coordinative definition' and reichenbach's semantic framework- a reassessment*

8/13/2019 'Coordinative Definition' and Reichenbach's Semantic Framework- A Reassessment*

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LIONEL STEFAN SHAPIRO

' C O O R D I N A T I V E D E F I N I T I O N ' A N DR E I C H E N B A C H ' S S E M A N T I C F R A M E W O R K :A R E A S S E S S M E N T *

1. INTRODUCTIONWide ly regarded as a landmark of logical posi tivism, H ans Reiche n-bach 's Philosophie der Raum-Zeit-Lehre of 1928 (henceforth PdRZLhas y et to benef i t f rom the recent awakening 1 of his tor ical interest inthis broad tradition, and sti l l awaits a reevaluation of accreted crit icalpreconceptions. Taking up this task in what follows, I will argue thatReichenbach 's analysis of space and t ime avoids most of the posi t ivis tpi t fa l ls i t i s near ly unanimously held to exemplify , notably both ver-i f icat ionism and convent ional ism. Thou gh such accounts of meaningand just i f icat ion are not to be found in PdRZL, Reichenbach does no tendo rse an y r ival accounts of com me nsura te phi losophical import . Inthis regard he resembles m any presen t phi losophers o f sc ience. Re cen tdecades have witnessed the progressive adopt ion of an approach toscientific theories known as the 'semantic view', defined largely inopposition to the 'syntactic view' associated with the posit ivists (oftenlabeled the ' received view ' for polemical con venience) . 2 While vers ionsof these views may be mutual ly preclusive, they are not in themselvesconfl ic t ing concept ions of the sam e dom ain. The semantic view, ra ther,ref lects a convict ion that useful phi losophy of sc ience may be cond uctedindependent ly of the broader metaphysical issues the logical posi t ivis ttradition had largely chosen to pursue, unsuccessfully, within the con-text of an analysis of scientific languages. Writing prior to the emer-gence of a ful ly syntact ic concept ion of theor ies , Reichenbach employsin PdRZL a vers ion of the semantic view.Surely the ' received view' among his fe l low mathematic ians , i t i s asemantic concep t ion o f the mathem atical natural sc iences that is voicedby An drew Gleason when he expla ins tha t the mathemat ical metho dof dealing with the real world l ies in applying purely logical deductionto a precisely descr ibed m ode l of the s i tuat ion . 3 This project of mathe-matical model ing is taken to comprise three moments: the interpreta-t ion of some aspect of real i ty into a mathematical s t ructure belongingto a defined class, the explo ration of this class of structures by ded uctio nfrom i ts def init ion, and the re interpreta t ion of those proper t ies d edu cedErkenntnis 41: 287-323 1994. 1994 Kluwer Academic Publishers Printed in the Netherlands


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288 L I O N E L S T E F N S H P I R Oas facts about the world . Gleason 's schema corresponds perfect ly tothe semantic f ramework of P d R Z L . In par t icular , Reichenbach 's not ionof the coord inat ive def ini t ion Zuordnungsdefinition) of concep t sby real th ings represents his specif icat ion of the f irst mo men t , theass ignment of precisely descr ib ed physical reference to the e lementsof a mathematical s t ructure . One mat ter the schema leaves unresolvedis the characterization of those aspects of reali ty that are to realize themathem atical objects and re la tions const itu t ing a mod el o f a theory. 4On com mon implementa t ions o f the semant ic v iew for space-t ime theo-ries, these real correlates are enti t ies as abstract as space-time manifoldspossess ing certa in affine and metr ic s t ructures. Mo tivate d by the analy-s is of re la t ivi ty theory occupying the bulk of his book, Reichenbachinstead presents a reduct ionis t account : the chief spat io- temporal re-lations realizing a mo del of physical geo me try, e.g. spatial cong ruen ce,are now analyzed as constructs of counterfactual condi t ionals and otherphysical relations, e.g. co incidences of ideally rigid bodie s. N ot surpris-ingly, th is has led Reichenbach 's views to be confla ted with those ofthe ' syntact ic ' t radi t ion concerned with re la t ing the ' theoret ical terms 'of a scientific language to i ts 'observ atio n terms' .5 Bu t i t is his reduction-ism, ra ther than any pecul iar ly suspect doctr ine in epis temology or thetheor y of meaning, that u l timately renders R eichen bach 's space- t imephi losophy un tenab le .

Contrary analyses, purport ing to reveal the col lapse of coordinat ivedef ini tion semant ics , have in effect bee n b ased on o ne o f the fol lowingtwo mutual ly opposed interpreta t ive premises:

(1)a. Reichenbach presents a verification theory of meaning. (Bythis and the synony m 'ver i ficationism' I mean any concept ionthat equa tes the meanings of sentences or larger bodies ofscientific theory with their possession as truth-condition ofpar t icular proposi t ions concerning possible experience).

b. His coordinative definitions determine the mean ing o f individ-ual theoretical sentences.(2) Reichenbach presents a radically holistic theory of meaning.(By this I mean a concept ion that denies that a s ta te ofaffa i rs may any more const i tu te the t ruth of one sentence ina scientific theory than that of any other).

Both assumptions , i t wi l l be argued, ar ise f rom misunders tandings ofthe form and funct ion of coordinat ive def ini tions. Premise (2) may


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R E IC H E N B A C I t S S E M A N T IC F R A M E W O R K 289

already s t r ike the reader of P d R Z L as bizarre: the book is in large parta plea for the formulat ion of coordinat ive def ini t ions with view towardendowing each theoret ical proposi t ion with determinate physical con-tent . Thus ( lb) is correct . But to those famil iar with Reichenbach 'ssubs eque nt work, my denial of ( la) may seem equa l ly surpr is ing. In hiswri t ings on general epis temology, notably in Experience and Prediction(1938), he end orse s a probab ilist ic verifiability the ory of the meaning -fulness and m eaning -identity of individual sente nces. 6 Th oug h this the-ory is more sophis t icated than ver i f icat ionism as def ined above, bothinvolve the ident i f icat ion of semantic not ions with ones of empir icalevidence. My claim is not that such an identification is expressly deniedin P d R Z L . The point is ra ther that Reichenbach is conspicuously (andin view of his subsequent posi t ion, sa lubr iously) unconcerned withformulat ing a theory of meaning, as contrasted with the specificationo f what is meant by the proposi t ions of space- t ime physics . Moreover ,we will f ind that the conception of verification implicit in P d R Z L andcommon to Reichenbach 's ear l ier works is essent ia l ly hol is t ic , whenceby (lb) i t is incompatible with a verificationist construal of coordinativedefinition.2 C O O R D IN A T IV E D E F IN IT IO N A N D C O N C E P T U A L D E F IN IT IO NThe examples by which Reichenb ach in t roduces the no t ion o f coord in-ative definit ion fail to impart a clear sense of how such a 'definit ion'will look. Contras ting coordin ative definit ion with con cep tua l defi-ni t ion or the determ inat ion of [conceptual] conte nt Inhaltsbestim-mung) , he insists that a unit of length can ult imately only be established

by re fe rence to [durch Hinweis auf] a physically given length such asthe s tandard me ter in Paris . ,,7 Bu t how is this referen ce to be pro vided?Reic henb ach is mo st expl ic i t in a separate p aper : In the end thiscoordinat ion can only be given ostensively [dutch Hinweis]; ' that thingthere ' i s to corr espo nd to such and such a conce pt . 8 Of course , suchcoordinat ion by point ing is a myster ious task: how do we know that i tis the Par is rod as an extended object, ra ther than as a colored object ,that is her eby coo rdinated to the 'conc ept uni t of length '? I t appears thatby this 'concep t ' Reic henb ach mean s a predicate to be lent extension byspecifying an operat ional proper ty of those physical things to which i tapplies. In par t icular , whe n an object of length one m eter is placedalongside the Par is rod, the tw o are local ly congruent . Such a reading


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290 L I O N E L S T E F N S H P I R Oaccords with Reichenbach's alternative coordinative definition of meter:

The unit is to be chosen in such a way that, placed end to end 40million times, it yields the earth's c ircumference .9 It also explains hissecond coordinative definition, that of general spatial congruence,where the declared ostensive coordination to something real becomeseven more obscure. Here, on my reading, it is stipulated that whenevera rigid rod locally congruent to one of a pair of congruent lengths islaid alongside the second length, it is locally congruent to the latter aswell.

Proceeding in this spirit, we might introduce 'is a meter long' and'are congruent' as predicates in a formal scientific language by meansof the following abbreviatory definitions: the sentence 'X is a meterlong' stands for 'X would be locally congruent to the Paris rod', whilethe sentence 'X and Y are congruent' stands for 'If a rigid rod locallycongruent (anywhere, anytime) to X were transported to Y, it wouldbe locally congruent to Y'. Here local congruence is declared an 'obser-vation term' in our language, accessible to immediate empirical determi-nation. Now we are unlikely to be satisfied with the counterfactualconditional, and might resort to Carnap's solution of 'reduction sen-tences', or conditional definitions, as developed in 'Testability andMeaning'. 1 There is, however, no hint in PdRZL that any such pro-gram is being embarked on. Reichenbach does not attempt to constructan artificial language whose theoretical terms are formally connectedthrough meaning postulates with a subset of directly verifiable 'obser-vation terms'. Rather, his scheme stresses a sharp delineation betweenan abstract system of so-called concepts and the real world to whichit is to be coordinated. Most importantly, his aim is not to give anaccount of the empirical verification of theoretical statements, but sim-ply to specify in well understood terms the real-world correlates of themathematical entities appearing in a theory. A geometric theory, forinstance, may involve defining a certain class of structures possessing arelation R on their elements. Reichenbach may now interpret theseelements as possible light-rays and assign to R the real structure [realesGefiige] 11 of spatial congruence, explained in terms of the hypotheticaltransport of rigid rods described above. Since this informal interpreta-tion of R is not a reduction of the term 'congruent' to observationterms, the above problem of counterfactuals (that of formulating theirempirical conditions of application) does not arise.The primary obstacle to an appreciation of Reichenbach 's project lies


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R E I C H E N B A C H S S E M A N T I C F R A M E W O R K 29

in the fact that the ear ly sect ions of P d R Z L never c lar i fy the nature ofthe rea lm of concep ts . A s a resu l t, one comm enta tor a rgues tha tReichenb ach ' s concep ts may on ly be unders too d as menta l en t i ti es , 12anoth er regards them as me re wo rds , ~3 whi le mo st cri tics a l togetheravoid distinguishing b etw ee n the 'c onc eptu al ' and th e 'physical ' . 14 W hathas inexplicably bee n igno red is a centra l po r t ion of the text (14-15)where Reichenbach explains that h is concepts are in tended as abstractent i ties , e lements in a system of re la tions [Beziehungsgefuge] with

self-consti tuting [in sich bestehende], pu rel y log ical significance . 25 (Ina footnote , he c i tes Carnap 's disser ta t ion Der Raum, where uninterpre-ted form al space is s imilarly pron oun ced a Beziehun gsgef i ige . ~6)The con tent of th is character izat ion beco me s appare nt once we examineReic henb ach 's und ers tanding of concep tual defini tion, e lsewhere de-scr ibed as math ema tical def ini tion : in each coordinat ive def ini t ion,

the mathematical def ini t ion is presupposed as a determinat ion of theconc ept . 17 Reic henb ach appeals to a not ion of defini tion der ived , viaMori tz Schl ick, f rom Hilber t ' s axiomatizat ion of c lass ical geometry -the implicit definit ion of a primitive term as a specification of allaxiom s involving tha t term . 18 Illustrating such d efinition in P d R Z L , hepresents Hi lber t ' s 'betweenness ' axioms in logical notat ion. This f rag-ment of a symbolic calculus serves merely to in t roduce the reader toabstract mathematics ; Reichenbach is not concerned with the syntact icformulat ion of physical theory. Ev en in this example, he careful lydis tinguishes the symbolic calculus f rom the re la t ional s t ructure i t

defines . I t is the concepts consti tuting this relational structure (ab-s t ract points , l ines, and the re la t ions of col inear i ty and b etwe enne ss) ,ra ther than the terms whose meanings they represen t, tha t we coor -dinate to the e lements of a physical system . 19 Thus the conc epts ofP d R Z L are best taken (a lbei t anachronis t ical ly) to represent the typesof objec ts specified in the d efinit ion of a class of mathematical structures,whose instantiations in each such structure satisfy the postulates speci-fied in this definit ion. 2 On ce this m uch is un de rsto od , the follow ingpassage f rom 15 reads as a summ ary of Gleaso n 's math ema ticalmethod of deal ing with the real world :

T h e m a s t e r y o f n a t ur a l p h e n o m e n a f o l l ow s t h r o u g h m a t h e m a t i c a l c o n c e p t s - t h e s e c o n -c e p t s a r e d e f i n e d t h r o u g h i m p li c it d e f i ni t i o ns a n d a r e n o t d e p e n d e n t o n a s p e c if i c a n du n i q u e k i n d o f v is u a l i z a ti o n [Veranschaulichung] W h a t e v e r v i s u a l i z a b l e [anschauliche]t h i n g s w e w i s h t o c o o r d i n a t e t o t h e m i s l e ft t o o u r c h o i c e ; t h e y m a y j u s t a s w e ll b e


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292 L I O N E L S T E F A N S H A P I ROpressure s or currents as rigid measuring rods This process of coordination is just theprocess we earlier formulated as coordinat ive def in i t ion 21

3 U N I V O CA L I T Y A N D E M P I RI CA L A D E Q U A CYDrawing on an idea from Schlick which had played a prominent rolein his earlier writings, Reichenbach emphasizes that the coordinationof concepts to things is not arbitrary: Since the concepts are mutuallyinterwoven in content [untereinander inhaltlich verflochten], this coordi-nation may become true or false, as soon as we add the requirementof univocality [Eindeutigkeit]; the same concept should always denotethe same object . 22 As an example of equivocality he cites the standardcoordinative definition of congruence by the hypothetical transport ofrigid rods, assuming a counterfactual world in which two rigid rodslocally congruent at one time and location need not remain locallycongruent upon transport. 23 Clearly, if the relation 'congruence' in amathematical structure is coordinated with a physical relation that isnot well-defined, the coordination is improper. Were we to concludethrough observation that the above hypothesis is correct, we wouldhence reject the coordinative definition. But this is only a degenerateinstance of the general situation that would lead us to revise our net-work of coordinative definitions and conceptual relations; the generalsituation obtains precisely when our theory proves empirically inade-quate.

How can the fact that the concepts are mutually interwoven incontent bear on a theory's empirical adequacy? Our coordinativedefinitions translate these relations among mathematical entities intoempirically ascertainable relations among physical things. As an exam-ple, suppose we coordinate an object al in the underlying mathematicalspace with a thing h, similarly aa with t2, and coordinate a mapping Mfrom the space to itself with a physically realized one P, such thatM al) = a2 but P h) turns out to be an object distinct from t2, say u.This would mean that a2 could be coordinated to ta or to u, dependingon whether we employ the coordinative definition of a2 or the coordin-ative definitions of M and al together with the above equality, thusviolating the 'univocality of coordination' (recognizable now as a con-dition of isomorphism). Assuming that the equality in question followsfrom our theory, the theory has been revealed faulty as interpreted byour coordinative definitions. For the special case of evaluation throughreal-valued functions, Reichenbach summarizes this conception in his


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R E 1 C H E N B A C H ~S S E M A N T I C F R A M E W O R K 2931920 book Relativitiitstheorie und Erkenntnis apriori: We always calla theory true when all chains of reasoning [and experience] lead to thesame number for the same phenomenon. This is our only criterion oftruth . . . . ,,24 Explicitly modeled after Schlick's slogan 'truth is univocal-ity of coordination', the criterion is here formulated in terms of truthrather than empirical adequacy. A distinction between these two notionswill prove essential in PdRZL but Reichenbach retains a Schlickianconception of empirical adequacy. 25

Once a proposed theory has been found faulty, we may in rareinstances be able to localize the problem in one equivocal coordinativedefinition. Usually, however, we will alter some of the relations amongthe concepts, maintaining their coordinative definitions, in order toreach univocality of the coordination as a whole. As most of our defi-nitions will not be empirically applicable without the interposition[Zwischenschahung] of conceptual connections (this holds for mea-surement based on a definition of the meter as the 40-millionth partof the earth's circumference), we will generally enjoy considerablelati tude, z6 Finally, we may always choose to revise a coordinative defi-nition that has not been rendered equivocal by direct empirical obser-vation (such would presumably have been the fate of the most naturalpre-relativistic definition of distant simultaneity, through the trans-ported clock). Citing Schlick, Reichenbach states that this ongoingprocess of the correction of models is what physics is all about: theprocess of attaining physical knowledge [physikalischer Erkenntnis-proze~8] ties precisely in establishing the univocality of this coordi-nat ion . 27 Thus the account of the empirical confirmation of scientifictheories implicit in Reichenbach's system of mathematical modelingalready begins to resemble the holistic process of underdeterminedreadjustments to the boundary conditions of experience described byQuine. Unlike Quine, however, Reichenbach demands that we alwaysbe able to specify a set of coordinative definitions relative to whichour mathematical propositions possess determinate physical content,content alterable only through revision of these coordinative definitions.

4 C O O R D I N A T I V E D E F I N I T I O N S A N D O B J E C T I V E ~A S S E R T I O N S

This notion of 'relatively possessed content' is best illustrated by re-sponding to Putnam's claim that Reichenbach is confused about theobjective significance of individual physical statements. 2s From Reich-


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94 L I O N E L S T E F N S H P I R O

e n b a c h ' s m o s t f o r c e f u l a n d e l o q u e n t s u m m a r y o f hi s b as ic f r a m e w o r k ,P u t n a m e x t r a c t s t h e f o l l o wi n g p r o b l e m a t i c s e n t e n c e s :The objective character of the physical statement [Aussage] is thus shifted to a statementabout relations. A statement about the boiling point of water is no longer regarded as anabsolute statement, bu t as a statement about the relation between the boiling water andthe length of the column of mercury. There is a similar objective statement about thegeometry of real space: it is a statement about the relation between the universe and rigidrods 29

P u t n a m r i g h t l y p o i n t s o u t t h a t t h is a r g u m e n t w i l l n o t d o : i f t h e le n g t ho f th e m e r c u r y c o l u m n d e p e n d s o n o u r a r b i t r a r y c o o r d i n a ti v e d e f in i ti o no f t h e u n i t o f l e n g th , n o r e l a t i o n of t he bo i l i ng wa te r t o t h i s l eng th wi l la c h i e v e a n y g r e a t e r ' o b j e c t i v i t y ' .

I t s e e m s c l e a r , t h o u g h , t h a t R e i c h e n b a c h s i m p l y u s e d t h e wr o n gwo r d s : h e c a n n o t p o s s ib l y h a v e i n t e n d e d t h e u n d e r l y i n g o b j e c t i v ea s s e r t io n a b o u t th e w a t e r' s t e m p e r a t u r e t o c o n c e r n a r e l a ti o n b e t w e e nt h e wa t e r a n d a f u r t h e r n u m b e r I n s t e a d , h e s u r el y p r o c e e d e d f r o m t h ec l a im t h a t ' a s t a t e m e n t a b o u t t h e b o i l in g p o i n t o f wa t e r i s a s t a t e m e n ta b o u t t h e r e l a t i o n b e t we e n t h e b o i l i n g wa t e r a n d a t h e r m o m e t e r ' , a n dt h e n o f f e r e d a n i n c o m p l e t e d e s c r i p t i o n o f t h e c o n s t r u c t i o n o f t h e t h e r m -o m e t e r . T h e f u ll e x p a n s i o n w o u l d i n s te a d h a v e b e e n : ' a s t a t e m e n t a b o u tt h e r e l a t i o n b e t w e e n a c o l u m n o f m e r c u r y a n d a r o d o f g la ss , wh e nt h e y a r e p l a c e d i n b o i li n g wa t e r ' . H e r e t h e ' l e n g th ' o f t h e m e r c u r yco lumn in t he o r ig ina l t ex t i s r ep l aced by i t s l oca l cong ruence wi th as t a n d a r d r i g i d b o d y . I n a p r e v i o u s s e c t i o n , R e i c h e n b a c h h a s e x p l a i n e dt h a t t h e t h e r m o m e t e r is b a s e d o n t he d i f f e r e n c e i n t h e e x p a n si o nc o e f fi c ie n t s o f m e r c u r y a n d g l a ss . 3 T h e p r o p o s e d e m e n d e d t e x t wo u l da ls o f it p e r f e c t l y w i t h t h e p a s sa g e ' s s e c o n d e x a m p l e : a r e l a t i o n b e t we e nthe un ive rse and r i g id rod s i s a l so a re l a t i on am ong th ings. Th i se x a m p l e is a g e n e r a l iz a t i o n o f R e i c h e n b a c h ' s p r e v i o u s c l a im t h a t i f wed e f i n e t h e m e t e r b y t h e P a r i s s t a n d a r d r o d a n d t h i s r o d i s c o m p r e s s e db y a n e a r t h q u a k e , t h e c o n c o m i t a n t e x p a n s io n o f o u r w o r l d is n o t a na b s o l u t e c h a n g e , t h e " f a c t u a l " s t a t e m e n t b e i n g a b o u t t h e ch a n g e i nt h e d i f f e r e n c e i n s iz e b e t w e e n t h e r o d a n d t h e r e s t o f t h e wo r l d . . . . ,3 1

I n R e i c h e n b a c h ' s e x a m p l e , t h e c o o r d i n a t i v e d e f i n it i o n o f th e u n i to f t e m p e r a t u r e i s s u p p l i e d b y a t h e r m o m e t e r ; h e n o w e x p la i n s t h a tt r a n s f o r m i n g a t h e o r e t i c a l s t a t e m e n t ( e . g . a s t a t e m e n t a b o u t t h e b o i li n gp o i n t ) i n t o a n o b j e c t i v e a s s e r t i o n r e q u i r e s e x p l i c i t r e f e r e n c e t o t hep h y s i c a l c o r r e l a t e s o f a l l a b s t r a c t e n t i t i e s i n v o k e d ( e . g . t o t h e m e r c u r y


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REICHENBACH~S SEMANTIC FRAMEWORK 95

and glass of the th erm om eter) . I t is jus t this s t ra ightforward senseof 'combinat ion ' that Reichenbach has in mind when he asser ts that[p]roperties of reality are reached only through the combination of astatement o f measur emen t with its underlying coordinative definition . 32We f ind here the th i rd m om ent of the schema ske tched by Gleason , thetransla t ion of asser t ions about the mathematical model into object iveasser tions abo ut things. Far f rom represent ing a des per ate a t temp tto straighten o ut [his] confu sion concernin g the 'objectivity ' of ou rs ta tements , the passage Putnam quotes i l lus t ra tes a centra l aspect ofReichenbach ' s p ro jec t .

5. DESCRIPTIVE SIMPLICITY AND REI CHEN BACH S~CONVENTIONALISM

Undoubted ly the bes t -known e lement o f Re ichenbach ' s space- t imephi losophy, though hardly i ts most or iginal , i s the supposedly 'conven-t ional is t ' thesis of the re la t ivi ty of geo me try (8 of P d R Z L ) , accord-ing to which physical space may be represented by many differentmathem atical s t ructures (of bo th Eucl idean and non-Eucl idean var ie-ties).33 E ach of these ge om etric the ories will involve a differen t coord in-at ive def ini t ion of the abstract metr ic , whence none is truer than anyother , though th e theor ies wil l d i f fer with respect to their descr ipt ivesimplicity . A t first sight, this argu me nt m ight ap pea r to exem plifywhat Putn am has cal led the convent ional is t p loy , by insist ing thatthe mathem atical postula tes for a metr ic are essential in a way thatthe othe r prop er t ies - or the s tandards of coherenc e - are not . 34Put nam r ight ly points out that a spat ia l metr ic according to which myleft l i tt le f inger is bigger than m y ho us e simply doe s not design ate the

ma gnitud e that we are referring to when we use the wo rd 'd is tance ' ,even should i t turn out that a complete descr ipt ion of a l l par t ic let ra jec tor ies may be based on such a met r icYFar f rom engaging in the convent ional is t p loy, Reichenbach employsthe centra l e lem ent of Putn am 's very refuta t io n of convent ion al ism .36

Putn am 's argum ent is that internal coh eren ce , consis t ing of s impli-c i ty of descr ipt ion and agre em ent with intui t ion , contr ibutes to thede te rmina t ion o f re fe rence , and therefore of t ru th (whence , somew hatconfusingly, he refuses to speak of descriptive simplicity). While notexplic it ly conc erned with Ge rm an language reference, Reic henb achaccords internal co heren ce m uch the sam e s ignificance. Thus he asser ts


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96 L I O N E L S T E F N S H P I R O

that our coordinative definit ion of the spatial metric is subject to restric-t ions f rom two sources : those based on the s t r ic t coord ina tion ofthe abstract concep t , which is arbi t rary, and others that arise bec ausewe demand tha t t he ob t a ined me t r i c su s t a in ce r t a in . . . con -c l us io ns . . , o f the 'phys ics o f everyday l i fe ' . 37 We re a coord ina t ivedefinit ion of the spatial metric to entail that our floors and ceil ings areno longer approximate ly p lanar , fo r example , we would reject that

scientific definit ion as unreflective of the hab its [Gewohnheiten] ofeve ryd ay life .38While these constra ints der iving from our hab i ts (Putnam 's in-

tui t ion ) are descr ibed as imposing only imprecise l imits on the choiceof metr ic , Reic henb ach also suppl ies a s t ronger constra int based o ndescriptive simplicity . In the first pages of his appendix to P d R Z L

he reminds us that the coordinat ive def ini t ion of congruence in termsof r igid rods is predica ted on a cont ingent fact , namely that the localcongruence of r igid bodies is independent of their means of t ransport .For this reason, the resul ting metr ic has the advantage that i t expressesa law of nature , namely the law of the t ransport of r igid bodies . Werewe to choose an arbi t rary nonstandard metr ic for space, he concludes,

the spat ia l metr ic would be def inable , but through this choice nolaw of na ture would be expressed ; the metric would lose its physicalsignificance [physikal ische Be deu tung ] . 39 H e offers an exam ple: usingthe standard metric definit ion, the length of a wall allows simple calcu-la t ion of how m any chairs of given width we can l ine up a long the wal l.An d w ere the coordinat ive def ini t ion of congruence in terms o f r igidrods not well-def ined, we wo uld f ind ourselves ra the r indifferenttoward some arbitrarily chosen metr ic ; we would instead search for ageom etr ic schem e expressive of the laws characteriz ing the n ow m yster i-ous beh avior of wal ls and chairs .This a rgument , one Reichenbach deems very impor tan t , r eveals asignificant dee pen ing of his doctrine of me re descrip tive simplicity .Though the concept 'd is tance ' i s ins tant ia ted in var ious geometr ic mod-els by funct ions that may be coordinated to any number of quant i t ies ,distance is really that physical quantity which among other things allowsstra ightforward determinat ion of how many chairs f i t a long a wal l .Viewed in th i s manner , Re ichenbach ' s much-mal igned ' conven-t ionalism' reduces to a forceful il lus tra t ion of the fact that mathem aticalstructures rem ain p hysically conte ntless pend ing specification of thereal-world correla tes of their abstract e lements . This should not be


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RE I CH E N BA CH S S E M A N T I C F RA M E W O RK 97

surpr is ing , i f we no te th a t Re iche nba ch ' s de fense o f the re la t iv i ty o fg e o m e t ry is f r a me d a s p a r t o f h is r e spo n se to th e n e o -K a n t i a n g e o m e t r i capr io r i s t . Here i t i s ins t ruc t ive to compare the anti-conventionalistMic h a e l F r i e d m a n : T h a t t h e g e o m e t ry asc r ib e d to ph y s ic a l sp a ce d e-p e n d s . . , o n o u r m e t h o d s f o r m e a s u r i n g l e n g t h ( d e t e r m i n i n g c o n g r u -ence re la t ions) i s c lea r and incontes tab le .4 This s i tua t ion would h ard lyh a v e b e e n a s c l ea r o r i n c o n te s t ab le to R e ic h e n b a c h ' s i n t e n d e d a u d ie n c e .

6 . T H E CO O RD I N A T I V E D E F I N I T I O N O F CO N G RU E N CE

R e ic h e n b a c h ' s a c k n o w le d g e me n t th a t t h e re i s a me t r i c p o s se s s in gp h y s ic a l s ig n if i ca n c e is n o t s imp ly a n e n d o r s e me n t o f P u tn a m ' s o w naccount o f the semant ics o f theor ies , accord ing to which the func t iond(x l , x2) in the m athe ma t ica l s t ruc tu re re fe rs s imply to a ce r ta in quan-t i ty distance a n d th e c o h e re n c e a c c o u n t r e v ea l s j u s t w h ic h p h y s ic a lquan t i ty th is i s. For reasons to be e xam ined in Sec t ion 12, Re ichen bachd e m a n d s a reductive characterization of the quantity distance itself o n ehe seeks to supply th ro ugh h is coord in a t ive def in i t ion o f spa t ia l congru-ence in terms of the r ig id rod. As i t is th is def ini t ion that is general lyadduced to i l lus t ra te the fundamenta l f laws of coord ina t ive def in i t ionsemant ics , i t is s tr ik ing tha t i t s ac tua l p resen ta t ion in P d R Z L h a s b e e na lmos t en t i re ly ignored . Only a ca re fu l exeges is o f the congruencedef in i t ion wi ll d i spel bo t h misco ncep t ions abou t R e iche nbach ' s sem ant icf r a me w o rk c i t e d in my in t ro d u c t io n .

W e hav e seen tha t R e ich enba ch re jec ts some log ica lly poss ib le coord-ina t ive def in i t ions on the g round tha t they do no t re f lec t phys ica l law.Unfor tuna te ly , even h is p re fe r red coord ina t ive def in i t ion o f spa t ia lcong ruence in te rms o f a r ig id rod th rea te ns no t to sa t i s fy th is c r i te rion .Clear ly , i t would no t be accep tab le to def ine congruence by po in t ingout an ac tua l near ly - r ig id rod never the less suscep t ib le to deformat ion ,as th is would fa i l to yie ld a def ini t ion of the equal i ty of distances.Refer r ing to the s imple r example o f the def in i t ion o f un i t o f leng th ,R e ic h e n b a c h c o n c lud e s th a t w e w o u ld n o lo n g e r vi e w th e P a r i s s t a n d a rdme te r a s a me te r , w e re i t t o b e d e fo rme d b y a n e a r th q u a k e . H e n o wasks a ques t io n fami l ia r f rom Schlick: B ut i s wha t we a re do ing s ti lldefining a t a l l , i f the def in i t ion may some day be ca l led fa l se? Doesn ' tthe no t io n of coord ina t ive def in i t ion lose a l l sense he re? ''41 Ra th er thanjo in Sch l ick in abandoning the no t ion (a move to be d iscussed be low) ,R e ic h e n b a c h a t t e mp t s to r e sc u e i t b y p ro p o s in g a mo re c o mp l i c a t e d


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298 L I O N E L S T E F A N S H A P I R Ocoordinat ive def ini tion. In orde r for the def ini t ion of congrue nce byrigid rods to express physical law we must f irst define the ideal rigidbody. A natural f i rs t a t tempt might be to def ine an ideal r igid body asone that follows Reic henb ach 's law of the t ransport of r igid bodie s :i f a t any t ime we f ind two or more such bodies local ly congruent toeach other , they wil l a lways remain local ly congruent . Unfor tunately ,the re la t ion of e ternal local congruen ce p ossesses infinite ly many equiv-alence c lasses . Given an arbi t rary theory of physical geometry, thisdefinit ion will be satisfied by any class of rods growing at a uniformrate re la t ive to the actual ' r ig id rods ' of that ge om etry.

Reichenbach employs instead a more res t r ic t ive physical law involv-ing rigid bodies. This law is the l imiting case of the empirical fact thatsol id bod ies chan ge their shape and s ize only very l it tle when s ubjectedto outs ide fo r ces . 4z Why does he not s imply s ta te as a law that anideal ly r igid body does not deform at a l l , regardless of the presence offorces? He explains that the sat isfact ion of this ' law' by a body woulddep end ent i re ly on the m etr ic we are using to descr ibe the bod y 's shape:we can always choose the metr ic so as to declare that our candidatefor ideal r igid body undergoes deformation. Next , he dis t inguishesbe tw een tw o kinds of deformations: those suffere d ident ical ly by bodiesof a l l mater ia ls , and those that dif fer according to the mater ia l ofthe body . Al l deformat ions a re to be unders tood as mani fes ta t ions of

forc es , and i t i s here that Reic henb ach introduces his notor io usdis t inct ion between universal forces those responsible for deformationsthat affect a l l mater ia ls in the same way, and the remaining differentialforces. On ce w e foreswea r a ll invocat ion of universal forces , it bec om espossible for a body to violate the above ' law' only when i t suffersdifferent ia l deformations, associated with dif ferent ia l forces . Accord-ingly, he defines ideal r igid bodies to be those not subjected to differ-ential forces:We define: r ig id bodies are sol id bodies prov ided they are subjected to no di f ferent ia lforces [wenn sie kein en differentiel len Kr~tften unterl iege n] or [bzw.] provided the e f fectsof d i f ferentia l forces are e l iminated by correct ive calculat ion; universal forces are heredisre garde d. 43

Fo r the present , I ignore the second clause of the dis junction, concern-ing corrective calculation.


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REICH ENBAC H ~S SEMANTIC FRAME WORK 2997. REICHENBACH~S FORC ES ~

Endless confusion has arisen over Reichenbach's vague characterizationof a 'force' as a something [ein Etwas] which we make responsible fora geometric cha nge . 44 At the root of the problem lies a hithertounnoticed equivocation in Reichenbach's use of 'force', neatly separableinto one usage in 3-6 and a second in 8. The division is one betweentwo distinct arguments; the former motivating and specifying thecongruence definition, and the latter expounding the thesis of the rela-tivity of geometry. Almost all commentary on the congruence definitionhas proceeded from 'Theorem 0' in 8, where Reichenbach points outthat we may accept any Riemannian spatial metric by positing theaction of an appropriate universal force on all physical bodie sY Inthis context, 'universal force' is used to refer to a specific mathematicalobject, to be incorporated into the formalism of the physical theorybased on our chosen metric (henceforth force1). 46 Reichenbach's analy-sis here matches an example from Camap's Der Raum where spatialremetricization is accommodated by an alteration to Newton's secondlaw formally equivalent to the positing of a ne w forc e. 47

Significantly, there is no mention of differential forces in 8. Werewe to interpret these as forces1, we would always be able to posit twodifferential forces such that their resultant yields an arbitrary universalforce (or zero). This would render the distinction between universaland differential forces utterly useless as a basis for the congruencedefinition.48 Fortunately, such a reading is irreconcilable with Reichen-bach's insistence that the classification of a 'force' as differential bedetermined by the material-dependent nature of the deformations suff-erable by transported measuring bo die s. 49 In the actual argumentationof 3-6, we find the name 'different ial force' standing in for the totalityof such sufferable deformations (henceforth differential force2). 5 Itmay be objected that this reading leaves little room for analogouslydefined universal 'forces', as these could no longer be associated withany region of space in which differential deformation occurs. Sincehowever differential deformation is indeed ruled out in Reichenbach'sintroductory examples of 'universal forces', as in the rigid body defi-nition itself, this need be no obstacle to a literal construal of 'universalforce' as subsuming sufferable universal deformations.

Still, a slight modification should prove more faithful to Reichen-bach's intent. Following his actual definition of rigid body, Reichenbach


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300 L I O N E L S T E F A N S H A P I R Ooffers an e labo rat ion of the con gruence def ini t ion in terms of the preser-vation of shape . H ere , his point is that (*) change of shape is to beattributed exclusively to the presence of differential forces whence theabsen ce of differential forces is a sufficient cond ition fo r shape-p reserva -t ion. But i f forces are taken as forces2 condition (*) fails to determinea unique spat ia l metr ic . However we choose to remetr ic ize the vic ini tyof a heat so urce (Reic henb ach s parad igmatic source o f di f ferent ia ldeformat ion) , the deformat ion of rods in th is region wil l remain ma-ter ia l -dependent . I t is perhap s for th is reason that R eichen bach pro-nou nce s the vanishing o f differential forces2, necessary for shape-preser-vat ion. 51 Bu t w e surely dem and of any theo ry of physical geo me try thati t supply a not ion of shape-preservat ion appl icable in the presence ofheat sources .

As a natural solut ion, I propose that universal forces2+ be taken assubsuming al l the deformat ions that would be sufferable by measur ingbodies were there no differential forces2+ (=def differential forces2)present . On this reading, condi t ion (*) does succeed in uniquely determ-ining a metric, provided this condition is coherent. For once we assumethat a given physical geometry satisfies the condition, any remetriciz-at ion must c lear ly invoke a universal forcez+. The modif ied readingthus renders the coordinat ive def ini t ion of congruence equivalent to astipulation that universal forces vanish. Though such equivalence is a tbest implicit in PdRZL 52 Reic henb ach s congrue nce def ini tion hasgenera l ly been taken to consist in the latter st ipulation. A benefit ofreading universal force s as forcesz+ is that doing so m ay allow for thisdefinit ion of congruence, unavailable on the strict ly l i teral reading ofthem s force s2. 53

8 I S T HE C ONGR U E NC E DE FI NI T I ON C OHE R E NT ?

Reic henb ach s off ic ia l formulat ion of the congru ence def ini tion remainsin terms of ideal rig id rods , and regardless of the req uirem ents forshape-preserv at ion, the absence of sufferable differentia l deformat ionis a necessary condition for ideal rigidity. Since the presence or absenceof such deformation in a given region is a matter of fact , satisfactionof the r igid body def ini t ion is indeed independent of physical theory.Adm it tedly, th is def init ion entai ls seemingly paradoxical consequ ences:under sui table c i rcumstances even a rubber band may approximate anideal r ig id body, and the mere re leasing of a s t re tched rubber band


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R E I C H E N B A C H S S E M A N T I C F R A M E WO R K 3 1

alongside a steel rod suffices to deprive the latter of ideal rigidity bymanifesting a 'differential force'. As viewed by Reichenbach, however,physical geometry does not articulate the relations among an ostensivelygiven class of bodies which are 'rigid' in the usual sense; it describesthe hypothetical coincident behavior of physical bodies made fromdifferent materials, 54 thus providing an idealized zero point for dy-namical th eor yY

Here we encounter the real vulnerability of the congruence definition.The question of physical geometry has assumed the following peculiarform: ho w wo uld solid bodies behave i f all solid bodies behaved thesame? What entitles us to suppose that there is a determinate answerto this question? Reichenbach appears to rely on a putative contingentfact: he insists that by means of technical manipula tion , it is alwaysphysically possible to el iminate differential forces to any desired degreeof approximation. 56 While this possibility may render the above coun-teffactual more tractable, we would also like it to be physically impossible to cause all materials to approximate an alternative geometry. Itcould be retorted that the general theory of relativity introduces pre-cisely such a possibility, to be realized by altering the distribution ofmass in addition to eliminating differential forces. In fact, this is thevery line taken by Reichenbach, who ignores the difficulty this situationmight present for the interpretation of his counterfactual definition (heeven suggests that were the coefficients of expansion for all materialsequal, the presence of a warm body would alter the geometry ofspace). 57 Contrary to Reichenbach, however, gravitation itself is mani-fested through differential effects on solid bodies of different ma-terials, 58 effects whose elimination is included in the antecedent of thecounterfactuals involved in geometric assertions. Consequently, even ifexplicable by means of a ceteris pa ribu s clause, Reichenbach's definitionof congruence would be unavailable as an interpretation of the metricstructure of general relativity theory. 59

Reichenbach confuses matters yet again when he allows the definitionof congruence to be supplied through calculation of how an actual rodwould behave if differential forces were not present. It is unclear howthis clause of the definition can be accommodated within his semanticframework: corrective calculation clearly presupposes a theory of phys-ics employing the quantity distance, whence it could not wi thout circu-larity be drawn upon for the real-world interpretation of the spatialmetric. Can Reichenbach, who boasts of having avoided the circle


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3 2 L I O N E L S T E F A N S H A P I R O

of defining the absence of forces through the preservation of shape,have overlooked so obvious an objection? Elsewhere, we find strongevidence that this clause represents no more than an unintentionalconflation of two issues which Reichenbach allots separate roles. Sup-plying the rigid rod definition in his Axiomatik der relativistischenRaum-Ze i t -Lehre (1924), he emphasizes that it utilizes only qualitative[i.e. theory-independent] physical characteristics , and even takes thisdefinition to refu te the view [one he had previously endorsed-L.S.]that it is impossible to define the rigid body without reference to ametr ic . 6 While the need for corrective calculation is fully acknowl-edged in the Ax ioma t i k such calculation does not figure in the definitionof rigid body itself but rather in an account of me asu rem ent. 61 Similarly,we find no appeal to corrective calculation in the definition of the idealnatura l clock in P d R Z L otherwise parallel to the rigid rod definition.62Here Reichenbach merely remarks that the astronomer uses such cor-rections to derive, based on observations, the flow of time that isimplicitly determined by the current physical laws. This poses no objec-tion to his semantics, as such corrective calculation is clearly essentialto measurement.

9 EINSTEIN S I N T E R P R E T A T IO N : R E I C H E N B A C HA S V E R I F I C A T I O N I S T

One interpretative tradition has nonetheless endeavored to illustratethe incoherence of Reichenbach's entire framework based on the issueof corrective calculation. Commenting in 1949 on a paper in whichReichenbach presents his 1928 rigid body definition as an advance overthe conventionalism of Henri Poincarr, Albert Einstein takes this issueas the starting point for a short dialogue between Reichenbach anda Non-Positivist initially identified as Poincar6. The consequencesPoincar r first draws are familiar as 'Duhemian' holism:

[ In providing the def in i tion of r ig id body based o n cor rec t ive ca lcula t ion] you have ma deuse of phys ical laws , the formula t ion of which pres up po se s . . , geometry . The ver if icat ion,of which you have spoken, re fers , therefore , not mere ly to geometry but to the ent i resys tem of phys ica l laws . . . An examinat ion of geometry by i t se l f i s consequent ly notthink able. 63

This conclusion need not by itself spell trouble for Reichenbach, al-though Reichenbach is predictably unaware of the reason. I have


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R E I C H E N B A C H S S E M A N T I C F R A M E W O R K 3 3

already suggested independent ly of the r igid body def ini t ion that hisSchl ickian account of empir ical adequacy may entai l Duhemian hol ism.Bu t the Non -Posi t ivis t now forces the issue with a new line of a t tack,one that c losely pref igures the centra l argum ent advanc ed two yearsla ter by Quine in 'Two Dogmas of Empir ic ism'64:[H]ow then is i t with your basic principle (meaning = verifiability)? Must you no t cometo the poin t where you deny the meaning of geometr ic s ta tements and concede meaningonly to the completely developed theory of relat ivi ty (which st i l l does not exist at al l asa f in i shed product )? Must you not grant tha t no meaning whatsoever , in your sense ,be longs to the indiv idual concepts and s ta tements of a phys ica l theory , such meaningbelonging to the whole sys tem insofar as i t make s in te l lig ib le w hat i s g iven in exper ience?Why do the indiv idual concepts tha t occur in a theory requi re any separa te jus t if icat ionat a l l , i f they are indispensable only wi th in the f ram ework of the logical s t ruc ture of thetheory , and i f i t is the theo ry as a whole tha t s tands the tes t? [Eins te in s use of Engl i shterms is indicated by i tal ics]65Einste in 's argument involves a move between two var ie t ies of hol ism,verification and radical m eanin g holism. 66 By verification holism I meanthe thesis Quine der ives f rom Duhem, that our theoret ical proposi t ions

face the tr ibuna l o f . . . exper ience no t indiv idua lly bu t as a corpora tebo dy and hence possess no determ inate 'empir ical content ' . 67 By rad-ical mean ing holism i t wi ll be recal led, I m ean the m ore fully Quin eanthesis that individual theoret ical proposi t ions possess no determinatecontent-about- the-world. Both Einste in and Quine argue direct ly f romverification holism to radical meaning hol ism. Ho we ve r , Einste in 's ver-s ion bet ter c lar i f ies the necessary premise: the argument presupposes aver if icat ion theory of meaning, f rom which Einste in ap pears to dis tancehim self. 6s

The en t i re purpose of Re ichenbach ' s semant ic f ramework ev ident lylies in a denial o f me aning holism (recall Section 4). Ein stein and(recent ly) Don Howard point out that he is unable to re ject ver i f icat ionhol ism. But this juxtaposi t ion need not embarrass Reichenbach. Con-trary to the readings of Einste in and Ho w ard (and near ly a ll o the rcommenta tors ) , Re ichenbach does no t defend a ver i f ica t ion theory ofmeaning. 69 The dif ference emerg es most vividly when Ho wa rd at tr i -butes to Reic henb ach the fol lowing cluster of doctr ines centra l to themature logical empir ic is t concept ion of the s t ructure and interpreta t ionof scientific theories :(1) the dist inct ion betw een analyt ic coord inat ing defini t ions and synthet ic empirical prop-os i tions ; (2) the asser t ion tha t the fo rmer are , a lone , convent ional ; and (3) the c laim tha t


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304 L I O N E L S T E F A N S H A P I R Oo n c e t h e f o r m e r a r e f i x ed b y c o n v e n t i o n e a c h o f t h e r e m a in in g e m p i r i c a l p ro p o s i t i o n s i si n v e s t e d w i th i ts o w n d e t e r m in a t e i n d iv id ua l e m p i r i ca l c o n t e n t such that the truth orfalsi ty of each em pirical proposi t ion is determined unamb iguously by experience correspo ndin g to tha t empirical content. 7It is the clause I have i tal icized, central to the cri t ique of Einsteinand H ow ard , that i s conspicuously lacking in P d R Z L . The process ofreaching a univocal ly coordinated model by progress ive correct ion wil lbe far more complicated than Howard 's reading al lows. In empir ical lyevaluating a theoretical claim based on certain coordinative definit ions,we will general ly ne ed to draw on fur ther theoret ical re la t ions , includingthose involv ed in corrective calculation. This will al low empirical recal-c i t rance to be shunted a long several d i f ferent 'chains of reasoning andexper ience ' . Of course , the es tabl ishment of any such chain ul t imatelyrequires that some coordinat ive def ini t ion be consul ted direct ly . ButReichenbach 's informal concept ion of coordinat ive def ini t ion preserveseven here th e underd eterm inat ion of the veri f icat ion process; we ma yfor ins tance re jec t a t roublesome measurement on any reasonable p leathat our measur ing rod is subject to dif ferent ia l deformat ion. Reichen-bach 's centra l con tent ions are that (a) every s ta tement of physicalgeo me try has a determ inate physical content , and that (b) our geometr ictheory is determined by the facts once a l l coordinat ive def ini t ions aregiven. These will not imply the rigidly posit ivist ic view of verificationHoward f inds in P d R Z L the view that we determine the t ruth-value oftheoret ical c la ims by s imply inspect ing whether or not their associated'empirical con tent ' obtains. 711 0 . T H E C A R N A P - P U T N A M I N T E R P R E T A T I O N : R E I C H E N B A C H

A S R A D I C A L M E A N I N G H O L I S TW e have seen that Re ich enb ach has grounds for re jecting the c laimof the No n-Po sit ivist that his con grue nce definit ion entails radicalmea ning holism. R esp ond ing specifically to Einstein 's dialogue in his1951 The Rise of Scientific Philosophy Reichenba ch h imse lf p lays ou this part quite differently. 72 Per hap s un der the influence o f the verifi-abi l i ty theory of meaningfulness he had come to hold, he appears tobi te the bul le t and accept radical meaning hol ism. The only not ion ofmeaning now in evidence is one which determin es whethe r empir icalobservat ion s are com pat ib le with a descr iption, and Reich enbac h ad-mits that such compat ibi l i ty can belong only to theor ies of geometry


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R E I C H E N B A C H S S E M A N T I C F R A M E W O R K 305and physics. Non etheless , he a t temp ts to rescue his coordina tive def i-ni t ion of con gru enc e by re interpret ing i t as implic i t in the con ventionalselection of a no rm al system from amo ng the c lass of equiva lentdescr ipt ions equally com patible with observations: he chooses thesupposedly unique theoretical descr ipt ion that includes no universalforces (here forces1). If this reading of the brief discussion is accurate,Re ichenbach ' s 1951 t rea tm ent of g eom etry represen ts a s tunning aban-do nm ent of the entire se mantic f ra me wo rk I have been describing. 73 I tis how ever jus t this reading that has shaped both Carnap 's and P utnam 'sanalysis of PdRZL T thoug h Put nam tell ingly replaces 'equal compati-bil ity with observation ' by 'agre em ent o n all poss ible par t ic le tra jecto-ries and prediction of all actual on es . 75

On their view, Reichenbach is interes ted not in the direct physicalinterpreta t ion of a metr ic function, but ra ther in the implic i t f ixing ofi ts interpreta t ion through a conventional res tr ic t ion on the form of ourempir ical ly ( in Putn am 's case , t ra jectory-predict ively) adeq uate theo ryof geom etry and physics. Analy ses of this sort were in deed co m m on atthe t ime Reichenbach was writ ing, though the s tandard res tr ic t ion isone of maxim al s implic i ty for physical law (such views were propo sedby both Schlick76 and CarnapV7). R eic hen bac h mo reo ve r aligns him selfwith this position in a 1922 synopsis of the philosophical debate aboutrela t ivi ty theory , deny ing here that a theory - ind epen den t def ini tion of'rigid body' is possible. TM But it is precisely these holistic analyses thathe seeks to repudiate in PdRZ L Th ey a re pa ten t ly incompat ib le withhis ins is tence that theoretical re la t ions are ren de red objective physicalfacts through the explic it repla cem ent of abstract enti t ies by their physi-cal inter preta tion s as specified by coo rdina tive definitions (recall Section4) .79

Admitt ing no such role for coordinative def ini t ions , the Carnap-Putnam reading no longer a l lows for construction of the chains ofreasoning and exper ience whose un iversa l agreement had cons t i tu tedthe cr i ter ion for empir ical adequacy, whence i t is not immediatelyevident in wha t the d esired 'compatibil i ty ' re la t ion betw een descr ipt ionand reali ty is to consist (we f ind no int im ation o f Carnap 's la ter analyticL- ru les for deriv ing pro tocol sen tences or o f Quine ' s unabashedlypsych olog ical accountS). H er e Pu tna m 's nonverif icationist sanitiz-at ion fares worst of a l l : while he may appeal to der ivation of par t ic letra jector ies descr ib ed in terms of [ the theory 's] me tr ic , th is c lear lyleaves the task of physically interpret ing geometrical descriptions of


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306 L IO N E L S T E F A N S H A P IR Otrajectories. Besides imputing intolerable insincer i ty to Reichenbach 'sat tempt a t def ining the ideal r igid body, the general Carnap-Putnamreading lays all weight on his apparent claim that there is a uniqueuniversal- force-free descr ipt ion of the universe . I t i s the unf or tu natefalsity of this claim on Putnam's reading of 'universal force' (force1)that he adduces in order to lay Reichenbach 's congruence def ini t ion torest . Once again, this claim is central to the discussion in The Rise ofScientific Philosophy but i s nowhe re em phas ized in Pd RZ L. 8111 T H E P O S IT IV IS T IN F E RE N C E A N D T H E A R G U M E N T F R O M

F R U S T R A T E D M E A S U R E M EN T A T T E M P T S

Let us now return to my character izat ion of Reichenbach as a ver-ification holist , a claim that may appear unconvincing as I have yet toproduce an expl ic i t endorsement in P d R Z L . Certainly, i t would bemisleading to regard his embrace of the re la t ivi ty of geometry as amanifesta t ion o f Du hem ian holism ;82 this thesis is an ingredient evenof Ho ward ' s in terpre ta t ion of P d R Z L on which a complete set ofcoordinative definit ions suffices to invest each proposition of physicswith determinate observat ional t ruth-condi t ions . The ver i f icat ion hol-ism I have b een ascribing to R eichen bach is far s t ronger ; i t leaves openthe possibil i ty that we might make conflicting revisions to physicaltheory in the face of empir ical recalc i t rance such that each would becompat ible with a l l possible observat ions, but none would involve anychange in the meanings o f terms, w hence a t mo st one wou ld be correct.Here my reading runs direct ly counter to an overwhelming t radi t ionaccording to which P d R Z L endo rses a radical verifiabili ty the ory ofmea ning (Clark Glym our) , manifested in the s tandard posi t ivis t infer-ence f rom empir ical equivalence to ful l equiva lence (Fr iedman) . s3We have a lready found a non-ver i f icat ionis t reading the only char i t -able one of Reichen bach 's coordinat ive def init ion of congruence in l ightof his acknowledgment that corrective calculation is essentially involvedin measurement . But the a l leged 'posi t ivis t inference ' i s independent ofReich enbac h 's account of the real-world interpreta t ion of mathem aticalmodels - i t i s compat ible with both Howard 's a tomist ic and Carnap 'shol is t ic readings, s4 M ost com mon ly, the inference has s imply beenequated with Reichenbach 's so-cal led convent ional ism, as manifestedin the thesis of the re la t ivity of geom etry. Con trary to received opinion,though, this 'convent ional ism' is base d not on any vers ion of Leibniz 's


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R E I C H E N B A C H S S E M A N T I C F R A M E W O R K 3 7

pr inc ip le bu t on Reichenbach ' s semant ics a lone . Toward the end ofP d R Z L , he pauses to r igorous ly formula te the ep is temologica lcom pon ent of an analogous 'convent ional is t ' thesis, the re la t ivi ty ofmo t ion :T h e t r a d i ti o n a l e x p o s i t i o n h a s o n l y o b s c u r e d t h i s s u b j e c t m a t t e r . W h e n i t i s s a i d t h a t o n l yr e l a t i v e m o t i o n i s r e c o g n i z a b l e [erkennbar] a n d h e n c e o n l y i t m a y b e a d m i t t e d a s a no b j e c t i v e d e t e r m i n a t i o n , t h i s a s s e r t i o n , b a s e d o n t h e principle of the identity of indiscern-ibles m a y b e d i s p u t e d , b e c a u s e i t a s s u m e s a m e t a p h y s i c a l c h a r a c t e r : i f w e c a n n o t r e c o g -n ize [erkennen] a d i f f e r e n c e , i s t h e n n o d i f f e r e n c e present i n t h e o b j e c t i v e p h e n o m e n a ?B u t t h i s e x p o s i t i o n o v e r l o o k s t h e f a c t t h a t w e a r e d e a l i n g w i t h a p u r e l y l o g i c a l m a t t e r .T h e q u e s t i o n W h i c h r e f e r e n c e f r a m e is m o v i n g ? i s n o t e v e n a defined question a n dtherefore n o a n s w e r i s p o s s ib l e . . . . [ T ] he t w o c o n c e p t io n s b e t w e e n w h i c h w e a r e s u p p o s e dt o d e c id e c a n n o t t h e m s e l v e s e v e n b e m e a n i n g f u l l y f o r m u l a t e d , a n d t h e r e f o r e a n a n s w e rs e l ec t in g o n e o f t h e t w o c a n n o t p o s s e s s an y s e n s e e i t h e r Y

In order for our theoret ical c la ims to acquire any s ignif icance beyondtheir purely mathematical conten t , their e lements must f i rs t be preciselyinterpreted through coordinat ive def ini t ions , in this instance throughthe coord inat ive def init ion of res t .

I t may be ob jec ted tha t Re ichenbach ' s bes t -known argument for thenecessi ty of coordinat ive def ini t ion is based on concerns of empir icalverification. Introducing his metrical coordinative definit ions, he arguesthat without such def ini t ions al l me asure me nt w ould be impossible inpr inciple . In part icular , he proceed s by the notor ious argument fromfrustrated measurement attempts, painstakingly demonstra t ing each pro-posed m ethod of de te rmin ing a ' t rue ' congruence or s imul tane ity re-la t ion to be defeasible by assumptions about universal forces or thebehavior of signals such as l ight. Even without the 'posit ivist inference' ,this argument clearly succeeds in establishing that some specificationof referenc e is ne ed ed in order to ensure that a t ransported r igid rod,ra ther than a t ransported rub ber ban d, wil l count as congruent . In theabsence of a sentence-by-sentence ver i f icat ionism stronger than the'posi t ivis t inference ' ) , i t does not however mandate that this specif ic-a t ion app eal direct ly to the beha vior of rigid rods.

Stil l , i t is not difficult to account for the argument from frustratedmeasurement a t tempts . Once aga in , we mus t keep in mind tha t Re ich-enbach is addressing a philosophical public largely unfamiliar with thedual i ty of mathematical and physical geometry. Temporar i ly beggingthe quest ion of how the physical interpreta t ion of the metr ic is to bespecified, the frustration argument graphically i l lustrates the depen-


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308 L IO N E L S T E F A N S H A P IR Oden ce of the ge om etr y o f physical space on such a specification. 86 Asecond funct ion of the a rgume nt eme rges dur ing i ts lengthiest e labor-ation, the passage introducing the coord inative d efinition of simultan-eity. 87 Th rou gh ou t P d R Z L , Reic henb ach cla ims as the phi losophicalachievem ent of the theory of re la t ivi ty the real izat ion that coordinat ivedefinit ions are required in more places than might init ially seem evi-dent . 88 The argum ent f rom frustra t ion is Reic henb ach 's tool for demo n-strat ing that the co ncept o f simultanei ty is left undefined by those spatialand tempo ral coordinative definitions already in place.

12. R E IC H E N B A C H S S P A T IO -T E M P O R A L R E D U C T IO N IS MI have arg ued that the need for coordinat ive def ini tions res ts sole ly onthe logical impossibi l i ty of making asser tions abo ut the world interms of a mathem atical s t ructure bef ore the e lements o f that s t ructurereceive physical interpreta t ion. 'But ' , the reade r will be lef t wond ering,'what is to prevent us f rom simply interpret ing the metr ic funct ion ass tanding for the physical quant i ty distance? Is this not because we haveno theory- independent means of determining distances until we identifydis tance with the q uant i ty y ie lded by a cer ta in ostensively dem onstrab lemeasur ing procedure? ' We indeed possess no such means , bu t th i scannot be why Reichenbach disal lows a mere appeal to dis tance as thereal-world member of the coordinat ive def ini t ion of the metr ic . In theclosing section of P d R Z L , he argues that spat io- temporal coincidencesare among the e lementa ry rea l-wor ld memb ers em ployed in h is geomet -ric coordinative definit ions. Nonetheless, he insists that the determina-t ion of which physical things are coincidences is not given through anykind of se lf -evidence in an unimpeachable manner; about this as wellonly the entire theoretical context [Zusammenhang] m ay decide , s9 Thisexpression of Reichenbach 's thoroughgoing ver i f icat ion hol ism con-tras ts sharply with Carnap 's view in Der Raum, where spa t io -tempora lcoincidences are pronounced a Tatbestand of exper ience (whose to-pological re la t ions repres ent Kan t 's nece ssary formal condi t ions forthe possibi l i ty of exper ience, while the metr ical re la t ions are a mat terof arbitrarily elect ive for m ) . 9For Reichenbach, the t rouble with a direct appeal to dis tance is thatwe have no unders tanding of wh at it is for two lengths to be congruent-a t-a-dis tance other than for them to be potent ia l ly local ly congruent to


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R E I C H E N B C H ~ S S E M N T I C F R M E W O R K 309an ideal r igid rod t ranspo rted betw een them. By contrast , he doescredit us with clear and distinct understanding of what i t is for there tobe a spat io- temporal coincidence, and (of ten) of what i t is for it to bethe case that one state of affairs would obta in provided another ob-ta ined. Is this s imply metaphysical prejudice? Given how suspect thiscol lection of theses may appe ar once explic it ly formulated, i t is remark-able how much credibi l i ty Reichenbach succeeds in affording i t . Much,no dou bt , arises f rom his e labo rate psycholog ical account of ourgrasp of what i t is for two lengths to b e con gruen t, involving an implicitcoo rdina tion of the relations of parallelism a nd right angle to rigidlybehav ing physical structures. 91 Ka nt 's pu re intuit ion [reine Anschauung] of space and t ime is thus unmas ked as the visualiz ing[Veranschaulichung] of mathematical re la t ions using imagined physicals t ructures . Leaving aside this account of our grasp of cer ta in not ions,Re ichenbach ' s spa t io - tempora l reduc t ion ism provides a ready means ofexpl icat ing the phenomenon of seemingly incompat ible but equivalentdescriptions en co un ter ed in the special the ory of relativity. 92 Con sider,for example, Einste in 's re la tivization o f the re la t ion o f s imultanei ty toinertial refere nce fram es. Co nflicting attr ibution s of simultan eity arereconci led, so Reichenbach, once we recognize that they are merelydifferent theoret ical expressions o f the sam e physical c laims abou t thecounterfactu al beha vior of light-s ignals and ideal clocks 93

W e ma y be surpr ised a t the dis tance t raversed in P d R Z L f rom Reich-enb ach 's init ial charac terization of coor dinativ e definit ions as ostensivecoordinat ions, as contrasted with discursive Inhaltsbestimmungen.While a f i rm dis tinction b etw een conceptua l and coordinat ive def ini tionremains , the form er has evolved from the 'determ inat ion of conceptualconten t ' to the characterizat ion of a c lass of mathem atical models , thelatter from a simple pointing gesture to the (now discursive) interpreta-tion of an element of such a model as a specific physical quantity orre la t ion. I ronical ly , Reichenbach here fa l ls vic t im to his consummatelypedagogical app roach, his pervasive s tra tegy of gradual ly developingand differentiating concepts f irst introduced in deliberately simplifiedguise. 94 The original ostens ive/discu rsive distinction serves m erely todramatize the dis t inct ion b etw een a mathem atical m odel and i ts physicalinterpreta t ion.

Reichenbach 's pr imary phi losophical goals in P d R Z L are threefold:(1) to dis t inguish between mathematical and physical geometry and to


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31 L I O N E L S T E F A N S H A P I R O

argue that this distinction vitiates neo-Kantian geometric apriorism, (2)to promote a specific reductionist account of certain spatio-temporalnotions and of our (typically obscure and confused) grasp of them, and(3) to rely on this account in interpreting aspects of Einstein's theoryof relativity. What we do not find in PdRZL, however, is any attemptto elucidate the nature of reference, that is pace Putnam) to explainhow term s can refer t o som ethirtg at all . 95

N O T E S* M y g r e a t e s t d e b t i s t o P r o f . H i l a r y P u t n a m , w i t h o u t w h o s e i n s p i r a ti o n a n d e n c o u r a g e -m e n t t h i s p a p e r w o u l d n o t h a v e b e e n w r i t t e n . Th a n k s a r e a l s o d u e t o P r o f . M i c h a e lF r i e d m a n f o r d e t a i l e d a n d h e l p f u l c o m m e n t s o n a n e a r l i e r v e r si o n , a n d t o t w o a n o n y m o u sr e f e r e e s . Th i s p a p e r i s b a s e d i n p a r t o n r e s e a r c h c o n d u c t e d w h i l e s u p p o r t e d u n d e r aN a t i o n a l S c i en c e F o u n d a t i o n G r a d u a t e F e l l o w s h ip .1 See F r ied man (1991) fo r an ex tens ive l is t o f re levan t au thors .e See Suppe (1989) , van F raassen (1989 , pp . 217-32) .3 G l e a s o n ( 19 88 ). F o l l o w i ng G l e a s o n ' s e x a m p l e , t h i s p a p e r u s e s t h e w o r d ' m o d e l ' i n b o t ht h e c o l l o qu i a l a n d t h e m o d e l - t h e o r e t i c s e n s es : m a t h e m a t i c a l s t r u c t u re s s u p p l y m o d e l s f o rphys ica l rea l i ty a s we l l a s fo r a theory .4 A n i n d e p e n d e n t q u e s t i o n i s t h a t p o s e d b y Ba s v a n F r a a s s e n : s h o u l d w e r e q u i r e o f at h e o r y t h a t i t b e true, i . e . tha t one o f i t s mode ls be phys ica l ly rea l ized in i t s en t i re ty , o rs h o u l d w e m e r e l y r e q u i r e t h at a c e r t a i n e m p i r i c a l s u b - s tr u c t u r e o f t h e m o d e l b e r e a li z e db y a s t r u c t u r e o f o b s e r v a b l e p h e n o m e n a ? I n t e r e st i n g l y , v a n F r a a s s e n v i e w s P d R Z L as ap recur so r to h i s empiricist v e r s i o n o f t h e s e m a n t i c v ie w : t h e r e l a t io n s h i p b e t w e e n e m p i r ic a ls u b s t r u c t u re a n d p h e n o m e n a c o r r e s p o n d s ex a c tl y t o th e o n e Re i c h e n b a c h a t t e m p t e d t oiden t i fy th rou gh h is concep t o f coord in a t ive de f in i t ions , once w e abs t rac t f ro m th e l inguis -t i c e le me n t (van F raass en , 1989 , pp . 227-8 ) . I wi ll deny bo th the ex is ten ce o f a ' lingu ist ice l e m e n t ' i n P d R Z L a n d t h e c o r r e s p o n d e n c e t h a t v a n F r a a s s e n h e r e i d e nt i fi e s.5 See Hem pel (1965b , p . 184n) , Horw ich (1982 , p . 72 ) . Th is fea tu re i s no t definitionalof a ' syn tac t ic v iew ' , a s tha t des igna t ion a l lows fo r two sep ara te senses o f 'syn tac t ic ' : ( i )a theory i s to be p resen ted as an ax iomat izab le fo rmal language , ( i i ) the co r re la t ions o f' t h e o r e t i c a l t e r m s ' w i t h ' o b s e r v a t i o n t e r m s ' a r e t h e m s e l v e s t o b e ( a na l yt i c) s e n t e n c e s inth i s l anguage . I t i s sense ( i i ) f rom which I am mos t concerned to d i s soc ia te P d R Z L ,though ( i ) i s equa l ly a misa t t r ibu t ion .6 Re ichenbach (1938 , p . 55 .7 Re i che nbac h (1928 /1958, pp . 31 -2 /14-5 ) . The page num bers to be g iven fo r Re ic hen-b a c h ' s G e r m a n w o r k s a r e t h o s e o f t h e o r i g i n al e d i ti o n s , w h i c h a ls o a p p e a r i n t h e Gesam-melte Werke vo lumes . Un less o the rwise no ted , a l l t r ans la t ions a re mine .8 Re i chen bac h (1978b , p . 161 [Schneewin d t rans la t ion ] ) . R e iche nbac h in fo rms us tha tth is ar t ic le for the Handbuch der Physik was wr i t t en in 1923 and lay unpub l i she d fo r s ixyea rs (R e iche nbac h , 1951a , p . 46) . The b r ie f sec t ion on coord ina t ive de f in i t ion i s how evernea r ly iden t ica l to 4 o f P d R Z L , wh ere the c i ted c la im ap pears on ly s l igh tly le ss fo rce fu l ly


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R E I C H E N B A C H ~ S S E M A N T I C F R A M E W O R K 3 11(Reichenbach, 1928/1958, p. 23/14). Concerning the account of 'concepts' in this article,which diverges substantially from that of P d R Z L , see note 12 below.9 Reich enba ch (1928/1958, pp. 46/34, 24/15). In the presen t context, i t is imm aterialthat Reichen bach also contrasts this definition with the direct definition through the Parisrod, ident ifying the former as an example of the interposi t ion of conceptual connect ionsadmissible in the specification of coord inative definitions. Af ter all , the con cept interp osed(the concept '40 million times as long') is itself physically interpreted through the oper-ation 'lay end to end 40 millio n ti m es ' (1928/1958, p. 152/128).a0 Carnap (1936-37, pp. 441-54).11 Reich enba ch (1928/1958, p. 25/16). In the 1923-29 pape r, he admits the real ity notonly of substant ial (elemental) objects but also of relat ions thereof , s ince i t mustbe possible to coordinate some object with every concept (Reichenbach, 1978b, pp.149-50 [Schneewind trans.]).12 Andreas Kamlah (1979, pp. 254-8). This reading is surprising, as Kamlah acknowl-edges that the source for Reichenbac h's 'concepts ' i s Mori tz Schl ick, who in introducing

Begriff e emphasizes that they are not mental (Schlick, 1925/1974, 5, pp. 19-20/20-1). The only initially credible suppo rt ad duced from R eichen bach 's ow n writings is hisrem ark in the 1923-29 paper that concep ts are configurations of perc eptio ns , a classof spec ial men tal things that are coordinate d as symbols to the totality of things(Reich enba ch, 1978b, p. 148). Ironically, Kam lah ne ver men tions that this equation , withwhich he aims to disqualify any langu age orien ted reading, i tself arises as part of anexplicit recipe for transcribing thing-talk into perceptual-experience-talk (Reichenbach,1978b, p. 140). No trace of this program remains in P d R Z L . Moreover , Kamlah 's ownconclusion is absurd: correct ly refusing to saddle Reichenbach with Ado lf Grt inbaum'sthesis of the intrinsic metrical amorphou sness of spac e-tim e , he instead identifies asReic henb ach's new messag e (Kam lah, 1979, p. 259) a thesis of the intrinsic contentless-ness of thoughts

My reason for belaboring Kam lah's views is that they point to o ne elem ent of Reichen-bach's argument indeed neglected by some language oriented readings. AlthoughReichenbaeh's 'concepts ' are not mental ent i t ies , conceptual relat ions are the contents ofour purely mathematical thoughts , and these thoughts are devoid of content about thephysical world (1928/1958, p. 118/97). Th e contra ry position, exem plified by Ka ntiangeometr ic apriorism, is one Reichenbach is concerned to refute throughout much ofP d R Z L . But the only though o riented compo nent of his response, his denial that weenjoy any pure intui t ion that can apply to Euclidean geometry alone (13), is a self-containe d argum ent, logically inde pen den t (as Reich enba ch insists) ol the preced ingaccount of the semantics of theories o f physical geome try (1928/1958, p. 44/32).13 Putnam (1975c, pp. 171-6; 1975b, pp. 120-4).14 See especially Glymour (1980, pp. 53-58) and Friedman (1983, pp. 296-301).15 Reichenbach (1928/1958, p. 129/107).16 Carnap (1922, pp. 7-8).17 Reichenbach (1924/1969, p. 5/8).1~ Rei che nba ch (1928/1958, p p. 11 3-4/93 ).19 Reichenbach remarks that the axiomatic calculus defining a Beziehungsgefage is itselfonly a coordinatio n of that abstract system of relations to a visualizable system of symbols("Zeichen"): Reichenbach (1928/1958, p. 129/107).


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3 2 L I O N E L S T E F A N S H A P I R O20 Assimilat ion of PdRZL to the ' semant ic v iew' i s not threa tened by Reichenbach ' sinclusion of the logical connectives in h is l is t of the conce pts f rom which a l l geometr icconcepts are to be defined (Reichenbach, 1928/1958, p. 114/93). The logical connectives,whi le not concepts assoc ia ted wi th the class of geometric structures the i r symbols he lpdef ine , a re themselves concepts , nam ely the meanings of the co nnect ive symbols. U nl ikeal l other symbols, which acquire meanings through implici t defini t ion ( i .e . the defini t ionof a c lass of s t ruc tures), the logica l symbols have an indep ende nt meaning .21 Reichenbach (1928/1958, p. 124/103). This passage occurs in the context of Reichen-bach ' s reduct ion of spa t ia l v i sua liza t ion (Kant ' s re ine Ansc hauu ng ) to imagined physi-cal coordination of pure ly logical concepts.22 Reichenbach (1928/1958, p. 23/14). See Schlick (1925/1974, 10) for the criterion of

e indeut ige Zuordnung . Only br ie f ly summar ized in PdRZL the Schlickian conceptionis elab orate d in far greater detai l , thou gh with signif icant differences, in cha pter IV( 'Erk enntn is a l s Zuo rdnu ng ' ) of Reichen bach (1920) , and in the 1923-29 paper (Reichen-bach, 1978b, 8).23 Reichenbach (1928/1958, pp . 25-6/16-7) .24 Re iche nba ch (1920/1965, p. 41143 [ the ful l phra se Obe rlegun gs- und Erfahrun gsket -te appears thre e sentences ear l ie r ] ). The res t r ict ion to rea l -va lued funct ions i s of meta-physical s ignif icance in the Kant-influenced Relativitdtstheorie und Erkennmis aprioriwhere Re ichenba ch holds tha t e lements of rea l ity are in some sense f ir s t def ined orcons t i tu ted through ou r coordina t ion . T herefore , cont rary to Schl ick 's emphat ic requi re-me nt (Schlick, 1925/1974, p. 63/68), we are n ever in a prior posi t ion to judge the id enti tyof two such elements (Reichenbach, 1920/1965, p. 43/45). Instead, so Reichenbach, al lwe can establ i sh i s wh ethe r two numbers der ived f rom two d i f ferent measu remen ts a reequal . In PdRZL however , Reichenbach expl ic i t ly coordina tes mathemat ica l en t i t iesto de term inate phys ica l th ings conceived of as ava i lab le pr ior to the co ordina t ion .25 Rei chen bac h inten ds his 1920 cri te r ion to be constitutive of t r u th (Re i chenbach ,1920/1965, p. 43/45). The sam e claim figures in the 1923 -29 paper (al thou gh Reic hen bac hnow emphas izes tha t such t ru th i s only approximate ly a t ta inable in sc ient if ic inqui ry) . H edraws the appropr ia te hol i s tic consequence: Onc e we note tha t every i tem of sc ienti f icknowledge depends on every o ther , tha t a ll scient if ic propos i t ions a re in terc onnected , wecan say that t ruth , according to this concep tion, is a characteris t ic of the system; tru thper ta ins only to the sys tem as a whole , and only f rom th is s tandpoin t can t ru th betrans ferre d to individual assert io ns (Re iche nba ch, 1978b, p. 156 [Schneew ind trans.]) .In PdRZL by co ntrast , the ant i-holis t ic role of co ordinat ive defini t ions in specifyingreference implies that the Schlickian holist ic conception can only be serving as a charac-terizat ion of empirical adequacy.26 Reic hen bac h (1928/1958, pp. 152/128, 24/15). S imilarly Reich enb ach (1978b, p. 161).27 Reichenbach (1928/1958, p. 23/14).28 Putnam (1975b, p. 122).29 Reichenbach (1928/1958, p. 50/37 [M. Reichenbach translat ion]) .30 Reichenbach (1928/1958, p. 35/24); see similarly (1928/1958, p. 21/13) and (1928/1958,p. 128/106).31 Re ich en ba ch (1928/1958, p. 30/21 [original italicsl).32 Reichenbach (1928/1958, p. 47/35 [original italics]).33 Reich enbach credi ts He rm ann von Helmhol tz a nd Henr i Poincar6 wi th the e labora t ion


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R E I C H E N B A C H ~ S S E M A N T I C F R A M E W O R K 3 3of th i s thes i s , one tha t had been embraced by Schl ick , Eins te in , and Carnap a l ike .Poincar6 ' s convent ional i sm (according to which cer ta in elements of a theory mus t beregarded as a rb i t ra ry convent ions) i s however c r i t ic ized for neglec t ing the semant icro le of the coordina t ive def in i t ion of congruence in de termining the geometry of space(Reichenbach, 1928/1958, p . 48-9/36-7) . This i s the most subs tant ive of Reichenbach ' srepea ted a t tempts to d is tance h imsel f f rom Poincar6: in works both pre- and pos tda t ingcoordinat ive defini t ion semantics, Poincar6 is rather unfair ly accused of a fai lure toemphas ize the fac t tha t the classes of cotenable conventions are de l imi ted by objec t iverea l i ty . See Reichenbach ' s 1920 cor respondence wi th Schl ick ( repr in ted in Howard ,for thcoming; i tem H R 015-63 -21 in the Archive of Sc ienti fic Phi losophy, Univers i ty ofPi t t sburgh) , and the ident ica l compla in t in Reichenba ch (1951, pp . 152-7) .34 I employ th e des ignat ion ' convent iona l i sm' in the sense used by Pu tnam in h is 'Refut -a t ion of Conven t ional i sm' (1975c), a sense tha t does n ot presupp ose a syntac tic concept ionof physica l theory . 'Convent ion al i sm' is a l so the n ame of a separa te v iew according towhich part icula r sentence s in a scientif ic theory are assigned the status of conventions.As we have seen , the la t te r is a lso a v iew comm only a t t r ibuted to R eichenb ach in P d R Z L .3s Putnam (1975c , pp . 165-8) ; the a rgument der ives f rom his ear l ie r paper (Putnam,1975b, pp. 110-1).36 Al tho ugh he is c r it iciz ing v iews of Reic henb ach l , al ias Adol f Gr i in bau m tha t a re

widely a t t r ibuted to Reichenbach , Putnam's explanat ion of how Reichenbach h imsel feludes cri t icism is unconvincing, as i t rests on a reinterpretat ion cri t icized in Sect ion i0below.37 Reichenbach (1928/1958, p. 30/20)38 Rei che nba ch (1928/1958, p. 30-1 /21). Pu tna m misses the significance of this dis-cussion: Th ere occurs on p . 21 the as tounding asser tion tha t the s ta tements tha t thef loors and ce il ings of our rooms are p lanes , [etc .] . . . a re not synthe t ic s ta tements butdefini t ions, and 'have nothing to do with cognit ion as one might at f i rs t bel ieve ' . This isclearly just a mis take (Put nam , 1975b, p. 122). W hile his rheto ric is certainly unfortu-na te , Reichen bach i s rea l ly saying tha t we choose our coordina t ive def in i t ions based o nthe cons t ra in t tha t our floors turn out to be approximate ly p lanar . Only once thecoord inat ive defini t ions are chos en can we t hen speak of scientif ic cognit ion.39 Reichenbach (1928, p. 332 [my i tal ics]) . The appendix is missing from the Englisht rans la tion . In h is com men tary on P d R Z L Kam lah notes tha t th i s passage represents animp or tant qual if icat ion of Reichenba ch ' s convent ional i sm (Kamlah, 1977, p . 430) .4o Friedman (1983, pp. 295-6).41 Rei chen bac h (1928/1958, p. 30/20). See Schiick 's discussion of a defini t ion of the unitof t ime according to the pulse of the Dalai Lama (Schlick, 1925/1974, pp. 66-7/71-2).I t might app ear tha t the fac t tha t Reichen bach i s t roubled by th is s ta te of a f fa i rs cont rad-ic ts my previous asser t ion tha t Reiche nbach ' s u nders tand ing of sc ient if ic met hod inc ludesrevising coordin at ive defini t ions in accordan ce with expe rime ntal resul ts (Sect ion 3). B ut ,as Putna m has po in ted out , there i s a grea t d i f fe rence be tween 1) dec lar ing an arb i t ra rycoordina t ive def in i t ion , a l though the theory conta in ing it may be revised due to unfavor-able exper imenta l resu l t s , and the def in i t ion abandoned, and 2) dec lar ing an arb i t ra rycoordina t ive def in i t ion wi th the unders tanding tha t cer ta in phys ica l events envis ionedwithin the theory wil l cause us to al ter the defini t ion. See Putnam (1975a, p. 59-61).42 Reichenbach (1928/1958, p. 29/19).


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3 1 4 L I O N E L S T E F A N S H A P I R O43 Reichenbach (1928/1958, p. 32/22).44 Reichenbach (1928/1958, p. 38/27).45 The emp hasis on 8 in the l i terature derives from i ts direct continuity with the co nven-t i

coordinative definition' and reichenbach's semantic framework- a reassessment*

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