Theory Change and the Indeterminacy of reference

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46 T H E J OU RN L O F P H I LO S O P HY

T h e temptat ion to use these not ions of L- t ruth and L-fa ls ity sug-gests an oth er interesting point. If th e objects of a th eory could some-how be fixed a priori t o be the nu m bers (as here) or physical objec tsor space -time points, we could ge t a different relation of L-incom-patibil i ty for which the underdeterm ination thesis m ight hold. Y etsuch a priori fixation of th e obje cts of a the ory is the epito m e of w ha tQuine maintains is impossible or m eaningless. T h e prim ary thr us t ofhis indeterminacy argum entsq is th at there is no fact of the m att er,whether the objects of a theory are concrete things, their stages,their undetached parts , or even their Godel numbers. Craig 's examplefails to supp ort Q uine's und erdetermination thesis .

J NE ENGLISH

Harv ard Univers i ty

T H E O RY C H A N GE A ND T H E I ND E T ER M IN A C YO F R E F E R E N C E *

IN this paper I will argu e th a t considerations ab ou t scientific rev-

olutions show that many scientific terms are referentially in-

determinate-there is no fa ct of the m at te r as to w ha t th eyde no te (if th ey a re singular terms) o r as to wha t the ir extension is (ifthey are general terms). In the opening section I will t r y t o establishthis general point of view b y consideringa particu lar scientific revolu-t ion, th a t in which N ewtonian mechanics was replaced by the specialtheory of relat ivi ty. I will argue th a t this revolution reveals th a t theword 'mass' a s used before relativity theor y was discovered ha d nodete rm inate denotation. L ater o n in the paper I will suggest th at thisindete rm inacy in th e term s of earlier scientis ts is evidence for an in-

determinacy in many of our own scientific terms.I n addition to establishing th e existence of inde term inacy ,I w a n tto show its impo rt for sem antic theory. Th ere is a long tradit ion insem antics according to which th e tru th value of w ha t someone say sis determined by certain sem antic features of the words (orword-tokens) he uses in saying i t . T h u s the tr ut h value of an u tteran ce of' John loves Ma ry and M ary loves Bob ' i s determined by t he denota-tions of the utterer 's to kens of 'John ', 'M ary ', an d 'Bob' (i.e., by th epeople the utte rer referred to in using these nam es) and by the ex-

Especially in Ontological Relativity and Other ssays (New York: Columbia,1969

am grateful to bl ichael Friedman, Clark Glymour, and David Hil ls , forhelpful suggestions about this paper. M y work on the paper was supported in itsfinal stages by the National Endowment for the Humanities.



THEO RY CH NGE ND INDETERMIN CY OF REFERENCE 463

tension of his tok en of lov ed : t he ut te ra nc e is tr ue if an d only ifthe extension of loved contains both t he ordered pair whose first

mem ber is the denotation of ( the token of) John and t h at whosesecond member is the denotatio n of M ary , an d the ordered pairwhose f irst mem ber is the denotatio n of M ary an d whose secondmem ber is the denotation of Bob . l I t has seemed to m an y philos-ophe rs th a t it is only because ther e are linguistic rules for determin-ing the truth value of a sentence from the denotations of its com-pone nt nam es, extensions of its comp onen t predicates, etc., th a t thenotions of truth and falsity even make sense.

T h is point of view (I ll call it referential sem antics) was a dhered

t o by Frege, Ca rna p, and Tarsk i? and h as become increasingly com-mon in recent years. B u t referential indeterm inacy creates a seriousproblem for referential se ma ntics. Fo r we ll see th a t there are sen-tences with perfectly determinate truth values which contain refer-ential ly indeterminate names and predicates, so th at i t makes per-fectly good sense to ask whether the sentence is true or false eventhough i t doesn t make sense to ask wh at th e name really denotes orw ha t t he real extension of th e pred icate is. Clearly, th en , th e factth at i t makes sense to speak of the t ru th and falsity of such sentences

can no t be based on th e existence of linguistic rules th a t determ inetruth value from denotation and extension.S o if m y arg um ent for referential indeterm inacy works, it follows

th a t we have t o revise t he program of referential semantics t o someextent. T h e second pa rt of the pap er will be concerned w ith th e ques-tion of w hat sor t of revision is required in ord er t o han dle th e so rt ofindeterminacy whose existence is revealed by scientific revolutions.

Before Ein stein s special theo ry of re lativit y, phy sicists accepted a

great many assert ions involving the term mass th a t are no longeraccepted today. For instance, Newton and his successors acceptedth e following claims

(1) Th e mass of a particle is equal to twice its kinetic energy dividedby th e squa re of it s velocity.

I t would be possible to formulate referential semantics in terms of propert iesrather than sets : we could say th at the utterance 'John loves Mary' is true ifand only if the person denoted by 'John' bears the relation (2-place property)denoted by 'loves' to the person denoted by 'Mary'. I believe th at if propertiesare carefully distinguished from meanings, there are certain advantages to pro-ceeding in this manner; but for our present concerns it is irrelevant whether wechoose set s or properties, so I have stuck to t he more common policy of relyingon sets.

3 This is more true of what Tarski ou ht to have said (given his logical dis-coveries) th an of what he did say : cf. my paper Tarski's Theory of Truth,this JOURNAL, L X I X , 13 ~ 3,1972 347-375.



THE J O U R N A L O F PHILOSOPHY

and

2) Mas s is conserved in all interactions.Part of the novelty of Einstein s theory was that (1) and 2) andmost of Newton s other assertions involving mass were given up.This fac t has led some philosophers (e.g., Thomas Kuhn3) to claimtha t before relativi ty theory was discovered the term mass did notdenote (or refer the same physical quanti ty5 t denotes (or refersto) today. These philosophers, in other words, deny the followingclaim

(3) Newton's term 'mass ' denoted mass i.e., Newton was refer-

r ing to the same phys ical quan t i ty t ha t w e refer t o when w e useth e word 'mass' .

I t seems to me very unlikely tha t the falsity of (3) can be establishedsolely on the sorts of grounds that Kuhn utilizes, viz., on the facttha t Newton had many beliefs involving mass th at are no longeraccepted there is nothing at all incoherent in the position that New-ton was referring to mass even though he had a great many false be-liefs about it (cf. note 3). Moreover, we should note that the falsebeliefs about mass th at Newton must have had for (3) to be right areall afiproximately true-e.g., we can approximate (1) by the weakerclaim

(I*) A t low velocities, th e mass of a particle is almost precisely equa lt o twice i t s kinet ic energy divided by th e squar e of it s velocity.

8 The Structure of Scienti5c Revolutions (Chicago: University Press, 1962)pp. 100-101. A similar conclusion is suggested by a passage from Quine's Wordand Object (Cambridge, Mass.: M I T Press, 1960), p. 16, abou t th e ter m 'neutrino'.Judging from this passage we might expect that Quine would argue as follows:

Since Newton's and Einstein's theories differed so much, they cannot havebeen referring to the same quantity. The fact that both physicists used theword 'mass' is no t significant. To discern two phases here, the first an agreementas to what physical quanti ty is involved (viz., mass) and the second a disagree-ment a s to what it's like (what laws it obeys), is absurd.

But this would be an ignoratio elenchi: the issue is not whether Newton knewwha t mass is or whether he and Einstein agreed as to what mass is, bu twhether he referred to mass and whether he and Einstein referred to the samething. Even if one is not inclined to say that Newton knew what mass is, it isstill possible to say that he referred to mass, and saying so might be importantin enabling you to characterize t he tr uth value of his assertions in terms ofreferents of the component terms.

I use these terms more or less interchangeably. (Usually I say that a personrefers, and t ha t the word token he uses in referring to x denotes x.)

6 A physical quantity can be viewed as a function that assigns a value to eachphysical object (or measurable set of spatial points). A quantity-term like 'mass'can take t he role of a function symbol, as in (1) above, or it can ta ke th e role of asingular term, as in the abbreviated form of (I) 'Mass equals twice kinetic energydivided by velocity'. In either case I say th at it denotes the physical quantity.



THEORY CH NGE ND INDETERMIN CY OF REFERENCE 65

and this approximating claim is true according to relativity theory.And there is certainly nothing incoherent in the position t hat Newton

was referring to mass even though he had a great many false-but-approximately-true beliefs about it; indeed, the fact that most ofNewton's beliefs involving 'mass' come ou t approximately-true-though-strictly-false if we regard them as being about mass lookslike evidence for (3) rather than against it .

Nevertheless, there are other considerations about Newtonianphysics and its relation t o special relativity which do call (3) intoquestion: these considerations show, I contend, th at i t simplydoesn't make sense to ask what physical quanti ty Newton and other

pre-relativity physicists referred to when they used the term 'mass'.If one opens a textbook on special relativity, one may find asser-tions such as the following :

R) T h e mass of a particle is equal to th e total energy of the p articledivided by the sq uar e of the speed of l ight. Since the tota l energyof a p art icle with re spect t o one fra m e of reference differs fromthe to tal energy with respect to other fram es of reference, bu t thespeed of light is the sa m e in all fram es of reference, it follows t h a tth e mass of t he par ticle has different values in different fram es.

That's what one will find in some textbooks, but in others one willfind something quite different :

P) The mass of a particle is equal to the nonkineti energy of thepartic le divided by t he squ are of the speed of light. Since th enonkinetic energy of a partic le is the sa m e in all fram es of refer-ence, an d a similar claim holds for th e speed of light, it followsth a t the m ass of the p article has th e sam e value in all frames.

R) and P) appear to conflict with each other; but is this conflictgenuine? A closer examination of the two textbooks will reveal thatboth agree th at the total energy divided by c2 (where c is the speedof light) has a different value in different frames, and t hat the non-kinetic energy divided by c2 has the same value in all frames: per-haps, then, the disagreement is simply over which of these quanti-ties is to be called mass. This hypothesis is confirmed by the factth at the textbooks agree about the ratio of these quantities: theyagree tha t

nonkinetic energy/c2

total energy/c2(where is the speed of the particle). I n fact i t turns out that if youtake any formula of Textbook P (the textbook from which P) wasextracted) and replace 'mass' everywhere by 'mass times dl (v2/c2),



466 THE J O I J R N A I , OF PHILOSOPHY

you get a fornlula th at is acceptable accordiiig to Textbook R ,and if you t ake any formula of Textbook R and replace mass every-where by mass divided by (v3/cZ), you get a formula that isacceptable according to Textbook P. It seems reasonable to say,then, t ha t there are two physical quantities involved here: TextbookR uses the term mass for a quant ity th a t can be called relativisticmass, which is equal t o tota l energy/c2; and Textbook P uses theterm mass for a different quanti ty th a t can be called proper mass,wliicli is equal t o nonkinetic energy/c2. T he appearance of conflictbetween the two textbooks arises solely from the fac t th a t one usesthe word mass for one qua nti ty and th e other uses the same wordfor a different quantity.

Wit h these facts in mind, let us return to t he question of w hatphysical quantity Nexton was referring to when he used the termmass . I t is natural to imagine Physicist R making the following

claim

(3R) Sewton s term mass denoted mass i.e. , it denoted total en-ergy/c2.

Bu t it is equally natural to imagine Physicist P claiming

(3P) Newton s term mass denoted mass i.e., it denoted nonkinetic

energy/c2.Put tin g their claims into unambiguous terminology, we get

(HR) Newton s word mass denoted relativistic mass.

and

(HP) Newton s word mass denoted proper Inass.

How are we to decide between these claims?hIy claim is th a t we can t. Before relativ ity theory was discovered

I will argue) , th e word mass was referentially indeterminate: i t did

not lack denotation, in any straightfor~vard ense; on the contrary,there ar e two physical quantities t ha t each satisfy the normal criter iafor being the denotation of the term. T o put th e point more precisely,let a positive analytical hypotlzesis for Newton s use of t he te rm massbe a sentence of the form

Newton s word mass denoted X.

where X is the name of a physical qu anti ty , and l et the negativeanalytical hypothesis be the sentence

HA) Newton s word mass denoted nothing whatsoever.I claim that the negative analytical hypothesis must be rejected,and so must all positive hypotheses except for (H P) and H R ) . I also



T I I E O RY C H A N G E A N D I N D E T E R h I I h A C Y O F R E F E R E N C E 467

claim that HP) and (FIR) are each extremely plausible (or moreproperly, that each would be extremely plausible were it not for the

existence of the ot he r), and th at there i s n o basis for choosing betweenthem. I t isn't merely t ha t we don't k n o w whether Newton was re-ferring to proper mass or to relativistic mass ; I claim that there i s nojact of the mat ter as to ~ vhi ch f these quantit ies lie was referring to.

T he first point I will argue is tha t the re is no basis for choosi~ig etween (FIR) and B P ) , i.e., for accepting one of these hypotheses andrejecting the other. I n order t o app rec iat e the difficulty of choosing

en-ton-etween them, it is necessary t o k n o x two central tenets ofian mechanics

4 R ) RIolnentum = mats )and

(5P) F o r ny tw o f rames of reference , mass wi th respect to f ram e2= m a s s wi th r e sp e c t t o f r a m e 1.

The first of these was formulated qu ite explicitly in every presenta-tion of Newton's theo ry, often as the definition of mome ntu m; thesecond was considered so obvious t hat it never occurred t o anyone tost at e it, hut certainly an advoca te of the theory would have assented

to it had anyone thought to ask him, and its tru th was presupposedin all of th e theory and practice of Newtonian mechanics. NOW, werethese two tenets of Newtonian mechanics correc t? Th ey c an' t bothhav e been correct ; for, according to relativity theo ry, the momentumof a particle divided by its velocity has different values in differentframe s of reference, whereas (4R) and (5P) together entail that themomentum divided by the velocity has the same value in differentframes.

Relativity theory, then, shows th at the conjunction of the New-

tonian tenets (4R) and (5P) was false; and so it ~vo uld e natural toexpect th at it would also show th a t a particular one of these tenetswas false. Unfo rtuna tely , this natu ral expectation seems to be wrong.For the fact is th at momentum does equal relafi.Llisticmass times ve-locity, and does not equal proper mass times veloc ity; whereas (aswe've seen) relatzhisfic mass does not have the same value in allframes, whereas proper mass does. In other words, some physiciststoday use the word 'mass' in such a way th a t their tokens of (4R)are true and their tokens of (5P) false, and if Newton was using th e

word in the way that they do (i.e., for relativistic mass), then histenet 4R) was true and his tenet (5P) was false. Bu t other physicistsuse th e word 'mass' in such a way th a t their tokens of (4R) are falseand their tokens of (5P) are true, and if Newton used th e word



468 THE J O U R N A L OF PHILOSOPHY

'mass' in the way th at they use the word (i.e., for proper ma ss), the nhis tene t (4R) was false and his tenet (5P) was true.I contend tha t

there is no basis wh atever for decidingbetween these tw o possibilities.The conjunction of New ton s tenets 4R) and ( 5 P ) was objectively

false, but there i s n o fact of the matter a s to wh ich of the conjuncts wa stru e and wh ich false, an d hence no fact of the matter as to whether theword ma ss as it occurred i n them denoted relativistic m as s or propermass.

T h e difficulty of choosing between (H R) a nd (H P) arises, the n,f rom the fact that (4R) and (5P) were both extremely centra l toNew ton's theorizing an d to his scientific prac tice; andI can see no

basis for asserting that a particular one of them was more centralthan the other. Perhaps, however, we could decide between (HR)an d (H P) on the basis of othe r tenets of N ewtonian phy sics?I don ' tbelieve so. Most of thetheoretical claims of Newtonian physics, like

1) and ( 2 ) , come ou t false ( thoughapproximately t rue) w hether wetak e N ewton as referring to re la t ivis tic mass or t o proper ma ss; andmost of Newton's experimental claims, like

(6) T h e m a s s of O b j e c t A i s b e t w e e n 1 .2 1 a n d 1 .2 2 k i lo g r a m s [ s ai da f te r p u t t i n g O b j e c tA o n t o a p a n b a l a n c e a n d a c c u r a t e l y w e ig h -in g i t] .=

come out t rue e i ther way.Another way we migh t t ry to choose between (H R) an d (H P) is to

look, not a t New tonian mechanics, bu t a t special relat iv ity; for ifone were to f ind t h a t one of the q uan ti t ies played a m uch more im-portant role in special relat ivity than the other one played, someprinciple of charity m igh t provide some basis for asserting th a t th e

more imp ortant q uan t i ty was the one tha t Newton was real ly ta lkingabout. Unfortunately, however, proper mass and relat ivist ic massplay a bo ut equally impo rtant roles in special relat ivity theory.Somelaws of ph ysics come o u t looking simpler in term s of relativistic m asstha n in terms of proper m ass th us if we let 'mass' sta nd for relativis-tic ma ss we ge t (4R ), b u t if we let 'mass' s ta nd for proper m ass weget the more complicated formula:

I use here the fact that Newton made experimental asser t ions only aboutobjects tha t were moving slowly (in comparison w ith th e speed of l ight), an d fora slowly moving object the proper m ass and relativistic mass are virtually identi-cal. (I t might be asked Slowly moving with respect to wh at reference fra m e?

No specific frame is mentioned in (6) . But no specific frame is mentioned inassertions like 'Object A is t ravel ing a t 10 f t /sec ' e i ther, an d yet we often adjudi-cate th e t rut h or fals i ty of such assert ions. We d o so by supposing th at on e frameof reference is intended by th e speaker, a n d evaluat ing the t ruth or fals i ty of t heut terance with respect to the intended frame. So the answer to the quest ion is :s low-moving with respect to t he intended frame .)



T H E O R Y CH NCE ND I S D ET E R I vl IN A C Y O F R E F E R E N C E 469

(4P) M o m e n t u m(mass) v

41 V ~ / C Z )

B u t other l a ~ v sof physics come ou t simpler in term s of p roper m assth an in te rm s of relativistic m ass : when 'm ass' st an ds for propermass we get the simple transformation law (5P), but when 'mass 'stands for relativistic mass we get instead

(where v and z are the speeds of the particle in frame and frame2,respectively). Ta ke n togeth er, the laws of special relativity co me ou tlooking just ab ou t as simple when form ulated in ter m s of on e ofthese qua nti t ies as they look when formulated in term s of the oth erqu an ti ty. T his explains why the division between those physicistswho find it more aesthetically pleasing to formulate the theory interms of relativistic mass and those who prefer to formulate it interms of pro per mass is just ab ou t 50/50.

I th ink t h at m y las t four paragraphs m ake i t h ighly plausible th atthere is no basis for choosing between the hypotheses (HP) and( H R ) . B u t this con tention is com patible with a n um ber of positions

which I now wa nt to argue against . Th e f irst posit ion is(H N ) New ton w asn ' t r e fe rr ing e i the r to p rope r mass o r to r e l a tiv i s-

t i c ma ss ; i n s t ead he was r e fe rr ing to a qua n t i ty cal led New-ton ian mass which ha d som e of the proper t ies of each .

(M ore p rec ise ly, N ' ewtonian m ass is equa l t o m om entu m d i -v ided b y ve loci ty-in th is i t i s unl ike proper mass b u t l ikere la t iv is t ic mass . But , unl ike re la t iv is t ic mass , Newtonianmass h as th e sam e va lue in a ll r efe rence f r ames . K ewton ianm a s s a l so h a s s o m e p r o p er t ie s t h a t d i s t in g u is h i t b o t h f r o m

proper m ass and f rom re l a tiv i st i c ma ss : e .g ., i tis

e q u a l t otwice th e k ine ti c ene rgy d iv ided b yv2, a n d i t i s c on s er v ed i na l l in terac t ions . )

T h e view t h a t wh at Piewton was referring to was ' [Ne wto nian mass,as just characterized, seems to be advocated by K uh n. In discussingEinstein 's concepts of space, time, and mass, K uh n w rites:

T h e hysical referentsof t h es e E i n s t e i n ia n c o n c e p t s a r e b y n o m e a n si d en t ic a l w i t h t h o s e of t h e N e w t o n i a n c o n c e p t s t h a t b e a r t h e s a m ename . (New ton ian m ass is conse rved ; E ins t e in i an is conver tib l e wi thenergy . Cop cit. p. 101, emphasis mine]. '

I t is odd that Kuhn adopts this view. Onlya few pages earlier (97) he hadcorrectly asserted Einstein's theory can be accepted only with th e recognitionth a t Newton's was wrong ; bu t if Newton was referring to New tonian m assan d Einstein to Einsteinian mass, both theories would be right.



4 7 THE J O U R N A L O F PHILOSOPHY

B u t this view seems wholly unreasonable, for wh at E instein showedis that there is no such qu ant i ty as New tonian mass ; a nd unless

one holds that the world used to obey Newton's laws but startedobeying Einstein 's laws one da y, i t is clear th at there was no New-tonian mass in Newton's t ime either. I 'm n ot denying th a t in New-ton's time the word 'mass'meant something different than the word'mass' (or its cou nter par ts 'relativistic m ass' an d 'proper mass')means toda y on certain construals of th e term 'meaning' , this seemsto be perfectly true. W h at I 'm denying is not a claim ab ou t meaning,b u t a claim ab ou t reference or den otation: I 'm denying th at there isor ever was such a qu ant i ty as New tonian mass, and hence I 'm

denying th at Newton could have ever referred to New tonian masswhen he used the word 'mass' .Once we've rejected all appea ls to New tonian mass, i t becomes

clear th a t there are no posit ive analytical hypotheses th at a re moreplausible th an (HR ) and HP). B ut now we must examine the nega-tive analytical hypothesis (HA), that Newton's word 'mass ' wassimply denotationless, in the wa y t h at 'Sa nta Claus ' is denotation-less. I claim t h at , if we reg ard N ew ton 's toke ns of 'm ass' a s sim plydenotationless, we are forced t o assign the wrong tru th values to

Newton's sentence tokens.In order to m ake the argum ent good, we have to knowhow a de-notationless term like 'Santa Claus' affects the truth value of sen-tences th at contain i t . One view, sometimes at tr ib ute d to Frege, isth at al l sentences containing denotationless term s lack tr ut h va lue ;anoth er view is t h at sentences containing denotationless terms are al lfalse. If either of these views were true, my argument would besimple: I could merely point out that Newton made many ut ter-ances with th e term 'mass' t h at all cur ren t physicists would agree to,whichever way the y used the term 'mass' . F or instance, he doub tlessmade experimental assertions like 6 , and he doubt less made the-oretical asser tion s like

7 ) T o acclerate a body uniformly between a ny pair of differentvelocities, more force is required if th e mass of the body is greate r.

W hen N ewton made such assertions as these, he would certainlyseem to h ave been saying something tr ue ; an d, since his tokens of

6) and 7 ) were tru e, the tokens of 'mass' th a t occur in them ca n' ts imply have lacked denotat ion in the way th at 'Santa Claus ' lacks

denotation.As i t s tands , the above argument will not d o ; for i t depends on the

view th at a sentence containing a term like 'San ta Claus ' is alwaystruth-valueless or false, andI regard this view a s incorrect. H owever



THEORY CH NGE ND INDETERMIN CY OF REFERENCE 7 I

something lik th a t view is correct , and once we see wha t i t is we cansee how th e above argum ent can be patched u p so th at i t rea lly doesshow th a t Newton s tokens of mass were no t denotationless.

Consider the following three sentences which contain the wordSanta Claus

(8) Sa nta Claus doesn t exist.(9) Johnny saw Santa Claus today.(10) Sa nt a Claus had a wart on his left shoulder.

I would regard t he f irst of these as true , th e second as false, an d t hethi rd as t ruth-valueless. Others m ay have different a t t i tud es toward(9) or ( l o ) , bu t one thing will,I think, be generally agreed: if you

tak e an y other nondenoting s ingular term a nd sub st i tu te i t for San taClaus in 8), (9), and ( l o) , the resul ting sentences will have th esame t ru th value a s the or iginal, or have no t r ut h value if the or iginallacked t ruth value. For ins tance, le t s assume th at Moses doesn tden ote any one; then cer ta inly the sentence

(8 ) Moses doesn t exist.is true. Moreover, anyone who regards (9) as false will also regard

(9 ) Johnny saw M oses today.

as false, an d an yone w ho regards (9) as truth-valueless will regard(9 ) a s truth-valu eless. S imilarly,

(10 ) Moses had a w art on his left shoulder.will appear truth-valueless to those who regard (10) as truth-v alue-ess, a nd false to those who regard (10) a s false. Th ese examples sug-gest t h a t Leibniz s well-known principle

(LL) If two terms each denote the same object, then substitution ofone term for the other (in nonquotational, nonintentional, etc.,contexts) always preserves tru th value.

has a counterpar t for nondenot ing names:

(LL*) If two terms each denote nothing whatsoever, then substitu-tion of one term for the other (in nonquotational, noninten-tional, etc., contexts ) always preserves tru th value (or lack oftruth value).

I thin k t h a t (LL*) accords with nearly everyone s pretheoreticviews as to th e t ru th values of sentences containing term s l ike San taC laus a n d M o s e ~ . ~t i s for tunate t h at th is i s so , for (LL*) is jus t

I t might be objected that Santa Claus fliesreindeer is true, whereas Mosesflies reindeer is not. B u t t seems to me that Santa Claus flies reindeer is trueonly when it is elliptical for The story says that Santa Claus flies reindeer ; n

that sentence, Santa Claus occurs n an intentional context and so is immuneto (LL*).




as impor tan t a principle for the semantics of nondenot ing terms as(LL) is for the semant ics of denoting terms. If two names each have

no denotation whatsoever, they are completely alike from a denot a-tional poin t of v iew; so how could subst ituti on of one for the otheraffect tr ut h va lue? Th e answer t ha t will be given by a ny advocate ofreferential semantics is tha t it cou ldn t: if subst ituti on of one termfor another atiects truth value, these terms must be different fromeach other, denotationally speaking, and that means that they arenot both simply denotationless.

Using this principle, we can sho~v ha t the term mass (as used byS e ~ v t o n ) was no t denotationless. For suppose \Ire replace the wordmass in (6) and (7) by the denotationless term phlogiston ,

getting

(6 ) T h e phlogiston in Object is between 1.21 an d 1.22 kilograms.

and

(7 ) T o accelerate a body uniformly between a ny pair of differentvelocities, more force is required if th e phlogiston in t he bo dy is

greater.

Clearly no one will regard (6 ) or (7 ) as true so if mass were deno-

tationless, then (6) and (7) ~xou ld n t e true either. We re talking, ofcourse, about (6) and (7) as used by Newton: t he analytical hypothe-sis (HA) does not commit us t o the claim t ha t when (7) is used todayit is untrue, bu t only to the claim th a t when (7) was used by ewtonit was unt rue . Bu t even th at seems bad enough-since all relativitytheorists (whether they use mass for proper mass or for relativisticmass) agree to the tr ut h of (7), it seems grossly uncharitable t o den ytha t Newton can have said something t rue by ut tering (7). Similarly,it seems uncharitable to deny that when Newton referred to a slo\v-

moving object whose proper mass and relativistic mass were nearlyidentical and n-ere between 1 . 2 1 and 1.22 kilograms, he could havesaid something true by utteri ng (6). By calling Ne~vt on s tterancesof (6) and 7) false, (HA) conflicts with th e principle of ch ar it y; inthis respect it is vastlyg inferior both to (HR) and to (HP).1°

Note that (HA) is incompatible even with the view that (6) and 7) areapfiroxinzately true; for any approximating claim would also come out untrue ifevaluated according to (HA). Similarly, (1) and 2) come out approximately trueaccording to HP) and (HR) , but not according to (HA). (These remarks holdnot only on the conception of approximate tr ut h introduced earlier, but on any

other conception in which the approximate tr uth of a sentence depends on thedenotations and extensions of i ts parts .)

o I would prefer not to have to rest my argument on th e appeal to charity: Iwould prefer it if I could show that the purpose for which we want the notion oftru th would not be satisfied if we declared (6) and 7) false in these circumstances.

Q



THEORY CHANGE A N D INDETERMINACY O F REFERENCE 47

We now have all the components of t he argument for the referen-tial indeterminacy of Newton's word 'mass'. We've seen that, of all

the positive and negative analytical hypotheses, the only two withany plausibility are (HP) and (HR). Each of these two hypotheseswould be plausible, were it not for the existence of the other, but wehave found no basis whatever for choosing between the two. I t couldbe contended, I suppose, that our inability to choose between (H P)and (H R) is due simply to ignorance-that one of (HP) and (HR) iscorrect and the other incorrect, and the only trouble is that wedon't know which. But the only way to give this contention anyplausibi ity is to state what sort of information is likely to decide be-

tween the two possible denotations; and the only prima facie likelybases of choice which I can think of have been ruled out earlier in thepaper.

I t seems implausible, then, tha t one of (HP) and (HR) is correctand the other incorrect the situation is not tha t we don't know whatNewton's word denoted, but that Newton's word was referentiallyindeterminate. But can this conclusion be tolerated? Surely (HP)and (HR) can't both be correct, and so if it is not the case th at one iscorrect and the other incorrect, it follows that neither (HP) nor (HR)

is correct. Yet we have also rejected all the obvious alternatives to(HP) and (HR) (i.e., the other positive analytical hypotheses, andthe negative one), and this seems to show that there is simply no co-herent way of using the term 'refers' in connection with Newton'sword 'mass'. In spite of this, there are many of Newton's utterancescontaining the word 'mass' that we want to regard as true-(7) wasone example-and there are many also that we want to regard asfalse, e.g., the conjunction of (4R) and (5P). I t follows, then, th atthe truth and falsity of these utterances simply cannot be explained

on the basis of what Newton was referring to when he used the word'mass', for there is no coherent way of explaining what he was refer-ring to. In other words, indeterminacy rules out the possibility ofreferential semantics.

I

In Wo rd and Object Quine wroteIf there were a n unknown [ ideal theory 9 (say a l imit th at

would be attained by applying scientific method forever) which wecould regard as completely true, st ll this would no t set t le the trut h-

I don't know in detail how to show this, but I suspect that by further developingthe remarks on the purpose of the notion of truth in the last section of my Tarskipaper, op cit (and also arguing that we have good reason to suspect that manyof our o w words will someday be in the position that Newton's word 'mass' is intoday), we could get the desired proof.




v a l u e o f] a c t u a l s in g le s e n te n c e s . W e c o u ld n o t s a y t h a t a n ys ing le sen ten ce i s t ru e if i t o r a t r ans la t ion be longs to6 for the re i sin genera l no sense in equ a t in g a sen ten ce of a the ory0 w i t h a s e n t e n c e

g iv e n a p a r t f r o m6. Unless p re t ty f i rmly an d d i rec t ly cond it ionedtosensory s t imula t ion a sen ten ce i s mean ing less excep t r e l a t ive to i t sown the ory meaningless in ter theore t ica l ly 23/4) .

I t is inessential to Quine's claim th at 6 be taken as a limit theory ;we could equally well take to be current scientific theory , which istreated in most contexts as if it were completely true. Quine's pointthen, in the first par t of the passage, is tha t there are sentencesfrom theories not now accepted such th a t (i) we can not equate themwith an y sentences of current scientific theory and (ii) we can no tfind any objective grounds for deciding whether they are tru e of false.The preceding section provides a confirmation of this part of Quine'sclaim both 4R) and (5P) are examples of such an S. In other words,th e observations of th e preceding section show no t only a failure ofthe concept of reference to d o what i t was supposed to do (viz., ex-plain t ru th ), bu t also a failure of the concept of tr ut h a t least as ap-plied to certain single sentences of a theory: Newtonian physics as awhole is objectively false, but there is no fact of the m at te r as to howthe falsity of the theory a s a whole is to be distributed among the in-dividual sentences of th e theory.

Thi s much I agree, but still there is pa rt of Quine's claim that Ido not accept (or even fully understand) the part th at concludesthat is meaningless intertheoretically. In the rest of this paper Iwill sketch a way to handle referential indeterminacy (of the sortwe've been discussing) which does not accord with this last Quineanclaim.

My approach will be to try to preserve as much of referential se-mantics , and of th e claim 3) , as can be preserved in the face of in-determinacy. The argument of the last paragraph of the precedingsection shows, I believe, that there is at present no coherent way ofusing the term 'denotes' in connection with Newton's word 'mass'. Ithink th at in this situation we have to develop a new semantic ter-minology th at is capable of handling referentially indeterminate ex-pressions. Th e terminology I propose is 'partia lly denotes' I want tosay that Newton's word 'mass' partially denoted proper mass andpartially denoted relativistic mass ; since it partially denoted each ofthem, it didn't fully (or determinately denote either.

The novel fea ture of partial denotation is tha t a singular term can

l Except th a t the last sentence holds only if we restrict our consideration tome thods of d istribution th at accord with classical 2-valued seman tics. Thi s willbecome clearer shortly.




P a r t ia l ly d e n o t e more than one t h i n g , and a q u a n t i t y t e r m l ik e masscan P a r t ia l ly d e n o t e m o r e t h a n o n e q u a n t i ty . A t e r m that p a r t i a l l yd e n o t e s m o r e t h a n one q u a n t i ty i s ca l l ed r e fe ren ti a lly inde te rminate12a term that p a r t i a ll y d e n o t e s e x a c t ly o n e q u a n t i t y i s sa i d t ofully ( o rd e te rm i n at el y) d e no te t h a t q u a n t i t y ;and a t e r m that d o e s n t p a r t i a l l yd e n o t e a n y t h i n g i s s a i d to be denota t ionless . I do not try to d e f i n ed e n o te s i n t e r m s o f p a r t i a ll y d e n o te s , f o r I don t t h i n k that t h i s

can be d o n e i n any a c c e p t a b l e way. ( P r o b a b l y t h e best s u c h d ef i ni -t i o n i s to take denotes as e q u i v a l e n t to f u ll y d e n o t e s ; b u t t h i sw o u ld h a v e the u n a t t r a c t i v e f e a t u r e that i n d e t e r m i n a t e t e rms w o u l dnot d e n o t e a n y t h i n g and y e t w o u l d not be d e n o t a t i o n l e s s . ) I find i tm o r e n a t u r a l s im p l y to a b a n d o n the t e rm d e n o te s , e x c e p t whend e a l i n g w i t h terms that are p e r f e c t l y d e t e r m i n a t e ( o r can b e as-s u m e d , i n a g i v e n c o n t e x t , to b e p e r f e c t l y d e t e r m i n a t e ). 1 3

If the term d e no te s i s a b a n d o n e d , w ecan no l o n g er e xp r e s s ( H P ) ,( H R ) , and ( H A ). B u t of c o u r s e we can e x p r e s s c l o s e a n a l o g u e s ofthem, v i z , ,

(HP*) New ton s word mass fu l ly deno ted p rope r ma ss ; i.e ., i t pa r-t ia l ly denoted proper mass and noth ing e lse .

(H R* ) Ne wton s w ord mass fu l ly deno ted re la t iv is t ic m ass ; i .e .,i t pa r t i a l ly deno ted r e l at ivi s ti c m ass an d no th ing e l se .

(HA*) Newton s word mass was den o ta t ion les s ; i. e. , i t d idn tpa r t i a l ly deno te an y th in g a t all .

B u t none o f t h e s e a n a l y t i c a l h y p o t h e s e s a r e a c c e p t a b le ,for p r e c i s e l ythe s a m e r e a so n s that none of ( H P ) , ( H R ) , and ( H A ) w e r e a c c e p t -a b l e . T h e p r o b l e m w i t h ( H P * ) and ( H R * ) i s that each of them d i s -c r i m i n a t e s b e t w e e n proper mass and r e l a t i v i s t i c mass and there ap-

l This definition a nd th at which follows are intended t o apply to termtokensnot to term types. This is necessary in order to distinguish indeterminacy fromambiguity. A term is ambiguous if different tokens of i t have differe nt sem ant ic

featu res; thus mass a s used toda y is ambiguou s, since physicist R s tokensdenote relativistic mass while physicist P s tokens denote proper mass. There isthus a sense in which the term type mass a s used today denotes (and hencepartially denotes) m ore than one thing ; bu t this does not dem onstrate the exis-tence of indeterm inacy or show the failure of re ferentia l sem ant ics ; it merelyshows th at referen tial semantics has to be applied to tokens instead of to types.Fo r a case of in determ inacy one needs to look to pre-relativity physics: hereeach token of mass partially denoted two different quant ities .

l I would defend this last approach on the grounds tha t the word denote isitself referen tially indete rm ina te: it partially signifies th e relation of full denota-tion an d partially signifies the relation of partial d enota tion. For referentiallydeterminate terms, full denotation and partial denotation coincide, and so wecan safely apply the word denotes to these terms without having to take theindeterm inacy of denotes into account. B ut i a term t partially denotes anobject without fully denoting it, the statement th att denotes will lack tr ut hva lue ; an d so to avoid th e complication of truth-valueless me talinguistic sentences,it is best to drop th e indeterminate term denotes .




pears t o be no basis for such discrimin ation. In this respect, (HA*) isbet ter than (HP*) and (HR ) ,bu t only a t a h igh cost : according to

HA*), New ton's word 'mass' bears no seman tic relat ion to any thinga t all , an d a s a consequence 'mass' turns o ut to be just l ike 'phlogis-ton' , d enotat ionally speaking. These objections t o( H P ) , (H R*)an d (HA*) are not shared b y th e new an alytical hypothesis

(HI ) Newton ' s word 'mass ' pa r t i a l ly deno ted p rope r mass and pa r-t i a l ly deno ted r e l a t iv i s t i c mass and d idn ' t pa r t i a l ly deno tean yth ing e lse.

In part icular, (H I) rules th at 'mass' an d 'phlogiston' are not al ike,den otationa lly spe ak ing : for clearly 'phlogiston' either does no t par-

tially denote anything, or else partially denotes a whole bunch ofthings, none of which is either form of mass.

If we acce pt the idea th a t New ton was partially referring to prop ermass and partially referring to relativistic mass when he used theterm 'mass' , which of th ese partia l denotation s ar e we to say affectedth e tru th values of N ewton's utte ran ces ? T h e answer of course isboth. W hen Newton uttered the sentence

SP* M ass i s inde pend ent of t he f ra m e of reference .

did he s ay something t rue? Th e re levant fac ts , you 'l l recall , a re t ha trelativistic mass is not independent of the frame of reference, butproper mass is ; so the answer is tha t when N ewton uttered this sen-tence w ha t he said was so rt of true and sort of false-it was impre -c i se , an d th e imprec is ion mat te red . T he re a re a lso cases where theimprecision does not matter: (7) was such an example, s ince bothth e mo dern analog s of (7) are true .

In order to turn these observations in to an ad equate t ru th defini -tion for sentences containing indeterminate expressions, we have toextend o ur analysis of ind eterm inacy beyond singular term s an dqu an ti ty term s, to other p arts of speech such as general terms, for i tis plausible that indeterminacy can arise in them also. An example,I su spe ct, is th e word 'gene' a s used b y all biologists un til a ve ry fewyears ago: one analytical hypothesis governing the use of this termby earlier biologists is th a t it had th e set of cistrons a s its extension,a second is tha t i t had the se t ofmu tons a s i ts extension, and a thirdis th a t it had th e set of recons a s its extension.14 Th er e is also a neg-ative analytical hypothesis , that the extension of 'gene' was theemp ty set.15 Bu t I think i t could be argued , a s was argued before

l Cf. Kenneth Schaffner, Approaches to Reduction, Philosophy of cience

x x x ~ (June 1967) 137-147, pp. 142 /3; and references cited there.l6 For predicates actually, there are tw possible negative analytical hy-

potheses : (a) that the predicate has the em pty set as its extension, and (b)



THEOR Y CH NGE ND INDETERMIN CY OF REFERENCE 477

with the t erm mass , t ha t the negative hypothesis is inadequate,and that all the positive hypotheses are inadequate too, since theyall ascribe to the word gene (as used by earlier biologists) a de-terminate extension when the word was in fact indeterminate. T ohandle such cases of indeterminacy, I introduce the term partial ex-t ens ion; this allows us to express analytical hypotheses such as

T h e w o r d g e ne h a d t h e s e t of c i s tr o n s a s o n e p a r t i a l ex t e ns i o n, t h es e t of m u t o n s a s a n o t h e r, a n d t h e s e t of r e co n s a s a t h ir d .

I t is convenient also to introduce th e words s igni fy and partiallys igni fy by saying th at a determinate predicate signifies its extensionand tha t an indeterminate predicate partially signifies each of i ts

partial extensions.In order to give a semantics for indeterminate expressions, le t s

introduce the term struc ture ; a structure for a sentence is a functionth at maps each name or qua nti ty t erm of the sentence into some ob-ject or qua ntit y, and maps each predicate into some set. The struc-ture m corresponds to the sentence if each name or quant iy term of thesentence partially denotes the thing t ha t m assigns to i t, and eachpredicate partially signifies the set t ha t m assigns to i t. Now, for eachstruc ture m, we can apply the sta nda rd referential (Tarski-type) se-

mantics to determine whether the sentence is nz-true or nz-false i.e.,true or false relative to m. (To say th at the sentence is m-true is tosay that i t would be true if t he denotations and extensions of i ts termswere as specified by m.) We can then say that a sentence is t rue(false) if i t is m-true (m-false) for every struc tu re m tha t correspondsto it. Putting all these definitions together, we get definitions oftr ut h and falsity in terms of partial denotat ion and partial significa-tion.

A few examples will illustrate how the truth definition works and

show the plausibility of it. Consider first the sentence SP* , nd forthe sake of illustration regard everything after t he mass as a primi-tive predicate. Then there are two structures corresponding to thissentence both assign to the predicate is independent of the frameof-reference the same se t (viz., the set of frame-independent quanti -ties), bu t one (ml) assigns proper mass to mass , whereas the other

mz assigns relativistic mass to mass . Relative to ml the sentenceis true , and relative to m it is false, and , since these relative t ru th

th at i t doesn t have a n extension a t a ll . (b) sounds a bi t more reasonable th an (a),

bu t only because (b) is compatible with th e hypothesis of indeterm inacy set outlater in this pa ragr aph ; (b) is not, in othe r words, a viable alternative t o thehypothesis of in determ inacy, a n y more th an (a) is, for take n b y itself(i.e.,wit hou t use of th e concept of par tial extension) (b) would obli tera te the sem anticdifferences between a ny two referentially in determ inate predicates.



78 THE JOURN L O PHILOSOPHY

values differ, the sentence is n ot determ inately tru e o r false. A simi-lar analys is will show th at (4R) had n o determinate t ru th value for

Newton , bu t t ha t (6) and7 )

were determinately true.Now let s consider sentences in which the same in determ inateterm occurs twice. An interesting exam ple is the conju nction of (4R)and 5P . Again there are two structure s corresponding to th is sen-tence . Rela tive to th e one th a t ass igns proper mass to mass , thefirst conjunct is false and the second true, so th a t th e whole sentenceis fa lse; rela tive to the other s t ructu re the f irst conjunct i s t rue andthe second false, so that again their conjunction is false. The truthdefinition tells us , then, that the con junction of 4R and 5P was false-even though each conjunct lacked truth value (so tha t there is no fact ofthe matter a s to w hich conjunct was false). T h is is precisely th e con clu-sion t h a t seemed desirable earlier.

Finally, we hav e to consider the very imp ortan t case where thereare two different indeterminate expressions in the same sentence.On e such exam ple of d oub le indetermin acy is

11) T h e mass of a gene i s l es s th an a mic rogram.

(as used b y pre-1950 geneticists). H ere th e sem antics says , plausiblyenough, th at the ut terance was t ru e , s ince for c is trons , recons, and

mutons, both the proper mass and relat ivist ic mass are less than amicrogram. B u t it would be well to con sider also a case where a sen-tence conta ins two indeterminate terms f rom the same theory. Inorder to ge t such an example, let us suppose no t only th at was N ew-ton s word mass indeterminate , b ut th a t h is word velocity wasalso indeterminate-it was ind ete rm ina te between rate of change ofdistance w ith respect to norm al time t, and r ate of change of distanc ewith respect to proper t ime T. (Perh aps this is implausible, b u t i t i l-lustrates th e seman tics admirably.) Now let us reconsider sentence

(4R) on this supposit ion. W e find th at , s inced T = dtdl (v2/c2),momentum equa l s ( r e l a t iv i s t i c mass )d x / d t

mo me ntum does no t equa l ( r e la t iv is t i c mass)d x / d T

m o m e n t u m d o e s n o t e q u a l ( p ro p e r m a s s)d x / d t

m o m e n t u m e q u a l s ( p r o p e r m as s)d x / d T

As a result , (4R) comes ou t m -true for two of th e structures m th a tcorrespond to i t and m -false for the o ther tw o; therefore i t comes o uttruth-valueless, just a s i t did before. I t seems to m e th a t this is justw ha t we would intuit ively wa nt to say if we believed th a t mass an dvelocity were both indeterm inate in the way I ve supposed.16

l This m ay perhaps be controversial: some might w ant t o say th at Newton sutterances of (4R) were true, a nd th at only the first and last of the four facts




I think these examples make it plausible t ha t the truth definitionI've given, together with the appropriate hypotheses about what

things the earlier theorist was partially referring to or partially sig-nifying, leads to the sort of results we want. If so, then I have estab-lished the uti lity of the concept of partial denotation in dealing withtheory change, and shown that scientific revolution can affect the se-mantic features of scientific terms in more complicated ways thanmany philosophers have allowed. No longer are we confined to thethree alternatives (i) term t has switched denotations during revolu-tion r [as (HN) held]; (ii) t has acquired a denotation during r [as(HA) held] ; and (iii) t has kept the same denotation through r. Now

there ar e other possibilities, most notably (iv) t has undergone a de-notational rejinement during r ; .e., the set of things t ha t it partiallydenoted after r is a proper subset of the set of things it partially de-noted before. This added possibility is of considerable importance fordebates about incommensurability in science it shows that we canaccept the claim tha t we can 't always equate a term from one theorywith a term from a later theory, and still deny the incommensurabil-ity thesis, i.e., the thesis t ha t the earlier and later terms cannot ob-jectively be compared with respect to referential properties.

I t is worth making two final points about denotational refinement.First, the 'mass' example is not an example of denotational refine-ment pure and simple: it is an example of double rejinement, sincesome physicists have refined 'mass' into a word for relativistic masswhile others have refined i t into a word for proper mass. I hope thatby concentrating on this example I have not obscured the fact thatsimple refinement (where the term is refined in only one direction)is also a possibility. That this really is a possibility should be obvi-ous 'mass' would have undergone a simple refinement rather than a

double refinement if everyone had followed Einstein's example in ad-hering to (4R) and rejecting 5P). Simple refinement will doubtlessbe less obtrusive than multiple refinement (since there will be nolinguistic disagreement resulting from the revolution like the lin-

l isted above ought to be considered relevant t o the t ru th value of these ut terances.In other words, i t might be held that onlycertain com binatio ns of th e partialdenotat ions a nd par t ia l extensions of the term s ought t o affect the t ru th value ofthe whole sentences an d th a t therefore m y semantics needs to be complicated byimposing some restrictions on which com binatio ns are considered.

I don t object to th is content ion in pr inciple, bu tI a lso don t see an y very goodreason for suppo sing it to be true (for th e kind of inde term inacy u nder considera-t ion in this paper) . The re may beother sor ts of indete rmin acy for which th e morecomplicated semantics is necessary, but I will defer consideration of that morecomplicated kind of indeterminacy correlative indeter minac y, I call i t ) to a la terpaper.



48 THE JOURN L OF PHILOSOPHY

guistic disagreement between PhysicistsR and P) ; but i t seemsplausible th a t i t does sometimes occur.17

Second point: if I am right in thinking that denotational refine-m ent is a fairly common feature of scientific revolutions, t h a t sug-gests th a t futu re scientists m ay ve ry well refine m an y of o ur cur ren tscientific term s, an d hence th a t m any of our cu rre nt scientific term sare referential ly indeterm inate. (In fact , induction from the ind eter-minacy of term s in earlier theories may even suggest t h a t science willn v r reach th e stage where all of i ts terms a re perfectly deter min ate.)I do n't think th at this conclusion conflicts with a ny thing th a t is rea-so na bly called scientific realism ; but an adequate discussion of

this m at te r is beyond th e scope of t he presen t paper.I will concludeth e paper b y return ing briefly to t he comparison w ith Quine's viewsbegun earlier in this section.

I

B y modifying th e program of referential sem antics in th e w ayI havesuggested, we come to rath er different conclusions ab ou t indete rm i-nacy from those reached by Quine. Quine think s the existence of in-determ inacy shows th a t scientific term s ar e meaningless [and de-notationless] except relative to [their] own theory; meaningless [and

denotationless] intertheoretically. Th is claim is then used to bu t-tress his tenet th at tru th is im ma nen t [ i.e ., relat ive] to theconceptual scheme '* for the na tural way to get an objective (non-relative) notion of tr ut h is to tr y t o explicate th at notion in terms ofden otation an d signification, bu t if those seman tic notions were alsorelative to th e conceptual scheme then th e desired obje ctivity wouldno t be achieved. Now , wha tI contest in this argu m ent is the assump-tion th a t the sem antic relations of den otation an d signification areinan y interesting sense relative t o th e conceptual scheme ; onmy

T One might even be tempted to speculate tha t all scientific revolutions involvedenotational or significational refinement, but I think that that is unlikely.Consider t he sequence of revolutions leading from Thomson's theory of theatom t o our own. In all these revolutions, it is hard to see any significationalrefinement in the term 'electron': there is nothing th at Thornson can plausiblybe said to have partially signified, beyond th e set of electrons. Moreover, the kindof argument used against (HN) and (HA) rules out t he possibility tha t Thom-son's word signified Thomsonian electrons (things that satisfied all of Thorn-son's beliefs involving 'electron'), or th at it signified nothing a t al l; th e onlyalternative seems to be (iii), that the word kept the same denotation despite theradical change of theory. (Actually the matt er becomes a good deal more com-plicated when one reflects tha t 'electron' might be referentially indeterminatetoday (cf. next paragraph); but even so, the above considerations do not corn-pletely lose their force in showing that scientific revolution is possible withoutdenotational refinement.)

8 Reply to Davidson, p. 304, Synthese X I X 1/2 (December 1968) 303-305.This view is set out more fully in $6 of Word and Object.



481OTES AN D NEWS

view the y ar e perfectly objective relations which hold between term son th e one hand an d extralinguist ic objects or sets of objects on th e

other . T h e existence of referential indeterminacy shows only th a t th erelations of d en ota tion a nd signification ar e n o t well-defined in cer-tain si tuations, an d t h at if we wa nt t o app ly semantics to those si tu-ations we ha ve to invok e the m ore general relations of pa rtial den o-tation and partial signification. But these more general relations(like th e less general on es, in t h e situ atio ns in which those less gen-eral relations are well-defined) are perfectly objective relations be-tween words an d extralinguistic objec ts (or sets of objec ts), an d ar en o t in an y interesting sense relative to th e conceptual scheme.

T h is accou nt of t he differences between Quine's view of ind eter-minacy a nd my own view is m eant only to be suggestive;I will pro-vide a more detailed investigation of th e differences, a nd a n argu -m en t for my view as opposed to Q uine's , in a sequel to this paper.lgI also hope, in the sequel, to extend th e ab ove semantics to certainother sorts of indeterminacy which could not be discussed in thispaper.

HARTRY FIEL

Princeton University

NOTES ND NEWS

Th e Department of Philosophy of the Oh io State University regrets toannounce the death of Arthur Gluck, on January 23 1973. Mr. Gluck, aColumbus industrialist, endowed the Julius Gluck Memorial Library ofPhilosophy at Ohio State and contributed to the philosophy libraries ofseveral other institutions. A constant supporter of philosophy since hisgraduation from Ohio State in 1920 Mr. Gluck was founder and first

president of the Ohio State Philosophy Club and established the BinghamAward for excellent undergraduate work in philosophy at Ohio State.

The newly formed Society for the Advancement of American Philosophyplans two meetings during the Academic year 1973/74. The Society willhold a symposium entitled Ethics at the Eastern Division APA Meetingat Atlanta in December 1973. Th en on March and 2 1974 the Societyfor the Advancement of American Philosophy will meet at VanderbiltUniversity. Th e topic for the two-day meeting will be Human Rights andthe American Tradi tion. Membership is open to anyone interested in

American philosophy. Write to Joseph G. Grassi, Secretary, Department ofPhilosophy, Fairfield University, Fairfield, Conn., 06430.

But sections 111 and of my Tarski's Theory of Truth op. cit. are alsaof considerable relevance to our disagreement.

Theory Change and the Indeterminacy of reference

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Transcript of Theory Change and the Indeterminacy of reference