Review: [Untitled] Reviewed Work(s): Anti-realism and Logic. Truth as Eternal by Neil Tennant W. D. Hart The Journal of Symbolic Logic, Vol. 54, No. 4. (Dec., 1989), pp. 1485-1486. Stable URL: http://links.jstor.org/sici?sici=0022-4812%28198912%2954%3A4%3C1485%3AAALTAE%3E2.0.CO%3B2-2 The Journal of Symbolic Logic is currently published by Association for Symbolic Logic.
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/asl.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.
The JSTOR Archive is a trusted digital repository providing for long-term preservation and access to leading academic journals and scholarly literature from around the world. The Archive is supported by libraries, scholarly societies, publishers, and foundations. It is an initiative of JSTOR, a not-for-profit organization with a mission to help the scholarly community take advantage of advances in technology. For more information regarding JSTOR, please contact
[email protected].
http://www.jstor.org Sun Sep 2 01:13:36 2007
1485
REVIEWS
book under review he aims to explicate this "ill-defined idea" by developing its implications, one of which "is the emphasis on appropriate selections and arrangements" (p. x). At a more specific level, he hopes to focus on the "inadequacies [of analytic philosophy] to what we know" while contrasting it with his alternative perspective, "which at present remains more definite in its applications than in its articulate formulation." The author believes that he has obtained "a pretty conclusive refutation of the position, represented in different forms by Carnap and Quine,. . . along a line explained all too briefly by Godel" (pp. x-xi). Although the book contains a fairly detailed historical account of many of the views held by Russell, Wittgenstein, Carnap, and Quine, its author did not intend it as a history of the analytic movement in philosophy (or even the strand of it he dubs "analytic empiricism"). Rather his aim was to show us the various alternative paths analytic empiricism might have taken. He also states: "A major theme of the present book is that analytic empiricism does not and cannot give an adequate account of mathematics" (p. xii). The book opens with an introductory chapter that not only maps the territory to be covered but also presents the author's most succinct and precise statement of his refutation of analytic empiricism. According to the author, the problem with both Carnap's logical positivism and Quine's "logical negativism" is that each sees mathematics asdevoid of content. The latter does so by denying the analyticsynthetic distinction (and the existence of conceptual intuition as a source of knowledge in mathematics and logic), the former by identifying mathematical truths with those generated axiomatically from a set of conventions. In contrast to this, the author holds (apparently along with Godel) that logic, which he defines as the general theory of concepts, includes mathematics; that mathematics and logic are analytic in the sense that their assertions are true by virtue of the meaning of the concepts occurring in them; and, for this reason, mathematics and logic contain contentful assertions. The author concludes his introduction with a general metaphilosophical discussion. He characterizes Quine's and Carnap's positions as contractions in philosophy, that is, as movements that truncated the scope and methods of philosophy. He regards this as a turn for the worse and tries to use his historical examination to show where analytic philosophy went wrong. This examination starts in the next chapter on Russell. The author quotes with approval Santayana's evaluation of Russell: "He ought to have been a leader, a man of universal reputation and influence.. .. Yet on the whole, relative to his capacities, he was a failure" (p. 49). According to the author, after Russell wrote the Principia mathematica he sought in vain projects that would be both as definite and as important as his great work on logic. Unfortunately, he clung to empiricism and fell under the influence of Wittgenstein. This all but set the fatal course for Carnap to follow. With Wittgenstein's influential characterization of logic and mathematics as a system of empty tautologies there was no turning back. The author recounts this in a chapter on Wittgenstein. In the next chapter he explains how Carnap responded to the Russell- Wittgenstein project, and in the long sequel to that he describes the debacle of the program in Quine's hands. In the final short chapter the author records a number of "metaphilosophical observations." The book contains as much history of logic in both its formal and philosophical aspects as it contains straight history of philosophy. Readers of this JOURNAL might find interesting the author's discussions of the various systems of logic of Russell, Quine, Wang as well as his evaluation of Carnap, Tarski, and Quine as logicians. The author'scommand of the history of the movement hereviewed and thedepth of his understanding of its doctrines is most impressive. Although several of his more specific evaluations of analytic empiricism are quite plausible, this reviewer would have welcomed a more careful articulation of the author's D. RESNIK MICHAEL own views and arguments. NEIL TENNANT.Anti-realism and logic. Truth as eternal. Clarendon library of logic and philosophy. Clarendon Press, Oxford University Press, Oxford and New York 1987, xii 325 pp. Once upon a time one was taught that Brouwer urged abandoning classical logic by blaming it for the paradoxes of set theory. Subsequent events, such as the articulation of Zermelo-Fraenkel set theory, made the critical strategy imputed to Brouwer seem like using cannon to hunt sparrow. Since the logic and mathematics approved by those calling themselves intuitionists seemed so ugly, and in particular so to obscure under a fog of negation signs glories convincingly revealed classically, it then became natural to wonder whether there is any good reason for bothering with intuitionist logic and mathematics. But
+
1486
REVIEWS
Michael Dummett kept the ball in play. It is hard to be sure (and this may help keep the ball in play), but an outline of Dummett's position seems to be that there is a correct choice of logic, that which logic is correct is fixed by meaning, that meaning cannot "transcend verifiability, and that consequently intuitionist logic is to be preferred to classical. Neil Tennant follows the first three of these lines, but concludes that we are entitled to less than full intuitionist logic; we should also for the sake of relevance avoid the so-called paradoxes of implication associated with C. I. Lewis. Tennant does not deny us the right to say that there are stars independent of us out there in spacetime. But he does deny us the right to assert without further ado that either there are infinitely many stars in spacetime or there are not. Anti-realism in logic (and, it seems, mathematics, though Tennant seems less explicit about this) can go with thorough-going realism elsewhere. Logic is in this special position because it is answerable to meaning, which is our creature, and we are not entitled to mean anything by negation and disjunction that would enable us to assert without further ado that either there are infinitely many stars in spacetime or there are not. Onemight then expect by way of justification for this thesis at least statements of the meanings of these connectives, some sort of derivation from those statements of the laws of logic in which those connectives are salient, and a proof that the law of the excluded middle, or bivalence as Tennant calls it, is not so derivable. But like most who claim that logic answers to meaning, Tennant asserts that the meanings of logical constants are given, indeed constituted, by certain rules of inference. On page 151 he denies that this constitution impugns the claim that his rules are responsible to an antecedent notion of meaning. But if we cannot separate the meanings of negation and disjunction sufficiently from the laws of logic, then how are we supposed to see what laws are justified by those meanings, and that bivalence is not among them? Suppose we give two correct deductions of a claim, one from a supposition and the other from its negation, but we can prove neither the supposition nor its negation. One classically inclined should then be willing to assert the claim outright, and thus that it is true (Tennant accepts this last sort of inference on page 130). It would seem that this truth is objective only if there is out there a chunk of reality independent of us by virtue of which the claim is true. This independence from us requires that is not depend for its existence on even the possibility of our knowing it to exist. But in Chapter 14, Tennant seems to contend that the claim depends for its meaning on at least the possibility of our "direct" epistemic access to that in virtue of which it is true. (See especially page 152. In Chapter 11, Tennant replies to criticism of Dummett by Colin McGinn by distinguishing the possibility of discovering a verification from the possibility of checking a verification, and requiring only the latter for meaning; but how trustworthy is a check on verification that does not enable one to recover the verification?) Requiring for meaning, and thus truth, the possibility of "direct" verification seems to undermine objective truth. Perhaps it is no accident that Dummett, and Wittgenstein before him, seem to flirt with idealisms more wholesale than Tennant's. Tennant separates from Dummett over relevance. On page 239 he says he has earlier given an argument for relevant logic based on the compositionality of meaning. But when one looks back through the text, it is very hard to find the argument to which he refers. In Chapter 17 there is an assertion that compositionality requires intuitionist logic also to retract for the sake of relevance; but it is very hard to see any argument here or elsewhere. He tells us that intuitionistic logic comes from his favoured logic by permitting inference from "the absurd proposition" to whatever one likes. "Given a proof of the absurd, say whatever you please" seems to be a statement of an algorithm that, given per impossibile a proof of the absurd, yields a proof of whatever one likes. Why isn't our having, and having recognized as such, an algorithm for this empty computable function a sufficient justification for the rule by which Tennant distinguishes intuitionist logic? Part of why the tempest in the British teapot over realism versus anti-realism seems so hard to follow may be that everyone tries to unload the burden of proof on someone else; the less one shoulders, the less is accomplished. So where Dummett seemed to promise a positive defense of intuitionism, we get criticism to the effectthat the realist has not refuted the anti-realist. Tennant speculates on the evolution of quality control on the flow of information (a kissing cousin of meaning of which he makes free use) among us, but there is more of this "You can't catch me" than one would like in his book. It is also striking that his text of a bit more than 300 pages is divided into twenty-six chapters. Many short chapters can signal a highly cumulative and restrained progression of argument, but too often Tennant does not take care to show us that he is not simply wandering around. W. D. HART
