EDDY M. ZEMACH

THE WORLD IS TOO MUCH

According to Putnam, the notion of the world as it is in itself is incoherent.There can be no full description of the world as it really is but many incom-patible true world-descriptions, and there is no way to adjudicate betweenthem: even God could not decide between some competing accounts of theworld, for there is no one way the world really is. Had Putnam composedWordsworth’s famous poem he may have written it thus:

The World is too much with us; late and soonGetting and spending, we lay waste our powersLittle we see in Nature that is NOT ours.

In this paper I examine two of Putnam’s proofs that true world-descriptionsmay yet be incompatible with each other: the Basic Objects Argument(BOA)1 and the Deviant Interpretation Argument (DIA).2 First, BOA:

Consider a world with three individuals . . .x1, x2, x3. . . . Suppose, for example, that likesome Polish logicians, I believe that for every two particulars there is an object which istheir sum. . . . I will find that the world . . . containssevenobjects. . . . Now, the classicmetaphysical realist way . . . is to say that there is a single world (think of this as a piece ofdough) which we can slice into pieces in different ways. But this “cookie cutter” metaphorfounders on the question, “What are the ‘parts’ of the dough?” If the answer is that . . .x1,x2, x3, x1 + x2, x1 + x3, x2 + x3, x1 + x2 + x3 are all the different “pieces” then wehave not aneutraldescription, but rather apartisandescription – just the description of theWarsaw logician! And it is no accident that metaphysical realism cannot really recognizethe phenomenon of conceptual relativity – for that phenomenon turns on the fact thatthelogical primitives themselves, and in particular the notion of object and existence, have amultitude of different uses rather than an absolute “meaning”.

Putnam claims that the basic concepts of ontology used by Carnap andby the Polish logician are logically incompatible. Carnap’s basic conceptis individual and of those there are three in the assumed worldW , whilethe Polish logician’s basic concept isobject, and of those there are seven inW . Hence, these views are not commensurable: Putnam says that Carnapand the Polish logician cannot state their differences in a neutral languagethat is acceptable to both.

Suppose the Polish logician does hold that the 7 objects inW are allequally basic, andx1 6= x2 6= x3 6= x4 6= x5 6= x6 6= x7. In that case, the

Synthese120: 411–418, 1999.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

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view Putnam attributes to the Pole, that “for every two particulars there isan object which is their sum”, i.e.,

AXIOM 1:

(x)(y){(x 6= y) ⊃ (∃z)[(z = x + y)& (z 6= x)& (z 6= y)]},

yields absurd results. If the sum ofeverytwo distinct objects is a third thatis distinct from both, then not onlyx1 + x2, for example, is a new object,x4, that is distinct from bothx1 andx2, but alsox1 + x7, e.g., is a newobject (call it ‘x8’) that is distinct from bothx1 andx7. And so forth and soon, ad infinitum. It follows thatW has infinitely many objects and not justseven. But that is not what the Polish logician believes. Thus, the view thatPutnam attributes to the Polish logician is inconsistent. Rather, the situ-ation is this: Carnap talks of basic entities only, calling them ‘individuals’.The Polish logician calls these entities ‘atomic objects’, but adds that therealso are nonbasic entities, defined as sums of atomic objects; these he calls‘nonatomic objects’. The Polish logician agrees with Carnap that there areonly 3 individuals (atomic objects) inW . Had he denied that, he couldnot obtain the result that there are exactly 4 nonatomic objects inW . Forexample, mereologists hold thatx1 + x7 is not a new object,x8, but justx7 all over again. How can that result be obtained unless Carnap’s thesis,that there are only 3 Individuals (atomic objects) inW , is expressed in thelanguage of the Polish logician?

Axiom 1, then, does not correctly represent the Polish view, that whileevery sum of atomic objects (Carnap’s Individuals) is a new object, notevery sum of nonatomic objects is a new object. The correct formulationof that view is, rather,

AXIOM 2:

(x)(y){(Ix) & (Iy) & (x 6= y) ⊃ (∃z)[(z = x + y) & (z 6= x)& (z 6= y) & (∼I2)]}

The disagreement between the Polish logician and his opponent is,therefore, not about basic entities; they agree that of those there are 3and only 3 inW . The neutral formulation of the disagreement betweenthe Carnapian and the mereologist is, then, this: Are nonatomic objects(nonbasic entities) genuine objects too? The Polish logician calls bothbasic and nonbasic entities ‘objects,’ and therefore concludes that thereare 7 objects inW . His adversary (Putnam calls him ‘Professor Antipode’)thinks that the category of objects in general (atomic and nonatomic ones)is bogus, for, given individuals, one need not accord any ontological status

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to their sums. Is this a fundamental impasse, a basic ineffability excludinga nonpartisan description ofW? Let us listen to Antipode:

I know what you’re talking about if by an object you mean a cat,or a bee, or a human being, or the Eiffel Tower. . . . But whenphilosophers say that there is an “object” consisting ofthe Eiffeltower and my nose, that’s just plain crazy. There simply is nosuch object.

Need the Polish logician disagree? Not at all. He grants that sums are notbasic ontologically; that is a distinction he must insist on in order to countno more than 7 objects inW . So if Antipode distinguishes between verit-able individuals and mere sums (Roderick Chisholm, the closest real-worldcounterpart of Professor Antipode I know, calls the latter ‘conjunctiva’)the Polish logician is right there with him. Calling conjunctiva ‘objects’the Pole may still distinguish genuine objects (e.g., cats and bees) fromnongenuine ones (e.g., the sum of a cat and a bee). If Antipode riles thatconjunctiva are not truly objects for they are not ontologically basic, aPolish logician may just give him theword ‘object’ and use another, ‘F ’,instead. Antipode will have to agree, then, that there are 7Fs in W , ifindividuals and conjunctiva alike areFs. Disagreement on how to use theword ‘object’ (whether to apply it to conjunctiva or not) does not justifythe radical conclusion Putnam draws from it. That quibble is no reason toforego realism. Putnam’s claim that it makes no sense to ask “How manyobjects are there inW ”3 is, then, unjustified.

Putnam’s best known argument against realism is DIA. I quote:

[L]et T1 be an ideal theory, by our lights. . . . We can imagineT1 to have every propertyexcept objective truth– which is left open – that we like. For example,T1 can be imaginedcomplete, consistent, to predict correctly all observation sentences . . . to meet whateveroperational constraints there are . . . to be beautiful, simple, plausible, etc. The propositionunder consideration is thatT1 might be all thisand still be(in reality) false.. . . Pick out a modelM of the same cardinality as THE WORLD. Map the individuals ofM one-to-one into the pieces of THE WORLD, and use the mapping to define relations ofM directly in THE WORLD. The result is a satisfaction relation SAT – a correspondencebetween the terms ofL and sets of pieces in THE WORLD – such that the theoryT1comes out true – true of THE WORLD – provided we just interpret “true” as TRUE(SAT).So what becomes of the claim that even theideal theoryT1 might really be false?4

All and only the theorems ofT1 are TRUE(SAT); since “T1 has the prop-erty of meeting alloperationalconstraints,”5 Putnam argues that the claimthat TRUE(SAT) is not truth because SAT is not the intended satisfactionrelation is unintelligible.

Strictly speaking, what is satisfied in THE WORLD isT1I1: The theory

T1 under the interpretationI1. Some philosophers argue thatT1 may still be

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false because under some interpretation other thanI1 it comes out false,6

but Putnam replies that all we mean by saying a theory is true is thatthere is an interpretation under which it comes out true. Realists maintainthat a theory, that successfully negotiates all operational and theoreticalconstraints, has yet a major hurdle to overcome: correspondence to reality.Putnam says that this is no hurdle at all, for any c&cc (consistent and ofcorrect cardinality) theory is satisfied in reality under some interpretation.Correspondence is easy: a theory that meets the theoretical criteria is con-sistent; if it also has enough signs, there is an interpretation under which itis true, even if it is interpreted by an arbitrary assignment of objects to itssingular terms. Therefore, the requirement, that a methodologically goodtheory should also correspond to reality, is trivially met.

Putnam’s model-theoretical argument (DIA) generated much interest;the literature on it is copious. I shall not examine it any further, however,partly because Putnam has already refuted most of it, and partly becausemy reply takes an entirely different line – and is simpler – than extantobjections to DIA.

I claim that, given a body of formalized sentences constituting a theoryT , how to interpret it is a question for another theory, INT. INT investigatesusers and uses of the terms inT and proposes an assignmentI of com-plaints to the names and predicates inT . Like all theories, INT is subjectto theoretical and operational constraints: to pass muster it must, as Putnamputs it in the passage quoted above, “be beautiful, simple, plausible”. Thatterms inT1 be interpreted by assignmentI1 is a theorem of INT1 and isjustified only if INT1 is a good theory, that is, if it is prettier, simplerand more plausible than its alternatives. Putnam has shown that ifI1 is anarbitrary assignment of objects to the terms ofT1, T1 can still be satisfied inreality, but he did not show that the choice ofI1 to interpretT1 is justified,that is, that the theory INT1, which sanctions interpretingT1 by I1, is ourbest theory of interpretation. Clearly, that need not be the case.

Some thinkers try to rejectI1 on the ground that it is not what weintendedT1 to mean. Putnam answers that the only way to specify whatT1 is to mean is by language, and language is subject to unintended inter-pretations. Some of those thinkers reply that intending an interpretation is anonlinguistic, “magical” relation between interpreter and text; you directlyintend interpretationI1 for T1. Putnam, however, rejects such magical,nonlinguistic intending-relation as a myth. He concludes that, if all c&ccinterpretations ofT1 are equally legitimate, requiringT1 to be satisfied inreality is pointless, for every c&cc theory is satisfied in reality under someinterpretation. That makes correspondence to reality a pointless test, forno c&cc theory can fail it. Is realism doomed, then? No; I suggest that

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an interpretationI1 may be rejected forT1, not because you just magically“know” what interpretation is intended forT1, but becauseI1 is not the bestinterpretation ofT1. The theory, that sanctions interpretingT1 by I1, maybe a bad theory. That defeats Putnam’s argument, because the question,which theory is best, is never trivial, and deciding it requires no magic.

The wayward interpretation given in Chapter 2 ofReason, Truth andHistory is a perfect example of an interpretation that fails the theoreticalconstraints. It ingeniously interprets ‘cat’ as denoting cats∗, that is, in real-ity, cherries. Yet the very ingenuity of that interpretation inveighs against it:clever it surely is, but simpler or prettier than its alternatives it is not. Thecategorycats∗ is convoluted and unintuitive, hence a theory that assignscats∗ to ‘cat’ is an inferior theory. The definition of ‘cat∗’ takes Putnamten lines of tangled prose that, for humanitarian reasons, I spare the reader.ThusI1, which interprets our word ‘cat’ to mean cats∗, is unintuitive andperverse: we cannot learn to identify cats∗ by ostensive definitions. The setof cats∗ is a hodge-podge of dissimilar entities, having no unity or intuitiveappeal to us; it is as ugly as sin.

In the early seventies Putnam himself held that assigning a referencerelation, that is, an interpretation, to a theory, is a theoretical problemwhose solution is subject to the usual nontrivial constraints. Yet later heabandoned that view, alleging that it begs the question in two ways.

The first way is reminiscent of Goodman: Goodman answers those whocharged that in defining ‘grue’ and ‘bleen’ he uses, hence presupposes,‘green’ and ‘blue’, that ‘green’ and ‘blue’ may be defined by ‘grue’ and‘bleen’. Putnam’s move is similar: ‘cat’, he says, may be defined by meansof ‘cat∗’, so the conceptcat does not presuppose the conceptcat∗: eitherone may be taken as basic. But that is irrelevant to my objection. I didnot claim thatcat∗ presupposescat; I said that the theory, that ‘cat’ meanscats∗, is ugly, becausecat∗ is an unintuitive category. Putnam may retortthat cat∗ seems ugly only to us; those who use SAT to define referencewill find cat∗ prettier thancat. We find it natural to identify cats, theyfind it natural to identify cats∗. To them, the conceptcat∗ is plain whilethe conceptcat is unintuitive and gerrymandered. Suppose it is so; that isirrelevant to my point. The theory it behooves us to prefer is the onewefind most elegant; we should adopt theories we find most simple, unified,predictively powerful and rich enough to encompass our experience. Thata theory we find pretty may seem otherwise to another kind of creature isneither here nor there.

Putnam’s second way is of Quinean design. I claimed that an interpret-ation that assigns cats to ‘cat’ is theoretically preferable to one on which‘cat’ refers to cats∗. That, Putnam says, begs the question, for we cannot

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tell which term refers to which entity. The very question, whether by ‘cat’I referred to cats or to cats∗, is senseless. All evidence about interpretationis based on people’s assenting to and dissenting from sentences, and thatevidence is compatible with either interpretation of ‘cat’. There is no factof the matter which entity ‘cat’ refers to. Both hypotheses (that it refersto cats and that it refers to cats∗) are senseless, for either interpretationis necessarily equally supported by the evidence. Referential opacity isunavoidable.

I answer that unless there is a difference between these assignmentsPutnam’s argument cannot get off the ground. Löwenheim and Skolemproved that a theory can be satisfied in different domains; unless one under-stands how these domains differ one fails to understand the proof. Putnam,too, assumes that we can tell how cats differ from cats∗; otherwise, he hasno argument. Yet once we know how the set of cats differs from the set ofcats∗ (e.g., the first includes no cherries) we can evaluate interpretationsthat assign them to ‘cat’, and find thatI2, which assigns cats to ‘cat,’ issuperior toI1 which says that ‘cat’ denotes cats∗.

Putnam considered that move but rejected it on the ground that theor-etical constraints on interpretation can also be trivially satisfied by givingthem a deviant interpretation. In “Realism and Reason” he uses that ployon the causal theory of reference, according to which a term denotes thatobject which stands to it in the causal relation C. Putnam says that con-dition can be trivially met by assigning to ‘causes’ some epistemicallyequivalent relation that has nothing to do with causality. The same tactics,he thinks, can be used on metalinguistic terms that state theoretical con-straints: for example, assign to ‘simplicity’ not simplicity but simplicity∗,a totally different relation. First, he suggests:

The alternative is not to give up the search for a physicalistic theory of the reference rela-tion, but rather to look for a physicalistic relation which hasexplanatory value. . . . Whathappens if we impose pragmatic constraints – plausibility, preservation of past doctrine,simplicity – as additional requirements on a good explanation?7

Then, he rejects the suggestion:

What is expressed by the “simpler”, “more plausible”, etc., sentences of the metalanguagedepends on what thereal reference for the metalanguage is; and our problem, for themetalanguage as much as for the object language, was how . . . this could be singled out.. . . Simplicity, plausibility, and preservation of past doctrine make sense from the point ofview of the universe onlyif the metalanguage has a singled-out reference relation “fromthe point of view of the universe”.8

That, Putnam rightly says, is absurd. To know what Simplicity and Plaus-ibility are we need to know what relation maps the terms ‘simple’ and‘plausible’ onto the world. It does not help to define that relation as what

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the simplest and most plausible interpretation assigns to these terms, for toknow which interpretation is simplest and most plausible we need to knowwhat ‘simple’ and ‘plausible’ mean, and that depends on the relation usedto map the terms ‘simple’ and ‘plausible’ onto the world!

Putnam proved that a theoryT1 can get two interpretations,I1 andI2,that assign to predicates inT1 distinct sets ofn-tuples in some worlds, yetfor every worldW , TI1 is true inW iff TI2 is true inW . That result, hethinks, also applies to the metalanguage in which it is couched. Does it?I think not. The proof will still go through (a logically valid proof is notaffected by change of interpretation) but we no longer knowwhatit proves:does it prove that terms may be deviantly interpreted without affectingthe truth-value of sentences in which they occur, or that terms∗ may be∗deviantly∗ interpreted∗ without affecting∗ the truth-value∗ of sentences∗in which they occur∗? Putnam’s needs the first interpretation, for underthe second the proof says nothing about reference: we know not what itsays. Furthermore, if Putnam’s proof is not valid, but only valid∗ (whateverproperty that is), why pay any attention to it? That is, if Putnam proves thatwhat he says need not have the sense we think it has, we have no reason tobelieve that what he says need not have the sense we think it has.

Putnam may argue that Skolemization is only areductio ad absurdumof the classic theory of sense.If the sense of a term depends on its denota-tion, then terms have no sense; but terms do have sense; therefore, a term’ssense is fixed by its use and not by assigning it a reference. But that argu-ment is beside the point. Putnam assumes thatT1 meets the theoretical andoperational constraints better than other theories, i.e., it is the best theory.Therefore, Putnam must grant that we can rank theories by their simplicity,unity, elegance, etc. however these metalinguistic terms are interpreted. Yetif we can find thatT1 is a better theory thanT2, we can also find that INT2is a better theory than INT1, and if INT1 is an inferior theory (as shown bythe fact that it offers to interpretT1 by I1, which assigns cats∗ to ‘cat’) wehave a very good reason to reject it.

Putnam may shift referents around as long as he leaves truth-valueintact. But in order to treat all interpretations ofT1 as equal he needs totamper with the truth-value of the statement that INT2 is a better theorythan INT1, or else with the inference from that statement to the operationalconclusion that terms inT1 be assigned the objects specified byI2 ratherthan those specified byI1. Let me use ‘>’ for ‘is better than’; Putnamholds that ‘T1 > T2’ can be empirically established, and that ifT1 > T2

then we are justified in usingT1 rather thanT2 as our world theory. INT2 >INT1 has the same status: we evaluate competing theories of interpretationin the way we evaluate all other competing theories, and if we find that

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INT2 > INT1 we should useI2, rather thanI1, to interpretT1. Thus, ifT1

comes out true underI1 and false underI2, that is not good enough forestablishing the truth ofT1, for the interpretation under which it comes outtrue is inferior to the interpretation under which it comes out false. Becausenot all interpretations are equal, satisfaction under an inferior interpretationdoes not establish the truth of a theory. Correspondence to reality underthe best interpretation is not trivial at all: it is a hurdle that an otherwiseideal theory (one that meets all the theoretical and operational constraints)still needs to negotiate. Metaphysical realism, as defined by Putnam, istherefore vindicated.

NOTES

1 The Many Faces of Realism, Open Court, 1987, pp. 18–21. Expanded version: ‘Truthand Convention’, inDialectica 41, 69–77 (69–77), and inRealism With a Human Face,Harvard University Press, 1990, 96–104.2 ‘Realism and Reason’, inMeaning and the Moral Sciences, Routledge & Kegan Paul,1978, 123–38; ‘Models and Reality’, inJournal of Symbolic Logic15, 464–82;Realismand Reason(Vol. 3 of Philosophical Papers), Cambridge University Press, 1983, Chapter1; Reason Truth and History, Cambridge University Press, 1981, Chap. 2, ‘Modal Theoryand the “Factuality” of Semantics’,Words and Life, Harvard University Press, 1994, 351–75.3 The Many Faces of Realism, p. 20.4 Meaning and the Moral Sciences, pp. 125–6.5 Ibid.6 See, e.g., William P. Alston,A Realist Conception of Truth(Cornell University Press,1995), Chapter 5: ‘Putnam’s Model-Theoretic Argument’; especially pp. 138–9.7 ‘Model Theory and the “Factuality” of Semantics’, inWords and Life, HarvardUniversity Press, 1994, pp. 355, 357.8 Ibid., p. 358.

Department of PhilosophyHebrew University of JerusalemJerusalem 91905IsraelE-mail: mseddy@pluto.huji.ac.il