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Analyticity, Undeniability, and Truth

Published online by Cambridge University Press:  01 January 2020

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In his 1970 book Philosophy of Logic, Quine propounds what he calls ‘the deviant logician’s predicament’: when a reformist logician tries to deny a law of classical logic, he succeeds only in changing the subject. This position, summed up in the aphorisms’ deny the doctrine and change the subject’ and’ an illogical culture is a mistranslated one,’ has struck many of Quine’s readers as backsliding. The old Quine denied that any statements whatever are analytic in the sense of being true solely in virtue of what they mean; the new Quine holds that certain laws of logic cannot be denied without changing the meanings of the logical connectives. Does not the position of the new Quine invest logical laws precisely with the status ‘true solely in virtue of what they mean’?

Type
Research Article
Copyright
Copyright © The Authors 1992

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References

1 Quine, W.V.Philosophy of Logic (Englewood Cliffs, NJ: Prentice-Hall 1970), ch. 6Google Scholar

2 Putnam, Hilary’Two Dogmas” Revisited,’ in Realism and Reason (Cambridge: Cambridge University Press 1983), 87-97, at 92;CrossRefGoogle ScholarHaack, SusanDeviant Logic (Cambridge: Cambridge University Press 1974), 15;Google ScholarDummett, MichaelIs Logic Empirical?’ in Truth and Other Enigmas (Cambridge, MA: Harvard University Press 1978), 269-89, at 270Google Scholar

3 The ‘old Quine’ is of course the Quine of Two Dogmas of Empiricism,’ first published in 1951 and reprinted in From a Logical Point of View (New York: Harper Torchbooks 1963), 20-46. The views of the ‘new Quine’ (as Adam Morton points out in ‘Denying the Doctrine and Changing the Subject,’ The Journal of Philosophy 70 [1973] 503-10) actually go back at least to 1954. See Quine’s, Carnap and Logical Truth’ in The Ways of Paradox (New York: Random House 1966), 100-25, esp. 102 and 105.Google Scholar

4 There does appear to be at least one respect in which Quine has reversed himself. The Quine of ‘Two Dogmas’ held that no statement is immune to revision, not even the law of excluded middle. The Quine to be discussed here holds that the laws of classical logic cannot be rejected without changing their meanings, and that makes them unrevisable in the only relevant sense of ‘revision.’

5 The retained laws include the standard introduction and elimination rules for the logical constants, which in the opinion of some philosophers are the only laws that are essential to the meanings of the logical constants. See, for example, Putnam, HilaryThe Logic of Quantum Mechanics,’ in Mathematics, Matter, and Method (Cambridge: Cambridge University Press 1975), 174-97Google Scholar, and Tennant, NeilAnti-Realism and Logic (Oxford: Clarendon Press 1987), ch. 9.Google Scholar

6 In conversation, Felicia Ackerman has objected to principle A on the ground that there are logical and arithmetical operations that are equivalent (hence subject to the same laws), yet different in cognitive meaning, such as single and triple negation, subtracting a number and adding the corresponding negative number, etc.

7 Levin, MichaelQuine’s View(s) on Logical Truth,’ in Essays on the Philosophy of Quine, W. V.Shahan, R.W. and Swoyer, C. eds. (Norman, OK: University of Oklahoma Press 1979), 45-67Google Scholar

8 Quine, W.V.Word and Object (Cambridge, MA: MIT Press 1960), 59Google Scholar

9 I am setting aside here any verificationist doctrine that would admit no distance between ‘it could never be rational to believe p’ and ‘p could not be true.’

10 See Philosophy of Logic, 82 and 96-7.

11 He considers them under the same heading on 51-3 of ‘Quine’s View(s).’

12 See Quine, W.V.Replies to Eleven Essays,’ Philosophical Topics 12 (1981), esp. 231-3.CrossRefGoogle Scholar At 232 Quine says, ‘The reconciliation, as I see it, is as Levin suggests. In conformity with the empirical view we may in an extremity rescind a logical principle, and in so doing we do not contravene the mistranslation view as long as we do not adopt a contrary principle.’

13 Morton suggests that Quine wishes to oppose weak deviance (refusing to assent to a classical law) as well as strong deviance (assenting to its negation).

14 ‘Observing our laws’ is ambiguous; it can mean affirming them, manipulating symbols in accordance with them, or simply not denying them. The differences among these three do not matter for the present point, which is that none of them guarantees that the laws in question are true.

Incidentally, some readers may wonder how Quine, the repudiator of modality, can affirm either 1 or 2 given that each contains a ‘necessarily.’ I suspect the answer is that he cannot, in which case to get a consistent Quine we would have to retreat all the way back to Levin’s first reconciliation, back to the Humean version of the mistranslation thesis that merely says it is improbable that anyone should take exception to our logical principles. As we saw, however, Quine gives every impression of wanting to say something stronger- something not properly expressible without using modal operators.

15 Philosophy of Logic, 96

16 If you think the phrase ‘right-minded’ deflects my point, note that the translation argument makes the phrase redundant: a wrong-minded man would be a misunderstood one.

17 Pap, ArthurSemantics and Necessary Truth (New Haven: Yale University Press 1958), 123Google Scholar

18 Pap, 169. I venture to suggest that the conflation I am targeting may also be made by those writers who gloss Quine’s challenge to the analytic-synthetic distinction as a challenge to the distinction between change of meaning and change of belief. For how is the latter challenge supposed to be tantamount to the former? Evidently, those who equate the challenges are presupposing that a sentence S is analytic for a person J iff no person K (who could be a different person or J himself at a later time) could deny S without attaching to it a different meaning from that which J gives it. If (as many contend) there is no saying whether a difference in the verdicts K and J offer on S represents a difference in belief or a difference in meaning, it would then follow that there is no saying whether S is analytic. My point in the text is that the connection between analyticity in this sense and analyticity in the sense of ‘truth by virtue of meaning’ is problematic.

19 I find at least a hint of this objection in the first note appended to Putnam’s, HilaryThere is at Least One A Priori Truth,’ in Realism and Reason (Cambridge: Cambridge University Press 1983), 98-114, at 110-11.CrossRefGoogle Scholar

20 This assumes that if asserting ‘not-p’ changes the subject, so does asserting ’possibly, not-p.’

21 A referee has raised the following objection: suppose one held that every law of logic is undeniable and also that every law of logic is possibly false. Then one would have to say of any particular doctrine that one recognized as a law of logic (excluded middle, let us say) that it is both undeniable and possibly false, thus falling into precisely the paradox I am discussing. Reply: Perhaps Quine holds that every law of logic is possibly false, but I do not; I only hold that undeniability does not entail truth.

22 Prior, A.N.The Runabout Inference Ticket,’ Analysis 21 (1960)CrossRefGoogle Scholar

23 Davidson, DonaldThe Method of Truth in Metaphysics,’ reprinted in Inquiries into Truth and Interpretation (Oxford: Clarendon Press 1984), 199-214, at 200-1.Google Scholar There is another presentation of the argument in ‘A Coherence Theory of Truth and Knowledge,’ reprinted in Truth and Interpretation, LePore, Ernest ed. (Oxford: Basil Blackwell 1984), 307-19, at 317.Google Scholar

24 Note the nested modalities in this formulation. Quantifying over possible worlds, we would put it this way: given any world w in which a person S has a system of beliefs, there is a world w’ in which S’s beliefs are as before and an omniscient and infallible interpreter interprets his utterances. We need not suppose that w’ = w; that is, we need not suppose that every world, or every world with believers, contains an omniscient interpreter. (Thus we may give a negative answer to the title question of Richard Foley and Richard Fumerton’s ’Davidson’s Theism?’ Philosophical Studies 48 (1985]83-9.) We do need to suppose, however, that the contents, truth values, and linguistic hook-ups of S’s beliefs are the same in w’ as in w; otherwise, we would not be capturing Davidson’s claim that anyone’s beliefs and utterances must be interpretable such as they are.

25 From 1 and 3, it follows that there is a world w in which a law L is false, but correctly interpreted by infallible interpreter J; adding 2, we have it that in w J believes L; so J believes a falsehood.

26 It may appear that this argument works only if logical laws enjoy necessity of acceptance. What if, as in Levin’s reading of Quine, their only privilege is impossibility of denial? The answer is that we can still reach an absurdity, though not the same one as before. The contradiction is no longer that an infallible interpreter believes something false, but that an omniscient interpreter is debarred from believing something true (viz., that law Lis false). Alternatively, the contradiction is that J knows L to be false (because Lis false and J is omniscient), yet cannot believe L to be false (because L is undeniable).

27 On this point, see Grandy, RichardReference, Meaning, and Belief,’ The Journal of Philosophy 70 (1973) 439-52.CrossRefGoogle Scholar

28 If this point is not clear, consider the following syllogism: anyone who interprets our law L correctly takes it to mean what we mean by it (tautology); anyone who takes L to mean what we mean by it accepts it (Quine); therefore, anyone who interprets L correctly accepts it. If we substitute ‘does not deny’ for ‘accepts,’ the rest of the argument must proceed as in note 26, above.

29 Somewhat more accurately: there are worlds w such that worlds like w except for containing infallible interpreters are impossible.

30 Kim, JaegwonConcepts of Supervenience,’ Philosophy and Phenomenological Research 45 (1984) 153-76CrossRefGoogle Scholar

31 If it is held that indexical terms can be alike in meaning yet different in their reference, then what I just said must be restricted to indexical-free sentences.

32 This is not quite Kim’s ‘strong supervenience,’ for which we would need to put another ‘necessarily’ in front of the entire thesis just stated.

33 Two modal assumptions come into play here: (1) what is necessary is necessarily necessary, and (2) if p and q together entail rand q is necessary, then p by itself entails r.

34 I wish to thank Felicia Ackerman, Anthony Appiah, Carl Posy, Ernest Sosa, and two referees for helpful comments and criticisms.