Quine and the Limit Assumption in Peirce's Theory of Truth

Quine and the Limit Assumption in Peirce's Theory of TruthAuthor(s): Richard CreathSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 90, No. 2 (May, 1998), pp. 109-112Published by: SpringerStable URL: http://www.jstor.org/stable/4320842 .

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RICHARD CREATH

QUINE AND THE LIMIT ASSUMPTION IN PEIRCE'S THEORY OF TRUTH

(Received in revised form 13 September 1996)

ABSTRACT. Quine rejects Peirce's theory of truth because, among other things, its notion of a limit of a sequence of theories is defective in that the notion of a limit depends on that of "nearer than" which is defined for numbers but not for theories. This paper shows that the missing definition of "nearer than" applied to theories can be supplied from within Quine's own epistemology. The upshot is that either Quine's epistemology must be rejected or Peirce's pragmatic theory of truth is partially vindicated.

As is well known, Quine rejects Peirce's pragmatic theory of truth. In fact, in Word and Object Quine mentions four arguments against it, one of which is that

There is a faulty use of numerical analogy in speaking of a limit of theories, since the notion of limit depends on that of "nearer than," which is defined for numbers and not for theories. (Quine, 1960, p. 23)

It is the contention of this paper that the missing definition of 'nearer than' applied to theories (and hence of 'limit' applied to theories) can be supplied from within Quine's own epistemology. This means that if the above argument against Peirce is to be accepted, then Quine's epistemology must be rejected. More positively put, this paper provides a partial vindication of a pragmatic theory of truth given the intelligibility of Quine's epistemology.

Quine states both Peirce's theory of truth and his own objections to it quite succinctly:

Peirce was tempted to define truth outright in terms of scientific method, as the ideal theory which is approached as a limit when the (supposed) canons of scientific method are used unceasingly on continuing experience.' But there is a lot wrong with Peirce's notion, besides its assumption of a final organon of scientific method and its appeal to an infinite process. There is a faulty use of numerical analogy in speaking of a limit of theories, since the notion of limit depends on that of "nearer than," which is defined for numbers and not for theories. And even if we by-pass such troubles by identifying truth somewhat fancifully with the ideal

Philosophical Studies 90: 109-112, 1998. ? 1998 Kluwer Academic Publishers. Printed in the Netherlands.



110 RICHARD CREATH

result of applying scientific method outright to the whole future totality of surface irritations, still there is trouble in the imputation of uniqueness ("the ideal result"). For, as urged two pages back, we have no reason to suppose that man's surface irritations even unto etemity admit of any one systematization that is scientifically better or simpler than all possible others. It seems likelier, if only on account of symmetries or dualities, that countless alternative theories would be tied for first place. Scientific method is the way to truth, but it affords even in principle no unique definition of truth. Any so-called pragmatic definition of truth is doomed to failure equally. 'Peirce, vol. 5, paragraph 407. (Quine, 1960, p. 23)

The two objections very briefly touched on in the second sentence of the paragraph are distinctly minor. It is far from clear whether the first really arises or whether the second is really problematic. In any event, I shall not discuss them here.

The objection, taken up beginning with the fourth sentence, that there may be no unique result of scientific method, is not minor at all. In the decades since Word and Object was published, however, this objection has had a curious fate. Quine himself took up the question of what relation there might be between these various ideal outcomes, and his answers have oscillated. (Quine, 1986, pp. 155- 7, 1990a, pp. 14-5, and 1990b) He has held successively: that the outcomes are just distinct, that they can be joined into one super- theory, that they cannot be so joined, and finally that the outcomes are merely notational variations of one another even though the variations admit of no sentence by sentence mapping or translation. Having commented elsewhere (Creath, passim) on these changes in Quine's outlook, I need say here only that if the latest version holds there is not much left of this objection to Peirce.

What does not disappear in all this is the worry from the third sentence of the paragraph that the idea of limit in Peirce's notion of truth makes no sense when applied to theories. This, too, is a very serious worry, and Quine is not the only one to be concerned by it. (Cf. Scheffler, p. 72) Very possibly a pragmatic theory of truth can be reformulated so as to avoid appealing to limits. But in this paper, however, I shall accept the challenge and show that the concept of limit can be defined using only concepts already available within Quine's own epistemology.

The epistemology is readily summarized: Beyond the obviously sound advice to choose only theories consistent with the empirical evidence, there are two principles: simplicity and conservatism. Other things being equal, we should choose the simplest of avail-



QUINE AND THE LIMIT ASSUMPTION IN PEIRCE'S THEORY OF TRUTH I l l

able theories, and other things being equal we should choose theories which involve the least revision from our antecedent views. Now the principles of simplicity and conservatism often pull us in opposite directions, but such are the dangers of a scientific life.

While the notions of simplicity and conservatism are much discussed, they are little defined. Let us suppose for the time being that this latter task can be accomplished. If the principle of conservatism is indeed intelligible, there has to be some sense to the idea that one theory is a more conservative modification of our current theory than is a second theory. This is, in effect, a three-place relation among theories, that is among our current theory (whatever it may be) and two available modifications thereof. More specifically the three-place relation is a relation of greater similarity which might well be expressed by the phrase 'nearer than' in such contexts as "A is nearer to B than to C" where A, B, and C are theories.

So far I have only highlighted some of the obvious features of Quine's epistemology: that one of its two pillars is a principle of conservatism and that this involves, at the very least, a three-place nearer than relation among theories. It remains only to show that this is sufficient to define the requisite notion of limit. I could, of course, cite Quine as an authority here since the very sentence of Word and Object which expresses his objection to the limit notion also tacitly concedes that, given a nearer than relation, the notion of limit is indeed definable. We need not rely on authority, however, for the requisite definition is not difficult to devise. A theory T is the limit of a sequence theories iff for any theory T', where T $ T' there comes a point in the sequence such that for any theory T" thereafter in the sequence T" is a more conservative modification of T than T' is of T. This definition of limit follows quite closely that of Weierstrass even though the present one relies only on comparative notions rather than on quantitative ones.

Plainly, Quine is in no position to complain against this that his notion of conservatism is so undefined, so vague, or so rarely applicable that it cannot be used in such a definition. Vaporous the notion of conservativism may be, but if Quine is to employ it in his account of the apparent necessity of mathematical truth, then he must at least insist on its intelligibility. Nothing more is required for the above definition. This is because my argument has been only



112 RICHARD CREATH

that Peirce's idea of the limit of a sequence of scientific theories is itself meaningful or at least as much so as Quine's various notions are. I do not claim that the actual development of science will be a sequence having a limit or that we can now or ever know such to be the case. The only issue under contention is the intelligibility of Peirce's conception.

It has not escaped my attention that, besides providing a definition of the limit of a sequence of theories and therewith of truth along Peirce's lines, these devices may be useful in providing explications of the notions of approximation to truth which are much discussed in the literature on scientific realism. This, however, is not the place for such further explorations.

I recognize moreover that the definitions provided do not settle the question of the viability of Peirce's conception of truth. First, there are other objections that I have not tried to address. Even more to the point, I have, as lately noted, attempted only a relative adequacy argument: Peirce's notion of limit is at least as adequate as Quine's notion of conservatism. This leaves open the possibility that the latter has serious defects. Making such a claim, however, is not open to Quine, for conservatism is not a dispensable feature of his epistemology. Perhaps a relative adequacy argument is all we can ever hope for on behalf of a concept, but even if it is not, for the moment it will have to do.

REFERENCES

Creath, R. (1990): 'Camap, Quine and the Rejection of Intuition', in R. Barret and R. Gibson (eds.), Perspectives on Quine, pp. 55-66, Oxford: Basil Blackwell.

Quine, W.V.O. (1960): Word and Object, Cambridge, MA: M.I.T. Press. Quine, W.V.O. (1986): 'Reply to Roger F. Gibson, Jr.', in L.E. Hahn and P.A.

Schilpp (eds.), The Philosophy of W. V Quine, pp. 155-157, La Salle, IL: Open Court.

Quine, W.V.O. (1 990a): 'Three Indeterminacies', in R. Barret and R. Gibson (eds.), Perspectives on Quine, pp. 1-16, Oxford: Basil Blackwell.

Quine, W.V.O. (1990b): 'Comment on Creath', in R. Barret and R. Gibson (eds.), Perspectives on Quine, p. 67, Oxford: Basil Blackwell.

Scheffler, I. (1974): Four Pragmatists, New York: Humanities Press.

Department of Philosophy Arizona State University Tempe, AZ 85287-2004 USA



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Quine and the Limit Assumption in Peirce's Theory of Truth