"Arts, Faculty of"@en . "Philosophy, Department of"@en . "DSpace"@en . "UBCV"@en . "Kosub, Timothy Alexander"@en . "2010-09-07T16:46:36Z"@en . "1989"@en . "Master of Arts - MA"@en . "University of British Columbia"@en . "Kuhn's incommensurability thesis is the claim that successive scientific theories often conflict not only logically but also normatively: i.e. they differ both about nature and also about the use of common apparatus, concepts and experimental results, and what are proper scientific goals and methods. Critics commonly object that Kuhn's thesis attacks such traditional scientific values as objectivity and rationality. But their strongest response can be expressed as a dilemma: either, if taken literally, the incommensurability thesis is self-contradictory; or, if that literal reading is rejected, this thesis has no philosophical Import. Kuhn claims his critics have misinterpreted his thesis and he maintains both its intelligibility and relevance. The problem is whether his position can be sustained.\r\nIn support of Kuhn, I argue that his critics' reading of his thesis is based on a mistaken Identification of logic with formal logic and, more generally, of comparability with commensurabil-lty. I argue that logical comparison of theories that lack common concepts is possible if one can compare theories directly, as whole to whole, and that such direct logical comparison is actually commonplace in natural languages. I also argue more generally that Kuhn's critics' identification of comparison with com-mensuration leads to a vicious regress.\r\nMy attempt at resolving the dispute between Kuhn and his critics is informed by a simple \"hermeneutic\" principle: If one view seems either unintelligible or irrelevant to the other, then both sides probably disagree on the Interpretation of shared concepts. Once the focus of the dispute is located, arguments can often be given for preferring one interpretation over another. Thus if I am right that Kuhn's critics' view wrongly equates comparability with commensurability and logic with formal logic, that view clearly must be replaced by one that distinguishes them.\r\nI argue that if those distinctions are made, incommensurability can be seen to represent no essential threat to scientific rationality and objectivity. In this light, I suggest Kuhn's major analytic concepts be viewed as Improvements on more traditional notions drawn from formal logic. I also use a historical case study of the original discovery of geometrical incommensurability to illustrate further Kuhn's concepts and to develop a more general notion of a proof of incommensurability that is applicable to scientific theories."@en . "https://circle.library.ubc.ca/rest/handle/2429/28254?expand=metadata"@en . "A DEFENCE OF KUHN'S INCOMMENSURABILITY THESIS By TIMOTHY ALEXANDER KOSUB B . S c , The U n i v e r s i t y of B r i t i s h Columbia, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES (Philosophy) We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October 1989 \u00C2\u00A9 Timothy Alexander Kosub, 1989 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date 1 DE-6 (2/88) u A b s t r a c t Kuhn's incommensurability t h e s i s i s the c l a i m that s ucces-s i v e s c i e n t i f i c t h e o r i e s o f t e n c o n f l i c t not o n l y l o g i c a l l y but a l s o n o r m a t i v e l y : i . e . they d i f f e r both about nature and a l s o about the use of common apparatus, concepts and experimental r e -s u l t s , and what are proper s c i e n t i f i c g o a l s and methods. C r i t i c s commonly o b j e c t t h a t Kuhn's t h e s i s a t t a c k s such t r a d i t i o n a l s c i -e n t i f i c v a l u e s as o b j e c t i v i t y and r a t i o n a l i t y . But t h e i r s t r o n g -e s t response can be expressed as a dilemma: e i t h e r , i f taken l i t -e r a l l y , the incommensurability t h e s i s i s s e l f - c o n t r a d i c t o r y ; o r , i f t h a t l i t e r a l r e a d i n g i s r e j e c t e d , t h i s t h e s i s has no p h i l o s o -p h i c a l Import. Kuhn cl a i m s h i s c r i t i c s have m i s i n t e r p r e t e d h i s t h e s i s and he maintains both i t s i n t e l l i g i b i l i t y and r e l e v a n c e . The problem i s whether h i s p o s i t i o n can be s u s t a i n e d . In support of Kuhn, I argue t h a t h i s c r i t i c s ' r e a d i n g of h i s t h e s i s Is based on a mistaken I d e n t i f i c a t i o n of l o g i c with formal l o g i c and, more g e n e r a l l y , of c o m p a r a b i l i t y with commensurabil-l t y . I argue t h a t l o g i c a l comparison of t h e o r i e s t h a t lack com-mon concepts i s p o s s i b l e i f one can compare t h e o r i e s d i r e c t l y , as whole to whole, and t h a t such d i r e c t l o g i c a l comparison i s a c t u -a l l y commonplace i n n a t u r a l languages. I a l s o argue more gener-a l l y t h a t Kuhn's c r i t i c s ' i d e n t i f i c a t i o n of comparison with com-mensuration l e a d s to a v i c i o u s r e g r e s s . My attempt a t r e s o l v i n g the d i s p u t e between Kuhn and h i s c r i t i c s i s informed by a simple \"hermeneutic\" p r i n c i p l e : I f one view seems e i t h e r u n i n t e l l i g i b l e or i r r e l e v a n t to the other, then both s i d e s p r o b a b l y d i s a g r e e on the I n t e r p r e t a t i o n of shared con-c e p t s . Once the focus of the d i s p u t e i s l o c a t e d , arguments can o f t e n be g i v e n f o r p r e f e r r i n g one i n t e r p r e t a t i o n over another. Thus i f I am r i g h t t h a t Kuhn's c r i t i c s ' view wrongly equates c o m p a r a b i l i t y with commensurability and l o g i c with formal l o g i c , t h a t view c l e a r l y must be r e p l a c e d by one t h a t d i s t i n g u i s h e s them. I argue t h a t i f those d i s t i n c t i o n s are made, incommensur-a b i l i t y can be seen t o r e p r e s e n t no e s s e n t i a l t h r e a t t o s c i e n t i f -i c r a t i o n a l i t y and o b j e c t i v i t y . In t h i s l i g h t , I suggest Kuhn's major a n a l y t i c concepts be viewed as Improvements on more t r a d i -t i o n a l n o t i o n s drawn from formal l o g i c . I a l s o use a h i s t o r i c a l case study of the o r i g i n a l d i s c o v e r y of g e o m e t r i c a l incommensur-a b i l i t y to i l l u s t r a t e f u r t h e r Kuhn's concepts and t o develop a more g e n e r a l n o t i o n of a proof of incommensurability t h a t i s a p p l i c a b l e t o s c i e n t i f i c t h e o r i e s . Contents iv ABSTRACT i i TABLE OF CONTENTS i v FIGURES V i Chapter 1: Commensurability, C o m p a r a b i l i t y , and L o g i c 1 1.0 I n t r o d u c t i o n 1 1.1 The Incommensurability T h e s i s 3 1.1.1 H i s t o r y and The Incommensurability T h e s i s 7 1.2 The C r i t i c a l Response: L o g i c and Formal L o g i c s 14 1.3 Commensurability and C o m p a r a b i l i t y 18 1.4 I n t e r i m Summary 26 1.5 How to D i s t i n g u i s h C o m p a r a b i l i t y from Commensurability 27 1.5.1 Kuhn and D i r e c t Comparison 32 1.6 L o g i c and Formal L o g i c s 33 1.6.1 Argument 1: Formal Comparison of T h e o r i e s 36 1.6.2 Argument 2: Formal A n a l y s i s of T h e o r i e s 36 1.6.3 A G e s t a l t - S w i t c h Model of T h e o r e t i c a l I n c o m p a t i b i l i t y 40 1.7 D i r e c t Comparison: A Thought Experiment 44 1.8 Summary, S y n t h e s i s and C o n c l u s i o n 47 Notes to Chapter 1 50 Chapter 2: Kuhn's A l t e r n a t i v e A n a l y t i c Concepts 60 2.0 I n t r o d u c t i o n 60 2.1 Paradigms and U n i v e r s a l G e n e r a l i z a t i o n s 61 2.1.1 Normal Science as a Process of Paradigm A r t i c u l a t i o n 63 2.1.2 Paradigms, Commensurability and D i r e c t C o m p a r a b i l i t y 65 2.1.3 D i r e c t Comparison of Competing Paradigms 70 2.2 F e l t Anomaly 73 2.3 C r i t i c a l Anomaly and C r i s i s 75 2.4 Thought Experiment: I s o l a t i n g the Root of C r i s i s 77 2.4.1 A P i a g e t i a n Thought Experiment: Volume Conservation 80 2.4.2 G a l i l e o ' s Thought Experiment 83 2.5 Morals 87 Notes to Chapter 2 90 Chapter 3: P r o v i n g Kuhnian Incommensurability: A Case Study 95 3.0 I n t r o d u c t i o n 95 3.1 The Pythagorean Paradigms 96 3.2 Dot-Diagramme A r t i c u l a t i o n s 100 3.3 Rules f o r F i n d i n g Pythagorean T r i p l e s 104 3.4 A r i t h m e t i c & Geometric V e r s i o n s of Pythagorus Theorem 105 3.5 Thought Experiment: Proof of Incommensurability 107 3.6 C o n c l u s i o n : Kuhnian and Mathematical Incommensurability 108 Notes to Chapter 3 111 B i b l i o g r a p h y 113 vi L i s t of F i g u r e s 1. The d u c k - r a b b i t G e s t a l t f i g u r e 41 2. An i n c l i n e d plane 85 3. A pebble r e p r e s e n t a t i o n of twelve 101 4. A pebble r e p r e s e n t a t i o n of t h i r t e e n 101 5. The seventh t r i a n g u l a r number 101 6. The f i f t h square number 102 7. The f o u r t h oblong number 102 8. D i v i d i n g an oblong f i g u r e 103 9. D i v i d i n g a square f i g u r e 103 chapter 1 Commensurability, C o m p a r a b i l i t y and L o g i c 1.0 i n t r o d u c t i o n In The structure of Scientific Revolutions, T. S. Kuhn mar-s h a l s much h i s t o r i c a l , p s y c h o l o g i c a l and p h i l o s o p h i c a l evidence f o r h i s t h e s i s t h a t s u c c e s s i v e s c i e n t i f i c t h e o r i e s are o f t e n both l o g i c a l l y incompatible and incommensurable (Kuhn 1970a, 96, 103). Kuhn contends t h a t the e x i s t e n c e of incommensurable t h e o r i e s i s r u l e d out by t r a d i t i o n a l eplstemology and p h i l o s o p h y of s c i e n c e ; so he concludes t h a t the t r a d i t i o n a l v i e v must be r e p l a c e d by a \" v i a b l e a l t e r n a t i v e \" t h a t can accommodate incommensurability (Kuhn 1970a, 121). Kuhn's c r i t i c s have r a i s e d many, s e r i o u s o b j e c t i o n s t o the incommensurability t h e s i s . Most are methodological and \"moral\" ( S c h e f f l e r 1967, 8) o b j e c t i o n s , which c l a i m incommensurability leads t o such bogies as r e l a t i v i s m and i r r a t i o n a l i s m . But Kuhn's opponents' deepest c h a l l e n g e i s t h a t h i s t h e s i s i s e i t h e r s e l f -c o n t r a d i c t o r y , i f taken l i t e r a l l y , or p h i l o s o p h i c a l l y i r r e l e v a n t , i f not. Thus h i s opponents take the standard meaning of \"incom-mensurable\" to be \" a b s o l u t e l y incomparable\" and argue t h a t , be-cause l o g i c a l l y incompatible t h e o r i e s are comparable, Kuhn's t h e s i s i s \" s e l f - r e f u t i n g \" (e.g. Putnam 1981a, 114). And they counter t h a t i f , i n Kuhn's usage, \"Incommensurable\" does not mean \" a b s o l u t e l y Incomparable,\" then the evidence he musters f o r h i s 2 t h e s i s can have o n l y p s y c h o l o g i c a l or pragmatic s i g n i f i c a n c e . N e v e r t h e l e s s , Kuhn r e j e c t s h i s c r i t i c s ' a n a l y s i s and continues to maintain the p h i l o s o p h i c a l importance of h i s t h e s i s . In t h i s c hapter, I defend Kuhn's r e b u t t a l by shoving t h a t h i s c r i t i c s ' arguments depend on a mistaken i d e n t i f i c a t i o n of l o g i c v i t h formal l o g i c and, more g e n e r a l l y , of comparison v i t h comraensuratlon. I argue t h a t Kuhn's t h e s i s Is p e r f e c t l y i n t e l l i -g i b l e i f those n o t i o n s are d i s t i n g u i s h e d . In a d d i t i o n , I provide t e x t u a l evidence t h a t Kuhn h i m s e l f d i s t i n g u i s h e s those concepts i n h i s vork. My arguments cannot, by t h e i r n ature, provide p o s i -t i v e evidence f o r the a c t u a l e x i s t e n c e of incommensurable theo-r i e s . P r o v i d i n g such p o s i t i v e evidence i s not my aim here s i n c e Kuhn has a l r e a d y s a t i s f i e d t h i s demand, as shovn by the v i g o r o u s c r i t i c a l r e a c t i o n t o h i s t h e s i s . 1 Instead of a r g u i n g f o r a c t u a l Incommensurability, I seek to remove an important o b s t a c l e t o a f a i r e v a l u a t i o n of Kuhn's e v i -dence. But I b e l i e v e my arguments perform more than t h a t nega-t i v e f u n c t i o n . I f I am r i g h t t h a t the t r a d i t i o n a l p h i l o s o p h y of Kuhn's c r i t i c s p r e c l u d e s i n c o m m e n s u r a b i l i t y because i t i s founded on a mistaken i d e n t i f i c a t i o n of d i s t i n c t concepts, my arguments a l s o p r o v i d e p o s i t i v e support f o r Kuhn's c l a i m t h a t ve need a nev \" e p i s t e m o l o g l c a l paradigm\" (Kuhn 1970a, 121): one t h a t embodies those c o n c e p t u a l d i s t i n c t i o n s , and thus a l l o w s f o r incommensura-b i l i t y . I t t u r n s out t h a t , c o n t r a r y t o vhat some of Kuhn's c r i t -i c s have claimed, t h i s nev epistemology need not eschev t r a d i -t i o n a l s c i e n t i f i c v a l u e s such as o b j e c t i v i t y and r a t i o n a l i t y , 3 1.1 The Incommensurability T h e s i s On the t r a d i t i o n a l view, s c i e n c e Is seen ( i d e a l l y ) t o pro-gress through t h e o r y change by accumulating f a c t s whose char a c -t e r i z a t i o n i s t h e o r y - n e u t r a l and by an I n c r e a s i n g v e r i s i m i l i t u d e t o a theory-independent r e a l i t y . The r e j e c t i o n of a c u r r e n t s c i -e n t i f i c t h e o r y i n favour of a new one i s deemed r a t i o n a l on t h i s view i f I t can be shown neutrally\u00E2\u0080\u0094i.e. on grounds common to both t h e o r i e s \u00E2\u0080\u0094 t h a t the new th e o r y i n c o r p o r a t e s the p o s i t i v e r e s u l t s of i t s predecessor while a v o i d i n g i t s e r r o r s and t h a t the new th e o r y has g r e a t e r e x p l a n a t o r y and p r e d i c t i v e scope ( C o l l i e r 1984, 9 ) . A premise of such n e u t r a l comparison, and t h e r e f o r e , of t r a d i t i o n a l p h i l o s o p h y of s c i e n c e , i s t h a t s u c c e s s i v e s c i e n t i f i c t h e o r i e s have the same b a s i c l o g i c a l s t r u c t u r e , a t l e a s t f o r those domains i n which they compete. Thus t o compare s u c c e s s i v e t h e o r i e s n e u t r a l l y f o r e m p i r i c a l adequacy i n those domains, the t r a d i t i o n a l view r e q u i r e s t h a t the meanings of each theory's r e -f e r r i n g e x p r e s s i o n s and other n o n - l o g i c a l concepts do not change (Newton-Smith 1981, 10). But i t i s p r e c i s e l y t h i s b a s i c premise of c o n c e p t u a l s t a b i l i t y between s u c c e s s i v e t h e o r i e s t h a t Kuhn cl a i m s h i s h i s t o r i c a l s t u d i e s show to be mistaken. In f a c t , Kuhn's n o t o r i o u s Incommensurability thesis i s the c l a i m t h a t the-ory change i n s c i e n c e i s o f t e n , i f not always, so r e v o l u t i o n a r y t h a t s u c c e s s i v e t h e o r i e s l a c k the common concepts and r e f e r r i n g 4 e x p r e s s i o n s r e q u i r e d f o r n e u t r a l l o g i c a l comparison (Kuhn 1970a, 102).* H i s t o r i c a l l y , Kuhn argues, the cause of an e a r l i e r t h e o r y ' s 9 f a i l u r e t o cope with experience o f t e n l i e s not j u s t with t h a t theory's e m p i r i c a l content but a l s o with i t s concepts, which are i t s means of e x p r e s s i n g t h a t content (Kuhn 1970a, 53). That i s , o f t e n the d i s c o v e r y of an \"unexpected n o v e l t y \" ( I b i d . , 35) i s not o n l y e m p i r i c a l l y , but a l s o c o n c e p t u a l l y , anomalous because t h a t novel phenomenon appears to f a l l v i t h i n the t h e o r y ' s scope, but a c t u a l l y c o n f l i c t s v i t h assumptions i m p l i c i t i n the theory's c a t e g o r i e s ( i b i d . , 63-4). The nev t h e o r y , Kuhn c l a i m s , has \"to change the meaning of (such p r o b l e m a t i c ] c o n c e p t s \" ( i b i d . , 102) i f i t i s t o a v o i d both of i t s predecessor's d i f f i c u l t i e s ( i b i d . , 56, 64). 4 Moreover, Kuhn a l s o argues t h a t a s c i e n t i f i c theory's con-cepts form an \" i n t e g r a t e d \" vhole ( i b i d . , 129) or \"conceptual veb\" ( i b i d . , 149); so the r e q u i r e d change of meaning of the p a r t i c u -l a r l y p r o b l e m a t i c concepts a l s o changes the meaning of a l l the other concepts the nev t h e o r y r e t a i n s from i t s predecessor. Such a r e v o l u t i o n a r y conceptual change betveen s u c c e s s i v e t h e o r i e s , he says, makes them \"fundamentally i n c o m p a t i b l e \" (Kuhn 1970a, 98): i t s i m u l t a n e o u s l y r e s u l t s i n both \" s u b s t a n t i v e \" ( i . e . l o g i c a l ) and \"normative\" ( i . e . c o n c e p t u a l , m e t h o d o l o g i c a l , o b s e r v a t i o n a l ) i n c o m p a t i b i l i t y ( I b i d . , 103, 109). ...paradigms [or, t h e o r i e s ; see n3] d i f f e r i n more than substance, f o r they are d i r e c t e d not o n l y to nature but a l s o 5 back upon the s c i e n c e t h a t produced them. They are the source of the methods, p r o b l e m - f i e l d , and standards of s o l u -t i o n accepted by any mature s c i e n t i f i c community a t any given time. As a r e s u l t , the r e c e p t i o n of a new paradigm o f t e n n e c e s s i t a t e s a r e d e f i n i t i o n of the c o r r e s p o n d i n g s c i -ence ( i b i d . , 103. I t a l i c s mine). That r e d e f i n i t i o n of s c i e n c e , Kuhn c l a i m s , \"changes...the standards governing p e r m i s s i b l e problems, concepts, and explana-t i o n s \" (Kuhn 1970a, 106. I t a l i c s mine). As a r e s u l t , not o n l y does the t r u t h of one view imply the other's f a l s i t y ( i b i d . , 9 8 ) 3 but o f t e n the \"problems, c o n c e p t s , and e x p l a n a t i o n s \" of one view appear e i t h e r i ncoherent or s c i e n t i f i c a l l y i r r e l e v a n t by the standards of the other (Kuhn 1970a, 103-110). In b r i e f : \"The n o r m a l - s c i e n t i f i c t r a d i t i o n t h a t emerges from a s c i e n t i f i c r e v o -l u t i o n i s not o n l y [ l o g i c a l l y ] incompatible but o f t e n a c t u a l l y incommensurable with t h a t which has gone b e f o r e \" (Kuhn 1970a, 103. I t a l i c s mine). Kuhn draws the f o l l o w i n g g e n e r a l l o g i c a l and e p i s t e m o l o g i c a l c o n c l u s i o n s from the incommensurability t h e s i s : (1) because there are no t h e o r y - n e u t r a l grounds f o r determining which of two incom-mensurable views i s t r u e (or f a l s e ) , the concept of t r u t h has an \"unproblematic\" a p p l i c a t i o n o n l y l n t r a t h e o r e t i c a l l y (Kuhn 1970b, 264);' hence, (2) the t r a d i t i o n a l i d e a l of s c i e n c e p r o g r e s s i n g toward an a n t e c e d e n t l y - u n d e r s t o o d aim of t r u t h i s a chimaera. S t i l l , Kuhn b e l i e v e s t h a t , d e s p i t e the absence of a n e u t r a l s t a n d p o i n t , i t i s p o s s i b l e t o compare c u r r e n t t h e o r y with p r e v i -ous ones (Kuhn 1970b, 264). And such backward-looking comparison o f t e n shows l a t e r t h e o r y t o be an improvement on e a r l i e r ones 6 (Kuhn 1970b, 264). That suggests, Kuhn says, t h a t we should \" s u b s t i t u t e evolution-from-what-we-do-know f o r the ( t r a d i t i o n a l ] e v o l u t i o n - t o v a r d - v h a t - v e - v i s h - t o - k n o v \" (Kuhn 1970a, 171) and come to see pro g r e s s i n s c i e n c e as \"a process of e v o l u t i o n from p r i m i -t i v e b e g i n n i n g s \" ( i b i d . , 170. I t a l i c s i n o r i g i n a l ) . P h i l o s o p h e r s have r a i s e d v a r i o u s s e r i o u s o b j e c t i o n s t o the incommensurability t h e s i s : they have claimed t h a t i t Is simply f a l s e ; t h a t i t i s based on a vague t h e o r y of meaning; t h a t i t makes r a t i o n a l t h e o r y c h o i c e i m p o s s i b l e ; t h a t I t e l i m i n a t e s the c r i t i c a l Impact of experiment on theory; t h a t i t l e a d s t o i d e a l -ism and r e l a t i v i s m ; and t h a t i t i s otherwise \" m e t h o d o l o g i c a l l y and e p i s t e m o l o g i c a l l y u n d e s i r a b l e \" (Lodynski 1982, 91). But by f a r the s t r o n g e s t c r i t i c i s m p h i l o s o p h e r s have made of Kuhn's t h e s i s , and the most r e v e a l i n g of t h e i r b a s i c p h i l o s o p h i c a l com-mitments, i s t h a t i t i s e i t h e r \" u n i n t e l l i g i b l e \" because \" s e l f - r e -f u t i n g \" (e.g., Newton-Smith 1981, 148-9; Putnam 1981a, 126; Lo-dyn s k i 1982, 91); or p h i l o s o p h i c a l l y - i r r e l e v a n t because d e s c r i b -i n g p u r e l y \"humdrum,\" p s y c h o l o g i c a l f a c t s about s c i e n t i s t s (Mus-grave 1980, 51) or e n t i r e l y \"modest\" c o n c e p t u a l d i s p a r i t i e s be-tween s c i e n t i f i c t h e o r i e s (Davidson 1984, 184). Ne v e r t h e l e s s , Kuhn c o m p l e t e l y r e j e c t s both a l t e r n a t i v e s and the i n t e r p r e t a t i o n s of h i s t h e s i s t h e y are based on. 7 Kuhn's c r i t i c s ' p o r t r a y a l of the incommensurability t h e s i s , as e i t h e r s e l f - r e f u t i n g or p h i l o s o p h i c a l l y - i r r e l e v a n t , s t r i k i n g l y resembles those he says g e n e r a l l y \" c h a r a c t e r i z e d i s c o u r s e be-tween p a r t i c i p a n t s i n incommensurable p o i n t s of view\" 7 (Kuhn 1970b, 230; c . f . p5 above). Thus the f a i l u r e of h i s c r i t -i c s t o f i n d an i n t e r p r e t a t i o n of h i s t h e s i s t h a t makes i t both i n t e l l i g i b l e and p h i l o s o p h i c a l l y - r e l e v a n t suggests t h e i r views may simply be incommensurable wi t h h i s ( i b i d . , 230). In other words, Kuhn's view may not be u n i n t e l l i g i b l e or i r r e l e v a n t sim-p l i c i t e r . J u s t so relative t o h i s c r i t i c s ' p e r s p e c t i v e . And s i n c e , by d e f i n i t i o n , incommensurable p o i n t s of view i n t e r p r e t common concepts d i f f e r e n t l y (see pp3-4 above), we should expect t h a t Kuhn's p o s i t i o n , i f i t i s i n t e l l i g i b l e or philosophically-relevant, must Involve a d i f f e r e n t and coherent understanding of those concepts t h a t l e a d t o t h e i r argumentative impasse.\" Before defending the i n t e l l i g i b i l i t y and r e l e v a n c e of Kuhn's p o s i t i o n , however, I s h a l l f i r s t i l l u s t r a t e the h i s t o r i c a l argument f o r the incommensurability t h e s i s w i t h Kuhn's d i s c u s s i o n of the P r o u s t - B e r t h o l l e t c o n t r o v e r s y . T h i s d i s c u s s i o n w i l l h o p e f u l l y p r o v i d e both a c l e a r e r p i c t u r e of the n o t i o n of loglco-normatlve i n c o m p a t i b i l i t y and an i n d i c a t i o n of one source of the Impasse between Kuhn and h i s c r i t i c s : the nature of l o g i c . 1.1.1 H i s t o r y and the Incommensurability T h e s i s One h i s t o r i c a l example Kuhn c i t e s of a p a i r of \"fundamental-l y i n c o m p a t i b l e \" t h e o r i e s are those of the French chemists J . L. Proust and C. L. B e r t h o l l e t . \" P r o u s t h e l d t h a t a l l chemical r e -a c t i o n s take p l a c e i n f i x e d , i n t e g r a l r a t i o s but B e r t h o l l e t In-s i s t e d t h a t most occur i n c o n t i n u o u s l y - v a r y i n g p r o p o r t i o n s . On 8 the face of I t , these p r o p o s i t i o n s are examples of the more f a -m i l i a r , l e s s g l o b a l , n o t i o n of i n c o m p a t i b i l i t y s i n c e both seem t o be e x p r e s s i b l e as formal c o n t r a d i c t o r i e s u s i n g common ( l o g i c a l and n o n - l o g i c a l ) c o n c e p t s . 1 0 But Kuhn p o i n t s out t h a t not o n l y d i d P roust d i s p u t e B e r t h o l l e t ' s view of c h e m i c a l processes, he a l s o d i f f e r e d v i t h him about the meaning of the concept, chemical r e a c t i o n , used i n e x p r e s s i n g t h e i r a p p a r e n t l y Incompatible c l a i m s . Hence he a l s o d i f f e r e d v i t h him about the meanings of the r e l a t e d concepts of chemi c a l compound and p h y s i c a l m i x t u re. 1 1 Thus though both chemists allowed t h a t , \"when mixing (of chemicals] produced heat, l i g h t , e f f e r v e s c e n c e or something e l s e of the s o r t , \" a chemical r e a c t i o n had o c c u r r e d , o n l y B e r t h o l l e t took the behaviour of \" s a l t i n v a t e r , a l l o y s , g l a s s , oxygen i n the atmosphere, and so on\" as a l s o evidence of a chemical r e a c -t i o n (Kuhn 1970a, 131). Because t h i s l a t t e r c l a s s of substances can form combinations of smoothly-varying p r o p o r t i o n s , i n r a t i o s from zero t o a f i x e d l i m i t , B e r t h o l l e t argued t h a t they provided c l e a r evidence f o r h i s theory* And s i n c e such compounds are more commonly found than those combining i n f i x e d p r o p o r t i o n s , he con-cluded t h a t v a r i a b l e compounds vere the norm, f i x e d ones the ex-c e p t i o n (Meldrum 1910, 5). By c o n t r a s t , because he r e j e c t e d the idea t h a t s o l u t i o n s vere chemical compounds, P r o u s t denied t h a t B e r t h o l l e t had proved h i s p o i n t . And he i n s i s t e d t h a t o n l y those cases of mixing t h a t produced compounds of f i x e d p r o p o r t i o n s vere chemical r e a c t i o n s . 9 Kuhn here argues t h a t we should not construe t h i s d i f f e r e n c e of concepts as a t r i v i a l d e f i n i t i o n a l e q u i v o c a t i o n (Kuhn 1970a, 131). F o r , he c l a i m s , P r o u s t ' s and B e r t h o l l e t ' s r e s p e c t i v e c h o i -ces of d e f i n i t i o n of chemical reaction and compound had substan-t i v e , incompatible consequences f o r the ways i n which they ex-p l a i n e d t h e i r common environments. Thus, because he b e l i e v e d t h a t compounds of v a r i a b l e composition were the norm, B e r t h o l l e t sought t o f i n d i n s t a n c e s of them produced by chemical r e a c t i o n s meeting the c r i t e r i a t h a t P r o u s t a l s o accepted ( g i v i n g o f f heat, l i g h t , gas, e t c . ) . And such experimental evidence was not hard to f i n d . Thus B e r t h o l l e t was a b l e to show t h a t \"metals such as copper, t i n and l e a d , on h e a t i n g i n a i r can take up oxygen con-tinuously i n p r o p o r t i o n s I n c r e a s i n g to a f i x e d l i m i t , g i v i n g a continuous s e r i e s of o x i d e s , as shown i n some cases (e.g. lead) by v a r y i n g c o l o u r changes\" ( P a r t i n g t o n 1957, 156. I t a l i c s i n o r i g i n a l ) . On the other hand, because of h i s commitment to h i s \" d e f i n i -t i o n , \" Proust repeated B e r t h o l l e t ' s experiments and claimed t h a t the same o p e r a t i o n s showed \" t h a t these oxides were mixtures of two, or a s m a l l number, of d e f i n i t e o x i d e s , and he c a r e f u l l y d i s t i n g u i s h e d between mixtures and s o l u t i o n s . . . a n d chemical com-pounds\" ( i b i d . , 156). N e v e r t h e l e s s , the experimental evidence was c o m p l e t e l y e q u i v o c a l ; \"the two men n e c e s s a r i l y t a l k e d through each other and t h e i r debate was e n t i r e l y I n c o n c l u s i v e \" (Kuhn 1970a, 132). Thus i t seems t h a t Proust's and B e r t h o l l e t ' s con-f l i c t i n g d e f i n i t i o n s of concepts a l s o made t h e i r t h e o r e t i c a l con-10 e l u s i o n s incompatible. And, e q u a l l y , as ve s h a l l see, t h e i r c h o i c e of incompatible t h e o r i e s a l s o seemed t o f o r c e those s c i e n -t i s t s t o i n t e r p r e t shared concepts i n c o n f l i c t i n g vays. B e r t h o l l e t ' s c l a i m t h a t s a l i n e i s a chemical compound, and not a p h y s i c a l mixture, vas a n a t u r a l consequence of h i s nev t h e -ory of a f f i n i t y , v h i c h he c o n s t r u c t e d to overcome the f l a v s of the o l d e r v e r s i o n . A f f i n i t y t h e o r y took chemical compounds to r e s u l t from a mutual \" e l e c t i v e \" a f f i n i t y betveen t h e i r c o n s t i t u -ent elements. Thus lumps of elemental substances l i k e s i l v e r h e l d together because of the a f f i n i t y of t h e i r c o r p u s c l e s f o r each o t h e r ; mixed compounds formed because the c o r p u s c l e s of the d i f f e r e n t elements had a g r e a t e r mutual a f f i n i t y f o r each other than f o r those of t h e i r ovn s o r t ; and s o l u t i o n s formed because the s o l u t e ' s p a r t i c l e s had a g r e a t e r a f f i n i t y f o r those of the s o l v e n t than f o r each o t h e r . \"In the e i g h t e e n t h c e n t u r y the t h e o r y of e l e c t i v e a f f i n i t y vas an admirable chemical paradigm, v i d e l y and sometimes f r u i t f u l l y deployed i n the d e s i g n and a n a l y -s i s of chemical e x p e r i m e n t a t i o n \" (Kuhn 1970a, 130). P r i o r t o B e r t h o l l e t , chemists had combined a b e l i e f i n a f -f i n i t y t h e o r y v i t h an acceptance of the g e n e r a l i t y of R i c h t e r ' s l a v of c o n s t a n t p r o p o r t i o n s (Meldrum 1910, 2 ) . But the o l d a f -f i n i t y t h e o r y vas plagued by anomalies: f o r example, i t c o u l d n ' t e x p l a i n the phenomenon of \"mass a c t i o n . \" The chemist Bergman had shovn t h a t , f o r r e a c t i o n s of the form: \"Ad + c = Ac + d, where Ac i s p r e c i p i t a t e d \" (Meldrum 1910, 4 ) , 1 2 depending on the p a r t i c u l a r A, d and c i n v o l v e d , from t v o to s i x times the mass of c was needed to s a t u r a t e A when combined with d, than when A was uncom-bined. T h i s phenomenon was c l e a r l y incompatible with the o l d e r a f f i n i t y t h e o r y's acceptance of the d o c t r i n e of f i x e d composi-t i o n ; f o r under d i f f e r e n t circumstances f o r c e s of a f f i n i t y seemed to permit the formation of compounds of w i d e l y - v a r y i n g propor-t i o n s . B e r t h o l l e t chose t o r e s o l v e the o l d e r theory's anomaly by keeping the proven n o t i o n of chemical a f f i n i t y but \" o b l i t e r a t -[ ing] the ( t r a d i t i o n a l ] d i s t i n c t i o n between chemical and p h y s i c a l f o r c e s \" (Meldrum 1910, 4 ) . Thus he took \" a l l f o r c e s of a f f i n i t y [to be] m o d i f i e d g r a v i t a t i o n a l a t t r a c t i o n \" ( P a r t i n g t o n 1957, 157n*). That c h o i c e allowed B e r t h o l l e t t o keep i n t a c t much of the t h e o r e t i c a l apparatus of the o l d e r t h e o r y of a f f i n i t y but made i t impossible to d i f f e r e n t i a t e any longer between chemical compounds and s o l u t i o n s . Mere p h y s i c a l mixtures were now j u s t those combinations of substances t h a t f a i l e d t o show c o h e s i o n : f o r example, those whose c o n s t i t u e n t s \"could be d i s t i n g u i s h e d by eye or m e c h a n i c a l l y s e p a r a t e d \" (Kuhn 1970a, 131). And B e r t h o l l e t claimed the r e l a t i v e l y few compounds of f i x e d p r o p o r t i o n s oc-c u r r e d because of the ways i n which t h e i r s p e c i f i c s t r u c t u r e s I n t e r a c t e d with c e r t a i n environments. F i x e d compounds, he s a i d , \"were formed as a r e s u l t of the i n t e r f e r e n c e of extraneous phys-i c a l f o r c e s . For example, c e r t a i n p r o p o r t i o n s of the elements c o u l d produce a compound which was l e a s t s o l u b l e or of g r e a t e s t d e n s i t y ( i n f l u e n c e of c o h e s i o n ) , or the most v o l a t i l e ( i n f l u e n c e 12 of e l a s t i c i t y ) of a l l the p o s s i b l e compounds, and hence t h i s compound was formed i n p r e f e r e n c e \" ( P a r t i n g t o n 1957, 157). Instead of choosing to keep the t i m e - t e s t e d concept of a f -f i n i t y from the o l d e r theory, however, Pr o u s t opted to r e t a i n t h a t t h e ory's law of c o n s t a n t p r o p o r t i o n s and i t s d i s t i n c t i o n between s o l u t i o n (qua p h y s i c a l mixture) and chemical compound. However, t h a t l e f t him with no a l t e r n a t i v e p o s i t i v e account of what f o r c e s kept substances l i k e s a l t and sugar, as mere p h y s i c a l m i xtures, In s o l u t i o n ; he c o u l d o n l y r e p l y t h a t such s o l u t i o n s c l e a r l y d i f f e r e d i n nature from standard chemical compounds l i k e s a l t and sugar themselves. So the f o r c e s t h a t bound s o l v e n t and s o l u t e together were conceivably v e r y d i f f e r e n t from chemical f o r c e s . Hence, he argued, the behaviour of s o l u t i o n s should not be used as counterexamples to h i s t h e o r y ( P a r t i n g t o n 1957, 157). That r e b u t t a l d i d not i n i t i a l l y prove v e r y c o n v i n c i n g to chemists because B e r t h o l l e t ' s new a f f i n i t y t h e o r y was the o n l y method then a v a i l a b l e f o r e x p l a i n i n g \"mass a c t i o n \" (now under-stood as \"chemical r e a c t i o n r a t e s \" (Day, General Chemistry, 1974). Proust's s i d e had to wait f o r Dalton's atomic theory and the work of B e r z e l i u s before they c o u l d begin to match B e r t h o l -l e t ' s account i n t h i s area (Meldrum 1910, 8, 12). Dalton's new t h e o r y , based on a law of m u l t i p l e (as opposed to e i t h e r f i x e d or c o n t i n u o u s l y - v a r y i n g ) p r o p o r t i o n s had much g r e a t e r apparent scope and i m p l i c a t i o n s than e i t h e r B e r t h o l l e t ' s or P r o u s t ' s t h e o r i e s . I t made sense of a c l e a r demarcation of s o l u t i o n s from compounds; handled the formation of metal oxides and s a l t s i n a l e s s equivo-13 c a l manner than e i t h e r B e r t h o l l e t or Proust; accounted f o r Gay-Lussac's l a v of combining volumes of gases; and vas a l s o a b l e encompass the phenomenon of mass a c t i o n (Meldrum 1910, 12-14). Dalton's \"nev vay of p r a c t i c i n g chemistry...proved so r a p i d l y f r u i t f u l t h a t o n l y a f e v of the o l d e r chemists i n France and B r i -t a i n vere a b l e t o r e s i s t i t \" (Kuhn 1970a, 134). S t i l l , i t \" r e -s o l v e d \" ( f o r most chemists, but not B e r t h o l l e t ) the d i s p u t e by i n t r o d u c i n g a nev t h e o r y and s e t of concepts t h a t vere incompat-i b l e v i t h both those of B e r t h o l l e t and P r o u s t . And i t a l s o l e f t unsolved a problem B e r t h o l l e t ' s t h e o r y c o u l d handle: the beha-v i o u r of s o l u t i o n s ( i b i d . , 131). In summary, i t seems, a t l e a s t I n t u i t i v e l y , t h a t B e r t h o l -l e t ' s and P r o u s t ' s (and Dalton's) competing t h e o r i e s of chemical r e a c t i o n s and compounds a l s o i n v o l v e d competing concepts f o r p i c k i n g out i n s t a n c e s of those r e a c t i o n s and compounds. Kuhn p o i n t s out a s t i l l f u r t h e r aspect of t h i s p u t a t i v e logico-norma-t i v e i n c o m p a t i b i l i t y . Based on c o n c l u s i o n s he dravs from G e s t a l t psychology and the work of the p h i l o s o p h e r N. R. Hanson, he a r -gues t h a t the v i e v s of Proust and B e r t h o l l e t vere not o n l y l o g i -c a l l y and c o n c e p t u a l l y , but a l s o perceptually or observatlonally, incompatible (see Kuhn 1970a, 112-114). Thus he c l a i m s t h a t not o n l y vas i t i m p o s s i b l e f o r e i t h e r s c i e n t i s t t o understand or f o r -mulate the o t h e r ' s t h e o r y u s i n g h i s ovn concepts; i t vas a l s o im-p o s s i b l e f o r e i t h e r s c i e n t i s t t o p e r c e i v e the v o r l d i n the same vay as h i s opponent. Thus \"vhere B e r t h o l l e t sav a compound t h a t c o u l d v a r y i n p r o p o r t i o n , P r o u s t sav o n l y a p h y s i c a l mixture\" 14 ( i b i d . 132; c . f . i b i d . , 198). In other words, even t h e i r \"obser-v a t i o n languages\" were \" t h e o r y - l a d e n , \" and thus i n c o m p a t i b l e . Because of t h i s p u t a t i v e t o t a l i n c o m p a t i b i l i t y o f t h e i r p o i n t s of view, Kuhn concludes t h a t Proust and B e r t h o l l e t c o u l d not f i n d any common ground t o s e t t l e t h e i r d i s p u t e \"and t h e i r debate was e n t i r e l y i n c o n c l u s i v e \" (Kuhn 1970a, 132). 1.2 The C r i t i c a l Response: L o g i c and Formal L o g i c s I f Kuhn i s r i g h t t h a t there are t h e o r i e s , l i k e P r o u s t ' s and B e r t h o l l e t ' s , t h a t are s i m u l t a n e o u s l y l o g i c a l l y , c o n c e p t u a l l y and p e r c e p t u a l l y i n c o m p a t i b l e , i t seems c l e a r t h a t the l o g i c a l incom-p a t i b i l i t y of those t h e o r i e s c o u l d not be formally demonstrated. T h i s i s because: (1) t o show on the b a s i s of \" l o g i c a l form\" t h a t two e n t i t i e s (e.g. sentences, t h e o r i e s ) are i n c o m p a t i b l e , formal l o g i c s r e q u i r e t h a t those e n t i t i e s have common concepts;*\" and (2) the f a c t t h a t the concepts of two p u t a t i v e l y incommensurable t h e o r i e s form d i s t i n c t , \"conceptual webs\" means t h a t one cannot c o n s t r u c t commonly-acceptable concepts from the two t h e o r i e s from s p e c i f i c , l o c a l i n s t a n c e s of l o g i c a l c o n f l i c t or congruence be-tween them. That i s , because the meanings of the ot h e r , incom-p a t i b l e t h e o r y ' s concepts are giv e n by t h e i r e n t i r e r o l e i n t h a t theory, t h a t theory's content cannot be d e s c r i b e d except by con-cepts which presuppose t h a t content's t r u t h . 1 4 I t seems c l e a r , t h e r e f o r e , t h a t i f there are t h e o r i e s t h a t are both l o g i c a l l y and c o n c e p t u a l l y i n c o m p a t i b l e , s i n c e formal 15 l o g i c s a p p a r e n t l y cannot demonstrate t h a t i n c o m p a t i b i l i t y , the gen e r a l concept of l o g i c a l i n c o m p a t i b i l i t y must have a l a r g e r scope than the s p e c i f i c formal one. On the other hand, however, the f a c t t h a t Kuhn's c r i t i c s do not g e n e r a l l y r e c o g n i z e t h i s op-t i o n , suggests s t r o n g l y t h a t they b e l i e v e t h a t l o g i c a l incompati-b i l i t y i s a p u r e l y formal n o t i o n . 1 8 Thus a standard o b j e c t i o n to Kuhn's analyses i s t h a t , be-cause debates l i k e those of P r o u s t and B e r t h o l l e t seem s t a l l e d l a r g e l y by t h e i r e q u i v o c a l use of common e x p r e s s i o n s , Kuhn has not \" j u s t i f i e d \" the c l a i m t h a t such views are actually incompat-i b l e (Newton-Smith 1981, 149). Instead i t i s claimed t h a t I f they were t r u l y Incompatible, i t should be p o s s i b l e t o analyze f u r t h e r those t h e o r i e s ' concepts and express t h e i r c o n f l i c t as a formal c o n t r a d i c t i o n u s i n g common concepts. For example, i t might be the case t h a t Proust and B e r t h o l l e t shared t a c i t , common c r i t e r i a f o r d i s t i n g u i s h i n g c h e m i c a l compounds from p h y s i c a l mix-t u r e s , which might be made e x p l i c i t through formal a n a l y s i s ; i n which case, t h e i r views would d i f f e r o n l y l o g i c a l l y , not concep-t u a l l y . On the other hand, i f Pr o u s t ' s and B e r t h o l l e t ' s concepts were d i f f e r e n t , Kuhn's c r i t i c s i n f e r t h a t , t h e r e f o r e , appearances and i n t u i t i o n s t o the c o n t r a r y , t h e i r t h e o r i e s were r e a l l y com-p a t i b l e ( c . f . Newton-Smith 1981, 150). Kuhn's r e p l y to the f i r s t a l t e r n a t i v e i s to note t h a t s c i e n -t i s t s seldom r e c o g n i z e the r e s u l t s of such formal \" a n a l y s e s \" as e q u i v a l e n t with t h e i r own usage (Kuhn 1970a, 47; Kuhn 1977, 305). Moreover, he a l s o notes t h a t when a h i s t o r i a n l i k e h i m s e l f t r i e s 16 to analyse the l o g i c a l bases of o l d e r t h e o r i e s , he I n v a r i a b l y f i n d s t h a t \"phrased i n j u s t t h a t way, or i n any other way he can imagine, (those l o g i c a l r e c o n s t r u c t i o n s ] would almost c e r t a i n l y have been r e j e c t e d by some members of the group he s t u d i e s \" (Kuhn 1970a, 44). In other words, Kuhn i s s a y i n g t h a t , i n h i s e x p e r i -ence, formal r e c o n s t r u c t i o n s of h i s t o r i c a l t h e o r i e s always misre-present t h e i r content. And he appeals t o W i t t g e n s t e i n ' s work on \" f a m i l y resemblance\" concepts t o argue t h a t t h e r e need be no t a -c i t , formal s t r u c t u r e s u n d e r l y i n g s c i e n t i s t s ' r e a s o n i n g ( i b i d . , 4 7 ) . \" Of course, one might o b j e c t t h a t s c i e n t i s t s ' d e n i a l s of the Congruence of t h e i r concepts with the r e s u l t s of a n a l y s i s are beside the p o i n t s i n c e the i s s u e s i n v o l v e d i n those r e c o n s t r u c -t i o n s l i e o u t s i d e t h e i r e x p e r t i s e ( C o l l i e r 1984, 96). To see tha t t h i s o b j e c t i o n f a i l s t o address Kuhn's p o i n t one must keep separate the f o l l o w i n g i s s u e s : (1) whether or not s c i e n t i s t s are n e c e s s a r i l y q u a l i f i e d t o judge, say, the r e l a t i o n s between t h e i r own and h i s t o r i c a l t h e o r i e s or the p h i l o s o p h i c a l i m p l i c a t i o n s of t h e i r work; and (2) whether or not s c i e n t i s t s are e x c e p t i o n a l l y q u a l i f i e d t o determine when formal r e c o n s t r u c t i o n s change the meanings of t h e i r concepts i n t h e i r s c i e n t i f i c context. I t seems c l e a r t h a t the answer t o the f i r s t q u e s t i o n i s t h a t s c i e n t i s t s are not s p e c i a l l y q u a l i f i e d by t h e i r s c i e n t i f i c work i n e i t h e r h i s t o r i c a l r e c o n s t r u c t i o n or p h i l o s o p h i c a l a n a l y s i s . But i t seems e q u a l l y c l e a r t h a t the answer to the second q u e s t i o n i s t h a t s c i e n t i s t s are s u r e l y the most q u a l i f i e d to recognize the noncongruence of t h e i r ovn usage v i t h formal r e c o n s t r u c t i o n s (supposing t h a t they understand the formal language). And Kuhn o b v i o u s l y has the second q u e s t i o n i n mind (along v i t h i t s suppo-s i t i o n ) i n the above c l a i m (pl5-16; see a l s o Kuhn 1977c, 303nl3). Thus i f a \" r e l n t e r p r e t a t i o n i n the broader c o n t e x t \" ( C o l l i e r 1984, 96) seems to a s c i e n t i s t t o change h i s concepts, t h a t be-l i e f deserves s e r i o u s c o n s i d e r a t i o n . More important, s i n c e the p o i n t of such r e i n t e r p r e t a t i o n s i s t o provide a n e u t r a l framework f o r s c i e n t i f i c debate, the f a c t t h a t s c i e n t i s t s from both camps vou l d l i k e l y f i n d those r e i n t e r p r e t a t i o n s i n a c c u r a t e v o u l d o n l y d e f e a t the purpose of t h a t supposedly n e u t r a l r e l n t e r p r e t a t i o n . Kuhn's counter to the second c l a i m t h a t t h e o r i e s t h a t cannot be r e c o n s t r u c t e d as f o r m a l l y incompatible are simply d i f f e r e n t and compatible has been, as ve have seen, to t r y t o make the i n -c o m p a t i b i l i t y of such t h e o r i e s seem i n t u i t i v e l y obvious. And, though i n t u i t i o n s n o t o r i o u s l y d i f f e r , the t h e o r i e s he d e s c r i b e s as incompatible are u s u a l l y a l s o taken as such by h i s c r i t i c s (e.g., Nevton-Smith 1981, 158). Thus, again , Kuhn's c r i t i c s ' i n -s i s t e n c e t h a t t h e o r i e s t h a t seem i n t u i t i v e l y Incompatible are e i -ther r e c o n s t r u c t i b l e as f o r m a l l y incompatible or not r e a l l y i n -compatible suggests that the r e a l i s s u e betveen them and Kuhn i s vhether or not the canons of formal l o g i c s f u l l y capture the no-t i o n of l o g i c a l i n c o m p a t i b i l i t y . In the f o l l o w i n g s e c t i o n s , I use comments and arguments from Kuhn's c r i t i c s t o show t h a t , to preserve the i n t e l l i g i b i l i t y and r e l e v a n c e of h i s t h e s i s , he must d i f f e r with them not o n l y on the 18 nature of l o g i c but a l s o on the more g e n e r a l n o t i o n of compari-son. And I g i v e t e x t u a l evidence t o imply t h a t Kuhn would a c t u -a l l y want t o d i f f e r from h i s c r i t i c s i n the ways I suggest. I then l i n k t h a t d i s p u t e about comparison and l o g i c t o the a n c i e n t problem of u n i v e r s a l s and argue t h a t the p o s i t i o n of Kuhn's c r i t -i c s leads t o an i n f i n i t e r e g r e s s . 1.3 The C r i t i c a l Response: C o m p a r a b i l i t y and Commensurabillty As we have j u s t seen, one primary source of Kuhn's opponents problems with the incommensurability t h e s i s i s t h e i r i d e n t i f i c a -t i o n of l o g i c with formal l o g i c . But there i s a s t i l l more b a s i c source of h i s c r i t i c s ' d i f f i c u l t i e s : t h e i r e q u a t i o n of \"incommen-s u r a b l e \" with e i t h e r \" a b s o l u t e l y incomparable\" or \"not i n t e r -t r a n s l a t a b l e . \" As noted above (p6), o f t e n Kuhn's opponents' s t r a t e g y i s to c o n f r o n t him with a dilemma. With r e s p e c t t o the concept of incommensurability i t s e l f , they commonly argue t h a t e i t h e r (1) i f \"incommensurable\" i s read ' l i t e r a l l y ' \u00E2\u0080\u0094 a s meaning \" a b s o l u t e l y i n -comparable\"\u00E2\u0080\u0094Kuhn's t h e s i s t u r n s out to be the s e l f - c o n t r a d i c t o r y c l a i m t h a t c e r t a i n t h e o r i e s are both ( a b s o l u t e l y ) incomparable and comparable;* 7 or (2) i f t h a t prima f a c i e r e a d i n g i s r e j e c t e d , h i s t h e s i s i s not s e l f - c o n t r a d i c t o r y , but \"incommensurability\" turns out to be o n l y h i s m i s l e a d i n g e x p r e s s i o n f o r what are mere-l y p s y c h o l o g i c a l or pragmatic problems i n comprehending, compar-ing or t r a n s l a t i n g a l i e n v iews. 1 8 19 I t i s easy t o see why Kuhn's opponents' I n t e r p r e t a t i o n of \"incommensurable,\" as meaning l i t e r a l l y e i t h e r \" a b s o l u t e l y incom-p a r a b l e \" or \"not i n t e r t r a n s l a t a b l e , \" makes h i s t h e s i s seem u n i n -t e l l i g i b l e . F o r , given t h e i r Interpretation, s i n c e i t i s t r i v i -a l l y obvious t h a t to c a l l t vo t h e o r i e s incompatible i s both to compare and c o n t r a s t them,'9 i t f o l l o w s t h a t Kuhn c o u l d not pos-sibly f i n d h i s t o r i c a l examples of s u c c e s s i v e t h e o r i e s t h a t are \"not o n l y i n c o m p a t i b l e but o f t e n a c t u a l l y incommensurable\" (Kuhn 1970a, 103). F u r t h e r , on this Interpretation, s i n c e i n h i s v r i t -ings Kuhn r e p e a t e d l y t r a n s l a t e s , i n a common ( n a t u r a l ) language (contemporary E n g l i s h ) , t h e o r i e s he c l a i m s are incommensurable v i t h contemporary ones, i t f o l l o v s t h a t he c o u l d not p o s s i b l y use t h i s vork to prove those t h e o r i e s vere t r u l y incommensurable. Donald Davidson, vho takes \"incommensurable\" to mean \"not i n t e r t r a n s l a t a b l e \" (Davidson 1984b, 190), makes e x a c t l y t h i s l a s t p o i n t vhen he remarks i r o n i c a l l y : \"Kuhn i s b r i l l i a n t a t s a y i n g vhat t h i n g s vere l i k e before the r e v o l u t i o n u s i n g \u00E2\u0080\u0094 v h a t e l s e ? \u00E2\u0080\u0094 o u r p o s t - r e v o l u t i o n a r y idiom\" ( i b i d . 184). Even a p h i l o s o p h e r as sympathetic t o Kuhn's o v e r a l l v i e v of s c i e n c e as H i l a r y Putnam ( c . f . Putnam 1981b, esp. 69-78) f i n d s h i s t h e s i s to be \" s e l f -r e f u t i n g \" (Putnam 1981a, 114), and f o r e x a c t l y the same reasons as Davidson ( I b i d . , 116). Thus Putnam observes t h a t , s i n c e \" i n -commensurable\" means \"not I n t e r t r a n s l a t a b l e \" ( i b i d . , 114), f o r Kuhn (or P a u l Feyerabend) t o \" t e l l us t h a t G a l i l e o had 'incommen-s u r a b l e * n o t i o n s and then to go on to d e s c r i b e them a t l e n g t h i s Incoherent\" (Putnam 1981a, 115. I t a l i c s i n o r i g i n a l ) . Kuhn's c r i t i c s ' i d e n t i f i c a t i o n o f \"in-commensurable\" with \" a b s o l u t e l y in-comparable\" (and \" n o t - i n t e r t r a n s l a t a b l e \" ) pro-v i d e s a c l u e t o the deep source of t h e i r d i s p u t e with him: i t shows t h a t they take \"comparable\" (and \" i n t e r t r a n s l a t a b l e \" ) t o mean \"commensurable/\" which i t s e l f means l i t e r a l l y \"measurable [ b r o a d l y : comparable] by a common s t a n d a r d \" (Concise Oxford En-glish Dictionary, s.v. \"commensurable\"). But \"comparable\" and \"comparable by a common st a n d a r d \" are not s e l f - e v i d e n t l y synony-mous e x p r e s s i o n s . F u r t h e r , i t a l s o seems p o s s i b l e t o d i s t i n g u i s h the l o c u t i o n s \"comparable i n a common natural language\" ( i n t e r -t r a n s l a t a b l e ) and \"comparable i n a common system of concepts\" (commensurable) ( c . f . n8, n l 4 ) ; f o r natural languages may not be f u l l y uniform conceptual systems. So whether \"commensurable\" should be c o n f l a t e d with, or d i s t i n g u i s h e d from, e i t h e r \"compar-a b l e \" or \" i n t e r t r a n s l a t a b l e \" seems t o be a s i g n i f i c a n t p h i l o s o -p h i c a l i s s u e . And Kuhn has gone on r e c o r d as denying t h a t \" i n -commensurable\" means e i t h e r \"incomparable\" or \"not i n t e r t r a n s -l a t a b l e \" (e.g., Kuhn 1970b, 267; Kuhn 1976, 191; Kuhn 1970a, 201-4) . On the other hand, however, i f one took c o m p a r a b i l i t y to r e q u i r e commensurablllty, because l o g i c a l I n c o m p a t i b i l i t y c l e a r l y i n v o l v e s ( l o g i c a l ) c o m p a r a b i l i t y , he would n a t u r a l l y a l s o con-clude t h a t l o g i c a l l y incompatible t h e o r i e s cannot be incommensur-a b l e . Thus we f i n d t h a t one of Kuhn's main c r i t i c s , Dudley Sha-pere, who e x p l i c i t l y equates \"Incommensurable\" with \" a b s o l u t e l y incomparable\" (Shapere 1981, 55), a l s o says t h a t \" i n order f o r 21 Itwo t h e o r i e s ] t o be i n c o n s i s t e n t with one another, they must be formulated, or a t l e a s t f o r m u l a b l e , i n a common language.\" ( i b i d . 44nl0. I t a l i c s mine). Shapere concludes t h a t \" i t i s d i f f i c u l t t o see how one c o u l d c o n s t r u c t a t h e o r y which, while d i f f e r i n g i n the meanings of a l l i t s terms from another t h e o r y ( i . e . , i s i n -commensurable w i t h i t ] , can n e v e r t h e l e s s be I n c o n s i s t e n t w i t h t h a t other t h e o r y \" ( i b i d . , 44). As the f o l l o w i n g passage r e v e a l s , another prominent opponent of Kuhn's views, I s r a e l S c h e f f l e r , a l s o i d e n t i f i e s \"comparable\" with \"commensurable\"; thus he wonders how paradigms t h a t are ...based i n d i f f e r e n t worlds, and address themselves to d i f -f e r e n t problems with the h e l p of d i f f e r e n t standards . . . l e a n be] s a i d t o be i n c o m p e t i t i o n ? To d e c l a r e them i n competi-t i o n i s , a f t e r a l l , t o p l a c e them w i t h i n some common frame-work, to view them w i t h i n some shared p e r s p e c t i v e s u p p l y i n g , i n p r i n c i p l e a t l e a s t , comparative and e v a l u a t i v e c o n s i d e r a -t i o n s a p p l i c a b l e t o both. I t i s i n f a c t to c o n s i d e r them as o r i e n t e d i n d i f f e r e n t ways toward the same purposes, as making r i v a l appeals from the s t a n d p o i n t of s c i e n t i f i c g o a l s taken t o be o v e r r i d i n g and with r e s p e c t to a common s i t u a -t i o n taken as a p o i n t of r e f e r e n c e . ( S c h e f f l e r 1967, 82. I t a l i c s mine). Thus both Shapere and S c h e f f l e r imply t h a t Kuhn's a s s e r t i o n t h a t incommensurable t h e o r i e s can be i n c o m p e t i t i o n i s s e l f - c o n -t r a d i c t o r y f o r t h e y c l a i m t h a t the v e r y n o t i o n of i n c o m p a t i b i l i t y presupposes t h a t of commensurability. Importantly, however, n e i -t h er Shapere nor S c h e f f l e r g i v e an argument f o r t h e i r c l a i m ; i n -stead they s i m p l y a s s e r t i t as though i t s t r u t h were s e l f - e v i -d e n t . 8 0 A c c o r d i n g to Ian Hacking, the deepest c r i t i c i s m of incommen-s u r a b i l i t y i s t h a t of Davidson (Hacking 1983, 73-4; Davidson 1984b, 183-198). Davidson a s s o c i a t e s the idea of incommensur-a b i l i t y w i t h the more commonly accepted view t h a t t h e r e can be more than one \"conceptual scheme\" ( i b i d . , 185, 190) but d enies t h a t t h i s i d e a makes sense a t all: t h a t i s , even when a p p l i e d t o t h e o r i e s or schemes t h a t a r e n ' t competing ( i b i d . , 198). L i k e Shapere and S c h e f f l e r , he understands \"incommensurable\" to mean \" a b s o l u t e l y incomparable\" ( i b i d . , 184) a t and, as we have a l s o seen, \"not i n t e r t r a n s l a t a b l e \" ( i b i d . 190). Davidson g i v e s a s u b t l e argument, based on h i s p h i l o s o p h i c a l s t u d i e s , t o t r y to show t h a t we cannot s e n s i b l y a t t r i b u t e any t h e o r i e s , b e l i e f s or concepts to o t h e r s unless we can f i r s t ( e x a c t l y ) t r a n s l a t e what they are s a y i n g \" i n t o a f a m i l i a r tongue\" such as E n g l i s h ( i b i d . 186). But Davidson's argument i s \"deeper\" j u s t because i t i s more e x p l i c i t l y committed than those of Kuhn's other c r i t i c s to an e q u a t i o n of c o m p a r a b i l i t y with commensurability. Thus, while he acknowledges t h a t the examples Kuhn (and o t h e r s ) p o i n t to of con-c e p t u a l change and d i s p a r i t y are \" [ o c c a s i o n a l l y ] i m p r e s s i v e \" (Da-v i d s o n 1984b, 184), he i n s i s t s t h a t they \"are not so extreme but t h a t the changes and the c o n t r a s t s can be e x p l a i n e d and d e s c r i b e d u s i n g the equipment of a single language\" (Davidson 1984b, 184. I t a l i c s mine). And t h i s c l a i m shows t h a t Davidson i m p l i c i t l y equates i n t e r t r a n s l a t l o n ( s u c c e s s f u l e x p l a n a t i o n and d e s c r i p t i o n of a l i e n views i n a s i n g l e , n a t u r a l language) with commensuration ( t h e i r s u c c e s s f u l e x p l a n a t i o n and d e s c r i p t i o n i n a n e u t r a l system of concepts: \"the equipment of a s i n g l e language.\") 8 8 However, as I have argued above (p20), i t Is j u s t t h i s p u t a t i v e I d e n t i t y of l n t e r t r a n s l a t a b i l i t y and commensurability t h a t Kuhn d e n i e s . That Kuhn's c r i t i c s i m p l i c i t l y i d e n t i f y \"comparable\" (and \" I n t e r t r a n s l a t a b l e \" ) v i t h \"commensurable\" i s a l s o made c l e a r by the o n l y a l t e r n a t i v e s they seem v i l l l n g t o c o n s i d e r i f t h e i r f i r s t c o n s t r u a l of \" i n c o m m e n s u r a b i l i t y \" i s not vhat he has i n mind. Thus they commonly counter t h a t i f , c o n t r a r y to f i r s t ap-pearances, h i s n o t i o n i s n ' t intended t o imply a b s o l u t e incompar-a b i l i t y or u n t r a n s l a t a b i l i t y , then the t h e o r i e s he terms \"incom-mensurable\" must, In the l i t e r a l sense, be commensurable. But, i n t h a t case, they say, Kuhn's t h e s i s cannot have any p h i l o s o p h i -c a l import; a t most i t can have o n l y e i t h e r p s y c h o l o g i c a l or pragmatic s i g n i f i c a n c e . For example, Alan Musgrave says t h a t i f comparison or t r a n s -l a t i o n of 'incommensurable' t h e o r i e s i s p o s s i b l e , \"incommensura-b i l i t y has ceased t o be a l o g i c a l a f f a i r and [ i t s import! has be-come a p u r e l y p s y c h o l o g i c a l . . . m a t t e r \" (Musgrave 1982, 50): i t merely r e f e r s t o the commonplace empirical f a c t t h a t o l d s c i e n -t i s t s o f t e n have c o n s i d e r a b l e d i f f i c u l t y i n a c c e p t i n g and even understanding nev t h e o r i e s . 2 3 S i m i l a r l y , Davidson argues t h a t examples Kuhn and others ad-duce to show t h a t , \"what comes e a s i l y i n one language may come hard i n another,\" can o n l y r e v e a l \"modest,\" pragmatic d i f f i c u l -t i e s i n s e c u r i n g adequate t r a n s l a t i o n s ; they cannot provide e v i -dence f o r c o n c e p t u a l d i s c o n t i n u i t i e s (Davidson 1984b, 184). I t f o l l o w s t h a t Kuhn's term \"incommensurable'' i s e i t h e r a m i s l e a d i n g e x p r e s s i o n f o r a n o n - l o g i c a l issue ( i f i t does not mean \"not i n t e r t r a n s l a t a b l e \" ) or embodies a c o n f u s i o n ( i f I t d o e s ) : \" i f t r a n s l a t i o n [of another's c o n c e p t u a l scheme] succeeds, we have shown t h e r e Is no need to speak of two conceptual schemes, while i f t r a n s l a t i o n f a i l s there i s no ground f o r speaking of two\" (Davidson 1980b, 243). 2 4 As a l r e a d y noted (p20), Kuhn denies h i s opponents' charge t h a t by \"incommensurable\" he ever meant \" a b s o l u t e l y incomparable\" or \"not i n t e r t r a n s l a t a b l e \" ; moreover, he c o n t i n u e s t o i n s i s t t h a t h i s t h e s i s has l o g i c a l and e p l s t e m o l o g i c a l r e p e r c u s s i o n s , not merely p s y c h o l o g i c a l or pragmatic ones (e.g. Kuhn 1970b, 232-3). But p h i l o s o p h e r s are o f t e n r e l u c t a n t to l e t go of even a straw man-opponent. Thus Kuhn's c r i t i c s have taken h i s d e n i a l s t o show simply t h a t he i s \"but a pale r e f l e c t i o n of the o l d , r e v o l u t i o n -a r y Kuhn\"; t h a t , i n the face of t h e i r cogent c r i t i c i s m , he beat a f u l l - s c a l e r e t r e a t from h i s o r i g i n a l , \" c h a l l e n g i n g \" ideas towards the t r a d i t i o n a l canons of r a t i o n a l i t y t h a t he o r i g i n a l l y s l u r r e d (e.g. Musgrave 1981, 51). 2 8 Kuhn's r e t o r t i s t h a t the debate be-tween him and h i s c r i t i c s has the c h a r a c t e r i s t i c \" t a l k l n g -through-each-other\" f e a t u r e of arguments between p r a c t i t i o n e r s of incommensurable paradigms l i k e Proust and B e r t h o l l e t (Kuhn 1970b, 231-2). Other p h i l o s o p h e r s are more sympathetic to Kuhn's view than Davidson and Musgrave but a l s o imply, l i k e Davidson, t h a t the d i f f i c u l t i e s he terms \" i n c o m m e n s u r a b i l i t i e s \" are not l o g i c a l and e p i s t e m o l o g i c a l but a r i s e o n l y from temporary pragmatic problems In p r e c i s e l y f o r m u l a t i n g the r e l a t i o n s betveen s c i e n t i f i c t h e o r -i e s . Incommensurability v o u l d be s o l e l y a pragmatic, and thus temporary, i s s u e i f , f o r example, the lack of common concepts vas o n l y apparent and removable by a n a l y s i s ; or i f \"metascience\" vere a b l e t o f i n d other common elements than concepts or phenomena f o r n e u t r a l t h e o r y comparison. 8' As noted above (ppl6-17), John C o l l i e r takes the f i r s t op-t i o n : he suggests t h a t ve can make a r t i c u l a t e the \" i m p l i c i t p a r t of a t h e o r y \" through \"the c r e a t i o n of a broader, more i n c l u s i v e language capable of e x p r e s s i n g the content of both t h e o r i e s \" ( C o l l i e r 1984, 8-9). Dale Moberg takes the second approach: he argues t h a t incommensurability because of \" r a d i c a l meaning v a r i -ance\" may simply p o i n t t o a need t o develop a nev \"theory of t h e -ory comparison\" (Moberg 1979, 261). Though there are no c o n c l u -s i v e a priori reasons vhy such p r o j e c t s must f a i l , ve have seen t h a t Kuhn argues i n e f f e c t t h a t there are no a p r i o r i reasons vhy they must succeed e i t h e r ; and th e r e are p l e n t y of e m p i r i c a l r e a -sons to b e l i e v e t h a t they v i l l not ( c . f . ppl6-17 above). S t i l l , i t i s m i s l e a d i n g t o see the d i s p u t e betveen Kuhn and h i s opponents as p u r e l y e m p i r i c a l . As ve have seen (ppl9-20), h i s c r i t i c s ' p h i l o s o p h y makes incommensurability a l o g i c a l impos-s i b i l i t y ; so t h a t p h i l o s o p h y can have no c r i t e r i a f o r d e c i d i n g vhether a g i v e n p a i r of t h e o r i e s vere or vere not commensurable. Kuhn's opponents' o f t e n unspoken, but c o n s i s t e n t , i d e n t i f i c a t i o n s of c o m p a r a b i l i t y with commensurablllty; and l o g i c a l i n c o m p a t i b i l -i t y with formal l o g i c a l i n c o m p a t i b i l i t y show t h a t those i d e n t i -f i c a t i o n s are not a r b i t r a r y , but b u i l t i n t o t h e i r whole p h i l o s o -p h i c a l approach. Davidson makes t h i s normally t a c i t commitment e x p l i c i t when he says a t the b e g i n n i n g of h i s c r i t i q u e of Kuhn: \" D i f f e r e n t p o i n t s of view make sense, but only i f t h e r e Is a com-mon co-ordinate system on vhich to plot them} y e t the e x i s t e n c e of a common system [standard] b e l i e s the c l a i m of dramatic incom-p a r a b i l i t y \" (Davidson 1984, 184. I t a l i c s mine). And Davidson, l i k e Shapere and S c h e f f l e r , never argues f o r t h i s a s s e r t i o n ; and he t a c i t l y assumes t h a t p h i l o s o p h e r s l i k e Kuhn a l s o accept i t . 8 7 1.4 I n t e r i m Summary We have seen t h a t the Incommensurability t h e s i s i s the c l a i m t h a t s u c c e s s i v e s c i e n t i f i c t h e o r i e s are o f t e n both l o g i c a l l y and n o r m a t i v e l y ( i . e . c o n c e p t u a l l y , o p e r a t i o n a l l y , o b s e r v a t i o n a l l y ) i n c o m p a t i b l e . We have a l s o seen t h a t Kuhn's c r i t i c s f i n d h i s t h e s i s e i t h e r u n i n t e l l i g i b l e or p h i l o s o p h i c a l l y i r r e l e v a n t be-cause they equate l o g i c with formal l o g i c s and c o m p a r a b i l i t y and i n t e r t r a n s l a t a b i l l t y with commensurablllty. T h i s leaves us with two ( m u t u a l l y - e x c l u s i v e ) o p t i o n s : (1) e i t h e r those n o t i o n s cannot be m e a n i n g f u l l y d i s t i n g u i s h e d ; i n which case, Kuhn's t h e s i s i s \"impaled on the dilemma\"; or (2) i t i s p o s s i b l e to d i s t i n g u i s h those n o t i o n s s i g n i f i c a n t l y ; i n which case, Kuhn \"escapes between 27 the horns\" but the t r a d i t i o n a l \" e p l s t e m o l o g l c a l paradigm\" l o s e s i t s p h i l o s o p h i c a l impetus. 2' In the f o l l o w i n g s e c t i o n , I show how to make a p h i l o s o p h i -c a l l y - s i g n i f i c a n t d i s t i n c t i o n between comparison and commensura-t i o n ; and, as p roof my i n t e r p r e t a t i o n i s on the r i g h t t r a c k , I g i v e t e x t u a l evidence to i n d i c a t e t h a t Kuhn a l s o makes such a d i s t i n c t i o n i n h i s p h i l o s o p h y . I then g i v e a more d e t a i l e d a n a l -y s i s of the p r e s u p p o s i t i o n s of s y s t e m a t i c , formal l o g i c s , l i k e the p r o p o s i t l o n a l and p r e d i c a t e c a l c u l i , t o h e l p p i n p o i n t those p r e s u p p o s i t i o n s which s p e c i f i c a l l y embody a commitment to commen-s u r a b i l i t y . That a n a l y s i s w i l l h o p e f u l l y y i e l d a c l e a r e r p i c t u r e of what a n o t i o n of l o g i c t h a t i s compatible with the Incommen-s u r a b i l i t y t h e s i s would be l i k e . 2 9 1.5 How to D i s t i n g u i s h C o m p a r a b i l i t y from Commensurability As a l r e a d y mentioned (p20), the most obvious p o t e n t i a l d i f -ference between \"comparable\" and \"commensurable\" i s t h a t the l a t -t e r e x p r e s s i o n i n v o l v e s an a d v e r b i a l q u a l i f i c a t i o n of the f i r s t : t h a t i s , \"commensurable\" means \"comparable by a common standard.\" And i f the a d v e r b i a l c l a u s e \"by a common standard\" i s not redun-dant, then \"incommensurable\" means \"not comparable by a common standard,\" not s i m p l y \"not comparable a t a l l \" (nor: \"absolutely incomparable\"). Hence, i f c e r t a i n t h i n g s were comparable, but not commensurable, they would be comparable, though not by a com-mon s t a n d a r d . 28 To get a more s p e c i f i c idea of what comparison without com-mon standards would be l i k e , f i r s t c o n s i d e r the n o t i o n of a standard of comparison. T r i v i a l l y , a standard of comparison i s a norm, paradigm, pattern, or r u l e f o r comparing t h i n g s (The Con-cise Oxford Dictionary). And two o b j e c t s are comparable Just i n case those o b j e c t s are r e l a t e d i n a p a r t i c u l a r way; t h a t i s , j u s t i n case they are both i n s t a n c e s of a particular b i n a r y r e l a t i o n : e.g. one of s i m i l a r i t y , d i f f e r e n c e , i n c o m p a t i b i l i t y , relevance, entailment, length, intensity, volume, e t c . Two o b j e c t s w i l l be commensurable, t h e r e f o r e , j u s t In case they are ins t a n c e s of a p a r t i c u l a r r e l a t i o n t h at i s determinable by a common standard. And, by c o n t r a s t , two o b j e c t s w i l l be comparable and incommen-s u r a b l e j u s t i n case they have such r e l a t i o n s , but those r e l a -t i o n s a re not determinable by a common standard. There are (at l e a s t ) two d i s t i n g u i s h a b l e cases of commensur-a b i l i t y : (1) a s i n g l e standard i s ab l e t o compare a given p a i r of o b j e c t s because each o b j e c t i s a simple, hence i r r e d u c i b l e or d i -r e c t , i n s t a n c e of i t s c a t e g o r i e s ; and (2) a s i n g l e standard i s ab l e t o compare a given p a i r of o b j e c t s because each o b j e c t i s a complex, hence \" d e f i n l t i o n a l l y - e l i m i n a b l e \" or i n d i r e c t , instance of more p r i m i t i v e c a t e g o r i e s embodied In t h a t standard. In both cases, however, the comparison of one o b j e c t with the other by the standard i s i n d i r e c t : each o b j e c t i s s e p a r a t e l y compared with the standard t o determine how they compare with each other. In other words, commensuration Is comparison of two t h i n g s by t h e i r comparison with a t h i r d : t h e i r common standard. Thus, s i n c e i n -29 commensurability means t h a t t h e r e are no common standards of comparison, a f u r t h e r c o n d i t i o n on our n o t i o n of comparable and incommensurable o b j e c t s i s t h a t each such o b j e c t must be compared d i r e c t l y with the other t o determine t h e i r i n t e r r e l a t i o n s . However, d e f i n i t i o n (1) does not, as i t stands, g i v e us the resources f o r making a u s e f u l d i s t i n c t i o n between commensurabil-i t y and c o m p a r a b i l i t y ; f o r , s i n c e , by h y p o t h e s i s , the o b j e c t s that we are c o n s i d e r i n g a re comparable, they c o u l d a l s o be made \"commensurable\" by a t r i v i a l technique compatible with t h a t d e f -i n i t i o n . Thus even though t h e y shared no common s t r u c t u r a l e l e -ments, and so were incommensurable by our e a r l i e r d e f i n i t i o n (p4 above), those o b j e c t s would be, i n a weaker sense, comparable by a common st a n d a r d : one c o n s t r u c t e d from t h e i r mere u n i o n . 8 0 D e f i n i t i o n (2) i s more h e l p f u l . Thus, on the b a s i s of (2) and our e a r l i e r d e f i n i t i o n of \"Incommensurability,\" we may say: D e f i n i t i o n 3: Tvo structurally-complex objects are compar-able and incommensurable vhen they have relations that are not determinable on the basis of more p r i m i t i v e elements common to both.31 And s i n c e Incommensurable o b j e c t s ' r e l a t i o n s cannot be de-termined Indirectly as a f u n c t i o n of common p a r t s , t h e i r r e l a -t i o n s can o n l y be determined d i r e c t l y . That i s , the r e l a t i o n s between such o b j e c t s \u00E2\u0080\u0094 w h e t h e r of p a r t to p a r t ; part/whole t o part/whole; whole t o whole; e t c . \u00E2\u0080\u0094 c a n be determined and determin-able o n l y by the simple j u x t a p o s i t i o n of one o b j e c t or i t s a s -pects with the other. And ( i f such d i r e c t comparison makes 30 sense) t h a t s p a t i a l , temporal, e t c . , p a i r i n g w i l l be enough t o show t h a t those o b j e c t s c o n s t i t u t e an i r r e d u c i b l e i n s t a n c e of a p a r t i c u l a r comparative r e l a t i o n . \" In summary, then, the i n t e l l i g i b i l i t y of the n o t i o n of com-para b l e but Incommensurable o b j e c t s depends on the i n t e l l i g i b i l -i t y of the n o t i o n of d i r e c t comparison. T h i s attempt to b i f u r -c a t e the n o t i o n of c o m p a r a b i l i t y i n t o d i r e c t c o m p a r a b i l i t y and commensurablllty has p o t e n t i a l p h i l o s o p h i c a l s i g n i f i c a n c e : i t suggests t h a t comparison of s t r u c t u r a l l y complex e n t i t l e s need not r e l y on the presence of elements common to both; i t need not r e l y on common standards of comparison. To make t h i s r a t h e r a b s t r a c t d i s c u s s i o n more a c c e s s i b l e , c o n s i d e r the a p p l i c a t i o n of my f o r m u l a t i o n t o commensurablllty and i n c o m m e n s u r a b i l i t y i n geometry, where those n o t i o n s were f i r s t i n t r o d u c e d . In geometry, two lengths are s a i d to be com-mensurable (by length) i f one can c o n s t r u c t a common u n i t l e n g t h t h a t w i l l d i v i d e both e x a c t l y . Thus a s t i c k t h a t i s ten c e n t i -metres long i s commensurable with one seven c e n t i m e t r e s long be-cause, f o r example, a one cent i m e t r e l e n g t h w i l l d i v i d e both without remainder. And both lengths are, i n a sense, ' d e f i n i -t l o n a l l y - e l l m l n a b l e ' s i n c e each l e n g t h can be reduced to m u l t i -p l e s of ( \" l o g i c a l c o n s t r u c t i o n s on\") t h a t common u n i t (see p28 above). Thus the r a t i o of the l e n g t h of the f i r s t to the second s t i c k can be broken down f u r t h e r t o the r a t i o 10 : 7. On the other hand, as Is w e l l known, the hypotenuse and s i d e of a r i g h t angle i s o c e l e s t r i a n g l e are incommensurable: i t i s 31 impossible to c o n s t r u c t a common u n i t l e n g t h t h a t w i l l d i v i d e both hypotenuse and s i d e e x a c t l y . N e v e r t h e l e s s , those l e n g t h s are d i r e c t l y comparable, s i n c e by mere I n s p e c t i o n of the t r i a n g l e one can see immediately t h a t the hypotenuse i s longer than the s i d e ; and from s i m i l a r t r i a n g l e s one can a l s o see d i r e c t l y t h a t those lengths form a consta n t , and i r r e d u c i b l e , ratio ( c . f . Von F r i t z 1945, 261). The s i d e and hypotenuse are thus both incom-mensurable and d i r e c t l y comparable as i n my d e f i n i t i o n . More-over, i t i s a l s o p o s s i b l e t o compare d i r e c t l y the p a r t s of those l e n g t h s : e.g., every p a r t of the hypotenuse i s (approximately) 14,142/10,000 times the l e n g t h of a p a r t of the s i d e , i f both those p a r t s are i n t h e i r o r i g i n a l r a t i o s . 9 3 Moreover, i n l i n e with the comments I made on d e f i n i t i o n (1) (p29 above), there i s a l s o a simple way i n which those l e n g t h s can be made \"commensur-a b l e . \" That i s , there i s a \"common standa r d \" f o r comparing the lengths of the hypotenuse and s i d e : the r e a l number \"system\"; and ac c o r d i n g to t h a t common system, the r a t i o s of those lengths i s ^ 2 : 1 . But s i n c e t h a t r e a l number system i s simply the union of two d i s j o i n t s e t s : the r a t i o n a l (e.g. which c o n t a i n s 1) and i r r a t i o n a l numbers (e.g. which c o n t a i n s v 2 ) , t h e i r \"commensurabil-i t y \" i n that system does not e n t a i l t h e i r c o m p a r a b i l i t y by more b a s i c elements common to bo t h . 9 4 Before I extend my model t o the problem of l o g i c a l l y incom-p a t i b l e and incommensurable s c i e n t i f i c t h e o r i e s , I s h a l l f i r s t p resent evidence t h a t Kuhn a l s o makes use of a d i s t i n c t i o n be-32 tween (what I have c a l l e d ) d i r e c t and i n d i r e c t comparison i n h i s p h i l o s o p h y . 1.5.1 Kuhn and D i r e c t Comparison The most e x p l i c i t example of a d i s t i n c t i o n between d i r e c t and I n d i r e c t comparison, and thus c o m p a r a b i l i t y and commensura-b l l l t y , i n Kuhn's w r i t i n g s i s i n h i s n o t i o n of a s i m i l a r i t y s e t (see Kuhn 1970a, 192, 200; Kuhn 1977c, 305-18). However, t h a t n o t i o n i s I n t i m a t e l y r e l a t e d t o h i s a n a l y t i c concept of a s c i e n -t i f i c paradigm, which he i n t r o d u c e s to r e p l a c e the t r a d i t i o n a l , formal n o t i o n of a u n i v e r s a l g e n e r a l i z a t i o n . And s i n c e I s h a l l d i s c u s s Kuhn's a l t e r n a t i v e t o the t r a d i t i o n a l formal schema i n chapter two, I s h a l l here use more su g g e s t i v e evidence of the above d i s t i n c t i o n . As the f o l l o w i n g passage shows, Kuhn a p p a r e n t l y b e l i e v e s t h a t r e c o g n i t i o n of r e l a t i o n s between d i f f e r e n t p o i n t s of view does not r e q u i r e a common, n e u t r a l b a s i s of comparison. What occurs d u r i n g a s c i e n t i f i c r e v o l u t i o n i s not f u l l y r e d u c i b l e t o a r e i n t e r p r e t a t i o n of i n d i v i d u a l and s t a b l e ( i . e . , t h e o r y - n e u t r a l ] d a t a . In the f i r s t p l a c e , the data are not u n e q u i v o c a l l y s t a b l e . [A B e r t h o l l e t i a n compound Is not a P r o u s t l a n p h y s i c a l m i x t u r e ] , nor i s oxygen d e p h l o g l s -t i c a t e d a i r . . . . [ T h u s ] r a t h e r than being an i n t e r p r e t e r [of \" f i x e d \" d a t a ] , the s c i e n t i s t who embraces a new paradigm i s l i k e [a] man [who undergoes a g e s t a l t s w i t c h ] . C o n f r o n t i n g the same c o n s t e l l a t i o n of o b j e c t s as before and knowing that he does so, he n e v e r t h e l e s s f i n d s them transformed through and through In many of t h e i r d e t a i l s (Kuhn 1970a, 121-2). I t a l i c s mine). 33 1.6 Commensurability and Formal L o g i c s Thus f a r I have claimed, without much e l a b o r a t i o n , t h a t f o r -mal l o g i c s r e q u i r e t h a t the l i n g u i s t i c e n t i t i e s they compare or analyse be e x p r e s s i b l e w i t h i n a common v o c a b u l a r y (e.g. p l 4 ) : i n other words, t h a t those e n t i t i e s be commensurable. I now want t o suggest t h a t formal l o g i c s be taken q u i t e s t r i c t l y as l o g i c a l \"measures.\" I f I am r i g h t , t h i s means e n t i t i e s t h a t can be f o r -m a l l y compared are logically commensurable because they are com-par a b l e by a common l o g i c a l measure. By c o n t r a s t , i n my use of \"formal comparison,\" those e n t i t i e s t h a t cannot be f o r m a l l y com-pared are l o g i c a l l y incommensurable. 8 3 Of course, i f one i s to take the m e t r i c a l analogy s e r i o u s l y , formal l o g i c s have t o have \" u n i t s \" of l o g i c a l measure: i . e . they have t o have s p e c i f i c means f o r d e t e r m i n i n g l o g i c a l r e l a t i o n s h i p s . In what f o l l o w s , I sug-gest t h a t those u n i t s are the s o - c a l l e d logical concepts. And I argue t h a t the view t h a t language d i v i d e s i n t o s t r i c t l y l o g i c a l and n o n - l o g i c a l concepts, which i s e s s e n t i a l to formal systems, i s incompatible with the t r u t h of the incommensurability t h e s i s . There are two b a s i c uses made of formal l o g i c s l i k e the p r e d i c a t e c a l c u l u s i n t r a d i t i o n a l p h i l o s o p h y of s c i e n c e : (1) they are used to d e s c r i b e the i n t e r n a l l o g i c a l s t r u c t u r e of a theory; and (2) they are used to formulate the l o g i c a l r e l a t i o n s between s c i e n t i f i c t h e o r i e s (e.g. Popper 1968, 32 e t . seq.). The second use c l e a r l y depends on the f i r s t , s i n c e i n d i v i d u a l t h e o r i e s have f i r s t t o be f o r m a l i z e d before t h e i r l o g i c a l i n t e r r e l a t i o n s with others can be determined. Now, i n v a r i a b l y , formal l o g i c s d i v i d e t h e i r o b j e c t languages i n t o l o g i c a l and non- or e x t r a - l o g i c a l concepts (e.g. Suppes 1957, 3, 43, 48, 68; Mates 1972, 16, 45; Boolos and J e f f r e y 1980, 97). For example, i n the p r e d i c a t e c a l c u l u s the standard l o g i c a l concepts (words, terms, symbols) a r e : \"not, \"and,\" \" o r , \" \" i f . . . , t hen,\" \" i f and o n l y i f , \" \" a l l , \" and \"some,\" and t h e i r synonyms. And p h i l o s o p h e r s who a p p l y formal l o g i c s t o s c i e n t i f i c languages a l s o commonly speak of the l o g i c a l and n o n - l o g i c a l v o c a b u l a r i e s of those languages (e.g. Suppes 1957, 68).\" 8 The i m p l i c a t i o n of t h i s d i v i s i o n of language i s t h a t a l l (or a t l e a s t the c l e a r e s t , c . f . n l 3 ) l o g i c a l work i n t h a t language i s done by j u s t these concepts. Such a d i v i s i o n of language seems to be a p r e - c o n d i t i o n f o r any f o r m a l , ( n o n - t r i v l a l l y ) s y s t e m a t i c l o g i c ( c . f . Mates 1972, p l 6 ) . Unless l o g i c a l r e l a t i o n s between, f o r example, p r o p o s i -t i o n s and t h e o r i e s were based o n l y on the meanings of a r e l a t i v e -l y s m a l l number of concepts, i t would be g e n e r a l l y Impossible to determine those r e l a t i o n s f o r m a l l y . For, i n t h a t case, the l o g i -c a l r e l a t i o n s between many p a i r s of e n t i t i e s would given by the meanings of those e n t i t l e s a l o n e ; so there would o f t e n be no com-mon f e a t u r e l i n k i n g v a r i o u s i n s t a n c e s of a p a r t i c u l a r l o g i c a l r e l a t i o n l i k e i n c o m p a t i b i l i t y . N e v e r t h e l e s s , I s h a l l now argue t h a t the incommensurability t h e s i s presupposes t h a t l o g i c a l r e l a -t i o n s are i n f a c t l a r g e l y non-systematic and non-systematizable. 35 I t must be emphasized, however, t h a t t h i s p r e s u p p o s i t i o n does not imply the p a t e n t l y absurd c l a i m t h a t there are no s y s t e m a t i c l o g -i c a l r e l a t i o n s nor t h a t such l o g i c s are not Important and power-f u l tools of s c i e n c e ( c . f . Kuhn 1977, 313). Rather, i t s i m p l y means that such s y s t e m a t i c r e l a t i o n s o n l y c o n s t i t u t e a s m a l l p r o -p o r t i o n of l o g i c a l r e l a t i o n s proper. I argue f o r two c l a i m s : (1) t h a t the r e l a t i o n of l o g i c a l i n c o m p a t i b i l i t y between incommensurable t h e o r i e s cannot be cap-tu r e d by formal systems; and (2) t h a t , i f there were incommen-su r a b l e t h e o r i e s , I t c o u l d not g e n e r a l l y be t r u e t h a t e v e r y I n d i -v i d u a l s c i e n t i f i c t heory c o u l d be analysed by formal l o g i c s . Both arguments work by r e d u c t i o ad absurdurn. I have t r i e d t o make the arguments completely g e n e r a l and not dependent on the f e a t u r e s of p a r t i c u l a r formal systems l i k e the p r e d i c a t e c a l c u -l u s . One should keep i n mind t h a t , by d e f i n i t i o n (see pp4, 29), incommensurable t h e o r i e s , or incommensurable p a r t s of t h e o r i e s , have no common concepts. And because ve are here c o n s i d e r i n g the hypothesis t h a t formal l o g i c s can e i t h e r compare or analyse i n -commensurable t h e o r i e s , i t i s a l s o t h e r e f o r e assumed t h a t incom-mensurable t h e o r i e s share the same l o g i c a l concepts but have no common non-logical concepts. 1.6.1 Argument 1: L o g i c a l R e l a t i o n s Between T h e o r i e s Here we c o n s i d e r the hyp o t h e s i s t h a t f o r m a l l y comparable 36 t h e o r i e s can a l s o be incommensurable. By the h y p othesis of f o r -mal c o m p a r a b i l i t y , the l o g i c a l r e l a t i o n s between any p a i r of e l e -ments, e.g. ( t l j ; t 2 k ) , of any p a i r of such t h e o r i e s , e.g. ( T l ; T 2 ) , must depend only on the meanings of the l o g i c a l con-c e p t s . T h i s means th a t one such element i s e q u i v a l e n t to a l o g i -c a l f u n c t i o n , f , of the o t h e r : e.g. t l j = / ( t 2 k ) ; and t h a t means, s i n c e the t h e o r i e s share the l o g i c a l concepts, the t h e o r y ( T l ) t h a t c o n t a i n s the f i r s t element ( t l j ) a l s o c o n t a i n s the second element ( t 2 k ) . Which c o n t r a d i c t s the h y p o t h e s i s of incommensur-a b i l i t y . 1.6.2 Argument 2: Formal A n a l y s i s of I n d i v i d u a l T h e o r i e s Here we c o n s i d e r the h y p othesis t h a t any i n d i v i d u a l s c i e n t i -f i c t h e o r y can be f o r m a l l y analysed even though there are p a i r s of t h e o r i e s t h a t cannot be f o r m a l l y compared because of t h e i r i n c o m m e n s u r a b i l i t y . Consider a p a i r of incommensurable t h e o r i e s : s i n c e , by h y p o t h e s i s , each i s f u l l y a n a l y s a b l e f o r m a l l y , each w i l l share the same l o g i c a l c oncepts; s i n c e those t h e o r i e s are incommensurable, they w i l l share no n o n - l o g i c a l concepts. Now, by h y p o t h e s i s , those t h e o r i e s are l o g i c a l l y r e l a t e d . And, c l e a r -l y , those l o g i c a l r e l a t i o n s must be due e i t h e r to the meanings of the t h e o r i e s ' l o g i c a l or n o n - l o g i c a l concepts. By argument 1, those r e l a t i o n s can't be due to the l o g i c a l concepts, s i n c e t h a t would imply, c o n t r a r y to the h y p o t h e s i s of incommensurability, t h a t the t h e o r i e s share common n o n - l o g i c a l concepts. On the 37 , other hand, i f those l o g i c a l r e l a t i o n s f o l l o w from the meanings of the n o n - l o g i c a l concepts, then the n o n - l o g i c a l concepts a r e n ' t (at l e a s t a b s o l u t e l y ) n o n - l o g i c a l . Which i s a a l s o a c o n t r a d i c -t i o n . Hence i f there are incommensurable p a i r s of t h e o r i e s , the languages of s c i e n t i f i c t h e o r i e s do not d i v i d e i n t o s t r i c t l y l o g i c a l and n o n - l o g i c a l concepts. In other words, i f there are incommensurable t h e o r i e s , l o g i c i s not i d e n t i c a l with formal l o g i c . For each of the above arguments i t i s p o s s i b l e t o r e t o r t that l o g i c j u s t i s formal l o g i c and t h a t , t h e r e f o r e , the incom-m e n s u r a b i l i t y t h e s i s i s f a l s e . Or i n s t e a d I t might be claimed that i n d i v i d u a l t h e o r i e s form d i f f e r e n t l o g i c a l systems; and each such system does d i v i d e f u r t h e r i n t o d i f f e r e n t p u r e l y l o g i c a l and n o n - l o g i c a l concepts (e.g. Goodman 1984, 44-5; but c . f . ibid.f 94-5); hence, formal l o g i c s don't preclude incommensurability. But, with r e s p e c t to t h i s second o p t i o n , I have not here claimed t h a t Kuhn's t h e s i s i m p l i e s t h a t there are no r e l a t i o n s based on l o g i c a l form or even t h a t no t h e o r i e s may be f o r m a l l y analysed. I have o n l y s a i d t h a t the incommensurability t h e s i s means that f o r -mal l o g i c s do not exhaust l o g i c proper. In any case, even i f each of an Incommensurable p a i r of t h e o r i e s c o n s t i t u t e d a d i f f e r -ent formal systems vould s t i l l leave u n e x p l a i n e d \u00E2\u0080\u0094 i . e . unformal-i z e d \u00E2\u0080\u0094 t h e l o g i c a l r e l a t i o n s between those d i s c r e t e systems. With r e s p e c t to the f i r s t r e t o r t , i t should be noted t h a t there are i n s t a n c e s of statements i n o r d i n a r y language whose l o g i c a l r e l a t i o n s seem to a r i s e from the meanings of t h e i r \"non-38 l o g i c a l \" c oncepts. For example, the c l a i m , \"George i s a bachelor and George i s a married man,\" i s not c o n t r a d i c t o r y because of i t s form but because of the meanings of bachelor and married man. Moreover, t o t u r n t h i s c l a i m i n t o a formal c o n t r a d i c t i o n by f i r s t d e f i n i n g bachelor as unmarried man, presupposes t h a t one a l r e a d y knows those concepts t o be synonymous, and so begs the q u e s t i o n of the source of the i n c o m p a t i b i l i t y of bachelor and married man. Examples of such meaning-dependent l o g i c a l r e l a t i o n s are not mere c u r l o u s i t i e s . The s o - c a l l e d n a t u r a l l o g i c i a n , Steven Thom-as, c l a i m s t h a t \"samplings i n d i c a t e I that]...more than 90% of d e d u c t i v e l y v a l i d i n f e r e n c e s i n n a t u r a l language...depend on the semantics, r a t h e r than on the l o g i c a l form or syntax, of the premise(s) and c o n c l u s i o n \" (Thomas 1986, 448. I t a l i c s i n o r i g i -n a l ) . \" 7 Moreover, Davidson h i m s e l f i s a l s o aware of deep prob-lems formal approaches have with the most common f e a t u r e s o\u00C2\u00A3 n a t u r a l languages ( l i k e t h a t of s c i e n c e ) , though with the oppo-s i t e c o n c l u s i o n t o Thomas. Since I t h i n k there is no alternative, I have taken an o p t i -m i s t i c and programmatic view of the p o s s i b i l i t i e s f o r a formal c h a r a c t e r i z a t i o n of a t r u t h p r e d i c a t e f o r a n a t u r a l language. But i t must be allowed t h a t a s t a g g e r i n g l i s t of d i f f i c u l t i e s and conundrums remains (Davidson 1984, 35. I t a l i c s mine). What my arguments, Thomas's s t a t i s t i c s and Davidson's \"con-undrums\" suggest i s th a t the l o g i c a l r e l a t i o n s between incommen-su r a b l e t h e o r i e s must l i k e w i s e depend on the semantics of t h e i r \" n o n l o g i c a l \" c oncepts. That should not be s u r p r i s i n g i f we r e -c a l l Kuhn's c h a r a c t e r i z a t i o n of incommensurable t h e o r i e s as \"fun-39 d a m e n t a l l y i n c o m p a t i b l e \" (see p 4 ) ; f o r t h a t l o g i c o - n o r m a t i v e h y -b r i d n o t i o n i s , i n r e t r o s p e c t , c l e a r l y a t odds wi th any r i g o r o u s d i v i s i o n of the l o g i c a l from the n o n - l o g i c a l . And i f we a l s o r e -member t h a t Kuhn takes s c i e n t i f i c t h e o r i e s to be h o l i s t i c , \"con-c e p t u a l webs,\" we s h o u l d a l s o expec t t h a t the l o g i c a l r e l a t i o n s between those \"webs\" w i l l have to be a consequence of the seman-t i c s of those systems as c o n c e p t u a l who le s . I t i s t r u e t h a t sentences a r e n o r m a l l y h e l d to be the u n i t o f l o g i c a l r e l a t i o n s such as i n c o m p a t i b i l i t y ; so i t w i l l undoubt -e d l y appear p e c u l i a r to speak of w h o l e s a l e t h e o r e t i c a l incompat -i b i l i t y . But i f we s t a t e the n o t i o n o f l o g i c a l I n c o m p a t i b i l i t y q u i t e b r o a d l y a s : \" i f this were t r u e , then t h a t c o u l d not a l s o be t r u e , \" then the idea of d i r e c t t h e o r e t i c a l i n c o m p a t i b i l i t y may not seem so odd . Thus one c o u l d s a y t h a t two h o l i s t i c t h e o r e t i -c a l systems are ( d i r e c t l y ) l o g i c a l l y i n c o m p a t i b l e j u s t i n c a s e , i f the whole wor ld were as i n one t h e o r y , i t c o u l d not a l s o be as i n the o ther t h e o r y . S t i l l , g i v e n the obv ious l i m i t s of the human mind , s i n c e t h e o r i e s are e n t i t l e s w i t h v e r y complex i n t e r n a l s t r u c t u r e s , i t might seem i m p o s s i b l e t h a t t h e i r i n c o m p a t i b i l i t i e s c o u l d be d e -t ermined d i r e c t l y . To h e l p h i s r e a d e r s get an i n t u i t i v e u n d e r -s t a n d i n g of the u n f a m i l i a r i d e a of p r i m i t i v e t h e o r e t i c a l incom-p a t i b i l i t y , Kuhn employs the i d e a o f a \"swi tch i n v i s u a l g e s t a l t \" as I t s \"e lementary p r o t o t y p e \" (Kuhn 1970a, 1 1 1 ) . 9 0 1.6 .3 A \" G e s t a l t - S w i t c h \" Model of T h e o r e t i c a l I n c o m p a t i b i l i t y 40 A c l a s s i c example of a v i s u a l g e s t a l t s w i t c h i s the response to the s o - c a l l e d duck-rabbit f i g u r e . S u r p r i s i n g l y , t h i s s t r u c -t u r a l l y - c o m p l e x f i g u r e i s seen a l t e r n a t e l y as wholly e i t h e r a duck or a r a b b i t , though never both a t once. Hence, s i n c e i t i s c l e a r l y impossible to see the f i g u r e s i m u l t a n e o u s l y as both a duck and a r a b b i t \u00E2\u0080\u0094 a duck i s not a r a b b i t and v i c e v e r s a \u00E2\u0080\u0094 t h e s e seem to be d i r e c t l y incompatible c o n s t r u a l s of the same domain. The d u c k - r a b b i t f i g u r e thus appears to provide a v e r y good model f o r e x p l i c a t i n g how the d i r e c t l o g i c a l comparison of ( p u t a t i v e ) incommensurables can take p l a c e without implying t h e i r commensur-a b l l l t y . 41 The Duck-Rabbit F i g u r e 1. Thus, having experienced both g e s t a l t s , we can d i r e c t l y com-pare and c o n t r a s t the duck and r a b b i t views as f o l l o w s . The up-per b i l l of the duck p e r s p e c t i v e \" i s \" the l e f t ear of the r a b b i t p e r s p e c t i v e ; the l e f t duck eye of the duck p e r s p e c t i v e \" i s \" the r i g h t r a b b i t eye of the r a b b i t p e r s p e c t i v e ; the t h r o a t of the duck p e r s p e c t i v e \" i s \" the nape of the r a b b i t p e r s p e c t i v e ; the notch on the back of the head of the duck p e r s p e c t i v e \" i s \" the mouth on the r a b b i t p e r s p e c t i v e ; and so on. 3 9 I have used shudder-quotes around the word \" I s \" In each case to emphasize t h a t , while the r e s p e c t i v e p a r t s are i n a sense co-e x t e n s i v e , I t Is n e v e r t h e l e s s impossible t h a t they both o b t a i n (from e i t h e r p e r s p e c t i v e ) . For ducks have no f l o p p y ears and r a b b i t s no r i g i d beaks, and so on. N o t i c e f u r t h e r t h a t while both the duck and r a b b i t are i n a sense composed of t h e i r c o n s t i -tuent b i l l s , e a r s , e t c . , these p a r t s are what they are because they are p a r t s of the whole o b j e c t . Thus i t i s more acc u r a t e to say i n s t e a d t h a t the duck and r a b b i t d i v i d e into t h e i r c o n s t i t u -ent p a r t s . 4 0 For Kuhn, then, on analogy with t h i s \"elementary p r o t o t y p e , \" the comparison or c o n t r a s t of incommensurable t h e o r i e s must u l t i -mately i n v o l v e t h e i r d i r e c t comparison as whole to whole. That those t h e o r i e s are w h o l l y incompatible, however, does not mean t h a t t h e i r p a r t s cannot be compared or even found to be s i m i l a r . I t j u s t means t h a t any comparison of those p a r t s w i l l i n v o l v e the j u x t a p o s i t i o n , not of theory-independent terms, concepts and sen-tences, but of those e n t i t i e s as theory-dependent s u b d i v i s i o n s . Thus each element i n the comparison or c o n t r a s t p a i r s w i l l be there as a r e p r e s e n t a t i v e of the whole t h e o r y from which they are a b s t r a c t e d . For example, j u s t as the b i l l gua b i l l of the duck can be seen d i r e c t l y to be c o - e x t e n s i v e with the ears qua ears of the rabbit, so a l s o a chemical compound gua Bertholletian sub-stance of g r e a t l y variable proportions can be seen d i r e c t l y to be (often) c o - e x t e n s i v e with a p h y s i c a l mixture gua Proustian solu-tion. Two o b j e c t i o n s have been r a i s e d a g a i n s t the use of the ges-t a l t model f o r t h e o r y change ( C o l l i e r 1984, 109). The f i r s t ob-j e c t i o n \u00E2\u0080\u0094 t h a t the d u c k - r a b b i t example i n v o l v e s r e p r e s e n t a t i o n s , not r e a l o b j e c t s - - i s , I t h i n k , r a t h e r e a s i l y d isposed o f . For, mutatis mutandis, t h a t example works j u s t as w e l l If we think of the o b j e c t as e i t h e r a p icture-duck or a p i c t u r e - r a b b i t , which we do i n any case ( c . f . a l s o Feyerabend 1975, 258 & n98). The second o b j e c t i o n i s more s e r i o u s . Thus i t i s c l a i m e d , with some (I t h i n k mistaken) encouragement from Kuhn (Kuhn 1970a, 114), t h a t i n the d u c k - r a b b i t case, there i s a n e u t r a l base of comparison: \"the l i n e s which make up the f i g u r e \" ( C o l l i e r 1984, 109). I f so, the duck and r a b b i t views would be a l t e r n a t i v e , but compatible c o n s t r u a l s of a common domain. But j u s t as i t i s im-p o s s i b l e to see the f i g u r e s i m u l t a n e o u s l y as both a duck and a r a b b i t , i t i s a l s o impossible to see the f i g u r e s i m u l t a n e o u s l y as both mere l i n e s and as e i t h e r a duck or a r a b b i t . Thus, while the drawing i s , i n a sense, composed of the l i n e s on paper, and while one may draw the f i g u r e o n e s e l f , s e e i n g those l i n e s as e i -ther a duck or a r a b b i t , or v i c e v e r s a , must a l s o take p l a c e \"as a r e l a t i v e l y sudden and u n s t r u c t u r e d event\" (Kuhn 1970a, 122). T h i s second o b j e c t i o n i s a more s p e c i f i c v e r s i o n of such c l a i m s as: \"what the d u c k - r a b b i t shows i s that r e a l i t y can have a l t e r n a t i v e or complementary r e p r e s e n t a t i o n s , each of which grasps some a s p e c t , but which are not o n l y not i n c o n f l i c t but are each needed i f one i s to get 'the whole p i c t u r e ' (so to speak)\" ( S a v l t t 1989, 2; see a l s o Hacking 1981, 4). But t h i s more g e n e r a l c l a i m I t s e l f c o n t a i n s an i m p l i c i t demand f o r commen-s u r a b l l l t y In making judgements about c o n f l i c t . Thus i t suggests t h a t unless there are common standards f o r showing views to be i n c o n f l i c t , those views are compatible by d e f a u l t . On the other hand, as we have seen, there are two b a s i c ways i n v h i c h one might judge v i e v s to be e i t h e r c o n f l i c t i n g or com-plementary: by i n d i r e c t or d i r e c t comparison. But i n cases l i k e the d u c k - r a b b i t f i g u r e , and incommensurable t h e o r i e s , I have argued, there i s no n e u t r a l p e r s p e c t i v e f o r making an i n d i r e c t judgement. T h e r e f o r e , i n such cases, the judgement must be made by d i r e c t comparison; and such comparison shovs those perspec-t i v e s to be c l e a r l y incompatible. That i s , i t i s im p o s s i b l e , from one p o i n t o f view, t o have the other p o i n t of v i e v ; and there i s no t h i r d s t andpoint from v h i c h one might have both. Hence t o c a l l incommensurable v i e v s compatible by d e f a u l t i s t o imply t h a t comparison i s commensuration. But as I s h a l l nov argue, such an i d e n t i f i c a t i o n leads t o a b s u r d i t i e s . 1.7 D i r e c t Comparison: A Thought Experiment From the f a c t t h a t commensuration i n v o l v e s the comparison of tvo t h i n g s by t h e i r comparison with a t h i r d t h i n g (see SI.5, p28-29), i t should be c l e a r t h a t t o d e f i n e \"comparison\" as \"commen-s u r a t i o n \" vould y i e l d a v i c i o u s r e g r e s s . 4 ' In vhat f o l l o v s , I argue t h a t t o demand that to e s t a b l i s h s i m i l a r i t y and d i f f e r e n c e of r e f e r e n c e ; to determine s i m i l a r i t y and d i f f e r e n c e of meaning; and t o r e c o g n i z e l o g i c a l i n c o m p a t i b i l i t y always r e q u i r e s common elements leads i n each case to a v i c i o u s r e g r e s s . On the other hand, I argue t h a t i f Kuhn's c r i t i c s were t o agree t h a t such com-p a r i s o n s w i l l a t some p o i n t have to be d i r e c t , but hold t h a t t h i s p o i n t i s o s t e n s i v e d e f i n i t i o n , a \"common c o - o r d i n a t e system\" 45 (Davidson 1984b, 184), or formal l o g i c they must o f f e r an i n d e -pendent argument t o prove t h a t t h i s i s so. And, t h e r e f o r e , i f the prima facie evidence i s t h a t no such system does or c o u l d e x i s t , t h a t evidence w i l l have t o be taken a t face v a l u e . F i r s t , i f the c o - r e f e r e n c e of two terms always depended on each one's being c o - r e f e r e n t i a l with some common t h i r d term, then we should a l s o r e q u i r e a s t i l l f u r t h e r term t o mediate c o - r e f e r -ence between each of the f i r s t two terms and the t h i r d ; and so on. On the other hand, i f the c o - r e f e r e n c e of the f i r s t two terms w i t h the t h i r d can be determined d i r e c t l y , we have t o be give n a reason why t h i s c o u l d not a l s o be the case f o r the f i r s t two. For example, c o n s i d e r the f o l l o w i n g c o - r e f e r e n t i a l expres-s i o n s , \" B r i a n Mulroney\" and \"the prime m i n i s t e r of Canada.\" I f we hold t h a t t o e s t a b l i s h t h e i r c o - r e f e r e n c e we f i r s t have t o show t h a t each i s c o - r e f e r e n t i a l with a \"more p r i m i t i v e \" expres-s i o n l i k e a demonstrative pronoun (e.g. t h i s ) , we s h a l l a l s o need a s t i l l \"more b a s i c \" e x p r e s s i o n to mediate the c o - r e f e r e n c e of both \" B r i a n Mulroney\" and \"the prime m i n i s t e r of Canada\" with t h a t demonstrative pronoun. 4 2 On the other hand, i f these l a s t r e l a t i o n s h i p s can be determined d i r e c t l y , 4 3 we need a reason why t h i s c o u l d not, In p r i n c i p l e , a l s o be done with \" B r i a n Mulroney\" and \"the prime m i n i s t e r of Canada\" alon e . Second, i f the s i m i l a r i t i e s or d i f f e r e n c e s of meanings of two concepts always r e q u i r e d a \"common co - o r d i n a t e system\" (Da-vidso n 1984, 184) t o determine those r e l a t i o n s , then we should a l s o r e q u i r e a s t i l l f u r t h e r c o - o r d i n a t e system t o show t h a t those concepts vere i n s t a n c e s of t h a t f i r s t system; and so on. Again, i f i t Is admitted t h a t the r e l a t i o n s the tvo concepts have v i t h the c o - o r d i n a t e system must be determined d i r e c t l y , ve need a f u r t h e r reason vhy t h i s c o u l d not a l s o be the case f o r the r e l a t i o n s betveen the concepts themselves. F i n a l l y , I f the i n c o m p a t i b i l i t y of tvo concepts, sentences, t h e o r i e s , e t c . a l v a y s had to be determined by a standard l i k e l o g i c a l form, then ve should a l s o need s t i l l f u r t h e r standards to shov t h a t one such e n t i t y Is i d e n t i c a l i n meaning v i t h the nega-t i o n of the o t h e r . And, on the other hand, i f i t i s countered t h a t the r e c o g n i t i o n t h a t one such e n t i t y i s synonymous v i t h the negation of the other i t s e l f needs no standard, ve need an inde-pendent reason vhy t h e i r i n c o m p a t i b i l i t y c o u l d not be judged d i r e c t l y . The f o r e g o i n g e x e r c i s e i s not meant to e s t a b l i s h t h a t a l l uses of terms, concepts, sentences, and t h e o r i e s i n v o l v e no com-mon s t a n d a r d s . That i s c l e a r l y f a l s e . Appeals to standards, pa-radigms, r u l e s , t r a d i t i o n , e t c . o f t e n p l a y an extremely important r o l e i n s c i e n c e , law, l i t e r a t u r e , a r t , e t c . 4 4 My argument o n l y makes the obvious p o i n t that such appeals must end somewhere; and so even those p r a c t i c e s t h a t Involve appeals to standards must at some p o i n t i n v o l v e d i r e c t comparison. T h e r e f o r e , when h i s t o r i -c a l , a n t h r o p o l o g i c a l , s o c i o l o g i c a l and conceptual evidence shows th a t c e r t a i n communities and t r a d i t i o n s use a p p a r e n t l y q u i t e d i f f e r e n t standards o f , say, t r u t h , meaning, or j u s t i c e , and determined attempts to a t t r i b u t e more b a s i c , common standards to 47 those groups are always \" r e j e c t e d by...members of the group\" (Kuhn 1970a, 44), t h a t evidence must be taken a t face v a l u e . The a b i l i t y to compare t h i n g s d i r e c t l y , however, should not be thought of as a \"mysterious\" (Shapere 1980, 32) c a p a c i t y to i n t u i t t h e i r r e l a t i o n s (see a l s o n28). That would be tantamount to i n t r o d u c i n g i n t u i t i o n as a commensurating f a c u l t y ; but as we have j u s t seen, the demand t h a t any such standards are necessary leads to a b s u r d i t i e s . W i t t g e n s t e i n puts t h i s l a s t p o i n t as f o l -lows: \" I f i n t u i t i o n i s an inner v o i c e \u00E2\u0080\u0094 h o w do I know how I am t o obey i t ? And how do I know t h a t i t doesn't mislead me? For i f i t can guide me r i g h t , i t can a l s o guide me wrong. ( ( I n t u i t i o n an unnecessary s h u f f l e . ) ) \" ( W i t t g e n s t e i n 1953, 8213). i n the f i n a l a n a l y s i s , then, a l l t h a t can be s a i d to e x p l a i n d i r e c t comparison i s simply to remark t h a t i t i s a b a s i c f a c t of human \" n a t u r a l h i s t o r y \" ( i b i d . , \u00C2\u00A725) t h a t we group c e r t a i n t h i n g s as s i m i l a r , i d e n t i c a l , d i f f e r e n t , i n c o m p a t i b l e , and so on. No more can be s a i d without redundancy. 1.8 summary, Sy n t h e s i s and C o n c l u s i o n In t h i s chapter I have t r i e d t o show t h a t the argumentative impasse between Kuhn and h i s c r i t i c s on incommensurability a r i s e s from a fundamental d i f f e r e n c e about the I n t e r p r e t a t i o n of two concepts: l o g i c and comparison. Thus i t turns out t h a t Kuhn's c r i t i c s i m p l i c i t l y I d e n t i f y l o g i c with formal l o g i c s ; but h i s ho-l i s t i c n o t i o n of t h e o r e t i c o - c o n c e p t u a l i n c o m p a t i b i l i t y c o n f l i c t s 48 with the i d e a , b a s i c t o formal l o g i c s , t h a t there i s a completely r i g o r o u s d i s t i n c t i o n between the l o g i c a l and n o n - l o g i c a l . More d e e p l y s t i l l , I t tu r n s out t h a t Kuhn's c r i t i c s I d e n t i f y l o g i c w ith formal l o g i c s because they i d e n t i f y comparison with commen-s u r a t i o n . But I showed, by p o i n t i n g out t h a t commensuration i s comparison of two t h i n g s by t h e i r comparison with a t h i r d , t h a t such an i d e n t i f i c a t i o n would make commensuration i t s e l f impos-s i b l e (see pp28-9, 44-6). One proof t h a t the d i s t i n c t i o n between ( d i r e c t ) comparison and commensuration i s on the r i g h t t r a c k i s i t s a b i l i t y t o r e -s o l v e a r e s i d u a l p u z z l e Kuhn f e e l s about the c h a r a c t e r i s t i c s of the new \" e p l s t e m o l o g l c a l paradigm\" (see 1.0 above). Kuhn says t h a t \"I am convinced t h a t we must l e a r n t o make sense of [seem-i n g l y p a r a d o x i c a l ] statements t h a t a t l e a s t resemble t h e s e . . . though the world does not change with a change of paradigm the s c i e n t i s t a f t e r w a r d works i n a d i f f e r e n t world\" (Kuhn 1970a, 121). These a p p a r e n t l y c o n t r a d i c t o r y c l a i m s can be made sense of as f o l l o w s . On the one hand, j u s t as d i r e c t comparison of the duck and r a b b i t views shows them t o be coe x t e n s i v e (p41), so too d i r e c t comparison of incommensurable t h e o r i e s shows t h a t t h e i r domains are o f t e n l a r g e l y o v e r l a p p i n g ; so i n one sense those t h e o r i e s d e s c r i b e the same world. On the other hand, j u s t as d i r e c t comparison of the duck and r a b b i t views does not r e v e a l a f u r t h e r , common d u c k - r a b b i t view, one can a l s o say th a t Incom-mensurable t h e o r i e s d e s c r i b e d i f f e r e n t worlds. Kuhn's r e j e c t i o n of a primary r o l e f o r (formal) l o g i c i n 49 a n a l y s i n g s c i e n c e has been construed by many c r i t i c s to i n v o l v e \"denying o b j e c t i v i t y to the processes by which s c i e n t i f i c t h e o r -i e s are c r i t i c a l l y e v a l u a t e d \" ( S c h e f f l e r 1967, 88). By c o n t r a s t , I suggested e a r l y i n t h i s chapter t h a t Kuhn should be understood i n s t e a d as o f f e r i n g an alternative c o n s t r u a l of s c i e n t i f i c o b j ec-t i v i t y and r a t i o n a l i t y t h a t i s not based on formal l o g i c , and thus commensurability. In t h i s r e g a r d , S c h e f f l e r a l s o notes, though with some p e r p l e x i t y , t h a t \" P r o f e s s o r Kuhn himself con-c l u d e s by r e i n t r o d u c i n g the v e r y [ e v a l u a t i v e ] ideas he has been a t pains to deny i n the main tendency of h i s work...[for example] he opposes r e c e i v e d n o t i o n s of f a l s i f i c a t i o n , but h i m s e l f i n t r o -duces the concepts of anomaly and c r i s i s , which have a parallel f u n c t i o n i n h i s account\" ( i b i d . , 89. I t a l i c s mine). The main reason Kuhn r e j e c t s a primary a n a l y t i c r o l e f o r formal l o g i c i n s c i e n t i f i c epistemology i s , as we have seen, t h a t he b e l i e v e s t h e o r i e s are o f t e n incommensurable. In the next c h a p t e r , I s h a l l b r i n g out s t i l l other reasons Kuhn has f o r the demotion of formal l o g i c . Thus i n chapter two I d i s c u s s Kuhn's n o t i o n s of paradigm, normal s c i e n c e , anomaly, c r i s i s , thought ex-periment and s c i e n t i f i c r e v o l u t i o n and show how they p a r a l l e l , and d i v e r g e from, more t r a d i t i o n a l c a t e g o r i e s drawn from formal l o g i c . I s h a l l a l s o show th e r e how Kuhn embodies a d i s t i n c t i o n between commensuration and what I have c a l l e d d i r e c t comparison i n those a l t e r n a t i v e a n a l y t i c n o t i o n s . Notes 50 1. I f Kuhn had not made a p e r s u a s i v e case f o r incommensurability, i t i s d o u b t f u l t h a t opposing p h i l o s o p h e r s would have made such co n c e r t e d e f f o r t s to respond t o h i s work. I s r a e l S c h e f f l e r , a noted c r i t i c of Kuhn, admits t h a t , a t f i r s t g l a n c e , Kuhn's r e -s u l t s seem undeniable: \"For the c l a i m s i n q u e s t i o n are supported by d e t a i l e d c o n s i d e r a t i o n s t o which we o u r s e l v e s are i n c l i n e d to ass e n t , a t l e a s t i n i t i a l l y \" ( S c h e f f l e r 1967, 22). 2. In t h i s paper, I s h a l l i n c l u d e under the d e s c r i p t i o n s \" t r a d i -t i o n a l image,\" \" r e c e i v e d view,\" e t c . not o n l y the c l a s s i c s t a t e -ments of the L o g i c a l E m p i r i c i s t s and K a r l Popper but a l s o more r e c e n t v a r i a t i o n s formulated i n response to Kuhn's (and other like-minded p h i l o s o p h e r s ' ) c r i t i c i s m s . Thus the p h i l o s o p h i e s of Lakatos, Laudan and Newton-Smith, f o r example, may be seen as \" t r a d i t i o n a l \" f o r my purposes s i n c e they a l s o seek what Kuhn argues does not and need not e x i s t : t h e o r y - n e u t r a l c r i t e r i a f o r e v a l u a t i n g progress i n s c i e n c e . Of course, such a schematic a c -count of 'the' t r a d i t i o n a l view i s bound to be o v e r l y s i m p l i s t i c and lump together incompatible p h i l o s o p h i e s , s t i l l i t i s s a f e to conclude t h a t , whatever the d i f f e r e n c e s of those p h i l o s o p h i e s , they are u n i t e d i n being attempts to f i n d t h e o r y - n e u t r a l compara-t i v e c r i t e r i a , and thus i n t h e i r r e j e c t i o n of incommensurability. 3. I s h a l l u s u a l l y use the term \"theory\" and Kuhn's p r e f e r r e d ex-p r e s s i o n \"paradigm\" as though they were synonymous. T h i s i s i n keeping with Kuhn's usual p r a c t i c e , though, given what he means by \"paradigm,\" i t does not agree with h i s opponents' understand-ing of \"theory.\" Thus t h e o r i e s t r a d i t i o n a l l y are thought to be u n i v e r s a l g e n e r a l i z a t i o n s ( c . f . G i e r e 1983, 271); but Kuhn holds t h a t h i s concept of a paradigm, or \"concrete s c i e n t i f i c a c h i e v e -ment\" (Kuhn 1970a, 11) i s more b a s i c t o s c i e n c e than i s t h a t t r a -d i t i o n a l c o n c e p t i o n ( I b i d . , 182). I s h a l l d i s c u s s paradigms i n chapter two. 4. By c o n t r a s t , i f the e m p i r i c a l anomaly does not i m p l i c a t e the theory's c a t e g o r i e s , theory change need not i n v o l v e c o n c e p t u a l change, and so a l s o need not i n v o l v e incommensurability. For example, the theory's concepts may a l l o w f o r the f o r m u l a t i o n of d i f f e r e n t e m p i r i c a l laws, so the replacement of the f a l s e law with a more adequate one can leave the b a s i c theory unchanged. On the t r a d i t i o n a l view, however, s i n c e t h e o r i e s are taken to be g e n e r a l i z a t i o n s , such a change of l a v s would a l s o be taken as a change of theory. But, as I poin t e d out i n note 3, Kuhn takes paradigms to be the b a s i c u n i t of s c i e n c e . And he suggests t h a t 51 change of t h a t p u t a t i v e l y more b a s i c u n i t almost always produces the conceptual and e v a l u a t i v e change he c a l l s incommensurability (Kuhn 1970a, 103). 5. I t i s o c c a s i o n a l l y claimed t h a t Kuhn cannot r e a l l y mean t h a t incommensurable t h e o r i e s are logically incompatible; so he must have some other n o t i o n of i n c o m p a t i b i l i t y In mind. Thus Newton-Smith says t h a t \" K u h n . . . i n c o n s i s t e n t l y e x p l i c a t e s the n o t i o n of c o m p e t i t i o n (between incommensurable t h e o r i e s ] i n terms of the n o t i o n of l o g i c a l i n c o m p a t i b i l i t y \" (Newton-Smith 1981, 159). Newton-Smith k i n d l y o f f e r s what he b e l i e v e s to be a more s u i t a b l e n o t i o n of i n c o m p a t i b i l i t y to get Kuhn's i n t e n t i o n s a c r o s s : \"prag-matic t e n s i o n \" ( i b i d . , 159). But, pace Newton-Smith, Kuhn e x p l i -c i t l y s t a t e s t h a t the t h e o r i e s he deems incommensurable\u00E2\u0080\u0094e.g. Newtonian and E i n s t e i n i a n d y n a m i c s \u00E2\u0080\u0094 a r e a l s o logically incompati-b l e : \" E i n s t e i n ' s t h e o r y (Kuhn argues] can be accepted o n l y with the r e c o g n i t i o n t h a t Newton's was wrong\" (Kuhn 1970a, 98; see a l s o ibid., 97). In any case, i n t h i s paper I s h a l l take Kuhn a t h i s word and t r y to g i v e an i n t e r p r e t a t i o n of the n o t i o n of \" f u n -damentally i n c o m p a t i b l e \" t h e o r i e s t h a t coheres both with Kuhn's e x p l i c i t l y - s t a t e d I n t e n t i o n s and with good sense. 6. That i s , though Kuhn a l l o w s t h a t i n comparing two incommen-s u r a b l e t h e o r i e s one can see t h a t , from the vantage of one theo-ry's standards, t h a t t h e o r y i s t r u e while the other i s f a l s e , he c l a i m s there i s no common, theory-independent perspective f o r s e t t l i n g which of them are i n f a c t true or f a l s e . 7. Kuhn a l s o denies most of h i s c r i t i c s ' other c l a i m s : v i z . , t h a t h i s p o s i t i o n means t h a t experiment p l a y s no c r i t i c a l r o l e i n s c i -ence (e.g. Kuhn 1970a, 132); t h a t i t leads to i d e a l i s m (Kuhn 1970b, 2); (strong) r e l a t i v i s m ( i b i d . , 264-5); l r r a t l o n a l l s m (ibid., 263-4); and he a l s o b e l i e v e s t h a t theories of meaning p l a y no e s s e n t i a l r o l e In these Issues ( i b i d . , 266n2). In t h i s paper, however, I s h a l l not d i s c u s s these more s p e c i f i c q u e s t i o n s i n any d e t a i l s i n c e I b e l i e v e t h a t they are a r e f l e c t i o n of the more g e n e r a l d i f f e r e n c e s Kuhn has with h i s c r i t i c s over l o g i c and comparison. That Is, I hope I t w i l l become c l e a r t h a t Kuhn does not r e j e c t the fundamental concepts of e m p i r i c a l s c i e n c e , o n l y p a r t i c u l a r c o n s t r u a l s of them. 8. Kuhn suggests t h a t when seek i n g the source of incommensurabil-i t y between two views t h a t one \"can f i r s t attempt to d i s c o v e r the terms and l o c u t i o n s t h a t , used u n p r o b l e m a t i c a l l y w i t h i n each com-munity, are n e v e r t h e l e s s f o c i of t r o u b l e f o r i n t e r - g r o u p d i s c u s -s i o n s \" (Kuhn 1970a, 202). Kuhn i s here o f f e r i n g a hermeneutic p r i n c i p l e t h at i s s i m i l a r to t h a t of Quine: \"The maxim of t r a n s -l a t i o n u n d e r l y i n g a l l t h i s Is t h a t a s s e r t i o n s s t a r t l l n g l y f a l s e 52 on the face of them are l i k e l y t o t u r n on hidden d i f f e r e n c e s of language\" (Quine I960, 59). Kuhn's p r i n c i p l e d i f f e r s from Quine's, as we s h a l l see, i n not r e q u i r i n g t hat the t r a n s l a t e d c l aims make sense from the s t a n d p o i n t of the home language's c u r -r e n t concepts ( c . f . Feyerabend 1987, 77 and note 14). 9. Kuhn d e s c r i b e s t h e i r views as being \"fundamentally a t c r o s s -purposes\" (Kuhn 1970a, 132). R e c a l l t h a t \"fundamentally incom-p a t i b l e \" means \"both l o g i c a l l y i n c o m p a t i b l e and incommensurable.\" A l s o note t h a t , i n t h i s essay, I s h a l l o n l y be concerned with those p u t a t i v e cases of p h i l o s o p h i c a l l y - I n t e r e s t i n g incommensura-b i l i t y : those which a l s o i n v o l v e l o g i c a l i n c o m p a t i b i l i t y ; thus t h e o r i e s here d e s c r i b e d as Incommensurable w i l l a l s o be assumed to be l o g i c a l l y i n c o m p a t i b l e . 10. For example, i f we l e t R and c stand f o r , r e s p e c t i v e l y , the 1-place p r e d i c a t e s \" i s a c h e m i c a l r e a c t i o n \" and \"takes p l a c e i n constant ( i n t e g r a l ) p r o p o r t i o n s , \" and i f we take the p r e d i c a t e \"takes p l a c e i n c o n t i n u o u s l y - v a r y i n g p r o p o r t i o n s \" to be l o g i c a l l y e q u i v a l e n t to ->Cf then i t seems t h a t we can r e p r e s e n t Proust's and B e r t h o l l e t ' s p o s i t i o n s as (formal) l o g i c a l c o n t r a d i c t o r i e s u s i n g the same concepts: Proust: (x)(Rx -\u00E2\u0080\u00A2 Cx) B e r t h o l l e t : -\"(x)(Rx - Cx) = (3x)(Rx & ->Cx) 11. A l t e r n a t i v e l y \u00E2\u0080\u0094 i n the \" m a t e r i a l mode\"\u00E2\u0080\u0094Proust d i s a g r e e d with B e r t h o l l e t over which pr o c e s s e s were chemical r e a c t i o n s and over which t h i n g s were chemical compounds as opposed to p h y s i c a l mix-t u r e s . The t h r e e concepts, chemical reaction, chemical compound and physical mixture are l o g i c a l l y - i n t e r r e l a t e d as f o l l o w s : a chemical compound i s formed when two or more chemical substances are mixed together i f and o n l y i f t h e y undergo a chemical reac-tion} otherwise they c o n s t i t u t e a mere physical mixture. 1 2 , A, d, and c are c h e m i c a l s u b s t a n c e s ; Ad and Ac are compounds of those substances. 1 3 . T h i s has been noted by most of Kuhn's c r i t i c s , though t h e i r arguments are u s u a l l y expressed as the c o n t r a p o s i t l v e of mine. That i s , Kuhn's c r i t i c s g e n e r a l l y i n f e r t h a t , s i n c e formal l o g i c s would show no l o g i c a l i n c o m p a t i b i l i t y between p u t a t i v e l y - i n c o r a -mensurable t h e o r i e s , those t h e o r i e s c o u l d not be l o g i c a l l y incom-p a t i b l e (e.g. Shapere 1 9 8 1 , 4 3 - 4 ; Newton-Smith 1 9 8 1 , 1 4 9 , 1 5 9 ; S c h e f f l e r 1 9 6 7 , 8 2 ; Davidson 1 9 8 4 , 1 8 4 ) . However, g r a n t i n g t h a t formal l o g i c s would not show Incommensurable t h e o r i e s to be i n -53 compatible, one may argue i n s t e a d t h a t those l o g i c s are simply inadequate t o d e s c r i b i n g l o g i c a l r e l a t i o n s between incommensur-abl e t h e o r i e s . I s h a l l p r ovide a more complete a n a l y s i s of the source of c o n f l i c t between Kuhn's t h e s i s and assumptions of f o r -mal l o g i c s i n s e c t i o n s 1.6 e t . seg., where I s h a l l a l s o argue th a t the e x i s t e n c e of incommensurable t h e o r i e s means t h a t formal l o g i c s c o u l d not, as a general r u l e , g i v e the l o g i c a l s t r u c t u r e s of a l l i n d i v i d u a l t h e o r i e s . 14. The problem (2) of f i n d i n g common concepts f o r incommensur-able t h e o r i e s i s s i m i l a r to the problem of t r a n s l a t i n g between c e r t a i n n a t u r a l languages. Thus t r a n s l a t o r s o f t e n f i n d t h a t f o r many words of one language there e x i s t s no s i n g l e word, or w e l l -d e f i n e d s e t of words, t h a t matches the meaning of the other i n a l l c ircumstances of i t s a p p l i c a t i o n ; to t r a n s l a t e they must a d j u s t t h e i r c h o i c e of word from s i t u a t i o n to s i t u a t i o n . But s i n c e those s i t u a t i o n - v a r i a n t c h o i c e s o f t e n proceed a c c o r d i n g to an a l i e n p a t t e r n of thought, such t r a n s l a t i o n s o f t e n r e s u l t In cla i m s t h a t seem b i z a r r e to the speakers of the home ( t r a n s l a t -ing) language ( c . f . Quine 1960, 57-9; Nida 1964, 92; Hacking 1983, 69-71). And i f , pace Quine (Quine 1960, 58), such t r a n s l a -t i o n s are c o r r e c t , but seem b i z a r r e o n l y because they r e p r e s e n t non-standard usage of e x i s t i n g concepts, t h i s l a s t f a c t suggests t h a t t r a n s l a t i o n may a l t e r the home language by i n t r o d u c i n g i n t o i t concepts t h a t are incommensurable with c u r r e n t ones (see a l s o Feyerabend 1977 and note 8 ) . 15. T h i s i s not s t r i c t l y t r u e . Thus, to borrow a l o c u t i o n of Kuhn's, those c r i t i c s o c c a s i o n a l l y \"dimly r e c o g n i z e \" t h a t there are phenomena t h a t seem incompatible with t h e i r views. For ex-ample, the l o g i c i a n s P a t r i c k Suppes and Benson Mates acknowledge as a \" s u b t l e and complicated matter\" the f a c t t h a t some l o g i c a l r e l a t i o n s seem not to be p u r e l y formal, but to d e r i v e from the meanings of ' n o n - l o g i c a l * e x p r e s s i o n s (Suppes 1957, 68; Mates 1972, 14-5, 80). And Shapere wonders b r i e f l y I f \"Feyerabend [and Kuhn have] i n mind some s p e c i a l sense of ' i n c o n s i s t e n t ' (though [they] c l a i m not to be abandoning the law of n o n c o n t r a d i c t i o n ) or 'meaning'\" (Shapere 1981, 44). But such b r i e f acknowledgements of problems are i n v a r i a b l y taken back; f o r such p h i l o s o p h e r s im-mediately go on to disparage u n f o r m a l i z a b l e l o g i c a l i n t u i t i o n s as i r r e l e v a n t to l o g i c (Mates 1972, 9-10); or irredeemably vague (Suppes 1957, 4); or f a r too \"broad\" (Shapere 1981, 54). 16. Because i t o f t e n seems Impossible to analyse f o r m a l l y a c t u a l s c i e n t i f i c t h e o r i e s , Kuhn o f f e r s h i s own a l t e r n a t i v e which he b e l i e v e s i s more a c c u r a t e . I s h a l l d i s c u s s Kuhn's a l t e r n a t i v e a n a l y t i c schema i n chapter two. 54 17. C o r r e l a t i v e l y , Kuhn's c r i t i c s a l s o b e l i e v e t h a t , read a t face v a l u e , \"incommensurable\" means \"not i n t e r t r a n s l a t a b l e , \" and t h a t on t h i s c o n s t r u a l , t h e r e f o r e , h i s t h e s i s amounts to the s e l f - c o n -t r a d i c t o r y c l a i m t h a t c e r t a i n t h e o r i e s are both not i n t e r - t r a n s -l a t a b l e and I n t e r t r a n s l a t a b l e . 18. F o r m a l l y , Kuhn's c r i t i c s ' argument i s a \"complex c o n s t r u c t i v e dilemma\" (Encyclopedia of P h i l o s o p h y , s.v. \" T r a d i t i o n a l L o g i c , \" and \" G l o s s a r y of L o g i c a l Terms\"). Thus, on the f o l l o w i n g symbol-i z a t i o n , ct: prima facie c o n s t r u a l of the Incommensurability thesis': \" i n -commensurable\" means e i t h e r \" ( a b s o l u t e l y ) incomparable\" or \"not i n t e r t r a n s l a t a b l e . \" Ci\ a l t e r n a t i v e c o n s t r u a l : t h e o r i e s can be both incommensurable, comparable and i n t e r t r a n s l a t a b l e . I: the incommensurability t h e s i s i s i n t e l l i g i b l e ; i n p a r t i c u l a r , not s e l f - r e f u t i n g . R: the incommensurability t h e s i s i s p h i l o s o p h i c a l l y - r e l e v a n t ; i n p a r t i c u l a r , i t r e q u i r e s changes i n the r e c e i v e d , p h i l o s o p h i c a l view of s c i e n c e . the argument of Kuhn's c r i t i c s I s : 1. Ci - ->l 2. Ci - ->R 3. c, v c* C. T v \"\u00C2\u00BBR As I argue l a t e r ( s e c t i o n s 1.4, 1.5 and 1.5.1), Kuhn's r e -sponse to h i s c r i t i c s amounts to an attempt to \"escape between the horns of the dilemma\": he e f f e c t i v e l y denies t h a t e i t h e r c o n s t r u a l c a p t u r e s h i s i n t e n t i o n s . 19. T r i v i a l l y , two views are incompatible I f they make opposing c l a i m s about the same s i t u a t i o n . Kuhn a l s o a c c e p t s t h i s d e f i n i -t i o n ( c . f . Kuhn 1970a, 122). 20. S c h e f f l e r acknowledges t h a t Kuhn may be r i g h t about incommen-s u r a b i l i t y between the standards of s c i e n t i f i c t h e o r i e s a t a \" f i r s t - o r d e r \" ( i . e . i n t r a t h e o r e t i c a l ) l e v e l ; but he hypothesizes t h a t e v i d e n t c o n f l i c t between two t h e o r i e s presupposes a \"second-order r e f l e c t i v e and c r i t i c a l l e v e l of d i s c o u r s e , \" which \"presup-poses a c e r t a i n s h a r i n g of standards a t the second-order ( i n t e r -t h e o r e t i c a l ] l e v e l \" ( S c h e f f l e r 1967, 83). 21. Davidson's a c t u a l e x p r e s s i o n i s \" d r a m a t i c a l l y incomparable.\" 55 22. What Davidson Is r e f e r r i n g to with the l o c u t i o n \"the equip-ment of a s i n g l e language\" are a language's p u t a t i v e \" r e f e r e n t i a l a p p a r a t u s . . . p r e d i c a t e s , q u a n t i f i e r s , v a r i a b l e s , and s i n g u l a r terms,\" and i t s \"equipment\" f o r d e a l i n g v i t h the t r u t h of \"whole sentences,\" as d i s p l a y e d i n T a r s k i ' s Convention T ( I b i d . , 193-4). In other words, Davidson b e l i e v e s there i s a s t r o n g resem-blance betveen n a t u r a l and formal languages ( c . f . Davidson 1984a, 29-30). In f a c t , much of Davidson's p h i l o s o p h y of language i s based on a b e l i e f t h a t n a t u r a l languages must have an u n d e r l y i n g s t r u c t u r e v e r y much l i k e t h a t of formal ones ( c . f . i b i d . , 3, 17, 30, 55). I t i s t r u e t h a t , i f n a t u r a l languages had the s t r u c t u r e formal languages are supposed to have, they vould form a s i n g l e system of concepts, and t r a n s l a t i o n vould imply commensuration (See s e c t i o n 1.6 e t . seg.). Hovever, the Chomskyan argument Da-v i d s o n o f f e r s f o r t h i s a priori n e c e s s i t y ( i b i d . , 3 ) \u00E2\u0080\u0094 t h a t l a n -guages vould not be l e a r n a b l e v i t h o u t formal r e c u r s i v e r u l e s \u00E2\u0080\u0094 i s a v e r s i o n of the demand f o r commensurability, and so begs the q u e s t i o n . 23. I t i s I r o n i c t h a t , though s c i e n t i s t s o f t e n disparage the con-cerns of t h e i r opponents as \"mere metaphysical s p e c u l a t i o n \" (Kuhn 1970a, 103), Kuhn's p h i l o s o p h i c a l c r i t i c s o f t e n s l a n d e r h i s vork as \"mere e m p i r i c a l s p e c u l a t i o n . \" 24. R e c a l l t h a t Davidson l i n k s the ideas of d i s t i n c t c o n c e p t u a l schemes v i t h t h a t of Incommensurable s c i e n t i f i c t h e o r i e s . 25. Musgrave somevhat d i s a p p o i n t e d l y concedes t h a t \"Kuhn's 'I never s a i d i t ' p l o y o f t e n c o n v i n c e s . \" I b i d . p51. For s i m i l a r v i e v s on Kuhn's ' r e t r a c t i o n s ' see, Putnam (1981a) pl26 and W.H. Nevton-Smith (1981) p l 0 3 . 26. One should keep i n mind here t h a t , though Kuhn b e l i e v e s i n -commensurable t h e o r i e s address a common v o r l d , he does not h o l d that t h i s commonality can be expressed i n terms ac c e p t a b l e to both t h e o r i e s . That means, i n p a r t i c u l a r , t h a t even s o - c a l l e d \" o s t e n s i v e d e f i n i t i o n \" i s not n e u t r a l between t h e o r i e s . See s e c t i o n 1.7. 27. T h i s should a l r e a d y be c l e a r from h i s equation of Kuhn's no-t i o n \"incommensurable\" v i t h \" d r a m a t i c a l l y incomparable\" and \"not i n t e r t r a n s l a t a b l e . \" In f a c t , the s t r a t e g y of Davidson's much di s c u s s e d paper, \"On the Very Idea of a Conceptual Scheme\" (Da-v i d s o n 1984b, 183-198), i s not t o show t h a t comparison and t r a n s -l a t i o n e n t a i l common st a n d a r d s , and thus meet Kuhn head on; i n -stead, he argues t h a t other standards f o r i n d i v i d u a t i n g concep-t u a l s c h e m e s , p u t a t i v e l y independent of t r a n s l a t i o n , t u r n out to 56 presuppose the a b i l i t y to l n t e r t r a n s l a t e those schemes: \"Studying the c r i t e r i a of t r a n s l a t i o n i s . . . a way of f o c u s i n g on criteria of i d e n t i t y f o r c o n c e p t u a l schemes ( i b i d . , 184)....Can we then say t h a t two people have d i f f e r e n t c o n c e p t u a l schemes i f they speak languages t h a t f a i l of i n t e r t r a n s l a t a b i l i t y ? . . . M y s t r a t e g y w i l l be t o argue t h a t we cannot make sense of t o t a l f a i l u r e , and then to examine more b r i e f l y cases of p a r t i a l f a i l u r e \" ( i b i d . , 185). 28. The t r a d i t i o n a l e p i s t e m o l o g l c a l paradigm would l o s e i t s p o i n t because there would then be no reason to s t r u g g l e to f i n d e l u -s i v e , common bases f o r e v a l u a t i n g s c i e n t i f i c t h e o r i e s . For i f I am r i g h t , r a t i o n a l theory c h o i c e would not need those common bases. 29. I should c a u t i o n t h a t the f o l l o w i n g d i s c u s s i o n , while i n t e n -ded to be i l l u m i n a t i n g and c o m p e l l i n g , must n e v e r t h e l e s s be con-s i d e r e d as programmatic. I t would, i n any case, be f o o l h a r d y to expect t h a t p r o p o s a l s f o r modifying c u r r e n t l y - a c c e p t e d concepts w i l l not themselves have to be r e f i n e d c o n t i n u a l l y t o f a c i l i t a t e what Nelson Goodman c a l l s \"the t r a n s i t i o n from s t a t i c a b s o l u t i s m to dynamic r e l a t i v i s m i n epistemology\" (Goodman 1984, 19. I t a l i c s mine) . 30. T h i s relativity of commensurablllty i s not, however, a com-p l e t e l y u n d e s i r a b l e r e s u l t . Thus Kuhn notes t h a t \" s c i e n t i f i c r e v o l u t i o n s . . . n e e d seem r e v o l u t i o n a r y o n l y to those whose para-digms are a f f e c t e d by them. To o u t s i d e r s they may, l i k e the B a l -kan r e v o l u t i o n s of the e a r l y t w e n t i e t h c e n t u r y , seem normal p a r t s of the developmental process\" (Kuhn 1970a, 92-3). And Kuhn a l s o suggests t h a t \"we may come to see ['the t r a n s i t i o n from Newtonian to E l n s t e l n i a n mechanics'] as a prototype f o r r e v o l u t i o n a r y r e -o r i e n t a t i o n s i n s c i e n c e \" ( I b i d . , 102. I t a l i c s mine). Thus we may come to c o n s t r u c t prototypes or standards f o r comparing t h e o r i e s by u s i n g t h e o r y p a i r s l i k e t h a t of Newton and E i n s t e i n as i r r e d u -c i b l e Instances of the r e l a t i o n o f, f o r example, fundamental the-o r e t i c a l I n c o m p a t i b i l i t y . 31. The e x p r e s s i o n \" s t r u c t u r a l l y - c o m p l e x \" i s i n c l u d e d i n the d e f -i n i t i o n to exclude from the c l a s s of Incommensurable o b j e c t s t h i n g s l i k e phenomenal c o l o u r s . Thus, without t h a t q u a l i f i c a -t i o n , i t might be argued t h a t , s i n c e one cannot determine the r e l a t i o n s between, say, blue and y e l l o w on the b a s i s of t h e i r more p r i m i t i v e p a r t s \u00E2\u0080\u0094 t h e y have none--blue and y e l l o w are incom-mensurable. But, at l e a s t i n t h i s paper, speaking of c o l o u r s as incommensurables would introduce unnecessary c o m p l e x i t i e s . On the other hand, s i n c e incommensurability i s c l e a r l y r e l a t e d to i r r e d u c i b i l i t y , i t might be p o s s i b l e to i n c l u d e such I r r e d u c i b l e t h i n g s as phenomenal c o l o u r s as l i m i t i n g cases of incommensurable 57 p a i r s of o b j e c t s ( c . f . note28). 32. I t should be noted t h a t d i r e c t c o m p a r a b i l i t y does not mean untutored c o m p a r a b i l i t y ; t h a t i s , I am not implying t h a t people who know nothing about, say, p a r t i c u l a r s c i e n t i f i c t h e o r i e s c o u l d j u s t look a t them and judge t h e i r r e l a t i o n s . In f a c t , I am im-p l y i n g j u s t the o p p o s i t e . To be a b l e to compare d i r e c t l y two t h e o r i e s one c l e a r l y must f i r s t have an independent, sympathetic, f u l l understanding (verstehen) of each. (I owe a r e c o g n i t i o n of t h i s problem to Rudy Vogt.) 33. T h i s l a s t remark may be more f a m i l i a r as the c l a i m t h a t the r a t i o of the hypotenuse to the s i d e of a r i g h t i s o c e l e s t r i a n g l e i s approximately 1.4142 : 1. I n c i d e n t a l l y , i t should not be thought t h a t , because t h e r e i s a r u l e f o r approximating v2 with r a t i o n a l numbers, t h i s r u l e makes them commensurable. For the s e r i e s of approximations always remains d i f f e r e n t from ^2; and the o p e r a t i o n ( m u l t i p l i c a t i o n ) by v h i c h the approximation i s compared v i t h v2 i s a l s o d i s j o i n t i n i t s separate a p p l i c a t i o n s . Thus, f o r example, one compares "Thesis/Dissertation"@en . "10.14288/1.0097741"@en . "eng"@en . "Philosophy"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "A defence of Kuhn's incommensurability thesis"@en . "Text"@en . "http://hdl.handle.net/2429/28254"@en .