0(c)TZJ->not-0(e) are true i f f e depends c a u s a l l y on c. I f c and e a c t u a l l y occur, then the f i r s t c o u n t e r f a c t u a l i s t r u e , and the causal dependence of e on c i s r e l a t i v e to the second c o u n t e r f a c t u a l : i f c had not been, then e never had e x i s t e d , i . e . , Hume's second d e f i n i t i o n . The f i n a l step i n t h i s approach i s the move from causal dependence to c a u s a t i o n : i f e i s c a u s a l l y dependent on c, then c i s a cause of e. Causal underdetermination shows the converse does not hold: c may be a cause of e, yet e i s not c a u s a l l y dependent on c — e may be brought about i n some other manner. Lewis proceeds, at t h i s p o i n t , to d i s t i n g u i s h c o u n t e r f a c t u a l and causal dependence from nomic dependence — a c e n t r a l feature of t r a d i t i o n a l r e g u l a r i t y accounts of c a u s a t i o n . He a l s o points out some of the favorable consequences of h i s approach over these t r a d i t i o n a l accounts. Although I b e l i e v e there are some minor flaws i n these f u r t h e r accounts, I w i l l not pursue them here. Rather, I would l i k e to r a i s e an o b j e c t i o n of K i m ' s 6 0 which p o i n t s out a c r u c i a l d e f i c i e n c y i n Lewis account, one which I b e l i e v e may be met by the adoption, w i t h i n Lewis' theory, of an ontology of causal processes. As w i t h Mackie's theory, we hope to show the e f f i c a c y of such an ontology. 91 Kim's o b j e c t i o n i s t h i s : c o u n t e r f a c t u a l dependency i s too broad to capture what we intend by s t r i c t causal dependency — there are many heterogeneous groups of p a i r s of events whose d e s c r i p t i o n s are c o u n t e r f a c t u a l l y dependent, c a u s a l l y dependent p a i r s being only one among them. Kim mentions four types of counterexamples and provides the f o l l o w i n g i n s t a n c e s : (1) (a) I f yesterday had not been Monday, today would not be Tuesday. (b) I f George had not been born i n 1950, he would not have reached the age of 21 i n 1971. ( l o g i c a l dependency) (2) I f I had not w r i t t e n ' r ' twice i n succession, I would not have w r i t t e n ' L a r r y ' . ( c o n s t i t u e n t dependency) (3) I f I had not turned the knob, I would not have opened the window. ( a c t i o n dependency) (4) I f my (only) s i s t e r had not given b i r t h a t t , I would not have become an uncle a t t . ( s o c i a l dependency) According to Kim, although each case shows c o u n t e r f a c t u a l dependency, i n no case would we be w i l l i n g to a s s e r t the corresponding causal dependency. Let us examine each supposed counter-example i n t u r n . The dependency expressed i n (1)(a) i s symmetric. Whatever reasons s u b s t a n t i a t e the t r u t h of (1)(a) a l s o serve to make true (1)(a') I f today had not been Tuesday, then yesterday would not have been Monday. However, f o r Lewis c o u n t e r f a c t u a l dependency i s not thus r e v e r s i b l e . The reasons f o r t h i s are complex; i t may be best understood v i a a c o n t r a s t w i t h nomic dependency. Consider the c o u n t e r f a c t u a l dependence of the readings of a barometer on the pressure of the surrounding a i r . I f the pressure were hi g h e r , the readings would be hi g h e r . We might al s o describe t h i s as nomic dependency: the readings depend on the pressure i n v i r t u e of c e r t a i n laws 92 (along w i t h statements of i n i t i a l c o n d i t i o n s . ) Given these laws and i n i t i a l c o n d i t i o n s we may a l s o i n f e r the pressure from the reading, as w e l l as the reading from the pressure. Nomic dependency i s thus r e v e r s i b l e . C o u n t e r f a c t u a l dependence, however, has a p r e f e r r e d d i r e c t i o n — i n t h i s case from the pressure to the readings — stemming from a measure on the "departure from a c t u a l i t y " one must make i n order that such c o u n t e r f a c t u a l s be t r u e . Indeed i t i s more of a departure to make the pressure agree w i t h the readings, than the reading w i t h the pressure. As Lewis puts i t , "when something must give way to permit a higher reading, we f i n d i t l e s s of a departure from a c t u a l i t y to hold the pressure f i x e d and s a c r i f i c e the accuracy [of the barometer]...being more l o c a l i z e d and more d e l i c a t e than the weather, [ i t ] i s more vulnerable to s l i g h t departures from a c t u a l i t y . " ^ 1 i The p o i n t here i s that some p a i r s of events have d e s c r i p t i o n s which are n o m i c a l l y dependent as w e l l as c o u n t e r f a c t u a l l y dependent. The dependency among such p a i r s i s r e v e r s i b l e , as i n example ( 1 ) ( a ) . I f we narrow the category of c o u n t e r f a c t u a l dependence to j u s t those i r r e v e r s i b l e i n s t a n c e s (by t h e i r asymmetric distance from a c t u a l i t y ) we can r u l e out non-causal counterexamples such as ( 1 ) ( a ) . In a d d i t i o n , as Kim po i n t s out, (1)(a) might be r u l e d out simply because the pa i r e d f a c t o r s are not r e a l l y events, a requirement of Lewis' a n a l y s i s . What then of example (1)(b)? George's b i r t h i s s u r e l y an event, and one e x p l i c i t l y countenanced by Lewis. Is t h i s dependency r e l a t i o n r e v e r s i b l e ? Is i t as much of a departure from a c t u a l i t y to hold the antecedent true when the consequent i s f a l s e , as i t i s to hold the consequent true when the antecedent i s f a l s e ? I t h i n k not, f or George may have died i n i n f a n c y . Does t h i s i r r e v e r s i b l e c o u n t e r f a c t u a l dependency imply causal dependency? C e r t a i n l y cause of George being 21 i n 93 1971 i s t h a t he was born i n 1950. Kim's o b j e c t i o n seems to r e s t on the f a c t t h a t these two events are non-contiguous. But are they? I t i s here that the adoption of a piece of Salmonian metaphysics becomes h e l p f u l . I f we view George as a four-dimensional, s p a t i o - t e m p o r a l l y continuous process, then the temporal s l i c e of t h a t process which i s the event of h i s b i r t h can be seen as a bona f i d e c a u s a l antecedent of the event which i s George on h i s 21st b i r t h d a y . Taking t h i s 'long' view of events permits us to understand example (2) c a u s a l l y as w e l l . Perhaps Kim does "not see a causal r e l a t i o n s h i p 62 between these events" because the question, "Why d i d you w r i t e 'Larry'?" as a search f o r explanatory causes i s not answered by " F i r s t I wrote an 'L', then an 'a', e t c . " (A c o n f u s i o n , perhaps, of formal and e f f i c i e n t causation.) But i f we take the w r i t i n g of a p a r t i c u l a r word as a c a u s a l process c o n s i s t i n g i n the complex movements of w r i s t , hand and f i n g e r s while h o l d i n g a pen, or while poised above a type w r i t e r keyboard, then a s l i c e of that complex motion, say the w r i t i n g of an ' r ' twice i n succession, can be seen as a c a u s a l l y l o c a t e d c o n s t i t u e n t of that process. Viewed t h i s way, then, we can a l s o understand what i s strange about the causal c l a i m at i s s u e here. I t i s simply that we u s u a l l y don't c l a i m a c o n s t i t u e n t as c a u s a l l y responsible f o r the whole of which i t i s a p a r t , unless i t happens to be the i n i t i a l segment of a sequence of events, or ( i n Salmon's terms) the e a r l i e r terminus of a causal process — g e n e r a l l y a causal i n t e r a c t i o n . We would not c a l l the event of 'making the clubhouse t u r n ' the cause of a horse race — although i t s u r e l y i s c a u s a l l y i n t e g r a t e d i n the causal process which i s g a l l o p i n g around the t r a c k — but we might very w e l l claim that the causal i n t e r a c t i o n at the s t a r t i n g gate ( i n c l u d i n g the s t a r t e r ' s b e l l , jockeys and 94 the c a u s a l processes that a c t u a l l y do the running) was the cause of the race. With t h i s refinement of our cau s a l discourse i n mind, then, we could speak of the 'clubhouse t u r n ' as both c a u s a l l y i n t e g r a t e d i n the race as a whole, as w e l l as the cause, or i n i t i a t i n g segment, of the process described as 'the s t r e t c h f o r home'. Can we say the same about the i n i t i a l segment of the process i n example (2)? Why don't we c a l l ' w r i t i n g an L 1 the cause of w r i t i n g "Larry"? For Lewis, i f . t h e r e i s c o u n t e r f a c t u a l dependence, then there i s causal dependence. With our notion of causal process at hand we see i n example (2) what t h i s dependence amounts t o . I f there i s a chain of events, each c a u s a l l y dependent on i t s predecessor, then we may, according t o Lewis, c a l l any event i n t h a t chain a cause of any subsequent event i n the c h a i n . But t h i s , then, r u l e s out counterexamples l i k e (2), f o r the event of " w r i t i n g 'Larry'" i s not subsequent to the event of " w r i t i n g ' r ' twice i n succession"; there i s no chain of events, each c a u s a l l y dependent on i t s predecessor, l e a d i n g from the one event to the other. Rather, " w r i t i n g 'Larry'" describes an e n t i r e c a u s a l process, which inc l u d e s " w r i t i n g ' r ' twice" as a proper c a u s a l p a r t . In case (3) one a c t i o n (of an agent) depends c o u n t e r f a c t u a l l y on some other a c t i o n , yet we would not (according to Kim) want to c l a i m that the former causes the l a t t e r . Kim i n s i s t s that one might c l a i m that my turning the knob caused the window's being open, but not my opening of the window. Presumably, my opening the window was caused by my d e s i r e f o r f r e s h air,' to see more c l e a r l y whether i t was going to r a i n , or whatever. Lewis himself presages t h i s o b j e c t i o n : 95 . . . i f I am i n c o n t r o l over what happens i n some respect, then there must be a double c o u n t e r f a c t u a l dependence, again over some f a i r l y wide range of a l t e r n a t i v e s . The outcome depends on what I do, and that i n turn depends on which outcome I want. 6^ In terms of causal processes, then, we may describe t h i s s i t u a t i o n as a complex causal process (the agent) extending from the s t a t e of the agent, i n c l u d i n g h i s wants and d e s i r e s , through the event which i s h i s a c t i o n , up to and i n c l u d i n g the outcome of such a c t i o n . "Turning the knob" then becomes the middle term i n t h i s sequence and can be understood c a u s a l l y much l i k e the c o n s t i t u e n t dependency described above as a response to Kim's counterexample ( 2 ) . Kim r i g h t l y a s c r i b e s the g r e a t e s t importance to example (4), f o r here we have not only c o u n t e r f a c t u a l dependency, but a l s o the i r r e v e r s i b i l i t y t y p i c a l of causal contexts, yet we are not i n c l i n e d to c a l l my nephew's b i r t h 64 the cause of my becoming an uncle. Kim has elaborated elsewhere a theory of events as ordered t r i p l e s , [x,P,t] of an o b j e c t , a property and a time. I have argued above (pp. 86) t h a t t h i s conception i s compatible with an ontology of processes. And I b e l i e v e t h i s c o m p a t i b i l i t y i s undisturbed by e i t h e r of the two p o s s i b l e responses that might be made here. The f i r s t response i s the more r a d i c a l of the two: that there are not two d i s t i n c t events here, but only one event under two d e s c r i p t i o n s . 6 ^ That i s , the b i r t h of my nephew and my 'unclehood' are one and the same happening. Kim d i s t i n g u i s h e s these because they appear to occur i n d i f f e r e n t places — my nephew's existence began i n P h i l a d e l p h i a w h i le I never l e f t Vancouver — and t h e i r d e s c r i p t i o n s a t t r i b u t e d i f f e r e n t p r o p e r t i e s to these l o c a t i o n s — being a son i n Pennsylvania, being an uncle i n B r i t i s h Columbia. However, I b e l i e v e i t i s e q u a l l y as p l a u s i b l e and i n t u i t i v e to regard t h i s s i t u a t i o n as 96 a s i n g l e event, l o c a t e d where my s i s t e r gave b i r t h , and which has p r o p e r t i e s ( i n c l u d i n g r e l a t i o n a l ones) which, because of the event which occurred there, are now a p p l i c a b l e elsewhere. I t i s only i n a very u n r e s t r i c t e d sense might we say that the existence of these new p r o p e r t i e s are something which 'happened' to me. Denying the d i s t i n c t i o n between these two events, of course, r u l e s out (4) as a counterexample to Lewis' theory. The second a l t e r n a t i v e e n t a i l s a f u r t h e r s l i g h t m o d i f i c a t i o n of Lewis' theory. For Lewis, c o u n t e r f a c t u a l dependence between events e n t a i l s c a u s a l dependence between those events. Kim does not see my 'unclehood' as an e f f e c t of the b i r t h of my s i s t e r ' s son as cause. But i f we broaden 'causal dependence' i n a Reichenbachian f a s h i o n to in c l u d e events connected by a common cause, then these two events ( i f they are d i s t i n c t , pace our f i r s t response) can be seen as c a u s a l l y r e l a t e d by t h e i r common ance s t r y . What makes me an uncle on the b i r t h of my s i s t e r ' s c h i l d i s the branching causal process which made us s i b l i n g s i n the f i r s t p l a c e . I see no prima  f a c i e reason why Lewis cannot accommodate causal dependence i n v i r t u e of common causes between events. Co u n t e r f a c t u a l dependence would then imply e i t h e r d i r e c t causal dependence or common causal dependence To conclude t h i s s e c t i o n i t remains only to note that the adoption of an ontology of processes here seems to help counter Kim's o b j e c t i o n s , j u s t as i n the previous s e c t i o n where such an ontology was suggested i n a i d of Mackie's r e g u l a r i t y theory. Lewis and Mackie do not d i r e c t l y address questions of ontology. However, Mackie does discus s causation i j i the o b j e c t (as any good Humean might) and the appending of any o n t o l o g i c a l device to h i s theory seems more d i r e c t . A sympathetic (to our i n t e r e s t s ) reading of Mackie might even 'see' the groundwork f o r such an ontology already there (as we 97 have argued at the c o n c l u s i o n of the previous s e c t i o n . ) Lewis' b r i e f a r t i c l e o f f e r s no such i n s i g h t . In the next two s e c t i o n s we s h a l l d i s c u s s these two t h e o r i e s , not w i t h respect to t h e i r o n t i c presuppositions or amendment, but r a t h e r with regard to t h e i r c a p a c i t y to embrace an i n d e t e r m i n i s t i c world. To t h i s end we w i l l introduce a t h i r d p a r t y , Anscombe, who r e f l e c t s on j u s t what some of the 'causal' d i f f i c u l t i e s of t h i s world might be. We s h a l l postpone u n t i l S e c t i o n 6 our examination of the i s s u e , c e n t r a l to our concerns i n these f i r s t two chapters and mentioned i n passing by Lewis, whether any a n a l y s i s of causation countenances undetermined events to be caused. 5. C a u s a l i t y and Indeterminism: A Reprise. Anscombe c o r r e c t l y p o i n t s out that any a n a l y s i s of causation e i t h e r i n terms of the necessary connection between events, or i n terms of the d e r i v a b i l i t y of e f f e c t s from u n i v e r s a l g e n e r a l i z a t i o n s and instances of them, makes at l e a s t t a c i t reference to the f o l l o w i n g p r i n c i p l e : I f any e f f e c t occurs i n one case and a s i m i l a r e f f e c t does not occur i n an apparently s i m i l a r case, there must be a •relevant f u r t h e r d i f f e r e n c e . To provide a d i f f e r e n t account of causation would be to supply one which denies t h i s p r i n c i p l e or assumption, that i s , one which c l e a r l y separates the concept of causation from both n e c e s s i t y and determinism. Anscombe attempts t h i s task, and the f i r s t p a r t of t h i s s e c t i o n w i l l address that attempt. Later we w i l l examine whether the p a r t i c u l a r t h e o r i e s we have examined are amenable to Anscombe's non-necessary, n o n - s u f f i c i e n t , non-deterministic c a u s a l conception. 98 Anscombe argues ag a i n s t analyses of causation that r e q u i r e (the t r a d i t i o n a l ) terms of necessary and/or s u f f i c i e n t c o n d i t i o n s . I f we take ' s u f f i c i e n t ' c o n d i t i o n s i n the s t r i c t sense, such that i f the s u f f i c i e n t c o n d i t i o n s f o r X are there, then X occurs, then i t would seem i l l e g i t i m a t e to ask "May not the s u f f i c i e n t c o n d i t i o n s f o r an event be present, and the event 69 yet not take place?" However, i f we consider a " s u f f i c i e n t c o n d i t i o n " i n the sense of "enough", we may very w e l l ask "May there be enough to have 70 made something happen — and yet i t not have happened?" I take t h i s to mean that we may know what c o n d i t i o n s are " s u f f i c i e n t " ( i n the l a t t e r sense) f o r an event, and yet not know these c o n d i t i o n s to be " s u f f i c i e n t " ( i n the former sense). This i s not such much an argument, however, as a piece of l e g i s l a t i o n as to how we are to describe causal s u f f i c i e n c y . One might respond that t h i s weakened v e r s i o n of s u f f i c i e n c y i s simply not what we mean here. We should view her remarks, then, as an attempt to d r i v e a (small) wedge between " s u f f i c i e n c y " and "causation." Anscombe then turns to " n e c e s s i t y " . The n e c e s s i t y Anscombe argues aga i n s t here i s not the n e c e s s i t y of the sine qua non approach of Lewis. Her t a r g e t i s the n e c e s s i t y which a l l e g e d l y attaches to the e x c e p t i o n l e s s g e n e r a l i z a t i o n s of the laws of nature. She seems to equate t h i s 71 " u n i v e r s a l i t y " w i t h n e c e s s i t y . C e r t a i n l y the two are d i f f e r e n t . Thus we w i l l take her argument to show only that a knowledge of causes i s independent of the knowledge of the corresponding u n i v e r s a l g e n e r a l i z a t i o n . Against these " u n i v e r s a l i z a b l e " c o n d i t i o n s she o f f e r s the f o l l o w i n g example. We know c e r t a i n diseases to be contagious, I have had contact with someone s u f f e r i n g such a disease, and I get i t myself. We suppose we know the cause of my c o n t r a c t i n g the disease, here the necessary c o n d i t i o n of 99 being i n contact with the c a r r i e r . Yet, given the contact, do we know t h a t I w i l l get the disease? I t i s l i k e l y that we won't know t h i s . Yet, one might o b j e c t , the knowledge of causes here i s only p a r t i a l — we j u s t don't know a l l the sets of c o n d i t i o n s under which one i n v a r i a b l y gets a d i s e a s e . But t h i s remark assumes that there i s such a t h i n g to know, and even i f there were, "the question whether there i s does not have to be s e t t l e d before we can know what we mean by speaking of the contact as cause of my g e t t i n g the 72 disease." So f a r Anscombe has shown that n e i t h e r a knowledge of s u f f i c i e n t c o n d i t i o n s , nor of e x c e p t i o n l e s s g e n e r a l i z a t i o n s , are necessary f o r an understanding of c a u s a t i o n . Neither are they s u f f i c i e n t , f o r suppose we do have such knowledge: we w i l l s t i l l be ignorant of what Anscombe claims i s the "core" feature of c a u s a l i t y , the d e r i v a t i v e n e s s of an e f f e c t from i t s causes. Our a n a l y s i s i n terms of n e c e s s i t y or u n i v e r s a l i t y does not t e l l us of t h i s derivedness of the e f f e c t ; rather i t f o r -gets about t h a t . For the n e c e s s i t y w i l l be that of the laws of nature; through i t we_ s h a l l be able to derive knowledge of the e f f e c t from knowledge of the cause, or v i c e versa, but that does not show us the cause as source 73 of the e f f e c t . What i s l e f t out, i n s h o r t , from d i s c u s s i o n s of c a u s a l i t y l i m i t e d to these concepts i s the connection between cause and e f f e c t . I t i s t h i s 'connection' t h a t Mackie attempts to e s t a b l i s h v i a "forms of p e r s i s t a n c e " i n h i s r e p a i r of a r e g u l a r i t y approach to c a u s a t i o n ; i t i s t h i s 'connection' t h a t , we argued, Kim f i n d s l a c k i n g i n Lewis' c o u n t e r f a c t u a l approach; and i t i s t h i s 'connection' t h a t Salmon attempts to c h a r a c t e r i z e with h i s ontology or processes. We s h a l l r e t u r n to t h i s p o i n t below. 100 Anscombe a l s o r e j e c t s any d e t e r m i n i s t i c requirements i n the a n a l y s i s of c a u s a t i o n . There are two arguments here. F i r s t , an event's being "determined" i s often used as i f i t meant "caused". To d i s p e l t h i s i d e a Anscombe remarks that the two are at l e a s t d i f f e r e n t i n the f o l l o w i n g way: something i s n ' t caused u n t i l i t has happened, but i t may be determined 74 before i t happens. This remark seems g r a t u i t o u s at best; we may a l s o say of any p a r t i c u l a r event that i t was both caused and determined. Or, l i k e w i s e , before i t s occurrence: here are the causes which together determine such an event. The language here does not seem p a r t i c u l a r l y u s e f u l or d e c i s i v e i n d e l i n e a t i n g these concepts. Of more use here i s her d e f i n i t i o n of determinism: When we c a l l a r e s u l t determined we are i m p l i c i t l y r e l a t i n g i t to an antecedent range of p o s s i b i l i t i e s and saying that a l l but one of these i s d i s a l l o w e d . Or, when speaking of d e t e r m i n i s t i c laws of nature: ...to be determined i s f o r them, together with the d e s c r i p t i o n of the s i t u a t i o n , to e n t a i l unique r e s u l t s . . This d e f i n i t i o n accords w e l l with Salmon's conception of determinism we noted i n Chapter I . There an event was s a i d to be determined only i f , given the circumstances, the p r o b a b i l i t y of i t s occurrence was 1 or 0. And although i t has long been thought that i f these circumstances i n c l u d e the cause of the event i n question, then the knowledge of these causes would e n t a i l knowledge of t h i s event, no argument to t h i s general conclusion has been put forward. As a matter of f a c t , we often speak as i f t h i s were not the case. We say that the cause of the accident was the i c y highway (although t h i s r e s u l t was not determined, given the circumstances); the disease was caused by contact with i t s c a r r i e r (although not a l l so contacted c o n t r a c t t h i s d i s e a s e ) ; a 1 01 Geiger counter r e g i s t e r s a c e r t a i n reading because i t was placed near a source of r a d i a t i o n (although i t i s not determined to do so.) Anscombe's second maneuver, a f t e r d i s t i n g u i s h i n g c a u s a l i t y from determinism, i s a d e s t r u c t i v e a n a l y s i s of the reasons f o r t h e i r h i s t o r i c a l concommitance. This she traces to the p r e d i c t i v e success of Newtonian mechanics as ap p l i e d to our s o l a r system. Not only d i d our s o l a r system provide a r e l a t i v e l y good causal model of Newton's dynamics, but t h i s system was a l s o r e l a t i v e l y well-behaved h i s t o r i c a l l y — l a c k of abberation meant p r e d i c t i v e success as w e l l . Any abberation of the system, a comet, say, or the e x p l o s i o n of a p l a n e t , would s t i l l i l l u s t r a t e Newton's laws, but could not have been p r e d i c t e d from them (along with i n i t i a l c o n d i t i o n s . ) But t h i s , a d e t e r m i n i s t might c l a i m , i s merely because Newton's mechanics do not cover these other c o n t i n g e n c i e s , the r e s u l t s perhaps of non-mechanical thermal, e l e c t r i c a l , or chemical f o r c e s . Given a l l the laws, and i n i t i a l c o n d i t i o n s , the outcome i s thus determined. But t h i s c l a i m , Anscombe argues, i s an 77 " i l l u s i o n " . I t s t r u t h depends on the assumption that there " i s always a law of composition of such a kind that the combined e f f e c t of a set of 78 f o r c e s i s determined i n every s i t u a t i o n . " The force of t h i s assumption i s a r e s u l t of the f o r t u i t o u s model provided by the s o l a r system. Thus, even given the f a m i l i a r d e t e r m i n i s t i c assumption of " a l l the laws" a c t i n g i n some domain, one cannot i n s u r e p r e d i c t a b i l i t y . Now i f the p o s s i b i l i t y of no n - n e c e s s i t a t i n g , i n d e t e r m i n i s t i c laws of nature i s a r e a l one, then can these laws s t i l l be described as "causal laws". And what, then, might we mean by "causal" here? Take the standard n o n - d e t e r m i n i s t i c example: the reading of a Geiger counter as a r e s u l t of a sample's r a d i o a c t i v e emission. Of t h i s example Anscombe remarks: 102 I t was random: i t "merely happened" that the r a d i o a c t i v e m a t e r i a l emitted p a r t i c l e s i n such a way as to a c t i v a t e the Geiger counter... . C e r t a i n l y the motion of the Geiger counter's needle i s caused; and the a c t u a l emis-s i o n i s caused too; i t occurs because there i s t h i s mass of r a d i o a c t i v e m a t e r i a l here... . But a l l the same the cau s a t i o n i t s e l f i s , one could say, mere hap. I t i s d i f f i c u l t to e x p l a i n t h i s idea any f u r t h e r . Thus we are l e f t w i t h the f o l l o w i n g problem: the i n d e t e r m i n i s t i c laws w i t h i n the theory which describes the behaviour of Geiger counters are s u r e l y " c a u s a l " laws — seemingly because the behaviour they describe i s "caused" — yet causation i t s e l f , when s t r i p p e d of i t s d e t e r m i n i s t i c assumptions, d e f i e s a n a l y s i s , i t i s "mere hap". But i f t h i s i s the case, then the a n a l y s i s of laws as "causal" must s u r e l y s u f f e r , since i t seems that we don't know what t h i s could mean. There are, however, other ph i l o s o p h e r s , v i z . , Mackie and Lewis, who c l a i m both an a n a l y s i s of c a u s a l i t y , and one which i s compatible with an i n d e t e r m i n i s t i c p h y s i c s . We have already seen how these analyses can be b o l s t e r e d a g a i n s t c e r t a i n o b j e c t i o n s by the adoption of Salmonian c o n s t r u c t s . Our l a s t task i n t h i s chapter, save summation, w i l l be to assess t h i s success a g a i n s t Anscombe's view that without the support of d e t e r m i n i s t i c assumptions causation can only be a p r i m i t i v e n o t i o n , "mere hap" . Before I t u r n to t h i s matter, l e t me emphasize the juncture at which we have now a r r i v e d by a b r i e f comparison between Anscombe's d e s c r i p t i o n of t h i s s i t u a t i o n and Salmon's. Anscombe's remarks are c h i e f l y n e g a t i v e . Her attempt i s to separate the concept of c a u s a l i t y from i t s a s s o c i a t i o n w i t h , or i t s a n a l y s i s i n terms of, n e c e s s i t y and determinism. Through h i s t o r i c a l c o n s i d e r a t i o n s she demonstrates how we have a r r i v e d at the unhappy s t a t e of viewing 20th century physics through 17th century g l a s s e s . Given t h i s viewpoint, i s i t any wonder we f i n d the p h i l o s o p h i c a l s t a t e of 103 physics a p p a l l i n g ? Salmon, on the other hand, represents a more p o s i t i v e a t t i t u d e . He asks, given the success of 20th century p h y s i c s , how are we to understand i t ? What concepts or analyses does i t force us to change or even j e t t i s o n ? Both agree that a progressive s h i f t i n our t h i n k i n g about causation i s r e q u i r e d . Anscombe's s h i f t p r o s c r i b e s the use of the concepts of n e c e s s i t y and determinism from appearing i n any a n a l y s i s of c a u s a t i o n . For Salmon, t h i s s h i f t e n t a i l s f i n d i n g a b a s i s f o r causation other than n e c e s s i t a t i o n or a f a i t h i n determinism. He p o s i t s other 'basic' o bjects (processes, i n t e r a c t i o n s ) which a l l e g e d l y solve the Humean problem of necessary connections without recourse to determinism ( v i a " p r o b a b i l i s t i c " c ausal p r o c e s s e s ) . The bottom l i n e , i t seems, i s that they both lean h e a v i l y on unanalyzed p r i m i t i v e s . P r i m i t i v e s , i n any system, are only j u s t i f i a b l e to the extent t h a t they make the e n t i r e system both v i a b l e and i n t e l l i g i b l e ( s i nce they can have no l o g i c a l l y p r i o r assessment.) "Process" c e r t a i n l y comes to us l e s s encumbered, by any metaphysical s u p e r s t r u c t u r e , than c a u s a t i o n . Whether t h i s f a c t makes i t any e a s i e r to understand i s a f u r t h e r q u e s t i o n . However, any a n a l y s i s of causation ( i f there i s one, pace Anscombe) w i l l have to address the arguments against n e c e s s i t a t i o n and . determinism r a i s e d by Anscombe and Salmon, i f i t i s to be amenable to developments i n 20th century s c i e n c e . Both Mackie and Lewis make the claim t h a t t h e i r analyses are so amenable, Mackie i n some d e t a i l , Lewis only i n p a s s i n g . We w i l l now attempt to assess such c l a i m s . 6. P r o b a b i l i s t i c C a u s a l i t y . I now hope to complete our examination of these contemporary t h e o r i e s of causation by d i s c u s s i n g each of t h e i r attempts at embracing the 104 s t a t i s t i c a l nature of the world as presented by modern p h y s i c s . We s h a l l consider Mackie f i r s t , then Lewis. The problems r a i s e d here by the p a r t i a l success and p a r t i a l f a i l u r e of these th e o r i e s w i l l set the stage f o r Chapter I I I , where Salmon's a n a l y s i s of p r o b a b i l i s t i c c a u s a l i t y w i l l be assessed and defended ag a i n s t recent o b j e c t i o n s . Mackie sets the question t h i s way: i f there are such things as 80 s t a t i s t i c a l laws, over what are such laws q u a n t i f i e d ? This question goes deep, and i f we are to understand i t f u l l y , we must f i r s t compare and c o n t r a s t some p u t a t i v e s t a t i s t i c a l laws. Suppose i t i s a law, i n a c e r t a i n p l a n t species S d i s p l a y i n g g e n e t i c a l l y determined c o n t r a s t i n g c h a r a c t e r i s t i c s A and a, where A i s dominant, that approximately 3/4 of the o f f s p r i n g of a s e l f - p o l l i n a t e d f i r s t generation p l a n t of pure parentage w i l l d i s p l a y A. Note that t h i s 'law' i s not the r e s u l t of q u a n t i f y i n g merely over i n d i v i d u a l second generation members of S, but rather i s the r e s u l t of q u a n t i f y i n g over c e r t a i n b a s i c  groups, a l l second generation p l a n t s of species S produced i n the p r e s c r i b e d manner. However, t h i s law can be considered only a derived law — i t s r e s u l t s f o l l o w from an i n t e r a c t i o n w i t h i n the basic group, an i n t e r a c t i o n which may (or may not) be known to be governed by u n i v e r s a l d e t e r m i n i s t i c laws at another l e v e l . Or consider a law that s t a t e s that the chance of r o l l i n g a s i x on any p a r t i c u l a r toss of a f a i r d i e i s 1/6. Here the domain, or basic group, i s the r o l l s of a die which are ' p h y s i c a l l y ' randomized by the s c a t t e r i n g of i t s i n i t i a l p o s i t i o n s over a f a i r l y wide range of p o s s i b i l i t i e s . A c t u a l l y , i t i s from w i t h i n t h i s randomizing procedure that t h i s s t a t i s t i c a l law d e r i v e s — i t , too, can be seen as the r e s u l t of a conjunction of p h y s i c a l 105 symmetry and, i n t h i s case, known but p r a g m a t i c a l l y u n a v a i l a b l e u n i v e r s a l d e t e r m i n i s t i c laws. Nei t h e r of these two p u t a t i v e s t a t i s t i c a l laws w i l l serve as an 81 example of a genuine s t a t i s t i c a l law. For d i f f e r e n t reasons they both obscure the same f a c t : that a f u r t h e r s p e c i f i c a t i o n of the antecedent ( i . e . , a f u r t h e r q u a l i f i c a t i o n of the basic group involved) w i l l reduce these 82 p u t a t i v e s t a t i s t i c a l laws to genuine (or a t l e a s t mixed ) d e t e r m i n i s t i c laws. In a genuine s t a t i s t i c a l law no f u r t h e r s p e c i f i c a t i o n of the antecedent w i l l be r e l e v a n t . But why i s t h i s a problem? S p e c i f i c a t i o n , l i k e e x p l a n a t i o n , must come to an end somewhere. Where i s the d i f f i c u l t y ? The d i f f i c u l t y i s t h i s : a s t a t i s t i c a l law not o n l y d e s c r i b e s , i n i t s antecedent, the domain of i t s a p p l i c a t i o n , i t a l s o assigns a p r o b a b i l i t y to the occurrence of an a t t r i b u t e i n that domain. I f that domain i s made up of b a s i c groups which r e f l e c t that p r o b a b i l i t y due to t h e i r u n s p e c i f i e d (but u l t i m a t e l y s p e c i f i a b l e ) i n t e r n a l i n t e r a c t i o n or s t r u c t u r e , then t h i s assignment of p r o b a b i l i t y i s unproblematic. I t derives from w i t h i n these b a s i c groups and i t has the added f u n c t i o n of serving as an explanatory guide i n approaching deeper l e v e l laws which describe t h i s i n t e r n a l s t r u c t u r e . However, i n a genuine s t a t i s t i c a l law, the b a s i c group becomes somewhat i r r e l e v a n t : f u r t h e r s p e c i f i c a t i o n of the i n t e r n a l s t r u c t u r e of, or i n t e r a c t i o n s w i t h i n , the basic group i s p r o h i b i t e d by our t h e o r i e s . Without t h i s i n t e r n a l , or deep, s t r u c t u r e to basic groups the p r o b a b i l i t i e s i n v o l v e d can only be assigned to the i n d i v i d u a l members of the c l a s s of events described i n the antecedent. The question of how t h i s i s p o s s i b l e i s the question of the s i n g l e case — and the answer to t h i s question w i l l i n turn r e f l e c t on j u s t what we take a s t a t i s t i c a l law to be. 106 This question might be best approached o b l i q u e l y . A n a t u r a l law describes a u n i v e r s a l l y q u a n t i f i a b l e p a t t e r n — as Mackie puts i t , they are 83 "the immanent patterns of being and becoming." And i f they are d e t e r m i n i s t i c laws, they place each and every member of t h e i r domain i n t o the p a t t e r n d e s c r i b e d . Thus we can say of any i n d i v i d u a l member of the domain ( i f there are any) that i t i n s t a n t i a t e s t h i s p a t t e r n . S t a t i s t i c a l laws, however, d e s c r i b e a p a t t e r n t h a t i s a c o l l e c t i v e r e s u l t of the i n d i v i d u a l s t h a t f a l l under i t , and as such t h i s p a t t e r n would seem i n a p p l i c a b l e to any p a r t i c u l a r member of that domain. In what sense, then, can we say that a property or p a t t e r n of a domain which i s thus c o l l e c t i v e l y generated can be assigned to a s i n g l e case? In other words, a n a t u r a l law i s a t once c o l l e c t i v e — i t speaks of a l l members of a s p e c i f i e d group — and d i s t r i b u t i v e — i t assigns a f e a t u r e , property, or place i n a c h a r a c t e r i s t i c p a t t e r n , to each member of that group. I f t h i s place i n a pat t e r n can only be s t a t i s t i c a l l y assigned, how, then, can a s t a t i s t i c a l law be d i s t r i b u t i v e ? Mackie's answer i s that "a s t a t i s t i c a l law assigns the corresponding p r o b a b i l i t y or chance to each i n d i v i d u a l t h a t f a l l s under i t , t h a t i t has the form 'Every A has an x per cent chance of becoming B (or of 84 producing a B)'." Mackie then adopts the l i m i t i n g frequency i n t e r p r e t a t i o n of p r o b a b i l i t y and suggests that t h i s assignment of p r o b a b i l i t i e s to i n d i v i d u a l s i s j u s t the f a c t that "long runs of such 85 i n s t a n c e s . . . u s u a l l y e x h i b i t frequencies close to the l i m i t i n g one." The frequency i n t e r p r e a t i o n of p r o b a b i l i t y i s a t t r a c t i v e here because of i t s obvious c o m p a t i b i l i t y with quantum mechanical examples. The p r o b a b i l i t y matrix assigned to i n d i v i d u a l s i n QM can be seen to be j u s t such a f u n c t i o n of the r e l a t i v e frequency of long runs of i d e n t i c a l l y prepared 107 i n d i v i d u a l s . Mackie's view attempts to overcome the d i f f i c u l t y most f r e q u e n t i s t s had i n speaking of the s i n g l e case** 6 — here the meaning of an assignment of p r o b a b i l i t y to a s i n g l e case i s exhausted by reference to long runs of such cases. And i f meanings are exhausted then one might think no more need be s a i d . Yet even Mackie admits that when s t a t i s t i c a l laws are thus " c l a r i f i e d and d i s t i n g u i s h e d , something rather mysterious i s l e f t . " 8 7 What remains mysterious f o r Mackie i s that no amount of refinement to h i s admittedly crude f o r m u l a t i o n of a s t a t i s t i c a l law w i l l a l low us to get "behind the brute f a c t of a c t u a l approaches to the l i m i t i n g frequency." For some t h e o r i s t s , however, there i s a qui t e n a t u r a l means of reducing t h i s b r u t i s h n e s s : When we say that the p r o b a b i l i t y of a baby's being male i s 0.52, we think i t proper to look f o r an explanation of t h i s a s s e r t i o n i n the physiology of repr o d u c t i o n . If t h i s demand f o r explanation i s to be met by a look a t physiolo g y (and i f the explanation i s to be l e s s mysterious than that which i t i s to exp l a i n ) then what we discover there needs be more than " p r o p e n s i t i e s " or d i s p o s i t i o n s . One i s tempted to say that i f t h i s explanatory debt i s to made good, i t must i s s u e bona f i d e c a u s a l currency, with the f i n a l r e s u l t being the d e r i v a t i o n of the s t a t i s t i c a l f a c t i n question from the j o i n t e f f e c t of d e t e r m i n i s t i c causal laws and random c o l l o c a t i o n s of i n i t i a l c o n d i t i o n s . I t i s only when there are _no causes to be found that we might s i t s t i l l f or an i n d e t e r m i n i s t i c explanation v i a s t a t i s t i c a l laws. I f , however, a coherent account of p r o b a b i l i s t i c c ausation could be d e l i v e r e d , then the o b j e c t i v e i n t e r p r e t a t i o n of p r o b a b i l i t y assignments may w e l l f i n d a foundation, j u s t as p h y s i c a l n e c e s s i t y d i d with s u f f i c i e n t 108 causation, and without recourse to deterministic, deeper level correlations. For the frequentist this account would go a step towards reducing the mystery l e f t in the wake of his analysis; for the objectivist i t would provide the 89 explanatory ground that Kneale has described as needed above. The point here is that in an indeterministic universe the concept of a probabilistic cause (1) reduces what is mysterious for the frequentists 1 position, and (2) helps make coherent the objectivists' position. Salmon has remarked that s t a t i s t i c a l causation is neutral among interpretations of probability. Yet i t must be remarked that "neutrality" does not eliminate or reduce the mystery — i t merely postpones i t until we can provide the called for account of s t a t i s t i c a l or probabilistic causation. We have begun this task in the previous chapter and w i l l expand this account through our response to objections in the following chapter. Our second protagonist is David Lewis. Although Lewis claims that the compatibility of his account with indeterminism to be one of i t s important advantages, his remarks on this subject are so brief they may be reproduced here in f u l l : I shall be content, for now, i f I can give an analysis of causation that works properly under determinism. By determinism I do not mean any thesis of universal causation, or universal predictability in principle, but rather this: the prevailing laws of nature are such there do not exist any two possible worlds which are exactly alike up to some time, which differ thereafter, and in which these laws are never violated. Perhaps by ignoring indeterminism I squander the most striking advantage of a counterfactual analysis over a regularity analysis: that i t allows undetermined events to be caused. I fear, however, that my present analysis cannot yet cope with a l l varieties of causation under indeterminism. The needed repair would take us too far into 90 disputed questions about the foundations of probability. 109 The f i r s t t h i n g to n o t i c e here i s t h a t Lewis' d e f i n i t i o n of determinism i s i n complete accord with Anscombe's d e s c r i p t i o n of the d e t e r m i n i s t i c assumptions 91 t a c i t i n many accounts of ' s u f f i c i e n t ' c a u s a t i o n . Lewis at l e a s t claims h i s a n a l y s i s to be free of any such assumptions and, th e r e f o r e , to a l l o w a caus a l d e s c r i p t i o n of undetermined events. Let us add some d e t a i l to t h i s c l a i m and see whether i t w i l l wash. The reader w i l l r e c a l l that i n Lewis' a n a l y s i s causal dependence between events c and e i s i m p l i e d by the corresponding c o u n t e r f a c t u a l dependence of the p r o p o s i t i o n 0(e) on the p r o p o s i t i o n 0 ( c ) , the p r o p o s i t i o n s t h a t e and c occur, r e s p e c t i v e l y . And c o u n t e r f a c t u a l dependence r e s u l t s i f and only i f some 0(e)-world where 0(c) holds i s c l o s e r (to the a c t u a l world) than any 0(e)-world where 0(c) does not h o l d . Causal dependence i n a phrase: 92 whether e occurs or not depends on whether c occurs or not. Now there i s at l e a s t prima f a c i e c o m p a t i b i l i t y between causes as necessary c o n d i t i o n s and an i n d e t e r m i n i s t i c world: c o u n t e r f a c t u a l dependence, as described above, r e s t s on the assumption that the e f f e c t occurs ( i . e . , the existence of some 0(e)-world) and t h e r e f o r e , even i f t h i s event occurs only s t a t i s t i c a l l y , we are only concerned, i n t h i s a n a l y s i s , w i t h the p o s s i b l e worlds i n which i t does occur. This seems to be what i s meant by necessary c o n d i t i o n analyses not d i s a l l o w i n g i n d e t e r m i n i s t i c events to be caused, but only when, and i f , they occur. What i f they do not occur? That i s , i f the occurrence of the e f f e c t event i s t r u l y s t a t i s t i c a l , then i t must be the case that even i f a l l the necessary c o n d i t i o n s f o r i t s occurrence be present, i t yet may not occur. As Lewis might put i t : i f c and e are c a u s a l l y , yet s t a t i s t i c a l l y , r e l a t e d , i n a world where 0(e) does not hold, a not-0(c)-world i s n e c e s s a r i l y c l o s e r to a c t u a l i t y than an 0(c) - w o r l d . I 110 Let's t r y t h i s on. Suppose 0(e) i s the p r o p o s i t i o n that r a d i a t i o n i s emitted — o r , i n Lewis' terms, a world where t h i s i s the case — and 0(c) i s the p r o p o s i t i o n d e s c r i b i n g the presence of a radium atom. For 0(e) to be c o u n t e r f a c t u a l l y dependent on 0(c), some not-0(c)-world where not-O(e) holds must be c l o s e r to a c t u a l i t y than any not-O(c)-world where 0(e) does h o l d . For the r a d i a t i o n case t h i s would appear to be so: i n a l l those p o s s i b l e worlds that c o n t a i n no radium, there are none that contain r a d i a t i o n and no radium (and that are c l o s e r to us than those that contain n e i t h e r . ) Now consider a l l those p o s s i b l e worlds where 0(c) holds: c o u n t e r f a c t u a l dependence then demands that some 0(c)-world where 0(e) holds be c l o s e r (to the a c t u a l world) than any 0(c)-world where not-O(e) h o l d s . That i s , i n a l l those worlds where radium i s present, those where there i s a l s o r a d i a t i o n are l e s s d i s t a n t than those which c o n t a i n radium and no r a d i a t i o n . In the r a d i a t i o n case, however, t h i s i s not g e n e r a l l y t r u e . What has gone wrong-here? The p o i n t of Lewis' a n a l y s i s , indeed of any necessary c o n d i t i o n a n a l y s i s , i s t h a t causes are to be i n f e r r e d from t h e i r e f f e c t s . I f an e f f e c t does not occur, can we then i n f e r the non-existence of i t s cause? No, not i f the l o g i c a l r e l a t i o n between effect-statements and cause-statements i s one of i m p l i c a t i o n , f o r we would simply be f a l l a c i o u s l y denying the antecedent. And i n the s t a t i s t i c a l case, where a cause does not produce i t s e f f e c t each and every time, t h i s i s j u s t as i t should be. But Lewis' c o n s t r u c t i o n i s more complex: i f i t hadn't been f o r the cause c, then we wouldn't have had the e f f e c t e. Why does t h i s c o u n t e r f a c t u a l a n a l y s i s s u f f e r the defect of the preceeding paragraph? Because although causal dependence i s a f u n c t i o n of c o u n t e r f a c t u a l depenedence, and c o u n t e r f a c t u a l dependence runs, as required 1 1 1 i n s t a t i s t i c a l cases, from e f f e c t to cause, c o u n t e r f a c t u a l i m p l i c a t i o n (between p r o p o s i t i o n s ) , on the other hand, runs the reverse course from 0(c) to 0(e). That i s , e depends c a u s a l l y on c j u s t i n case the f o l l o w i n g c o u n t e r f a c t u a l s are both tr u e : ( 1 ) 0 ( c ) Q +0(e) (2) not-O(c) Q -*not-0(e) As above, suppose that c and e do not a c t u a l l y occur, thus (2) i s t r u e . Then c i s a cause of e i f and only i f ( 1 ) i s t r u e . What are the t r u t h c o n d i t i o n s f o r ( 1 ) ? Simply that i t be " l e s s of a departure from a c t u a l i t y " to make 0(c) true along w i t h 0(e), then to make 0(c) true without 0(e): a world w i t h radium and no r a d i a t i o n must be more d i s t a n t than a world with both. The t r u t h c o n d i t i o n s f o r the c o u n t e r f a c t u a l operator on p r o p o s i t i o n s are simply too c l o s e to the t r u t h c o n d i t i o n s f o r the m a t e r i a l c o n d i t i o n a l . In sum, then, c o u n t e r f a c t u a l dependence, as captured by the c o u n t e r f a c t u a l i m p l i c a t i o n operator " ->-" cannot accommodate s t a t i s t i c a l c a u s a t i o n . I t i s not c e r t a i n whether some re p a i r e d v e r s i o n of t h i s a n a l y s i s w i l l do, even though some necessary c o n d i t i o n a n a l y s i s seemed i n i t i a l l y more 93 s u i t e d to t h i s task. In the next chapter we s h a l l defend Salmon's a n a l y s i s , t a i l o r e d to f i t s t a t i s t i c a l c ausation, against some recent o b j e c t i o n s . Salmon, as with Mackie, adopts a f r e q u e n t i s t . p o s i t i o n towards p r o b a b i l i t y , yet u n l i k e Mackie's, h i s system leaves no 'mysterious' r e s i d u e . Salmon b e l i e v e s , as Lewis does, that undetermined events can be caused, yet, u n l i k e Lewis does not t i e h i s a n a l y s i s to the correspondence of p r o p o s i t i o n s . We s h a l l now turn to a defence of t h i s view. 11 2 Notes: Chapter I I 1. E.g., Mackie (1965), r e p r i n t e d i n Sosa, ed. (1975), pp. 15-38; see a l s o Mackie (1974), pp. 59-87; Scri v e n (1975) pp. 3-16; Taylor (1966), r e p r i n t e d i n Sosa, ed. (1975), pp. 39-43. 2. M a r t i n (1972) . 3. Lewis (1973), r e p r i n t e d i n Sosa, ed. (1975), pp. 180-191; S e l l a r s (1958). 4. Thus Brand and Swain (1970), p. 223 are i n c o r r e c t i n saying that an a n a l y s i s " i n terms of necessary and s u f f i c i e n t c o n d i t i o n s " i s an a l t e r n a t i v e to a r e g u l a r i t y theory. 5. Martin (1972). 6. Lewis (1973) p. 557. 7. In Sosa, ed. (1975), p. 16. 8. Following Marc-Wogau (1962). 9. Cf. Mackie (1965) (In Sosa (1975), p. 25): "...our formal analyses do not insure that a p a r t i c u l a r r e s u l t w i l l have a unique cause, nor does our o r d i n a r y causal t a l k r e q u i r e t h i s . " 10. In Sosa, ed. (1975), p. 19. 11. Marc-Wogau's term, (1962), pp. 226-227. 12. In Sosa, ed. (1975), p. 23. 13. Chapter I , p. 18. 14. Or r u l e out genuine s t a t i s t i c a l , yet c a u s a l , s i t u a t i o n s . See Hesslow (1981), Katz (1983). 15. Below, Chapter I I , Section 6. 16. In Sosa, ed. (1975), p. 27. 17. Marc-Wogau (1962), p. 227, n. 8. 18. A general a l t e r n a t i v e to s u f f i c i e n c y analyses of "A i s the cause of B" i s o f f e r e d by Raymond Mar t i n (1972) where he argues f o r the d i s j u n c t i o n : E i t h e r A i s s u f f i c i e n t c e t e r i s paribus f o r B, or A i s c o n t i n g e n t l y necessary f o r B. 19. Mackie (1974), pp. 196-218. 113 20. Since a c o u n t e r f a c t u a l i s true only i n an attenuated sense (because i t s antecedent i s f a l s e or u n f u l f i l l e d ) we w i l l not say that a law of n a t u r a l e n t a i l s , but rat h e r supports i t s c o u n t e r f a c t u a l form. The nature of t h i s support w i l l be made c l e a r below. 21. We should note here that the l i m i t e d l o c a l e of the former u n i v e r s a l c l a i m w i l l not, i n general, d i s t i n g u i s h i t from the l a t t e r . We may avoid i t s l i m i t a t i o n s by a s u i t a b l e choice of p r e d i c a t e s ; on the other hand we might j u s t p o i n t out that a l l laws are l i m i t e d to some degree. 22. Mackie (1974), p. 178. 23. Here Mackie o f f e r s what I take to be a bad argument against t h i s Humean o p t i o n . He co n s t r u c t s a s i t u a t i o n where an a c c i d e n t a l c o r r e l a t i o n e x i s t s u n i v e r s a l l y , yet access to p r i o r causal laws from which i t may be deduced i s cut o f f by an underlying indeterminism. The Humean w i l l then have to accept t h i s c o r r e l a t i o n as a new, fundamental, law of nature. This argument does not get at the heart of the matter (the p o s s i b l e f a l s i t y of determinism) and only serves to make t h i s option look more r i d i c u l o u s f o r the Humean. See Mackie (1974), p. 198-199. 24. L i k e w i s e , consider the m a t e r i a l c o n d i t i o n a l " I f t h i s c o in i s i n my 1 pocket, then i t i s shiny" b e l i e v e d s o l e l y on the grounds that i t s antecedent i s u n f u l f i l l e d , i . e . , because there are no coins i n my pocket. I t could h a r d l y be used i n conjunction with the a s s e r t i o n "This c o i n i s i n my pocket" to conclude "This c o i n i s shiny" f o r much the same reason. 25. This argument i s presaged i n Chisholm (1955), p. 149, who c r e d i t s i t to Strawson. Chisholm d i s t i n g u i s h e s nomic and non-nomic statements by v i r t u e of t h e i r epistemic status — on what evidence they are b e l i e v e d . (This view i s a l s o found i n Chisholm (1946), r e p r i n t e d i n F e i g l and S e l l a r s (1949), p. 495.) 26. Mackie (1962), p. 66. 27. Mackie (1974), p. 204. 28. Op. c i t . , p. 205. 29. This sketch of M i l l i s perhaps too b r i e f — h i s account i s more subtle than i s needed here. For example, c e r t a i n u n i f o r m i t i e s of coexistence, those r e s u l t i n g from common causes, were considered derived causal laws. Laws of a r i t h m e t i c too were u n i f o r m i t i e s of coexistence f o r M i l l — and a r i t h m e t i c an e m p i r i c a l d i s c i p l i n e , u l t i m a t e l y derived from deeper l e v e l p s y c h o l o g i c a l laws. 30. Popper (1959), quoted i n Mackie (1974), p. 209. 31. Mackie (1974), p. 210. 32. Op. c i t . , p. 211. 114 33. Mackie (1974), p. 211. R e c a l l that our i n i t i a l task was to separate c a u s a l from non-causal c o r r e l a t i o n s , and t h a t t h i s d i s t i n c t i o n i s somewhere among the f o l l o w i n g : laws of succession/laws of coexistence ( M i l l ) ; s t r u c t u r a l p r i n c i p l e s / i n i t i a l c o n d i t i o n s (Popper); laws of w o r k i n g / c o l l o c a t i o n s (Mackie). But i t w i l l not do to s o r t out the l a t t e r , v i a r e l e v a n t c o n d i t i o n s s i m p l i c i t e r , i n order to e x p l i c a t e the former. For i n what way are they relevant? And to what are they r e l e v a n t ? I suggest that 'relevant' here presupposes a concept of a caus a l law, and causal connections, which we are supposed to be e x p l i c a t i n g . Furthermore, as Mackie notes, t h i s d i s t i n c t i o n works only i f we " f u l l y understand" how a system works, as we do i n the Newtonian example. Besides relevancy d i f f i c u l t i e s , other problems with t h i s proposal become acute when the system i n question i s an i n d e t e r m i n i s t i c one. For example, Mackie remarks that i t i s reasonable to suppose that there are pure laws of working underlying any mixed law, even i f we don't know what they are, and thus don't know what are the r e l e v a n t features whose e x p l i c i t mention v i a the method i n the t e x t would p u r i f y these mixed laws. T h i s , I b e l i e v e , i s the same as suggesting that i n the i n d e t e r m i n i s t i c case such as death by r a d i a t i o n induced cancer, i n i t i a l c o n d i t i o n s can be s u c c e s s f u l l y screened o f f , r e v e a l i n g some un d e r l y i n g , p u r e l y d e t e r m i n i s t i c , law of working. 34. Kneale (1949) . 35. Kneale (1949), p. 71, quoted i n Mackie (1974), p. 214. 36. Mackie (1974) makes s e v e r a l cogent Humean c r i t i c i s m s here, p. 216. 37. Mackie c r e d i t s d'Alembert with a s i m i l a r view, and ably defends i t from c r i t i c i s m due to Nagel. A n a l y s i s of t h i s debate would take us too f a r a f i e l d . D'Alembert (1921), p. 3-6, Nagel (1961), pp. 175-178. 38. Mackie (1974), p. 221. 39. Mackie (1974), p. 224. This remark ends "...which i s i t s e l f a form of p a r t i a l p e r s i s t a n c e , " (my emphasis) engendering j u s t the s o r t of m a t e r i a l / f o r m a l confusion I am r e f e r r i n g t o . What i s meant by " p a r t i a l p e r s i s t a n c e " i s never made c l e a r . 40. Whether Mackie i s s t i l l to be considered a good Humean r e g u l a r i t y t h e o r i s t w i l l be taken up at the end of t h i s s e c t i o n . 41. Kim (1971). See a l s o Kim (1973a). 42. Kim (1971), p. 59. P r i o r to t h i s passage Kim d i s s e c t s Mackie's a n a l y s i s , c o n v i n c i n g l y showing how and where confusion r e s u l t s from the f a i l u r e to n o t i c e t h i s o n t o l o g i c a l d i s t i n c t i o n . I have omitted a d e t a i l e d d i s c u s s i o n of t h i s c r i t i q u e here for a d i s c u s s i o n of the general p i c t u r e i t presents w i l l take us too f a r a f i e l d . S u f f i c e to say that Kim's remarks are w e l l taken, however, i t i s only the s o l u t i o n to Mackie's o n t i c confusion which i s of i n t e r e s t here. ( 115 43. Kim (1971), i n Sosa, ed. (1975), p. 56. 44. A paraphrase gleaned by Kim ( i n Sosa, ed. (1975), p. 57) from Mackie's d e s c r i p t i o n of h i s example of the short c i r c u i t and the f i r e , Mackie (1965) i n Sosa, ed. (1975), p. 31. 45. Kim (1971) i n Sosa, ed. (1975), p. 57. 46. Op. c i t . , p. 59. 47. Here 'x' may be an obje c t or a region of space-time. Kim opts f o r the former, I would advocate the l a t t e r , f o r i t s e x p l i c i t l o c a t i o n of the event — but t h i s w i l l make no d i f f e r e n c e i n what f o l l o w s . 48. Kim (1971) i n Sosa, ed. (1975), p. 60. 49. Kim's f o r m u l a t i o n , op. c i t . , p. 61. 50. Mackie (1974), Chapter 3. 51. Kim (1971) i n Sosa, ed. (1975), p. 60. 52. Here I am t r a d i n g on the vagueness of a process/event d i s t i n c t i o n . Kim's 'events' might be best taken as Salmon's ' i n t e r a c t i o n s ' . And although i n t e r a c t i o n s are c l e a r l y d i s t i n c t from the processes which form them, i t seems n a t u r a l to take processes as somehow ' i n c l u d i n g ' them. 53. In Salmon (1970), (1978), and i n a seminar given a t Simon Fraser U n i v e r s i t y where he expressed t h i s idea i n terms of a continuum which i s mathematically "dense". 54. Salmon a l s o answers Hume's query v i a processes, see Chapter I , Section 3a. This c a u s a l s t r u c t u r e has been r e c e n t l y examined by Levy (1982) and Humphreys (1980). The problems they r a i s e w i l l be discussed i n Chapter I I I . 55. The source f o r much of what f o l l o w s i s Lewis (1973), r e p r i n t e d i n Sosa, ed. (1975), pp. 180-189. 56. Oddly enough, Mackie n o t i c e s t h i s r e l a t i o n s h i p (of o v e r a l l s i m i l a r i t y ) when he argues f o r the d i r e c t i o n of causation with respect to a 'hammer blow — f l a t t e n e d chestnut' sequence. He points out that i t i s le s s " n a t u r a l " to a s s e r t " I f the chestnut had not been f l a t t e n e d , the hammer blow would not have happened" than to a s s e r t the converse c o u n t e r f a c t u a l " I f the hammer blow had not occurred, the chestnut would not have been f l a t t e n e d " , but denies t h a t t h i s c o n t r a s t i n "naturalness" can provide an a n a l y s i s of causal p r i o r i t y . Perhaps i f he had Lewis' apparatus of p o s s i b l e worlds... . (His own attempt i s drawn i n terms of ' e f f e c t i v e n e s s ' or c o n t r o l — we can manipulate a cause to produce an e f f e c t , but not vi c e versa, see (1974), p. 168.) 116 57. Lewis (1973) i n Sosa, ed. (1975), p. 185. 58. Loc. c i t . 59. In Sosa, ed. (1975), p. 187. Co u n t e r f a c t u a l dependence r e l a t e s p r o p o s i t i o n s w h ile causal dependence r e l a t e s events. They are r e l a t e d by the p r o p o s i t i o n '0(a)', the p r o p o s i t i o n that a occurs. 60. Kim (1973b), r e p r i n t e d i n Sosa, ed. (1975), pp. 192-194. 61. Lewis (1973) i n Sosa, ed. (1975), p. 189. 62. Kim (1973b) i n Sosa, ed. (1975), p. 193. 63. Lewis (1973) i n Sosa, ed. (1975), p. 185. 64. Kim (1973a). 65. This p o s i t i o n i s , of course, incompatible with Kim's theory of events where event i d e n t i f y i s defined as [x,P,t] = [ y , R , f ] i f f x=y, P=R, t=t'. I am not prepared to argue for any one theory of events here; s u f f i c e i t to say that there remains these kinds of problems f o r any theory, and t h e i r r e s o l u t i o n does not seem to a f f e c t d i r e c t l y our r e s u l t s above. 66. We may even propose a r u l e of " c o u n t e r f a c t u a l screening o f f " : c c o u n t e r f a c t u a l l y screens o f f a from b i f f i f c had not occurred then b would not c o u n t e r f a c t u a l l y depend on a. 67. Lewis (1973) i n Sosa, ed. (1975), p. 183. 68. Anscombe (1971) r e p r i n t e d i n Sosa, ed. (1975), p. 63. This p r i n c i p l e i s r e a d i l y comparable to the p r i n c i p l e of explanation suggested i n Chapter I , p. 39. 69. Op. c i t . , p. 66. 70. Op. c i t . , p. 66. 71. S t r i c t l y speaking, the u n i v e r s a l i t y of n a t u r a l laws expresses only one aspect of the r o l e of n e c e s s i t y w i t h i n the context of c a u s a l i t y . Mackie (1974, p. 192ff) catalogues at l e a s t 7 d i s t i n c t "jobs" f o r the concept of n e c e s s i t y . Anscombe's remarks here seem to concern only #5 i n that catalogue: n a t u r a l n e c e s s i t y , the marking of nomic from a c c i d e n t a l r e g u l a r i t i e s . 72. Anscombe (1971) i n Sosa, ed., (1975), p. 67. 73. Op. c i t . , p. 67. 117 74. Op. c i t . , p. 73. 75. Loc. c i t . 76. Op. c i t . , p. 81 . 77. Op. c i t . , p. 75. 78. Op. c i t . , p. 76. There are two other " d e t e r m i n i s t i c " assumptions Anscombe d e s c r i b e s , but I b e l i e v e i t i s only t h i s l a s t which does the work she i n t e n d s . The other two are that i n "many c r o s s i n g contingencies whatever happens next must be determined: o r . . . t h a t the generation of forces (by human experimental procedures, among other things) i s always determined i n advance of the generating procedure." These assumptions, I f e e l , represent merely pragmatic d i f f i c u l t i e s . In c o n t r a s t , the l a s t assumption, quoted i n the t e x t above, makes reference to the kind of laws which might or might not be discovered. 79. Op. c i t . , p. 78. 80. Mackie (1974), p. 238. 81. The f i r s t because of u n s p e c i f i e d higher l e v e l i n t e r a c t i o n s which occur and produce the r e l e v a n t p r o b a b i l i t i e s ; the second because the p h y s i c a l set-up i t s e l f generates them ( i n an unknown f a s h i o n ) . 82. See Mackie (1974), Chapter 8. 83. Mackie (1974), p. 232, quoting Bunge (1963), p. 249. 84. Mackie (1974), p. 239. 85. Op. c i t . , p. 241. 86. As von Mises (1939), p. 15, puts i t : "We have nothing to say about the chance of l i f e and death of an i n d i v i d u a l , even i f we know h i s c o n d i t i o n s of l i f e and hea l t h i n d e t a i l . The phrase ' p r o b a b i l i t y of death', when i t r e f e r s to a s i n g l e person, has no meaning at a l l f o r us." 87. Mackie (1974), p. 246. 88. Kneale (1949), p. 164. 118 89. Such an account would a l s o serve to 'dis-equivocate' the p r o p e n s i t y explanatory schema suggested by Mackie as a p o s s i b l e (but untenable) a l t e r n a t i v e to h i s f r e q u e n t i s t approach. Mackie supposes we might i d e n t i f y the assignment of p r o b a b i l i t y not with a 'propensity' or d i s p o s i t i o n , but rather with the "ground of that d i s p o s i t i o n . " (1974, p. 241) But i n order to f i g u r e i n a law of working, that propensity must be i n t e r p r e t e d as a d i s p o s i t i o n , not the ground of a d i s p o s i t i o n . And i f " d i s p o s i t i o n " i s analyzed v i a laws, then t h i s e f f o r t , as an a n a l y s i s of s t a t i s t i c a l laws, becomes c i r c u l a r . For example, suppose i t i s a s t a t i s t i c a l law that radium atoms e x h i b i t a c e r t a i n decay r a t e . This may be s t a t e d as ' A l l radium atoms have a c e r t a i n s t r u c t u r e such th a t x per cent of them decay ( a f t e r some time t ) . ' This ' c e r t a i n s t r u c t u r e ' , c a l l i t R, i s the ground of the d i s p o s i t i o n . That x per cent of them decay i s the d i s p o s i t i o n or propensity f i g u r e d i n the law, the same d i s p o s i t i o n f i g u r i n g e q u i v o c a l l y i n R, v i a our understanding of the ground of the d i s p o s i t i o n and of what a law of working must be. D i s a l l o w i n g 'propensity' i n R forces us to abandon an explanatory concept — instanced here by the s t r u c t u r e assigned to the antecedent — we must s u b s t i t u t e f o r the propensity i n R an unknown "that which would account f o r . " Our suggestion i n the t e x t i s to understand the ground of a d i s p o s i t i o n by way of a p r o b a b i l i s t i c cause — which would then make such a ground unproblematic i n an a n a l y s i s of a s t a t i s t i c a l law of working. 90. Lewis (1973) i n Sosa, ed. (1975), p. 183. 91. See above, p. 4 5 f f . 92. Lewis (1973) i n Sosa, ed. (1975), p. 187. 93. Anscombe argues that no a n a l y s i s w i l l do t h i s j o b . And she may be r i g h t i n at l e a s t the f o l l o w i n g way: no a n a l y s i s that depends on the l o g i c a l correspondence of p r o p o s i t i o n s which describe cause and e f f e c t w i l l do. This i s not because there are no unique d e s c r i p t i o n s of causes and/or e f f e c t s (See Lewis (1973) i n Sosa, ed. (1975), p, 186, f n . 9) but rather because (1) any l o g i c a l correspondence w i l l depend on some u n i v e r s a l i z a b l e ' r u l e of t r u t h ' which defines the p r o p o s i t i o n a l operator i n v o l v e d , and any such u n i v e r s a l i z a b i l i t y must remain i n h o s p i t a b l e to s t a t i s t i c a l r e l a t i o n s h i p s . (2) A p r o p o s i t i o n a l s t r u c t u r e to events demands that they (the events) be independent, as the p r o p o s i t i o n s a r e . I f Salmon i s r i g h t , and as the f a i l u r e of most r e g u l a r i t y t h e o r i e s of causation r e f l e c t s , these events may not be independent. 119 CHAPTER I I I PRODUCTION AND PROPAGATION "The t h i n k i n g man e r r s p a r t i c u l a r l y when he asks f o r cause and e f f e c t ; both together are the i n d i v i s -i b l e phenomena." ( i n Von Mises 1 P o s i t i v i s m , Chapter IV) 1. Doing I t the Hard Way (a) P o s i t i v e Relevance. The p r o b a b i l i s t i c conception of c a u s a l i t y , as e x p l i c a t e d i n the preceeding two chapters, faces a t l e a s t two r e l a t e d d i f f i c u l t i e s whose common o r i g i n l i e s i n the 'reduced' relevance of cause f o r e f f e c t , 'reduced' i n the sense that the p r o b a b i l i t y of the e f f e c t given the cause might be less than one. The f i r s t d i f f i c u l t y concerns cases of improbable c a u s a t i o n . The second d i f f i c u l t y i s based on the i n t u i t i o n that i n a causal chain of three or more events, any element of that chain which i s n e g a t i v e l y r e l e v a n t to l a t e r events w i l l "cut" the causal chain a t that p o i n t . That i s , the e a r l i e r event can no longer be considered a cause of the l a t e r event. This i n t u i t i o n w i l l be discussed i n p a r t (b) of t h i s s e c t i o n . Here we s h a l l consider i n t u i t i v e l y i n t a c t causal chains with n e g a t i v e l y r e l e v a n t l i n k s . C e n t r a l to the s t a t i s t i c a l a n a l y s i s of causation i s the i n t u i t i o n t h a t a cause i s an event which makes a_ d i f f e r e n c e i n the production of some e f f e c t - e v e n t . I f an event serves to lessen the p r o b a b i l i t y of some e f f e c t , we are normally w i l l i n g to r e f e r to that cause-event as a negative cause, or a p r e v e n t a t i v e . I t i s something that without which the e f f e c t would be more l i k e l y to occur. I t i s only with an extended notion of cause, extended to 120 i n c l u d e negative causes, that we are w i l l i n g to speak here of causation a t a l l . C e r t a i n l y t h i s negative cause makes a d i f f e r e n c e , but i n preventing, and not producing, i t s e f f e c t . A simple example w i l l s u f f i c e : t a k i n g q uinine lowers the p r o b a b i l i t y of a severe a t t a c k of malaria (perhaps to near z e r o ) . I f one, u n l u c k i l y , s t i l l s u f f e r s an acute attack of malaria a f t e r t a k i n g q u i n i n e , no one would normally c i t e the taking of quinine as the cause. Thus i t seems th a t p o s i t i v e s t a t i s t i c a l relevance i s a n a t u r a l requirement for p r o b a b i l i s t i c causes. Is t h i s g e n e r a l l y the case? P o s i t i v e relevance c e r t a i n l y doesn't e n t a i l c a u s a t i o n — does causation e n t a i l p o s i t i v e r e levance? 1 The answer seems to be no. Consider a s i t u a t i o n where an event B, a product of event A, i s n e g a t i v e l y r e l e v a n t to the occurrence of event C, yet B o b v i o u s l y l i e s c a u s a l l y between events A and C. That i s , P(C/A)>P(C) and P(C/B)<P(C/A) or even P(C/B)<P(C), even though i t i s c l e a r that A can produce B which can produce C. Examples of t h i s phenomenon are not r a r e ; I they are e x h i b i t e d whenever a r e s u l t i s produced 'the hard way'. The chance of winning money increases i f one wagers at the race track; t h i s chance drops d r a m a t i c a l l y when one bets on a 'long shot'; yet winning t h i s bet ( a l b e i t r a r e l y ) i s c e r t a i n l y c a u s a l l y dependent on p l a c i n g i t . Another example rebounding through the l i t e r a t u r e (and destined to be a c l a s s i c ) i s due to Deborah Rosen. A g o l f e r ' s approach shot (event A) i s headed f o r the green when i t s t r i k e s a tree branch (event B) and i s d e f l e c t e d d i r e c t l y i n t o the cup (event C) f o r a spectacular b i r d i e . The p r o b a b i l i t y r e l a t i o n s among these three events are as above: h i t t i n g the branch c e r t a i n l y seems n e g a t i v e l y r e l e v a n t to s i n k i n g the shot and j u s t as c e r t a i n l y seems to cause t h i s r e s u l t . I t seems, then, that p o s i t i v e relevance cannot be a 1 21 requirement of p r o b a b i l i s t i c causal relevance, and, i f not, what else i s there i n our a n a l y s i s which allows us to p i c k out l e g i t i m a t e causal antecedents from p r e v e n t a t i v e causes? \ Most p r o b a b i l i s t i c causal t h e o r i s t s make p o s i t i v e s t a t i s t i c a l relevance a necessary c o n d i t i o n of causal relevance and thus respond to t h i s q u e s tion by attempting to salvage p o s i t i v e relevance. In the remainder of 3 t h i s s e c t i o n we w i l l examine these attempts. There are three r e l a t e d attempts at r e s o l v i n g t h i s d i f f i c u l t y . The 4 f i r s t i s a method of more d e t a i l e d s p e c i f i c a t i o n , proposed by Rosen. Rosen argues that C may be the cause of E even though P(E/C)<P(E), provided t h a t some a d d i t i o n a l f a c t o r X y i e l d s P(E/CSX)>P(E). In the g o l f b a l l example we simply add to the antecedent of the c o n d i t i o n a l p r o b a b i l i t y f a c t o r s such as the speed and d i r e c t i o n of the approach shot which w i l l , together with the d e f l e c t i o n by the branch, r a i s e the p r o b a b i l i t y of the b a l l going i n the cup. This s o l u t i o n , however, i s inadequate. F i r s t , i t seems a r t i f i c i a l and ad hoc. In the causal chain A->B->C, as described above, the sample (or p r o b a b i l i t y ) space f o r event A was roughly the set of approach shots to the green. For event C i t was the set of b a l l s dropping i n the cup. The suggestion before us i s to provide a r e l a t i v e l y f i n e - g r a i n e d a n a l y s i s of event B, i n c l u d i n g d e t a i l s of the approach t r a j e c t o r y . These d e t a i l s a p parently serve no other purpose than the rescue of p o s i t i v e relevance as a necessary c o n d i t i o n on s t a t i s t i c a l causal c l a i m s . (Consider the punter's dream: the d e t a i l s necessary to render the long shot bet p o s i t i v e l y r e l e v a n t to winning.) 122 P r o v i s i o n of these d e t a i l s may be an admirable goal, or u s e f u l s t r a t e g y , but the need to provide them seems wrongly based i n the demand fo r p o s i t i v e relevance, f o r t h i s s o l u t i o n w i l l not work i n a l l cases. Salmon provides an example where f u r t h e r s p e c i f i c a t i o n of the n e g a t i v e l y r e l e v a n t c a u s a l f a c t o r i s impossible i n p r i n c i p l e . 5 As t h i s example w i l l prove worthwhile i n a l a t e r context we w i l l give i t i n d e t a i l here. We have an atom i n an e x c i t e d s t a t e which we s h a l l r e f e r to as the 4th energy l e v e l . I t may decay to the ground s t a t e (zeroeth l e v e l ) i n s e v e r a l d i f f e r e n t ways, a l l of which i n v o l v e intermediate occupation of the 1st energy l e v e l . L et P(m->n) stand f o r the p r o b a b i l i t y that an atom i n the mth l e v e l w i l l drop d i r e c t l y to the nth l e v e l . Suppose we have the f o l l o w i n g p r o b a b i l i t y values: P(4 -*3) = 3/4 P(3-M) = 3/4 P(4 +2) = 1/4 P(2 -M ) = 1/4 The f o l l o w i n g c o n d i t i o n a l p r o b a b i l i t i e s then hold (where (4->-0) i n d i c a t e s p o s s i b l e decay to the ground s t a t e from the e x c i t e d s t a t e ) : P(1/(4-K))) = 10/16, P(1/(4 -KD) & 2) = 1/4, thus the atom's occupying the 2nd energy l e v e l i n i t s decay to the ground s t a t e i s n e g a t i v e l y r e l e v a n t to i t s occupying the 1st l e v e l . "Nevertheless, i f the atom goes from the 4th to the 2nd to the 1st l e v e l , that sequence c o n s t i t u t e s a causal c h a i n , i n s p i t e of the negative 7 s t a t i s t i c a l relevance of the intermediate stage." The p o i n t of t h i s example i s simply t h i s : no f u r t h e r s p e c i f i c a t i o n i s a v a i l a b l e here (as i n the g o l f b a l l example) which w i l l render the s t a t i s t i c a l relevance r e l a t i o n i n question p o s i t i v e . Once we have s p e c i f i e d the atom, i t s energy l e v e l s , and the t r a n s i t i o n p r o b a b i l i t i e s , we have given a complete d e s c r i p t i o n of the events i n q u e s t i o n . g Rosen concludes i n favor of a p r o b a b i l i s t i c approach to c a u s a l i t y , yet her p r o f f e r e d s o l u t i o n to the problem of negative relevance places her on a s l i p p e r y slope to determinism. For what i f we could, by f u r t h e r 1 23 s p e c i f i c a t i o n of the circumstances surrounding the a l l e g e d causal f a c t o r , provide an increase i n i t s s t a t i s t i c a l relevance for i t s e f f e c t ? As we have seen, p o s i t i v e relevance alone i s not a s u f f i c i e n t c o n d i t i o n f o r c a u s a l r e l e v a n c e . Can we continue to demand a d d i t i o n a l r e l e v a n t f a c t o r s u n t i l we have reached a d e t e r m i n i s t i c s i t u a t i o n ? I t seems an unargued assumption that there w i l l be such f u r t h e r s p e c i f i c a t i o n to be had. In the atom decay example we have p l a u s i b l e grounds on which to deny any such assumption. A s i m i l a r f a t e b e f a l l s Good's proposed s o l u t i o n to the problem of 9 negative relevance. Salmon dubs t h i s approach "the method of i n t e r p o l a t e d 10 c a u s a l l i n k s . " Suppose that P has a tendency to prevent E, yet o b v i o u s l y caused E. Good suggests "we say that F was a cause of E because there was a chain of events connecting F to E, each of which was s t r o n g l y caused by the preceding one". 1 1 Good's b r i e f remark may be elaborated i n the f o l l o w i n g way: i f F ->-E (where ->• i n d i c a t e s negative re l e v a n c e ) , then + + there must be some event (or set of events) D such that F D E. Or, i n our usual n o t a t i o n , i f P(E/F)<P(E), then there i s some D such t h a t P(D/F)>P(D) and P(E/D)>P(E). But t h i s c o n t r a d i c t s our i n i t i a l assumption 12 t h a t F was n e g a t i v e l y r e l e v a n t f o r E s i n c e : P(E/F) - P(E) _ tP(E/D) - P(E)][P(D/F) - P(D)] P(D) I.e., our assumption of the p o s i t i v e relevance of D makes the r i g h t hand expression p o s i t i v e , thus P(E/F) must be greater than P ( E ) . (There are f u r t h e r i n t e r e s t i n g consequences of t h i s theorem which w i l l be discussed i n the next sub-section.) Furthermore, there are s i t u a t i o n s which are not amenable to Good's method of i n t e r p o l a t i o n . In Salmon's atomic decay example above Good's suggestion would amount to the p o s t u l a t i o n of hidden v a r i a b l e s — events 1 24 which l i e c a u s a l l y between the s p e c i f i e d energy l e v e l s . Good r e j e c t s the assumption of hidden v a r i a b l e s here and suggests an a l t e r n a t e a p p r a i s a l of 1 3 t h i s counter-example. In t h i s example, i f the atom's being at the 2nd energy l e v e l ( F ) , i s followed by the atom at the 1st energy l e v e l (E), we claimed that F caused E, even though F was n e g a t i v e l y r e l e v a n t f o r E. Good a s s e r t s that t h i s c a u s a l claim i s l e g i t i m a t e only i f we compare atoms at the 2nd energy l e v e l w i t h the absence of atoms at any energy l e v e l . In other words, we can recapture a sense of p o s i t i v e relevance by making the proper comparisons: i n t h i s case E i s more l i k e l y to be produced by F than i t i s to — — 14 be produced by F, where F i s to be taken as "no s t a t e of the atom." Notice that t h i s i s no longer an i n t e r p o l a t i o n of causal l i n k s but r a t h e r something we s h a l l c a l l the method of comparative u n i v e r s e s . Salmon himself proposes a s i m i l a r s o l u t i o n i n a r e l a t e d example, yet argues l a t e r that both Good's and h i s own method w i l l not work for the atom example. Consider the f o l l o w i n g chain of events, t h e i r r e s p e c t i v e p o s i t i v e and negative relevance represented as above by and -> : F -*G -*E. Imagine a game where one chooses to p l a y (F) by r o l l i n g a f a i r tetrahedron whose outcome (G or G) determines one's chance of winning (E). We suppose that a four on the tetrahedron (G) y i e l d s a 1/4 chance of E, any 1 5 other r o l l (G) gives a 3/4 chance. Thus (1) P(G/F)>P(G/F) (F i s n e g a t i v e l y r e l e v a n t f o r G) (2) P(E/G)>P(E/G) (G i s n e g a t i v e l y r e l e v a n t f o r E) This set of events i s a 2-state Markov process, i . e . , each event screens o f f f u t u r e events from the past, thus: (3) P(E/F&G) = P(E/G) and P(E/F&G) = P(E/G) What s h a l l we say of the player who wins "the hard way" — by f i r s t r o l l i n g a 125 four and then, against the odds, winning? I f F-> G->- E c o n s t i t u t e s a causal chain when i t occurs, can we not c a l l E c a s u a l when it occurs? Salmon suggests that we might salvage p o s i t i v e relevance, and thus our j u s t i f i c a t i o n f o r a causal c l a i m here, by a more c a r e f u l d e s c r i p t i o n of the sample space (rather than of the events themselves). In the present example the p r o b a b i l i t y that E w i l l occur should be c o n d i t i o n a l i z e d over a set of events that i n c l u d e s G, G and a f u r t h e r event H: the p l a y e r q u i t s a f t e r the game begins. ( I . e . , P(E/H) =0.) Likewise for G: the p r o b a b i l i t y of i t s occurrence should be compared not only with F, but a l s o F. I f we take U = {F,F} and R = {G,G,H}, we can regain the p o s i t i v e relevance between events i n the chain F->-G->-E because the f o l l o w i n g i n e q u a l i t i e s h o l d : (4) Pu(G/F) > P y(G) (5) P R(E/G) > P R(E) and even though (6) PytE/G) = P R(E/G) (Markovian) and (7) Py(E/G) < P^E) (5) i s true "because the p r i o r p r o b a b i l i t y of E i s q u i t e d i f f e r e n t i n the two u n i v e r s e s . " 1 6 In the atom decay example, i f we s e l e c t the proper universe or p r o b a b i l i t y space over which we c o n d i t i o n a l i z e , then we may again capture the sense of the p o s i t i v e relevance requirement. In t h i s case we compare the p r o b a b i l i t y of the occurrence of atoms a t the 1st energy l e v e l both w i t h t h e i r p r i o r occupation of the 2nd l e v e l , and with "the s i t u a t i o n i n which no 17 atom i s present at a l l . " Salmon recognizes the s i m i l a r i t y between h i s proposed s o l u t i o n and that o f f e r e d by Good yet suggests that there i s something misleading about t h i s s o l u t i o n . While i t appears to make sense i n 126 some cases to c o n s t r u c t and compare a l t e r n a t i v e sample spaces with respect to which we may c l a i m a sense of p o s i t i v e relevance between cause and e f f e c t , t h i s approach seems beside the p o i n t i n other cases. (And t h i s d i f f e r e n c e between cases does not f a l l , c ontra Salmon, along macroscopic/microscopic 18 l i n e s . See below, p. 127.) Salmon claims to have re-captured "an important sense i n which [the cause] possesses an i n t e r n a l p o s i t i v e relevance with respect to [the 19 e f f e c t ] . " What he has done (and, i n a p a r a l l e l f a s h i o n , what Good o f f e r s ) amounts to no more than reducing the p r i o r p r o b a b i l i t y of the e f f e c t to zero (or near zero) by e i t h e r (a) narrowing the universe with respect to the cause or (b) broadening the universe i n which the e f f e c t occurs. Method (a) i s employed i n the g o l f example: i f we r e l a t i v i z e the h i t t i n g of the branch to the universe s e l e c t e d by "errant shots from the rough", then, given shots such as these the branch becomes p o s i t i v e l y r e l e v a n t to the b a l l going i n t o the cup. In the tetrahedron example the a l t e r n a t i v e s t r a t e g y (b) i s used: broadening the sample space i n which the e f f e c t (winning) occurs by i n c l u d i n g q u i t t i n g the game as a p o s s i b l e outcome, lowers the p r i o r p r o b a b i l i t y of winning and makes r o l l i n g a f o u r , given that one might q u i t , p o s i t i v e l y r e l e v a n t . Neither of these approaches, Salmon maintains, w i l l work i n the atom decay example. Taking them i n reverse order, s t r a t e g y (b), as suggested above, would see the e f f e c t event (the atom dropping to the 1st energy l e v e l ) c o n d i t i o n a l i z e d over a universe broadened to inc l u d e the s i t u a t i o n where "no atom" i s present. But t h i s a l t e r n a t i v e seems beside the p o i n t — "we are concerned w i t h what happens to an atom, given that i t occupies the 4th 20 l e v e l . " Strategy (a) f a r e s no b e t t e r . There i s no way, short of 127 p o s t u l a t i n g 'hidden v a r i a b l e s ' , to narrow the reference c l a s s of atoms to those 'headed towards the 2nd energy l e v e l ' i n a fashion p a r a l l e l to the set of e r r a n t fairway shots 'headed towards the branch.' I t a l s o seems c l e a r that n e i t h e r of these approaches s a t i s f a c t o r i l y r e solves t h i s problem at the macroscopic l e v e l . Both s t r a t e g i e s depend on a r e - s t r u c t u r i n g of the p r o b a b i l i t y space i n which the events i n question take place i n a manner which seems both ad hoc and a r t i f i c i a l . There w i l l always be a c o n d i t i o n a l i z a t i o n r e l a t i v e to which the occurrence of any event can be viewed as h i g h l y probable. Consider a l o t t e r y w i t h 100 chances and only one winning t i c k e t . The' chances of winning having bought a t i c k e t , r e l a t i v e to the t o t a l t i c k e t s i s s u e d , are s l i m . However, the chance of winning i s greater given that we don't tear up the t i c k e t , or given that we have entered the l o t t e r y a t a l l . That i s , i f we compare the p r o b a b i l i t y of winning, given t h a t we've bought a t i c k e t , to that of winning whether we have bought a t i c k e t or not, then buying the t i c k e t becomes p o s i t i v e l y r e l e v a n t to winning. There i s both something wrong and something r i g h t about t h i s view. I t seems wrong, or at l e a s t m isleading, to search f o r p o s i t i v e relevance i n t h i s f a s h i o n , simply because i t i s not j u s t a p o s i t i v e l y r e l e v a n t s t a t i s t i c a l r e l a t i o n we are seeking but rather an explanatory account of events, given t h e i r negative relevance f o r each other. In other words, i f i t i s 'success the hard way' we are attempting to analyze, i t i s suspect to provide such an a n a l y s i s by e l i m i n a t i n g what i s 'hard' about the 'hard way 1. In the above l o t t e r y example, "Because I bought a t i c k e t (rather than not)" does not go very f a r i n e x p l a i n i n g one's success. In the tetrahedron example, i t i s winning given that we have r o l l e d a four that we are e x p l a i n i n g , and not j u s t 1 28 winning at a l l . ( R e c a l l GI Joe's dilemma (Chapter I, Secti o n 4a): we can e x p l a i n h i s c o n t r a c t i o n of leukemia, but not why he got i t rather than GI Jane. Likewise, there are two d i f f e r e n t questions here.) What may be r i g h t about t h i s view shows up when we focus on the c a u s a l , rather than s t a t i s t i c a l , aspect of these kinds of s i t u a t i o n s . There are p a i r s of events whose causal r e l a t i o n s h i p seems c l e a r , and whose s t a t i s t i c a l relevance to each other i s negative. I f so, then i t seems we can always c o n s t r u c t a universe with respect to which the e f f e c t i s more l i k e l y , given the cause. Such a c o n s t r u c t i o n would g e n e r a l l y be t a i l o r e d to each i n d i v i d u a l event p a i r , and might w e l l need to include a f a i r l y o u t l a n d i s h set of p o s s i b i l i t i e s . I t i s i n t h i s sense that t h i s s t r a t e g y seems ad hoc and a r t i f i c i a l . What i t does capture, however, i s how these s i t u a t i o n s are d i s t i n c t from those where negative s t a t i s t i c a l relevance i s evidence for the presence of a pr e v e n t a t i v e rather than a cause. I f two events are r e l a t e d such that the e a r l i e r event s t a t i s t i c a l l y prevents, rather than causes, the occurrence of the l a t e r event, then no such 'constructed' universe w i l l be found. In other words, i f the e a r l i e r of two events i s n e g a t i v e l y r e l e v a n t to the occurrence of the l a t e r event, and i f there i s no con s t r u c t a b l e universe w i t h respect to which t h i s negative relevance can be reversed, then the f i r s t event i s a pre v e n t a t i v e and not a cause. The atom decay example, however, s t i l l presents a problem i n th a t i t f u l f i l l s the antecedent but not the consequent of the above c o n d i t i o n a l . Salmon proposes an a l t e r n a t i v e e x p l i c a t i o n of the causal r e l a t i o n s h i p e x h i b i t e d here which i s independent of the s t a t i s t i c a l r e l a t i o n s h i p between the two events i n q u e s t i o n . The source of the d i f f i c u l t y , Salmon maintains, i s the attempt to co n s t r u c t causal r e l a t i o n s s o l e l y on the basis of 1 29 p r o b a b i l i t y r e l a t i o n s among d i s c r e t e events, without c o n s i d e r i n g t h e i r p h y s i c a l connection. Instead, according to Salmon, these cases should be analyzed as a s e r i e s of causal processes, succeeding one another i n time, each of which transmits a d e f i n i t e p r o b a b i l i t y d i s t r i b u t i o n — a d i s t r i b u t i o n which turns out to give the p r o b a b i l i t i e s of c e r t a i n types of i n t e r -a c t i o n s . Transmission of a determinate p r o b a b i l i t y d i s t r i b u t i o n i s , I b e l i e v e , the e s s e n t i a l f u n c t i o n of c a u s a l processes with respect to the theory of p r o b a b i l i s t i c c a u s a l i t y . I f we focus on the atom as a p h y s i c a l process e x i s t i n g through a p e r i o d of time, we can then describe the causal s t r u c t u r e of i t s drop to the ground s t a t e 'the hard way', d e s p i t e the negative relevance of cause to e f f e c t , i n the f o l l o w i n g manner: the atom transmits a p r o b a b i l i t y d i s t r i b u t i o n through time, i t makes a t r a n s i t i o n to a lower energy l e v e l i n accordance with t h i s d i s t r i b u t i o n (marked by the emission of a photon of c h a r a c t e r i s t i c frequency), t h i s t r a n s i t i o n transforms the atom, now i n a lower energy l e v e l , to a process with a d i f f e r e n t p r o b a b i l i t y d i s t r i b u t i o n f o r f u r t h e r changes. As Salmon points out, "the t h e s i s that causation e n t a i l s p o s i t i v e s t a t i s t i c a l 22 relevance i s not p a r t " of t h i s a n a l y s i s . Two p o i n t s are apparent here. The f i r s t i s the r e i t e r a t i o n of the c l a i m , f i r s t put forward i n t h i s context (of p r o b a b i l i s t i c c a u s a l i t y ) by Salmon i n 1978, that s t a t i s t i c a l relevance r e l a t i o n s alone are i n s u f f i c i e n t f o r understanding causal r e l a t i o n s . The second p o i n t i s r e f l e c t e d i n the emphasized words i n the previous paragraph. 'Transmission', ' t r a n s i t i o n ' , 23 'transformation' are d i s t i n c t l y causal concepts. The connection between these two p o i n t s i s t h i s : whatever i s provided i n order to f i l l out our conception of c a u s a l i t y (e.g. p h y s i c a l processes), i f i t i s to increase our understanding, must make c l e a r the r o l e of causal power or e f f i c a c y i n t h a t conception. And t h i s , of course, must be done without reference to 130 24 notions that are c l e a r l y causal i n nature. We s h a l l postpone the d i s c u s s i o n of t h i s p r o b a b i l i t y - process - power connection u n t i l the next s e c t i o n . In p a r t (b) below we w i l l look at an a l t e r n a t i v e account of 25 negative relevance suggested by Humphreys. Humphreys argues that the combination of s t a t i s t i c a l relevance and a connecting p h y s i c a l process i s not s u f f i c i e n t to e s t a b l i s h a causal r e l a t i o n . (b) C u t t i n g the Chain. Humphreys argues that i f A,B,C are events such that A i s p o s i t i v e l y r e l e v a n t to B and B to C, yet A, B and C occur, then even though A may be p o s i t i v e l y r e l e v a n t to C, "A i s not a cause of C, not even an i n d i r e c t cause, because A i n s t i g a t e d a process which ended i n an event which tended to 26 prevent C from coming about." On the face of i t t h i s conclusion seems to run contrary to the r e s u l t s of the preceeding s e c t i o n . In t h i s s e c t i o n we w i l l examine Humphreys' argument to t h i s conclusion to determine whether h i s f i n d i n g s are indeed incompatible w i t h our own. To a n t i c i p a t e , I b e l i e v e t h a t Humphreys' argument i s both i l l u m i n a t i n g and not unconvincing, yet does not c o n t r a d i c t what we have s a i d . The argument i s i n two p a r t s : there i s a t h e o r e t i c a l r e s u l t , and the i n t e r p r e t a t i o n of t h i s r e s u l t . The t h e o r e t i c a l r e s u l t i s a l s o i n two p a r t s , the f i r s t of which we have already found occasion to use (p.123). That i s , i n a two-state Markov chain, the relevance of the f i r s t member of the chain to the l a s t i s p o s i t i v e i f the i n t e r v e n i n g l i n k s are p o s i t i v e , or i f there are an even number of negative l i n k s . Thus, according to t h i s theorem, p o s i t i v e and negative relevance i n a chain of two or more l i n k s behaves i n the same manner as the m u l t i p l i c a t i o n of p o s i t i v e and negative 131 r e a l numbers. In a three s t a t e chain, comprised of elements A,B,C, where the f i r s t member A i s p o s i t i v e l y r e l e v a n t to the t h i r d member C, the + + - - «. -two p o s s i b l e chains are A ^ B ^ C and A-*B->-C. The second p a r t of t h i s t h e o r e t i c a l r e s u l t i s s i m p l y (1) that i f A i s not a s u f f i c i e n t cause of B, then upon the occurrence of A both B and B are genuine p o s s i b i l i t i e s , and (2) that i f A i s p o s i t i v e l y r e l e v a n t f o r B, then A i s n e g a t i v e l y r e l e v a n t f o r Humphreys i l l u s t r a t e s these r e s u l t s by means of an example: Two climbers at the top of a mountain have had t h e i r normal route back cut o f f by an avalanche. The only other way down i s v i a an easy rock face with one very dangerous overhang. Once over t h a t , the route i s c l e a r to the bottom, but i n e x p e r t climbers are l i k e l y to f a l l a t the overhang. A f a l l , of course, increases the pro-b a b i l i t y of i n j u r y at that p o i n t , and i f anyone i s i n j u r e d a t the overhang, i t i s h i g h l y u n l i k e l y that he could complete the journey. Of the two climbers, Axel i s f a r superior to h i s companion. So i t i s decided t h a t Axel w i l l go f o r help. Let A = Axel i s chosen to go, B = climber does not f a l l a t the overhang, C = climber i s not i n j u r e d a t overhang, D = climber fetches help. We see t h a t , i n t h i s s i t u a t i o n , A i s p o s i t i v e l y r e l e v a n t f o r D ( P(D/A)>P(D) ), and that when "things go as expected, we get + + + 30 A->B->-C->-D." But our theorem shows that the p o s i t i v e relevance of A ^ + f o r D remains even though A-^-B+C-^D occurs: despite h i s s k i l l , Axel f a l l s a t the overhang; l u c k i l y he escapes i n j u r y and e f f e c t s the rescue. "In t h i s sequence of events", Humphrey w r i t e s , "the f a c t t h a t Axel was chosen had nothing to do with help being fetched, d e s p i t e the f a c t that i n general, i t 31 would have." Nor w i l l A be countenanced as an i n d i r e c t cause of D. An i n d i r e c t 3 2 cause should at l e a s t p l a y "some r o l e i n b r i n g i n g about the e f f e c t , even though i n t e r v e n i n g events occurred ... because A i n s t i g a t e d a process 132 which ended i n an event which tended to prevent C from coming about", A should not be considered even as an i n d i r e c t cause. We can g e n e r a l i z e these r e s u l t s as f o l l o w s : (1) negative l i n k s i n a causal chain w i l l always cut that chain; (2) conversely, f or an event to be a d i r e c t , or i n d i r e c t , cause of a l a t e r event i n a chain, each event i n th a t c h a i n must r a i s e the p r o b a b i l i t y of the occurrence of i t s successor. The f o l l o w i n g f i g u r e i l l u s t r a t e s these g e n e r a l i z a t i o n s : * (C) «. ( O F i g . I: A s i m p l i f i e d 3 event 2 s t a t e Markov chain of the f i r s t three events i n the above example. A i s a genuine but i n d i r e c t cause of C when B occurs; when B occurs, even i f C occurs, A does not cause C. A i B X C c o n s t i t u t e s a causal chain; A B C i s a chain that has been c u t . Before commenting on Humphreys' i n t u i t i o n s regarding cut and uncut chains, one f u r t h e r r e s u l t w i l l be of i n t e r e s t . I f A i s n e g a t i v e l y r e l e v a n t f o r B, then P(B/A)<P(B/A). I f A i s necessary f o r B, then, presumably, P(B/A) = 0 . Thus i f A i s necessary f o r B, then A cannot be n e g a t i v e l y r e l e v a n t f o r B. Causes which are necessary, t h e r e f o r e , can never be n e g a t i v e l y r e l e v a n t f o r t h e i r e f f e c t s , and thus can never produce a cut c h a i n . I f we apply t h i s r e s u l t to Rosen's g o l f b a l l - t r e e branch example we see t h a t , under a minimal r e - d e s c r i p t i o n of the sequence of events, i f the b a l l had not h i t the branch, i t would not have gone i n the cup. Under t h i s sine^ qua non d e s c r i p t i o n , the h i t t i n g of the branch must have been necessary 133 f o r the b a l l going i n the cup, and, t h e r e f o r e , cannot have been n e g a t i v e l y r e l e v a n t to i t . Understanding t h i s example i n t h i s way i s roughly p a r a l l e l to Salmon's method of comparative un i v e r s e s : with both methods we recapture the sense of p o s i t i v e relevance needed to r e - e s t a b l i s h what we take i n t u i t i v e l y to be a causa l c h a i n . Humphreys, however, does not b e l i e v e that an appropriate r e - d e s c r i p t i o n of the rescue example can be made, and, that t h i s example i s 33 on a par with Salmon's tetrahedron example. There, we r e c a l l , r o l l i n g a four was n e g a t i v e l y r e l e v a n t to, yet a d i r e c t causal antecedent o f , winning. We s h a l l discuss each of these examples i n turn; i n both cases I b e l i e v e t h a t Humphreys' judgement i s premature. Let A = Axel's being chosen, o r , i n the p a r a l l e l example of the dice game, A = choosing to p l a y . Let B = s u c c e s s f u l l y n e g o t i a t i n g the overhang, or r o l l i n g other than a four on the tetrahedron; C = g e t t i n g help or winning the game. The s t a t i s t i c a l r e l a t i o n s among these three events i n each example are as represented i n F i g . I. In both examples A i s p o s i t i v e l y r e l e v a n t f o r C and, i n the dice example, A i s necessary f o r C: i f the pl a y e r had not chosen to pl a y , he would not have won. Is there a d e s c r i p t i o n of the events i n the rescue example that shows A to be necessary f o r C? There i s , and there i s n ' t . There i s , i f the sense of ' I f i t hadn't been f o r Axel being chosen' i s that someone was chosen, f o r then the r e d e s c r i p t i o n necessary would be something l i k e ' i f no one had been chosen, then the rescue would not have occurred.' There i s n ' t , i n the sense that Axel being chosen i s c e r t a i n l y not a necessary c o n d i t i o n f o r rescue — h i s partner A s t r i d could have a f f e c t e d a rescue. Necessary or not, however, A i s p o s i t i v e l y r e l e v a n t f o r C. 134 The c r u c i a l event i n both examples, f o r our purposes, i s the i n t e r v e n i n g one, B. Unlike the tree branch i n the g o l f b a l l example, the middle events of the rescue and dice examples are not necessary f or t h e i r s uccessors. ( I t i s f a l s e that i f he hadn't r o l l e d a four he wouldn't have won, j u s t as i t i s f a l s e that i f he hadn't f a l l e n , he wouldn't have been rescued.) Now, i n general, h i t t i n g a tree branch i s not a necessary c o n d i t i o n of g e t t i n g a b i r d i e ; i t i s only necessary 'given the circumstances'. And, given the circumstances, we see immediately the 'necessity' of the branch. Can we make a s i m i l a r move with respect to the middle event B i n the other two examples? Salmon seems to think so, at l e a s t f o r the dice example. To the d e s c r i p t i o n ' r o l l i n g a f o u r ' he adds 'and continues the game' which then makes t h i s event necessary f o r winning. We might suggest a s i m i l a r move f o r Humphreys' mountain c l i m b e r s : i f Axel hadn't s l i p p e d - y e t - e s c a p e d - i n j u r y , rescue would not have occurred. And Humphreys would agree that i t was the combination of these two u n l i k e l y events which "brought about the f i n a l r e s u l t . " 3 4 But the conc l u s i o n he draws from t h i s seems much too strong: that the " f a c t that Axel was chosen 35 had nothing to do with help being fetched." Surely, i f we are asking "What caused the rescue?" (and i t c e r t a i n l y wasn't uncaused), then, given 3 6 t h a t he gets past the overhang, Axel i s i t . What Humphreys notices i s that the events a t the overhang e l i m i n a t e Axel's s k i l l as a major f a c t o r i n the rescue, but not Axel h i m s e l f . Consider the s i t u a t i o n where A s t r i d i s chosen to go: the p r o b a b i l i t y r e l a t i o n s between A and B would then be reversed, and A then n e g a t i v e l y r e l e v a n t to C. Yet s u r e l y i f A C occurs, whether B or B occurs, we would c l a i m that A s t r i d , p o s s i b l y against the odds, caused the rescue. Even f o r Humphreys, Axel must count as a t l e a s t an 135 i n d i r e c t cause i n t h i s redescribed p i c t u r e of the rescue. Humphreys clai m s t h a t "an event as an i n d i r e c t cause s u r e l y e n t a i l s that the i n d i r e c t cause at 37 l e a s t p l a y some r o l e i n b r i n g i n g about the e f f e c t . . . " . And i t seems c l e a r that Axel had a s i g n i f i c a n t r o l e to p l a y here — even though he f e l l a t the overhang. A f t e r a l l , both f a l l i n g a t the overhang, and escaping i n j u r y , are things which happened to A x e l . Suppose, then, t h a t Axel makes i t as an i n d i r e c t cause, given that we have redescribed the i n t e r v e n i n g events and regained the appropriate sense of p o s i t i v e relevance. Our general qualms about negative relevance remain ( i n a s l i g h t l y a l t e r e d s t a t e ) . According to Humphreys, the reason why Axel d i d not appear to be even an i n d i r e c t cause of the rescue was "because A i n s t i g a t e d a process which ended i n an event which tended to prevent C from 38 coming about." As we have seen t h i s i s a s l i g h t mis-statement of the events i n t h i s sequence: the process i n s t i g a t e d at A d i d not end at B, the process was not c u t . The i n t e r a c t i o n a t the overhang modified t h i s process — i t lowered the p r o b a b i l i t y of i t going to completion r e l a t i v e to the p r o b a b i l i t y a s s o c i a t e d w i t h t h i s process should i t evolve normally. This normal p r o b a b i l i t y d i s t r i b u t i o n can be regarded as u n f o l d i n g according to a 39 " n o n - i n t e r a c t i v e law of e v o l u t i o n " f o r the process i n q u e s t i o n . What we must n o t i c e here i s the d i s t i n c t i o n between processes and events — events being the derived n o t i o n , with processes as b a s i c . This d i s t i n c t i o n w i l l be re-examined i n the next s e c t i o n — we w i l l postpone our d i s c u s s i o n u n t i l then. We are l e f t , however, with the problem of what, i n general, d i s t i n g u i s h e s negative l i n k s i n a c a u s a l chain of events from negative l i n k s 40 which i n d i c a t e the presence of p r e v e n t a t i v e s . From the above 136 d i s c u s s i o n we can generate a t l e a s t the f o l l o w i n g two c r i t e r i a which may be marshalled i n order to mark t h i s d i s t i n c t i o n . (1) I f B i s a genuine p r e v e n t a t i v e of C, then B cannot be redescribed as necessary f o r C. Of course, we cannot guarantee that no such r e d e s c r i p t i o n e x i s t s . (2) We must pay c a r e f u l a t t e n t i o n to the production of events, i n c l u d i n g the i n t e r a c t i v e or n o n - i n t e r a c t i v e e v o l u t i o n of processes. I f the above examples the occurrence of B or B i s an event t h a t marks the i n t e r a c t i o n of ( a t l e a s t ) two processes. The negative relevance f o r the f u r t h e r event C that r e s u l t s from t h i s i n t e r a c t i o n can be a product of e i t h e r of the two processes. I f the i n t e r a c t i o n y i e l d s only s t a t i s t i c a l r e l a t i o n s among these events then the e n t i r e sequence of events must be considered to determine whether we have a causal process which has- gone to completion despite i n t e r f e r e n c e , or whether the r e s u l t was produced by i n t e r a c t i o n with the i n t e r f e r i n g causal process. Often t h i s becomes a judgement c a l l -- a judgement based on s c i e n t i f i c c r i t e r i a of t o t a l evidence, maximum s p e c i f i c i t y , e t c . Consider, as a f i n a l example, the batsman who cannot h i t a major league curve. Going to bat (A) i s p o s i t i v e l y r e l e v a n t to g e t t i n g on base (C) — i n b a s e b a l l they provide the fan with t h i s p r o b a b i l i t y to three f i g u r e s — and i t i s a l s o necessary. Throwing a curve (B) w i l l lower t h i s p r o b a b i l i t y and, we say, tend to prevent the b a t t e r from reaching f i r s t base, without changing the p o s i t i v e relevance of A f o r C. The p i t c h e r d e l i v e r s h i s f i r s t p i t c h , a curve, and the b a t t e r swings and misses. We say h i s curve i s c e r t a i n l y e f f e c t i v e today. The p i t c h e r winds up and sends another curve to the p l a t e , another swing and a miss. We have grounds f o r saying that another curve w i l l s t r i k e the b a t t e r out — perhaps even cause the end of h i s career i f he can't ' f i g u r e i t out.' Another p i t c h , another 137 curve. This time, however, the b a t t e r raps out a s i n g l e . We say 'Atta boy, Casey,' g i v i n g c r e d i t to the b a t t e r for beating the odds and g e t t i n g a h i t despite the presence of a preventative causal process. Now (1) there does not seem to be an a l t e r n a t i v e d e s c r i p t i o n of t h i s sequence of events which would y i e l d ' I f i t hadn't been f o r t h a t p i t c h , Casey would not have got on base.' And (2) what we have are two p r o b a b i l i s t i c causal processes, one tending to produce C, and one tending to produce C. Both are i n v o l v e d i n the f i n a l outcome, whichever occurs. E.g., i f C occurs the b a t t e r i s c r e d i t e d wit h reaching base s a f e l y , the p i t c h e r i s charged with a l l o w i n g a h i t . p a r t of the reason f o r Humphreys' misperception of negative r e l a t i o n s among events i s h i s c o n s t r u a l of the causal processes i n v o l v e d as a sequence of events, events which are more p r o p e r l y viewed as being constructed out of the i n t e r s e c t i o n s and i n t e r a c t i o n s of processes. Focusing on the event which i s the i n t e r a c t i o n of these processes i s misleading. 'It i s the processes themselves which transmit the p r o b a b i l i t y r e l a t i o n s i n q u e s t i o n . Concentrating s o l e l y on events tends to obscure the r o l e played by the processes which serve to make up such events. Salmon remarks, "Transmission of a determinate p r o b a b i l i t y d i s t r i b u t i o n i s , I b e l i e v e , the e s s e n t i a l f u n c t i o n of causal processes with respect to the theory of p r o b a b i l i s t i c c a u s a l i t y . " 4 " 1 " The a n a l y s i s of t h i s property of processes w i l l be our next t o p i c . 2. Transmission L i n e s . (a) P r o b a b i l i t i e s and Processes The p r e s u p p o s i t i o n of the concluding remarks of the l a s t s e c t i o n i s that the p r o b a b i l i t y r e l a t i o n s among events are the r e s u l t of a more ba s i c p r o b a b i l i t y d i s t r i b u t i o n w i t h i n the processes themselves, processes whose 138 i n t e r a c t i o n s make up these events. Axel had a c e r t a i n p r o b a b i l i t y of g e t t i n g down the mountain and e f f e c t i n g a rescue; the overhang presented a c e r t a i n p r o b a b i l i t y of preventing t h i s process; the p r o b a b i l i t i e s a s s ociated w i t h both processes may w e l l be l e s s than d e t e r m i n i s t i c , thus l e a v i n g room f o r the success of the improbable on p a r t i c u l a r o c c a sions. The concern of the f i r s t p a r t of t h i s s e c t i o n w i l l be the nature of t h i s a s s o c i a t i o n of a p r o b a b i l i t y and a process. I take t h i s measure of p r o b a b i l i t y (as w i l l be shown) to r e f e r , a t l e a s t i n d i r e c t l y , to the i n f l u e n c e of one process on another. In p a r t , then, t h i s d i s c u s s i o n w i l l meet the task set by Salmon at the co n c l u s i o n of h i s " P r o b a b i l i s t i c C a u s a l i t y " : to give "an account of the propagation of caus a l i n f l u e n c e v i a causal p r o c e s s e s . " 4 ^ Most s o r t i e s i n t o the realm of p r o b a b i l i s t i c c a u s a l i t y f a i l to mark the d i s t i n c t i o n between s p e c i f i c and generic events, between events and event types, or between an event and a c l a s s of events. More a c c u r a t e l y , they a l l u d e to these d i s t i n c t i o n s and c l a i m that t h e i r remarks are not a l t e r e d by 43 t h i s choice of r e f e r e n t s f o r t h e i r v a r i a b l e s . Yet some d i s t i n c t i o n would seem to be appropriate here — we need only n o t i c e that i n the d e f i n i t i o n of conj u n c t i v e and i n t e r a c t i v e forks the p r o b a b i l i t i e s r e f e r to po p u l a t i o n frequencies , while the production and transmission of these p r o b a b i l i t i e s v i a processes suggests that these p r o b a b i l i t i e s are embedded i n the i n d i v i d u a l events themselves. This d i s t i n c t i o n w i l l make a d i f f e r e n c e , as w i l l be shown, with respect to our l i n g u i s t i c i n t u i t i o n s regarding the n e c e s s i t y of p o s i t i v e relevance i n causal e x p l a n a t i o n s . This, and other 44 d i f f e r e n c e s w i l l be our t o p i c here. Consider f i r s t the conj u n c t i v e f o r k . As formulated by Reichenbach t h i s p r i n c i p l e e x p l a i n s the increase i n frequency of the occurrence of p a i r s 139 45 of events by the p o s t u l a t i o n of a common cause. This increase i n frequency i s represented by: P(A & B)>P(A) • P(B) The p r o b a b i l i t i e s i n t h i s i n e q u a l i t y r e f e r to the frequency of the occurrence of events l i k e A and B from w i t h i n some reference c l a s s , or p o p u l a t i o n , of 46 events. Salmon's i n t r o d u c t i o n of the i n t e r a c t i v e f o r k followed much the same l i n e : p r o b a b i l i t i e s mentioned i n t h i s d e f i n i t i o n a l s o r e f e r to pop u l a t i o n frequencies Next consider the d e f i n i t i o n s of causal i n t e r a c t i o n s and causal 48 processes. Roughly , causal processes are spatio-temporal continua which can transmit m o d i f i c a t i o n s ; i n t e r a c t i o n s are co-mo d i f i c a t i o n s of two or more processes. T y p i c a l l y , these m o d i f i c a t i o n s ' a r e regarded as a change i n the property or p r o p e r t i e s which can be e x h i b i t e d by the process. Following 49 Rogers l e t the s t a t e of each process a t a p a r t i c u l a r time be the set of p r o p e r t i e s t h a t t h a t process possesses a t that time. For processes that do not i n t e r a c t with any other process, t h e i r e v o l u t i o n through time can be c h a r a c t e r i z e d by the d i s t r i b u t i o n of p r o b a b i l i t i e s over the p o s s i b l e s t a t e s of that process during that time. This d i s t r i b u t i o n may remain constant, or i t may "change i n a l a w f u l way as the process p r o g r e s s e s . " 5 0 "Such a law," Rogers t e l l s us, "gives a p r o b a b i l i s t i c c h a r a c t e r i z a t i o n of the n o n - i n t e r a c t i v e propagation of the process through space and time. Newton's f i r s t law of motion i s an example of such a law." ^  A causal i n t e r a c t i o n , then, can be more r i g o r o u s l y defined as a change i n the p r o b a b i l i t y d i s t r i b u t i o n s over the s t a t e s of the i n t e r s e c t i n g processes; that i s , a change of the p r o b a b i l i t i e s assigned those states by the process' own n o n - i n t e r a c t i v e law of e v o l u t i o n . Thus the source of the p r o b a b i l i t i e s 140 propagated through space-time by causal processes and modified by causal i n t e r a c t i o n s i s the d i s t r i b u t i o n of these p o s s i b l e states of the processes. The source of the p r o b a b i l i t i e s a s s o c i a t e d with the d e f i n i t i o n of caus a l f o r k s i s the frequency of events among c e r t a i n populations of events. Thus there are two p r o b a b i l i t i e s operating here: frequency among events y i e l d i n g c o n j u n c t i v e and i n t e r a c t i v e f o r k s ; d i s t r i b u t i o n s over p o s s i b l e s t a t e s y i e l d i n g n o n - i n t e r a c t i v e laws of e v o l u t i o n . This d i s t i n c t i o n between the r e f e r e n t s of the p r o b a b i l i t i e s i n the two cases i s masked by Salmon's d e f i n i t i o n of a causal i n t e r a c t i o n : "when two processes i n t e r a c t , and both are modified i n such ways that the changes i n one are c o r r e l a t e d with the changes i n the other -- i n the manner of an i n t e r a c t i v e f o r k -- we have a 52 c a u s a l i n t e r a c t i o n . " There are at l e a s t two morals to be drawn from t h i s d i f f e r e n c e — one f o r caus a l explanation and one f o r causal d e t e c t i o n . We have of t e n been asked, i n the f i r s t and cur r e n t chapters, to e x p l a i n an i n d i v i d u a l event: GI Joe's c o n t r a c t i o n of leukemia; the rescue of Axe l and A s t r i d from the summit; the spectacular b i r d i e v i a the overhanging branch; e t c . The focus i n d i s c u s s i n g these examples has been the low p r o b a b i l i t y or negative relevance of these events, given t h e i r circumstances. Whatever i t s value, that p r o b a b i l i t y was i n f e r r e d from, and those events e x p l a i n e d ( i n p a r t ) by, the r e l a t i v e frequency among c l a s s e s of events (along w i t h the appropriate causal p r o c e s s e s ) . The cl a s s e s of events r e f e r r e d to were a l l r e l e v a n t l y t y p i c a l : each member had a r e l e v a n t l y t y p i c a l causal h i s t o r y , sharing s i m i l a r causal i n t e r a c t i o n s among other events of a c e r t a i n k i n d . When the r e l a t i o n s h i p s among these events (both explanandum and explanans) were l e s s than d e t e r m i n i s t i c , there always remained the s u s p i c i o n t h a t our explanations were somehow incomplete. Various attempts to a l l a y 141 t h i s s u s p i c i o n were suggested, mostly aimed at breaking the strong i n t u i t i v e connection between c a u s a l i t y and determinism. We can now take yet another run a t t h i s i n t u i t i o n v i a the above d i s t i n c t i o n between p r o b a b i l i t i e s as a f u n c t i o n of p o p u l a t i o n frequencies and as f u n c t i o n of p r o b a b i l i s t i c laws. A causal explanation of an i n d i v i d u a l event need not r e f e r t h a t event to a c l a s s of events with a s i m i l a r causal h i s t o r y . Rather, e a r l i e r and l a t e r stages of the process which culminates i n the event to be explained can be shown to be r e l a t e d v i a some causal law of e v o l u t i o n . The causal h i s t o r y of the p a r t i c u l a r event — the h i s t o r y of the i n d i v i d u a l — can be r e t r a c e d , i n c l u d i n g i t s past i n t e r a c t i o n s with other processes. The p r o b a b i l i t i e s a s s o c i a t e d with t h i s d e s c r i p t i o n r e f e r to the s t a t e s of the process i t s e l f . As i n t e r a c t i o n s occur the d i s t r i b u t i o n of these p r o b a b i l i t i e s (over p o s s i b l e s t a t e s ) need not show an increase i n the p r o b a b i l i t i e s of c e r t a i n f u t u r e p o s s i b l e s t a t e s , but o n ly change these p r o b a b i l i t i e s . Thus the demand f o r p o s i t i v e relevance (of an e a r l i e r s t a t e f o r a l a t e r one) need not be maintained (although i t sometimes o c c u r s ) . Rosen's g o l f b a l l had a c e r t a i n d i s t r i b u t i o n of p r o b a b i l i t i e s f o r i t s f u t u r e p o s i t i o n s and momenta, given i t s present p o s i t i o n and momentum. These p r o b a b i l i t i e s were r a d i c a l l y a l t e r e d by the process' i n t e r a c t i o n with the branch — the p r o b a b i l i t y of i t s f i n a l s t a t e ( p o s i t i o n : i n the cup, momentum: zero) was increased i n t h i s case. Axel's i n t e r a c t i o n with the overhang lowered the p r o b a b i l i t y of h i s f i n a l s t a t e being one of 'down the mountain s a f e l y ' . Even so, we can s t i l l understand, and c a u s a l l y e x p l a i n , Axel's p a r t i c i p a t i o n i n the mountain rescue v i a the causal process i n which these p r o b a b i l i t y d i s t r i b u t i o n s inhere and i n which they are modified by c a u s a l i n t e r a c t i o n s . 142 Often, i n o f f e r i n g a causal explanation of an i n d i v i d u a l event, we do r e f e r that event to a c l a s s of s i m i l a r events. The causal behavior of the p a r t i c u l a r event may then be explained as t y p i c a l of a c l a s s of events, the ex p l a n a t i o n of these events c o n s i s t i n g i n accounts of the causal i n t e r a c t i o n s shared by i n d i v i d u a l events of a c e r t a i n k i n d . The causal explanation of the atom decay example provides an instance of a p r o b a b i l i s t i c explanation of t h i s s o r t . A c l a s s of i n d i v i d u a l processes with d i f f e r e n t causal h i s t o r i e s may yet e x h i b i t c e r t a i n e m p i r i c a l r e g u l a r i t i e s . The c o r r e l a t i o n s discovered among sets of h i s t o r i c a l l y heterogeneous processes are c o r r e l a t i o n s among i n t e r a c t i o n s of these processes, thus the focus here i s on events. I t i s here that the a p p l i c a t i o n of causal f o r k s , both conjunctive and i n t e r a c t i v e , i s appropriate f o r e x p l a n a t i o n . Some h i s t o r i c a l l y s i m i l a r sets of processes may al s o be c l a s s e d as e m p i r i c a l r e g u l a r i t i e s — and thus t h e i r explanation w i l l turn on t y p i c a l causal h i s t o r i e s . The d i s t i n c t i o n to be drawn here, however, i s between the explanations o f f e r e d f o r i n d i v i d u a l processes and those o f f e r e d f o r r e g u l a r i t i e s e x h i b i t e d by sets of processes. Thus, the attempts by Reichenbach and Salmon to c h a r a c t e r i z e causal r e l a t i o n s e n t i r e l y i n terms of the s t a t i s t i c a l r e l a t i o n s among events, and f a i l i n g to note the d i s t i n c t i o n among p r o b a b i l i t y r e l a t i o n s drawn here, f a i l e d f or at l e a s t the f o l l o w i n g two reasons. F i r s t , the g e n e r a l i z a t i o n of the r e s u l t s of t h i s i method to in c l u d e the s i n g l e case l e d to counterexamples when the c o r r e l a t i o n s were l e s s than d e t e r m i n i s t i c . As we have seen, and as the d i s t i n c t i o n we are attempting to draw i n t h i s s e c t i o n suggests, the assignment of p r o b a b i l i t i e s derived from these r e g u l a r i t i e s are often not even a p p r o p r i a t e l y assignable to the i n d i v i d u a l process. Second, the 143 p r o b a b i l i t i e s a s s o c i a t e d with the causal forks i n the a n a l y s i s of such r e g u l a r i t i e s r e f e r to the frequency of events o c c u r r i n g i n a p o p u l a t i o n . And any s t a t i s t i c a l r e l a t i o n between events i n a given population can be reversed i n a sub-population by the choice of a s u i t a b l e p a r t i t i o n i n g 53 c h a r a c t e r i s t i c . I t was Salmon's i n s i g h t to reduce the r o l e of mere s t a t i s t i c a l c o r r e l a t i o n as causal explanans, unless b u t t r e s s e d by the concepts of causal processes and i n t e r a c t i o n s . What we have t r i e d to show here i s that the ground of the p r o b a b i l i t y values i n the f i r s t c o r r e l a t i o n i s d i s t i n c t from the ground of the p r o b a b i l i t y values associated with processes and t h e i r i n t e r a c t i o n s . S t a t i s t i c a l c o r r e l a t i o n s , however, s t i l l have a r o l e to p l a y with respect to causal d e t e c t i o n . This leads to our second 'moral'. I f we are loo k i n g f o r causes among a set of r e g u l a r l y o c c u r r i n g phenomena, then we must, i n a d d i t i o n to assembling the s t a t i s t i c a l c o r r e l a t i o n s , give some causal c h a r a c t e r i z a t i o n of the processes and i n t e r a c t i o n s that make up the events to be exp l a i n e d . This can be done, as described above, through laws of n o n - i n t e r a c t i v e e v o l u t i o n f o r the processes i n v o l v e d . More often than not, however, the causal s t r u c t u r e which r e s u l t s i n such c o r r e l a t i o n s i s m u l t i v a r i a t e : the i n d i v i d u a l processes r e f l e c t a v a r i e d c a u s a l h i s t o r y . Thus the required causal c h a r a c t e r i z a t i o n i s often completely unknown, known to be incomplete, or too complex to be p r a c t i c a l . The usual procedure i n such s i t u a t i o n s c a l l s f or c o n t r o l groups s e l e c t e d i n some randomized f a s h i o n . As Rogers puts i t , "The r o l e of the c o n t r o l group 54 i s to provide a surrogate f o r the law of n o n - i n t e r a c t i v e e v o l u t i o n . " Random s e l e c t i o n of a c o n t r o l and experimental group from among a popu l a t i o n plays o f f causal laws (laws of n o n - i n t e r a c t i v e e v o l u t i o n , and u n i n t e r e s t i n g c a u s a l c o r r e l a t i o n s among events i n more complex cases) operating i n one 144 group ag a i n s t the (supposed) same laws operating i n the other. This helps to ensure, but does not guarantee, that the d i f f e r e n c e s detected between the two 55 groups i s a r e s u l t of the manipulation of the independent v a r i a b l e . Although a c o r r e l a t i o n thus exposed may p o i n t to a causal i n t e r a c t i o n , even i n t h i s simple s i t u a t i o n a s t a t i s t i c a l l y s i g n i f i c a n t increase i n the r e l e v a n t p r o b a b i l i t y d i s t r i b u t i o n among the experimental population may not j u s t i f y a c a u s a l i n f e r e n c e . In more complex cases, and e s p e c i a l l y i n non-experimental s i t u a t i o n s (where c o n t r o l groups are u n a v a i l a b l e ) , we are even f u r t h e r from j u s t i f i a b l e causal i n f e r e n c e s . Rogers maintains some hope f o r these areas of causal i n q u i r y by d e f i n i n g , independently of the s t a t i s t i c a l r e l a t i o n s among events, p r o b a b i l i s t i c laws of n o n - i n t e r a c t i v e e v o l u t i o n and p r o b a b i l i s t i c laws of i n t e r a c t i o n . The p r o b a b i l i t i e s here r e f e r not to the frequency of events i n a p o p u l a t i o n , but rat h e r to the st a t e s of the processes themselves."' 6 Thus the s h i f t i n reference that was e x p l o i t e d above i n order to avoid the p o s i t i v e relevance requirement i n p r o b a b i l i s t i c causal e x p l a n a t i o n , i . e . , reference to p r o b a b i l i s t i c laws rather than po p u l a t i o n frequencies, a l s o has a r o l e to play i n causal d e t e c t i o n . The question we wish to address here i s the extent to which these p r o b a b i l i s t i c laws of i n t e r a c t i o n , and n o n - i n t e r a c t i v e e v o l u t i o n , provide us with an a n a l y s i s of the "production and propagation" of caus a l processes. As Salmon puts i t : I t i s my view that knowledge of the mechanisms of production and propagation of s t r u c t u r e i n the world y i e l d s s c i e n t i f i c understanding, and that t h i s i s what ^ we seek when we pose explanation-seeking why questions. I take i t that t h i s " s t r u c t u r e " i s the network of conjunctive and i n t e r a c t i v e f o r k s which serve to make up the e m p i r i c a l r e g u l a r i t i e s we seek to e x p l a i n ; and t h a t these "mechanisms" are the causal processes that give r i s e to these 145 s t r u c t u r e s . Suppose, then, that we have the knowledge of these processes provided by the kinds of p r o b a b i l i s t i c laws suggested by Rogers and discussed above. That i s , we have knowledge of the l a w f u l changes of p r o b a b i l i t y d i s t r i b u t i o n s over the p o s s i b l e s t a t e s of these processes over time. Does t h i s knowledge i l l u m i n a t e the causal nature of these processes? Does t h i s knowledge y i e l d the "mechanisms of production and propagation"? The answer, I am a f r a i d , must be i n the negative. To see why t h i s i s so we must assemble s e v e r a l threads, not the l e a s t of which i s the d i s t i n c t i o n among the kinds of a n a l y s i s p r o f f e r e d as an e x p l i c a t i o n of the c a u s a l r e l a t i o n . For those of us who f e e l the need to analyze the causal r e l a t i o n s h i p (as a g a i n s t those who b e l i e v e i t to be merely C Q a n a c h r o n i s t i c ) there e x i s t s two usual routes. We might consider the r e l a t i o n to be a l o g i c a l one, to be analyzed i n terms of n e c e s s i t y and s u f f i c i e n c y . This strong r e l a t i o n s h i p has a weaker cousin: the causal r e l a t i o n might be a nomic one, p r o v i d i n g what i s o f t e n c a l l e d the r e g u l a r i t y theory. That i s , p r o p o s i t i o n s d e s c r i b i n g causal r e l a t i o n s h i p s are l a w - l i k e i n c h a r a c t e r , a l l o w i n g them to l i c e n s e i n d u c t i v e , but not deductive, i n f e r e n c e . With t h i s view arose issues concerning the nature of these l a w - l i k e c o r r e l a t i o n s — how they were d i f f e r e n t , say, from a c c i d e n t a l c o r r e l a t i o n s . C o unterfactuals were of t e n appealed to i n t h i s regard, but t h i s seemed to be a r e v e r s a l (or at l e a s t a w a f f l e ) to the l o g i c a l view of causes. In any case, as we saw i n Chapter I I , both Mackie's r e g u l a r i t y view, and Lewis' l o g i c a l view, were seen to be flawed — they were too broad, and could not ( e a s i l y ) handle l e s s than d e t e r m i n i s t i c circumstances. Salmon's view, at l e a s t as understood by Rogers, i s p a r t l y a resuLt. of the nomic conception. A l a r g e p a r t of causal e x p l a n a t i o n , f o r Salmon, c o n s i s t s i n p r o v i d i n g the c o r r e l a t i o n s between events, and the subsumption oi \; 59 events under these c o r r e l a t i o n s , or laws. The Salmonian v e r s i o n of the 146 ' l a w - l i k e n e s s ' problem f o r the nomic conception was the p a r a l l e l d i f f i c u l t y of d i s t i n g u i s h i n g causal processes from non-causal processes. Salmon's response r e f e r r e d to the 'transformation' and 'transmission' of 'm o d i f i c a t i o n s ' or marks through space-time -- a l l obviously causal concepts. Rogers does s l i g h t l y b e t t e r by c l a i m i n g an a n a l y s i s of causal processes i n terms of laws of i n t e r a c t i o n and e v o l u t i o n — t h i s time the laws r e f e r r i n g not to r e g u l a r l y o c c u r r i n g sets of events, but rat h e r to r e g u l a r l y ( i . e . , a ccording to a r e g u l a r succession of p r o b a b i l i t y d i s t r i b u t i o n s ) o c c u r r i n g sequence of st a t e s of processes. But t h i s w i l l not do: we can s t i l l ask (again p a r a l l e l to the nomic view) why these processes obey these laws and not some others, or, perhaps more to the p o i n t , "What makes t h i s r e l a t i o n s h i p , described by such laws, l a w - l i k e , and not merely a c c i d e n t a l (and a c a u s a l ) ? " As a p r e l i m i n a r y c o n c l u s i o n , then, we can c l a i m that although Rogers' approach goes some distance towards an understanding of the process -p r o b a b i l i t y r e l a t i o n s h i p , i t nevertheless e x h i b i t s the same kinds of problems with respect to the causal r e l a t i o n s h i p as the received nomic view. The source of these problems must then be something common to a l l these approaches. One suggestion has been that the d i f f i c u l t y a r i s e s from seeking some connection between cause and e f f e c t , some t h i r d t h i n g which w i l l guarantee that the l a w f u l correspondence among events (or p r o p e r t i e s ) i s no a c c i d e n t . This i s the legendary causal power Hume warned us a g a i n s t . I s h a l l o f f e r a d i f f e r e n t , two p a r t , d i a g n o s i s . (1) The need f o r a t h i r d t h i n g or 'power' a r i s e s from the d i s c r e t e nature of our d e s c r i p t i o n of r e a l i t y . Even when the re f e r e n t s of the 147 p r o b a b i l i t i e s are p r o p e r l y assigned, i n accordance with the d i s t i n c t i o n drawn above between events and s t a t e s , we seem constrained to c a s t our d e s c r i p t i o n i n terms of a succession of d i s c r e t e ' f a c t s ' . Whether one adopts Rogers' s t a t e s of processes view, or the more t r a d i t i o n a l r e g u l a r i t y a n a l y s i s i n terms of events, f o r the r e f e r e n t s of the p r o b a b i l i t i e s which describe the c a u s a l r e l a t i o n , one i s committed, i t seems, to a cinematographic view of r e a l i t y . Such a view i s the end r e s u l t of Bergson's c r i t i q u e of Zeno's 60 paradoxes of motion. According to Bergson these f a m i l i a r anomalies are a product of the f a c t that our d e s c r i p t i v e armoury contains no g e n e r a l i z e d n o t i o n of 'becoming' on which to a t t a c h the successive stages of an ongoing process, say, the f l i g h t of an arrow. In the present context the analogous d i f f i c u l t y i s the tension f e l t between our d e s c r i p t i o n of causal r e a l i t y i n terms of laws, which r e q u i r e a ( c e r t a i n k ind of) r e l a t i o n s h i p between d i s c r e t e events, and our d e s c r i p t i o n of the basic e n t i t i e s of that r e a l i t y as continua or processes. (The n o t i o n of continua i s the Salmonian v e r s i o n of a g e n e r a l i z e d notion of 'becoming'.) The force of continua, as an e x p l i c a t i o n of the production and propagation of causal i n f l u e n c e , seems to be l o s t when we are r e q u i r e d to describe them v i a d i s c r e t e s t a t e s . (2) The other side of t h i s c o in i s that Salmon's conception of the c a u s a l r e l a t i o n i n p a r t l y nomic — c a u s a l explanations are a v e r s i o n of 'covering law' explanations — and p a r t l y o n t i c -- c a u s a l i t y i s i s an o b j e c t i v e feature of c e r t a i n processes i n the world: I t i s my view that these processes transmit causal i n f l u e n c e (which may be p r o b a b i l i s t i c ) from one region of space-time to another. and 148 Transmission of a determinate p r o b a b i l i t y d i s t r i b u -t i o n i s , I b e l i e v e , the e s s e n t i a l f u n c t i o n of c a u s a l 62 processes. The tension here i s between causation as an explanatory c o n s t r u c t , whose l a w - l i k e r e l a t i o n s , or s t a t i s t i c a l relevance r e l a t i o n s , l i c e n s e c e r t a i n i n f e r e n c e s , and " c a u s a l i t y " or causal i n f l u e n c e as d e s c r i b i n g a general, but nonetheless r e a l , property of o b j e c t s . That t h i s i s a tension, and not an i n c o m p a t i b i l i t y , can be seen when we consider that to resolve i t one need only provide an account of the propagation of t h i s causal i n f l u e n c e (without, of course, l e a n i n g on p a t e n t l y causal concepts i n accomplishing t h i s ) i n order to ground our o n t i c view i n experience at some l e v e l , and then showing how t h i s grounding supports the explanatory framework we wish to c o n s t r u c t . The former task (pace our c o n f l i c t i n g i n t u i t i o n s described i n (1)) has been w e l l begun by Rogers, as described i n t h i s s e c t i o n . The ' o n t i c ' r o l e of causation i n e x p l a n a t i o n (Mackie's "causation i n the o b j e c t " ) , of which the d i s c r e t a / c o n t i n u a tension i s a p a r t , remains. There have been at l e a s t two attempts to resolve t h i s t e n s i o n . Salmon takes on t h i s problem, again v i a Zeno's paradoxes of motion, and i t i s 63 the subject of a recent a r t i c l e by David F a i r . F a i r ' s proposal i s the more r a d i c a l of the two. Neither approach i s completely s u c c e s s f u l , but both w i l l be the s u b j e c t of the concluding s e c t i o n of t h i s chapter. (b) Causal Influence The problem may be r e s t a t e d : How i s i t that causes explain? Or, more e x p l i c i t l y , what feature or features of the world are we p o i n t i n g to when we o f f e r an o b j e c t A (or set of o b j e c t s ) , and the r e l a t i o n s h i p expressed by 'A causes B', as an explanation of B? (We must be c a r e f u l to take 149 "features of the world" q u i t e g e n e r a l l y here i f we are not to beg any questions — some do not f e e l that "A causes B" r e f e r s to any o b j e c t i v e feature.) As we have seen, the t r a d i t i o n a l answers (that we are r e f e r r i n g to a l o g i c a l r e l a t i o n s h i p , or that we are r e f e r r i n g to a nomic r e l a t i o n s h i p (a set of laws)) do not capture what F a i r has c a l l e d "the core notion of cau s a t i o n ; a c e r t a i n r e l a t i o n of connectedness between objects i n the 64 p h y s i c a l world." This answer places F a i r f i r m l y i n the o n t o l o g i c a l camp — the causal r e l a t i o n s h i p i s a k i n d of p h y s i c a l connection. What F a i r proposes i s a p h y s i c a l i s t i c r eduction of our causal t a l k , our reference to causes to be replaced by, or reduced to, the flow of energy or the t r a n s f e r of momentum. Roughly, A causes B i f f A and B are r e l a t e d by energy -momentum t r a n s f e r . In order to make t h i s r e d u c t i o n s u c c e s s f u l l y we must f i r s t r edescribe the r e l a t a A, B such that they can be regarded as p l a u s i b l e candidates f o r such a t r a n s f e r . That i s , i f the r e l a t a are events, or p r o p e r t i e s , e t c . , they w i l l have to be redescribed as the p h y s i c a l objects which make up these events, or that have these p r o p e r t i e s . Less roughly then, A causes B i f f there are p h y s i c a l r e d e s c r i p t i o n s of A and B as some ma n i f e s t a t i o n of energy and momentum or r e f e r to objects manifesting these that i s t r a n s f e r r e d ( f l o w s ) , a t l e a s t i n p a r t , from the A-objects to the B-objects. F a i r sees i t as the task of science to provide us with these r e d e s c r i p t i o n s . The complete and u n i f i e d science that would allow such a red u c t i o n i n h i s t o r i c a l and s o c i a l contexts i s a long way o f f . (More w i l l b s a i d about t h i s below.) There i s a curr e n t debate about the p o s s i b i l i t y of such a red u c t i o n i n psychology. F a i r ' s p r o p o s a l , then, i s programmatic — the outcome of such a program to be p a r a s i t i c on the bas i c notion of energy 150 t r a n s f e r . F a i r does discus s c e r t a i n obvious 'extensions' of h i s theory, and describes the e s s e n t i a l r o l e played by t h i s b a s i c concept of causation w i t h i n 66 these c o n t e x t s . These w i l l not i n t e r e s t us here. We have enough on our p l a t e a t t h i s p o i n t with the problem of causal i n f l u e n c e . We have before us, then, a theory of causal 'connectedness' or causal i n f l u e n c e , the i n f l u e n c e c o n s i s t i n g of the t r a n s f e r of energy/momentum. Our s t r a t e g y w i l l be to show how Salmon's account of causal i n f l u e n c e , although o n t i c i n nature and sharing some features of F a i r ' s conception, manages to avoid the d i f f i c u l t i e s of t h i s system (and thus s u c c e s s f u l l y ground causal explanation i n good o n t i c s o i l . ) Although F a i r ' s conception f a i l s i n c e r t a i n c r u c i a l r e s p e c t s , i t s t i l l serves to i l l u m i n a t e Salmon's more fundamental approach. There are two areas where an o n t o l o g i c a l approach to causation might demonstrate i t s promise over other approaches, and a t h i r d area where i t may need to show that i t i s as adequate as those others. The f i r s t two are the s i n g l e case, and the d i r e c t i o n of c a u s a l i t y ; the t h i r d i s the extension of the o n t o l o g i c a l conception to causal contexts outside of p h y s i c s . Consider the s i n g l e case. Hume wr i t e s i n the I n q u i r y : I t i s i m p o s s i b l e , t h e r e f o r e , that the idea of power can be derived from the contemplation of bodies i n s i n g l e instances of t h e i r o p e r a t i o n . . . 6 7 and the same thought i s echoed 200 years l a t e r by Carnap: I t i s never p o s s i b l e to a s s e r t a causal r e l a t i o n on the ba s i s of observing one case alone. For Hume, the only observable evidence we have f o r causation i n the s i n g l e instance i s c o n t i g u i t y and temporal succession. The ideas of regular succession and necessary connection -- ideas which are a l s o p a r t of the 151 notion of power — cannot be grounded by our observation of one i n s t a n c e . Thus, we can have no "idea of power...in s i n g l e instances." I f causation, or the c a u s a l r e l a t i o n , i s taken to be an o b j e c t i v e feature of the world — a r e a l r e l a t i o n between observable events — then i t would seem that i t should be p o s s i b l e to observe, and thus have knowledge of, i t s existence i n the s i n g l e case. F a i r claims i t as an advantage of h i s system t h a t i t allows such judgements, that i s , h i s account provides an epistemology f o r these s i n g u l a r causal judgements. We are e n t i t l e d to the a s s e r t i o n of a causal r e l a t i o n between two objects when we note the r e q u i s i t e energy/momentum t r a n s f e r . This b i t of epistemic j u s t i f i c a t i o n i s an advantage, of course, only i f we do indeed make such s i n g u l a r causal c l a i m s . F a i r claims that we do. On the r e g u l a r i t y view, our judgement that A causes B i s , at l e a s t p a r t l y , grounded by the b e l i e f that there i s some r e g u l a r i t y (even i f unknown to us) t h a t A and B i n s t a n t i a t e . F a i r i n s i s t s that "we recognize unique occurrences as c a u s a l l y connected even i f they defy r e g u l a r i t i e s i n our 69 experience," and thus causal judgements need not presuppose such r e g u l a r i t i e s . His only example, however, seems i l l - c h o s e n . ( I t i s an open qu e s t i o n , as we s h a l l see, whether there could be a well-chosen example.) Watching a b a s e b a l l s h a t t e r a window, we would a l l agree that the b a s e b a l l was (at l e a s t apparently) the cause of the s h a t t e r i n g . I maintain we would conclude such even i f we f a l s e l y b e l i e v e d that glass was unbreakable. (Suppose we had never heard of p l a s t i c and thus d i d not d i s c r i m i n a t e i t from g l a s s . Suppose we had been very lucky with glass and our experiences with p l a s t i c had l e d us to our f a l s e b e l i e f . ) 7 0 There are s e v e r a l p o i n t s to n o t i c e here. I f F a i r ' s counterexample to the r e g u l a r i t y view i s to be p l a u s i b l e , we would have to b e l i e v e more than j u s t that g l a s s i s unbreakable. Our judgement that i t was the baseball,which 152 caused the s h a t t e r i n g may w e l l r e s t on other p r e s u p p o s i t i o n s , about the usual e f f e c t s of b a s e b a l l s g e n e r a l l y on f r a g i l e and n o n - f r a g i l e o b j e c t s , about the s h a t t e r i n g c a p a c i t i e s of massive p r o j e c t i l e s i n general, e t c . I b e l i e v e that to do j u s t i c e to Carnap's remark we must take i t l i t e r a l l y : "one case alone" must be taken to mean "without even an analogous i n s t a n c e . " In t h i s case i t would mean that we must have a preponderance of f a l s e b e l i e f s , about s h a t t e r i n g s i n g e n e r a l , about p r o j e c t i l e s , e t c . Considered i n t h i s l i g h t , i t seems to me odd that anyone witnessing the b a s e b a l l / g l a s s s h a t t e r i n g event p a i r could conclude anything about t h e i r causal connection. (Of course, the observation might w e l l lead to an i n v e s t i g a t i o n of such a p o s s i b i l i t y . ) A more general p o i n t can be made here. Suppose we have an account of energy/momentum t r a n s f e r , i n c l u d i n g the r e l e v a n t conservation laws. Given t h i s background knowledge, i t then seems f a i r to claim that we can observe causation i n the s i n g l e instance (and even contrary to some e s t a b l i s h e d r e g u l a r i t i e s . ) But then t h i s required background knowledge i s s u r e l y j u s t 71 the r e g u l a r i t i e s F a i r claims we can do without. I f F a i r were c l a i m i n g t h a t , i n the a s s e r t i o n of a causal connection between the b a s e b a l l and the shattered g l a s s , that we are j u s t i f i e d i n t h i s a s s e r t i o n without an appeal to l a w - l i k e r e g u l a r i t i e s , then he would seem mistaken. I f F a i r were c l a i m i n g to have provided the meaning of such an a s s e r t i o n ( i n v i r t u e of the t r u t h c o n d i t i o n s f o r i t s use, or i n v i r t u e of what any competent speaker ought to know) then h i s account would fare no b e t t e r than the nomic (or c o u n t e r f a c t u a l ) account. In f a c t , he i s c l a i m i n g to do n e i t h e r , but r a t h e r to have given a p h y s i c a l i s t i c r eduction of causation to energy f l o w . This r e d u c t i o n "has the l o g i c a l s t a tus of an e m p i r i c a l l y discovered i d e n t i t y , namely that the causal r e l a t i o n i s i d e n t i c a l r 153 72 w i t h a c e r t a i n p h y s i c a l l y s p e c i f i a b l e r e l a t i o n " ( i n the same sense that temperature i s reduced by i t s e m p i r i c a l equivalence to mean k i n e t i c energy.) Now t h i s has a more or l e s s r a d i c a l f l a v o r , depending on one's e m p i r i c a l bent. For F a i r i t means that attempts to analyze the concept of c a u s a l i t y v i a e m p i r i c a l r e g u l a r i t i e s have put the c a r t before the horse: i t i s t h i s " p h y s i c a l l y s p e c i f i a b l e r e l a t i o n " which serves to reduce our ca u s a l a s s e r t i o n s and ex p l a i n s the observed r e g u l a r i t i e s . What we have attempted to show here, i n the d i s c u s s i o n of the s i n g l e case, i s that the reducing r e l a t i o n o f f e r e d by F a i r assumes c e r t a i n r e g u l a r i t i e s . That he does make such assumptions, and thus i s not completely free of the nomic approach, 73 weakens h i s c l a i m to have p h y s i c a l l y reduced the concept of c a u s a t i o n . The supposed v i r t u e of t h i s o n t i c account of causation i s the explanation of the core notion of "connectedness" between c a u s a l l y r e l a t e d events, something that cannot be accomplished merely by reference to some law or set of laws. F a i r ' s account i s s u c c e s s f u l only i f there are no a d d i t i o n a l mysteries to be found i n the p r o f f e r e d r e d u c t i o n , that i s , i n the laws of energy/momentum t r a n s f e r . My p o i n t i s that jio account can s u c c e s s f u l l y e x p l i c a t e t h i s core connection by reference to laws, since the "connection" w i l l always reappear unanalyzed i n the analysans. The extent to which any o n t i c account r e s t s on r e g u l a r i t i e s i s the extent to which causation remains mysterious. Consider the d i r e c t i o n of c a u s a l i t y . A counterexample, based on the asymmetry of caus a l 'flow' and pu r p o r t i n g to show that the caus a l r e l a t i o n should not be i n t e r p r e t e d o n t o l o g i c a l l y or r e a l i s t i c a l l y , i s of f e r e d by Deiks: Imagine some i c e cubes placed i n a glass of water. Ordinary language provides two ways of speaking i n causa l terms about t h i s s i t u a t i o n : (a) the i c e cubes cause the water to grow c o l d e r ; (b) the water causes the i c e cubes to melt. 154 This i s a d i f f i c u l t y f o r any " o n t o l o g i c a l " theory of causation because on such a theory only one of the p o s s i b i l i t i e s can correspond to the ' r e a l ' d i r e c t i o n of the causal l i n k . 4 Again, there are s e v e r a l threads to untangle here. We could consider t h i s 75 example (and there are many others ) as c a l l i n g f o r a r e v i s i o n of or d i n a r y language. This seems extreme, given that the i c e cubes seem s i n g u l a r l y r e l e v a n t to the water growing c o l d e r , even though the energy flows i n the opposite d i r e c t i o n . F a i r seems content to r e v i s e h i s proposal to a l l o w f o r energy flow i n e i t h e r d i r e c t i o n between the cause and the e f f e c t . On t h i s (revised) view (a) and (b) are e q u i v a l e n t . But then we lose one n a t u r a l advantage of the energy-flow conception — t h a t the asymmetry of energy-flow n e a t l y captures the asymmetry of causal d i r e c t i o n . More t e l l i n g , however, i s the f a c t that (a) and (b) do seem d i f f e r e n t : we can use (a) to e x p l a i n why the water grows c o l d e r , and (b) to e x p l a i n why the i c e cubes 76 melt. This remark goes deep — i t i s meant to cut against any o n t o l o g i c a l conception of c a u s a t i o n . Since the same set of circumstances can be marshalled to e x p l a i n c a u s a l l y a v a r i e t y of 'why' questions, then the a t t r i b u t i o n of the causal connection cannot be ' r e a l ' — i t must be a f u n c t i o n of our explanatory i n t e n t i o n s and not d e s c r i p t i v e of the s i t u a t i o n as such. I f the concept of causation i s depicted as "the flow of energy", or any other r e a l connection, then, i t i s charged, t h i s concept cannot be put to the v a r i e t y of uses demanded of i t as an explanatory c o n s t r u c t i o n . This i s , then, the t h i r d problem f o r the o n t i c view and i t becomes more apparent as we move away from physics to p s y c h o l o g i c a l , s o c i a l , and h i s t o r i c a l e x p l a n a t i o n s . For example, we may w e l l c i t e "being a C a t h o l i c " as a cau s a l f a c t o r i n the explanation of l i b e r a l v o t i n g behavior, and t h i s e x p l a n a t i o n may remain good even though we underwent "a sudden upheaval i n 155 77 p h y s i c a l theory which would obviate the concept of energy...". There seems no obvious p h y s i c a l i s t i c r e duction of t h i s causal c l a i m to one of energy/momentum t r a n s f e r , and, even i f there were, i t would serve only to obfuscate the matter a t hand. F a i r ' s c l a i m that t h i s i n a b i l i t y to perform 78 the r e d u c t i o n i s merely a matter of "our ignorance" i s a r a t h e r sweeping b i t of arm-waving. Before we turn to an a n a l y s i s of Salmon's theory of causal 'connectedness' or i n f l u e n c e , and an assessment of i t s a b i l i t y to handle these problems, a few remarks are i n order on the above dichotomy between causation as an o n t i c versus explanatory category. On the o n t i c view we have been c o n s i d e r i n g , a causal r e l a t i o n i s an o b j e c t i v e feature of the world. I take t h i s to mean more than j u s t that c e r t a i n event p a i r s behave according to e s t a b l i s h e d , or l a w - l i k e , r e g u l a r i t i e s , or that there e x i s t s a c e r t a i n l o g i c a l r e l a t i o n s h i p between t h e i r d e s c r i p t i o n s . Rather, t h i s r e l a t i o n i s a r e a l , p h y s i c a l connection between such events, and that i t i s t h i s connection which accounts f o r the production and propagation, i n Salmon's terms, of ca u s a l i n f l u e n c e . Our task, then, i s to describe the nature of t h i s i n f l u e n c e . This does not e n t a i l 'reducing' t h i s r e l a t i o n to non-causal terms, as i n c o n t i g u i t y , constant c o n j u n c t i o n , or temporal succession, although these may serve as evidence f o r a causal connection. I t may i n v o l v e a form of "power" as a causal analysand, but one no more mysterious than the concepts of f o r c e , or energy. At i s s u e here i s whether any of t h i s i s incompatible with causation as an explanatory category, e s p e c i a l l y outside of the domain of physics (where the idea of "power" has long been demystified.) Of course, one might suggest that the l o g i c of causal explanations i s not the same outside of 156 p h y s i c s , or perhaps that there simply are no causal explanations i n these ' s o f t e r ' s c i e n c e s . Both of these are untenable -- there i s no reason to think that the canons of understanding should s h i f t from d i s c i p l i n e to d i s c i p l i n e , nor are there reasons to r u l e out the p o s s i b i l i t y of j u s t such an understanding outside of p h y s i c s . I see no r e a l problem f o r the 'hard' s c i e n c e s , given F a i r ' s a n a l y s i s i n terms of energy/momentum t r a n s f e r , i n f i t t i n g t h i s concept of causation with the idea of causal e x p l a n a t i o n . But I a l s o see no r e a l reason f o r attempting to reduce the core concept of t h i s explanatory schema — that of the 'connectedness' between events — to the terms of physics f o r every other d i s c i p l i n e . What i s needed, r a t h e r , i s a more general c h a r a c t e r i z a t i o n of t h i s connection that i s free from, but not incompatible w i t h , the idea of energy/momentum t r a n s f e r . (Salmon, I b e l i e v e , has o f f e r e d j u s t such a c h a r a c t e r i z a t i o n , as we s h a l l see.) Thus I b e l i e v e that Deik's c l a i m "that we must not conceive of causation as an o n t o l o g i c a l category, but rather must see i t as an 79 explanatory concept," i s wrong-headed. Rather, i t i s the concept of c a u s a l i t y that acts the c e n t r a l r o l e i n any explanatory schema, and thus the nature of the causal r e l a t i o n w i l l determine the nature of the explanatory schema. Suppose c a u s a l i t y i s taken to be a l o g i c a l r e l a t i o n s h i p between i d e s c r i p t i o n s of r e g u l a r l y o c c u r r i n g event p a i r s . Then the causal law which describes t h i s r e g u l a r i t y , together with a d e s c r i p t i o n of i n i t i a l and boundary c o n d i t i o n s , w i l l e n t a i l a statement that the e f f e c t occurs, and thus e x p l a n a t i o n s , on t h i s view of causation, are arguments. In a p a r a l l e l f a s h i o n , i f causal r e l a t i o n s are taken to be nomological i n nature, then explananda which describe such nomically r e l a t e d events w i l l not e n t a i l , but r a t h e r demonstrate how the r e g u l a r i t y and i n i t i a l c o n d i t i o n s p h y s i c a l l y 157 n e c e s s i t a t e the occurrence of the explanandum event. I f , as we have argued, causation i s considered as an o n t o l o g i c a l r e l a t i o n , then causal explanations w i l l again take a d i s t i n c t form, where the event to be explained w i l l be made i n t e l l i g i b l e by l o c a t i n g i t i n the space-time p a t t e r n of events i n the world. 80 In Salmon's most recent o f f e r i n g he develops these three types of explanation from a c o n s i d e r a t i o n of the r e l a t i o n s h i p between the explanans and explanandum. I have approached t h i s typology from another aspect: the candidates f o r the causal r e l a t i o n . On my view i t i s only the o n t i c conception of c a u s a l i t y that provides understanding of the connectedness of events. For Salmon, only the o n t i c conception of e x p l a n a t i o n w i l l do. That these accounts mesh i s no acident: (1) f o r Salmon, the r e g u l a r i t y appealed to i n the explanans i s , or must be supplemented by, a c a u s a l account; (2) i f the r e g u l a r i t y i s c a u s a l , then the nature of t h i s r e g u l a r i t y w i l l d i c t a t e the kind of explanatory impetus t h a t the explanation can provide. Since i n both the l o g i c a l and nomic views of causation a form of n e c e s s i t y i s conferred upon events which i s incompatible w i t h indeterminism, Salmon opts f o r the o n t i c conception. I t i s my view that an even stronger c o n c l u s i o n i s warranted here. Not only i s the o n t i c conception of explanation the only conception to handle i n d e t e r m i n i s t i c s i t u a t i o n s , but i t i s the only one (of these three) t h a t seems to f u r t h e r our understanding of events i n the world. A l i s t of n e c e s s i t a t i n g f a c t o r s may show an event to be expected, or to be p h y s i c a l l y compelled, but t h i s knowledge seems to do l i t t l e more than s c r a t c h the surface of our ignorance. What we would l i k e to know l i e s deeper — the ground, as i t were, of the n e c e s s i t y . 158 What, then, on Salmon's account, c o n s t i t u t e s the c a u s a l connectedness between objects? Again, the reader must be cautioned that Salmon takes a 'long' view of o b j e c t s : the fundamental c o n s t i t u e n t s of h i s ontology are processes, with the notion of an event being a d e r i v a t i v e of these as a temporal stage, or s l i c e , of a s p a t i o - t e m p o r a l l y continuous process. Within t h i s framework the problem of causal connectedness, or c a u s a l i n f l u e n c e , becomes analogous to the problem of c o n t i n u i t y i n g e n e r a l . Neither t h i s problem, nor i t s s o l u t i o n , are new: Salmon sees i t s o r i g i n i n the paradoxes of motion formulated by Zeno, and i t s s o l u t i o n f o l l o w s d i r e c t l y 81 from the s o l u t i o n o f f e r e d f o r these paradoxes. The problem, f o r our purposes, can be b r i e f l y s t a t e d . A process 82 can be considered c a u s a l i f i t has the a b i l i t y to transmit a mark. Both the marking of a process, and the transmission of such marks, seem s t r a i g h t f o r w a r d l y causal i n nature, and, t h e r e f o r e , are i n need of f u r t h e r e x p l i c a t i o n . The nature of the former has been c h a r a c t e r i z e d v i a the n o t i o n 83 of a causal i n t e r a c t i o n . The problem at hand i s to c h a r a c t e r i z e the transmission of marks: "how does the process make the mark appear elsewhere 84 w i t h i n i t ? " The proposed s o l u t i o n i s e q u a l l y simply s t a t e d : A mark th a t has been introduced i n t o a process by means of a s i n g l e i n t e r v e n t i o n at p o i n t A i s transmitted to p o i n t B i f i t occurs at B and at a l l stages of the process between A and B without a d d i t i o n a l i n t e r v e n t i o n . Thus "making" a mark appear continuously i s nothing more than the f a c t t h a t a t each moment i t appears _at the appropriate p l a c e . This i s a more general account of the ' a t - a t ' theory o f f e r e d as a s o l u t i o n to Zeno's paradoxes of motion. There, i t w i l l be r e c a l l e d , the problem was to get from the apparent zero v e l o c i t y a t each i n s t a n t of an o b j e c t i n motion, to the f a c t of i t s 159 motion. The s o l u t i o n i s to see that, a t each i n s t a n t , the apparent zero v e l o c i t y was r e a l l y a non-zero instantaneous v e l o c i t y . This non-zero v e l o c i t y at each i n s t a n t can be mathematically c h a r a c t e r i z e d by a f u n c t i o n t h a t maps places and times, f o r each i n s t a n t . I t i s t h i s one-to-one mapping which suggests the more g e n e r a l i z e d account o f f e r e d here f o r continua — there i s no mathematical f u n c t i o n which describes t h i s mapping, as i n the s o l u t i o n to the problem of motion, r a t h e r t h i s i s "a p a r t i c u l a r l y important 86 species of constant c o n j u n c t i o n . " " P a r t i c u l a r l y important" or not, t h i s l a s t remark might seem a b i t m i s l e a d i n g . Our i n q u i r y began as a search f o r a c h a r a c t e r i z a t i o n of causal i n f l u e n c e w i t h i n the concept of s p a t i o - t e m p o r a l l y continuous processes; the response, i n terms of the ' a t - a t ' theory, e s p e c i a l l y as understood as a form of constant c o n j u n c t i o n , seems d i s c r e t e i n nature. How can i t provide us with the idea of the connection between o b j e c t s , or, i n the case of Salmonian processes, with the idea of continuous causal i n f l u e n c e ? But t h i s question seems to miss the p o i n t . To look f o r a connection between elements of a s e r i e s i s to admit that these elements need connecting. To look f o r something that grounds the c o n t i n u i t y of a causa l process i s to miss j u s t that q u a l i t y of experience which d i s t i n g u i s h e s a process from an event. The 'connection' i s not something added — rather i t i s contained i n the process i t s e l f . The fundamental d i f f e r e n c e between a process and a pseudo-process i s that " i n the causal process the r e g u l a r i t y i s 87 produced w i t h i n the process i t s e l f . " The mode of t h i s "production" i s nothing more than the "persistence of something" — a p e r s i s t e n c e of q u a l i t y 88 or s t r u c t u r e . 160 Is t h i s idea of " p e r s i s t e n c e " an e m p i r i c a l matter? A f t e r a l l , the idea r e s t s on nothing more than "the uninter r u p t e d resemblance" of our 89 impressions. And though resembling one another, these impressions are d i s t i n c t , and, as impressions go, so go our i d e a s . But, again, I think t h i s 90 i s misguided. To paraphrase a conclusion of Aronson , the i d e n t i t y of a s t r u c t u r e over time, or p e r s i s t e n c e , i s not at a l l l i k e that of impressions, the l a t t e r being separate and d i s t i n c t a t each moment i n time. Our judgement that the same process i s co n t i n u i n g i s not an inference from the resemblance of i t s stages — r a t h e r , i t seems to me, that the idea of an ' a t o m i s t i c ' impression i s the derived n o t i o n , one that i s achieved only by approaching a l i m i t of some k i n d (as i n the case of determining v e l o c i t y a t a poi n t . ) To r e i t e r a t e , p e r s i s t e n c e seems to imply a succession of d i s c r e t e s t a t e s : A i s (or has) a p e r s i s t e n t s t r u c t u r e i f f A at t- resembles A a t t. ., . I t i s t h i s i m p l i c a t i o n I wish to deny. Given t h i s understanding of the propagation of causal i n f l u e n c e , what can we now say regarding the three problems o u t l i n e d at the beginning of t h i s section? (1) Can we observe, i n the s i n g l e case, a causal connection without any e s s e n t i a l reference to laws or r e g u l a r i t i e s ? This question can now be reduced to (?) whether there i s a more p r i m i t i v e non-persistent experience which grounds, and i s e s s e n t i a l t o , our causal experience of p e r s i s t e n t o b j e c t s . I f what we have s a i d above i s c o r r e c t , then the answer seems to be no, f o r any i n d i v i d u a l process. When we consider the b a s e b a l l / s h a t t e r e d window event, however, we are e a s i l y l e d to the reduction of t h i s event i n t o d i s t i n c t experiences whose connection, according to the received view, i s a f u n c t i o n of constant c o n j u n c t i o n , e t c . Even i f we look f o r the p e r s i s t e n t 161 p a r t of t h i s event p a i r , namely the constancy of energy, we are a c t u a l l y r e l y i n g on a complex of laws (of c o n s e r v a t i o n , etc.) and thus t h i s constancy does not seem to be given i n experience. I t i s not c l e a r whether Salmon's more a b s t r a c t and su b t l e account fares much b e t t e r . For Salmon there are two processes here, each capable of t r a n s m i t t i n g causal i n f l u e n c e , or i n f o r m a t i o n . When they i n t e r a c t both are modified i n some (more or l e s s permanent) way. Does t h i s mutual m o d i f i c a t i o n presuppose any laws? Although i t may w e l l act i n accordance with some n a t u r a l laws, i t does not seem to presuppose them. In Salmon's system causal i n t e r a c t i o n , or the mutual m o d i f i c a t i o n of causal processes, i s a p r i m i t i v e entry. As such i t need not appear mysterious, or as a necessary category of experience. We may simply t r e a t i t as an observable r e l a t i o n between some i n t e r s e c t i n g processes. Since experience may lack t h i s observable r e l a t i o n (and lack even the p e r s i s t e n t s t r u c t u r e s necessary f o r i t ) , i t cannot be considererd an a p r i o r i c o n d i t i o n on experience. (2) The Salmonian response to the i c e water counterexample i s s t r a i g h t f o r w a r d . Deiks claimed that there were two d i s t i n c t and e q u a l l y l e g i t i m a t e causal d e s c r i p t i o n s of the s i t u a t i o n -- a d i s t i n c t i o n that Rogers' theory could not produce. In Salmon's theory the two d e s c r i p t i o n s are indeed d i s t i n c t — they are of two d i f f e r e n t processes, the i c e and the water, which are i n t e r a c t i n g . Both processes are c a u s a l , and t h e i r mutual m o d i f i c a t i o n shows them both as e f f e c t s , i . e . , the colder water and the melted i c e . (3) Can the Salmonian concept of c a u s a l i t y and causal explanation be extended f o r use outside the context of p h y s i c a l science? I can only sketch the beginnings of an answer to t h i s question here, but I think t h i s w i l l s u f f i c e to suggest the a f f i r m a t i v e . 162 There are two p o i n t s to consider: causal claims and causal e x p l a n a t i o n s . The foundation of causal c l a i m s , on Salmon's view, r e s t s on the p e r s i s t e n c e of s t r u c t u r e and the transmission of i n f o r m a t i o n , that i s , on processes and marks. This i s a very general and a b s t r a c t c h a r a c t e r i z a t i o n . We can f i l l out t h i s general c h a r a c t e r i z a t i o n f o r any d i s c i p l i n e by s e t t i n g out the p a r t i c u l a r s t r u c t u r e s and mechanisms that f u l f i l l these r o l e s w i t h i n that area of study. In the v o t i n g behavior example c i t e d above we may o f f e r the s t a b i l i t y of church dogma and the s o c i a l i z i n g e f f e c t s on i t s adherents as the p a r a l l e l components i n the suggested causal c l a i m . And we needn't be saddled w i t h F a i r ' s f a n c i f u l proposal to reduce these claims to ones about energy t r a n s f e r , as i n h i s h i s t o r i c a l example "Antiwar demonstrations were a 91 cause of the Vietnam war ending." We need only show how c e r t a i n s o c i a l s t r u c t u r e s maintained s u f f i c i e n t coherence and s t a b i l i t y to have the c a p a c i t y to mutually modify each other through the transmission of i n f o r m a t i o n . S i m i l a r remarks seem appropriate when we turn to c a u s a l e x p l a n a t i o n . E x p l a n a t i o n , on t h i s view, does not proceed by l o g i c a l i n f e r e n c e or nomic n e c e s s i t y . Rather, to provide a causal explanation of an 92 event i s to l o c a t e i t w i t h i n an i n t e l l i g i b l e network of events and processes. The s t r u c t u r e of t h i s network i s provided by causal r e l a t i o n s as described above — through p e r s i s t e n c e and transmission of i n f o r m a t i o n . Both f u n c t i o n a l and s t a t i s t i c a l explanations can be accommodated w i t h i n t h i s schema. I t i s our knowledge of the s t r u c t u r e of the world — i t s s t a b i l i t y and c a p a c i t y to be modified — which grants us understanding. 163 Notes - Chapter I I I 1. R e c a l l the d i s c u s s i o n i n Chapter I , Section 3 and 4b. There i t was argued that the value of the p r i o r and p o s t e r i o r weights of the s t a t i s t i c a l relevance r e l a t i o n s that marked a causal connection need not show a p o s i t i v e relevance of cause f o r e f f e c t . Causal f a c t o r s need o n l y mark a r e l a t i v e d i f f e r e n c e i n the p o s s i b i l i t y of the occurrence of t h e i r e f f e c t s . S e c t i o n 4b was an attempt to r e c o n c i l e t h i s c l a i m with our i n t u i t i v e demands on causal e x p l a n a t i o n . Here our (perhaps more basic) concern i s the e f f e c t t h i s lack of p o s i t i v e relevance may have on sequences of i n t e r s e c t i n g and i n t e r a c t i n g causal processes. 2. Rosen (1978). 3. Salmon has catalogued some of these responses i n h i s (1980a). What fo l l o w s here w i l l r e l y on t h i s e x p o s i t i o n . 4. Rosen (1978). 5. Salmon (1980a), p. 65. 6. Loc. c i t . 7. Loc. c i t . 8. Rosen (1978). 9. I . J . Good (1961). 10. Salmon (1980a), p. 64. 11. Good (1961), p. 318. Good does not elaborate on t h i s suggestion. 12. See Humphreys (1980), Theorem 1 — proof i n appendix. P(D) i s w e l l d e f i n e d i f P(D) i s : P(D) = 1 - P(D). 13. Good (1980). 14. Op. c i t . , p. 303. 15. This i s a s i m p l i f i c a t i o n of Salmon's (1980a) example, p. 68. The suggested p r o b a b i l i t i e s y i e l d an example analogous to the atom-decay example. 16. Salmon (1980a), p. 69. 17. Op. c i t . , p. 74, f n . 24. 18. Op. c i t . , p. 69. 19. Op. c i t . , p. 68. 20. Op. c i t . , p. 74, f n . 24. (My emphasis.) 164 21. Op. c i t . , p. 70. 22. Loc. c i t . 23. Perhaps r e l a t e d to some Lockean notion of 'power' or ' a b i l i t y 1 . See Essay Concerning Human Understanding, Book I I , Chapter 21. 24. Hume's answer: "a h a b i t of the mind." 25. Humphreys (1980). 26. Op. c i t . , p. 309. 27. This "s i g n r u l e " f o r a chain of p r o b a b i l i t y r e l a t i o n s pre-dates Humphreys' proof — see Costner and L e i k (1964). 28. (1) i s obvious. (2) can be simply shown: I f P A(B)>P(B), since P(B) = 1 - P(B), P A(B)>1 - P(B), then P A(B) - 1>-P(B). M u l t i p l y i n g by (-1) y i e l d s 1 - P A(B)<P(B), but P A(B) = 1 - P A ( B ) . q.e.d. 29. Humphreys (1980), p. 308. 30. Loc. c i t . 31. Loc. c i t . 32. For the moment an i n d i r e c t cause w i l l be an event which r a i s e s the p r o b a b i l i t y of i t s e f f e c t - e v e n t , but which i s not the immediate predecessor of that e f f e c t - e v e n t . One of the r e s u l t s of t h i s example w i l l be to narrow t h i s d e f i n i t i o n . 33. Humphreys (1980), p. 309, f n . 7. 34. Op. c i t . , p. 308. 35. Loc. c i t . 36. This i s obvious i f we cut the chain at a d i f f e r e n t l i n k : suppose A ^ B D occurs. Surely Axel i s a cause of D. 37. Humphreys (1980), p. 309. 38. Loc. c i t . 39. The term i s Rogers' (1981). 40. As Humphreys puts i t , " A l l o w i n g [Axel as a cause].. .would erase the important d i s t i n c t i o n between ( p o s i t i v e ) causes and negative causes." (1980), p. 309. 41. Salmon (1980a), p. 70. 42. Salmon (1980a), p. 71. 165 43. See e s p e c i a l l y Humphreys (1980), f n . 5; Salmon (1980), f n . 3 and (1980b) ( c l a s s e s ) , (1978), p. 412 (event t y p e s ) . 44. A large debt i s owed, f o r much of what f o l l o w s , to Ben Rogers' (1981). Rogers' work was brought to my a t t e n t i o n a f t e r I had formed only the p r e l i m i n a r y i n t u i t i o n s of t h i s s e c t i o n — h i s d i s c u s s i o n has served t o c l a r i f y these ideas — although, as w i l l be seen, we are not e n t i r e l y eye to eye. The reader w i l l s u r e l y b e n e f i t , as I have, from t h i s a r t i c l e . 45. See above, Chapter I , p. 37. 46. In Salmon (1978) . 47. R e c a l l t h a t c o n j u n c t i v e forks are d i f f e r e n t i a t e d from i n t e r a c t i v e forks by r e p l a c i n g ( i ) P(A & B/C) = P(A/C)*P(B/C) w i t h ( i i ) P(A & B/C)>P(A/C)*P(B/C) i n the d e f i n i t i o n ; other d e f i n i n g i n e q u a l i t i e s and equations remain the same. See above, Chapter I , p. 4 0 f f . 48. The reader may see Chapter I , s e c t i o n s 3a and 3b f o r d e t a i l s . 49. Rogers (1981), p. 203. 50. Salmon (1980), p. 74, f n . 25. 51. Rogers (1981), p. 203. 52. Salmon (1978), p. 417. 53. This r e s u l t i s known as Simpson's Paradox. What t h i s amounts t o , i n our terms, i s that "screening o f f " s i m p l i c i t e r can no longer be ^considered a causal i n d i c a t o r . In experimental terms the two causal patterns the same r e s u l t : the c o r r e l a t i o n between X and Y disappears. 54. Rogers (1981), p. 220. 55. The s i t u a t i o n i s o b v i o u s l y more complex than t h i s simple sketch. For a more d e t a i l e d account of experimental s i t u a t i o n s see Giere (1979); o r f o r s i t u a t i o n s where v a r i a b l e s cannot be ( e a s i l y ) manipulated see B l a l o c k (1961). 56. Rogers (1981), p. 210. 57. Salmon (1978), p. 422. 58. R u s s e l l (1929). when c o n t r o l l e d for W, y i e l d 166 59. This i s not q u i t e as Hempelian as i t sounds. The subsumption c o n s i s t s i n the p l a c i n g of an explanandum event i n the proper " c e l l " of a pro p e r l y p a r t i t i o n e d (homogeneous) reference c l a s s of events. These ex p l a n a t i o n s , c o n t r a Hempel, are not arguments. 60. Henri Bergson (1970). This p o i n t was begun i n Chapter I I , pp. 87-88. 61. Salmon (1980a), p. 66. 62. Op. c i t . , p. 70. 63. Salmon (1977a); F a i r (1979). 64. F a i r (1979), p. 245. 65. Op. c i t . , p. 236. 66. They are not without i n t e r e s t , however. F a i r describes the causal r e l a t i o n between dynamic v a r i a b l e s — whose c o r r e l a t i o n s are o f t e n described as c a u s a l , e.g., the length of the pendulum caused i t s period — as " c o n t r o v e r s i a l " ; the r e l a t i o n s h i p between mathematical v a r i a b l e s — where a f u n c t i o n a l r e l a t i o n between values i s described as causal — i s " c l e a r l y metaphorical." C e r t a i n l y not a l l p h y s i c a l explanation i n v o l v e s a t r a n s f e r of energy. 67. Hume (1748), Section V I I , p a r t I . See al s o T r e a t i s e (Selby-Bigge) P a r t I I I , S e c t i o n XIV, p. 162. 68. Carnap, (1964) 69. F a i r (1979), p. 225. 70. Loc. c i t . 71. For s i m i l a r reasons, D. Dieks (1981) sees F a i r ' s proposal as a v e r s i o n of the nomic a n a l y s i s of caus a t i o n ; and w i t h i n t h i s view as an attempt to analyze the notion of a causal law. 72. F a i r (1979), p. 231. Cf. Richard Boyd i n a recent ms.: "Ma t e r i a l i s m without Reduction: Non-Humean Cuasation and the Evidence f o r Ph y s i c a l i s m " : " C e r t a i n l y the a n a l y s i s of causation i n terms of the i n t e r a c t i o n of microscopic causal f a c t o r s i s not an a n a l y t i c d e f i n i t i o n (or a d e f i n i t i o n a t a l l , f o r that matter), but an e m p i r i c a l a n a l y s i s or assay of the c o n s t i t u e n t s of p h y s i c a l c a u s a t i o n . On the s o r t of Non-Humean account we are c o n s i d e r i n g , causal terms r e f e r to features of the world, features whose p r o p e r t i e s are s t i l l being discovered." p. 47. 73. This presents no problem, however, f o r the confirma t i o n of causal hypotheses — one can simply 'bootstrap' i t — i . e . assume the r e l e v a n t conservation laws, observe a s u f f i c i e n t number of instances of appropriate causal r e l a t i o n s , and holding these 'new' r e g u l a r i t i e s constant, confirm the conservation laws. 167 74. Deiks (1981), p. 106. 75. E.g., any cases where the r e d e s c r i p t i o n of the cause i n terms of energy flow shows that the cause l o s e s , while the e f f e c t gains, energy. 76. This i s Deiks' (1981) c r i t i c i s m , p. 106. 77. Op. c i t . , p. 107. 78. F a i r (1979), p. 237. To be f a i r , F a i r r e a l i z e s only too c l e a r l y the programmatic nature of t h i s conception of c a u s a l i t y , p. 234. 79. Deiks (1981), p. 106. 80. Salmon (1982). 81. For a d i s c u s s i o n of Zeno's problems see Salmon (1970); and Salmon (1975). 82. 83. 84. 85. 86. See Chapter I , Section 3a f f . Chapter I , S e c t i o n 3b. Salmon (1977), p. 221 . Loc. c i t . Salmon (1977a), p. 220. These are not the constant conjunctions Hume requ i r e d of h i s causal connection. Later i n t h i s a r t i c l e (p. 223) Salmon b e t t e r c h a r a c t e r i z e s the r e l a t i o n s h i p s among these concepts: c a u s a l processes are d i s t i n g u i s h e d by t h e i r a b i l i t y to transmit marks; they (the processes) are governed by laws ( r e l a t i n g i n t e r a c t i o n s of processes); these laws are e m p i r i c a l r e g u l a r i t i e s ; such r e g u l a r i t i e s are the constant conjunctions required by Hume. 87. Salmon (1977a), p. 219. 88. The d e s c r i p t i o n i s R u s s e l l ' s from h i s (1948) p. 459, quoted i n Salmon, l o c . c i t . 89. Hume, T r e a t i s e , p. 164. 90. Aronson (1971), p. 156. 91. F a i r (1979), p. 237. 92. 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(1977): "Causation, E x p l a n a t i o n , and S t a t i s t i c a l Relevance", Philosophy of Science 44, pp. 136-145. Sosa, E., ed. (1975): Causation and C o n d i t i o n a l s , Oxford U n i v e r s i t y Press, Oxford. T a y l o r , C. (1966): "The Metaphysics of Causation", from A c t i o n and Purpose, P r e n t i c e H a l l , Englewood C l i f f s , N.J., r e p r i n t e d i n Causation and  C o n d i t i o n a l s , pp. 39-43. van Fraassen, B. (1978): "Review of Stegmuller, P e r s o n e l l e and S t a t i s t i c h e  W a h r s c h e i n l i c h k e i t , S p r i n g e r - V e r l a g , 1973, i n Philosophy of Science 45, pp. 158-163. (1980): The S c i e n t i f i c Image. Clarendon P r e s s , Oxford. Mises (1939): P r o b a b i l i t y , S t a t i s t i c s and Truth, W. Hodge. 

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