The most puzzling and intriguing aspect of intuitionism as a philosophy of mathematics is its claim that classical deductive reasoning in mathematics is illegitimate. The two most well-known proponents of this position are L. E. J. Brouwer and Michael Dummett. Both of their criticisms of the use of classical logic in mathematics have, by and large, been taken to depend on the thesis that the principle of bivalence does not apply to mathematical statements; and the difference between these criticisms is (...) taken to consist in their grounds for this thesis. Brouwer bases this thesis on an account of the nature of mathematics: it is an activity of mental construction essentially independent of language. Dummett, in contrast, bases the thesis on his anti-realist view of the nature of meaning. ;My first principal argument in this essay shows that the conception of anti-realism just outlined is problematic as a reading of Dummett. To begin with, Dummett explicitly rejects, not only the evidentiary restrictions of this conception, but also, more seriously, the use of specific epistemological theses in a philosophical account of meaning. Moreover, I give an alternative account of anti-realism, consisting of alternative interpretations of the manifestation requirement and of the rejection of realist truth conditions, that do not rely on an epistemology of meaning, and hence, a fortiori, not on evidential restrictions. ;My second principal argument in this essay consists of drawing a consequence of this conception of anti-realism, namely, that the failure of bivalence cannot, by itself, support a cogent criticism of classical logic. The basic reason is that, given my view of anti-realism, the claim that the legitimacy of applying classical reasoning to a class of statements depends on whether bivalence applies to that class already implies that the system of deductive reasoning applying to these statements is non-classical. Hence an argument against classical logic based on this claim is question-begging. ;Finally, I conclude by showing that Dummett's criticism of classical reasoning, as reconstructed by my third argument, fails. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Using Stanley CavellMichael FischerContending with Stanley Cavell, edited by Russell B. Goodman, 205 pp. Oxford: Oxford University Press, 2005, $45.00Reading Cavell, edited by Alice Crary and Sanford Shieh, 262 pp. London: Routledge, 2006, $120.00Stanley Cavell, edited by Richard Eldridge, 260 pp. Cambridge: Cambridge University Press, 2003, $24.99.Stanley Cavell often speaks of inheriting and carrying on the work of Ludwig Wittgenstein, Ralph Waldo Emerson, Henry David Thoreau, and other (...) writers. These writers help him move on in his own thinking, turning him around when he feels lost, provoking him when he gets discouraged or stuck. His indebtedness to J. L. Austin in the acknowledgements to Must We Mean What We Say? (1969) captures one way he benefits from all the writers who have influenced him: "To the late J. L. Austin I owe, beyond what I hope is plain in my work, whatever is owed the teacher who shows one a way to do relevantly and fruitfully the thing one had almost given up hope of doing."1 By taking up the work of the writers he values, Cavell hopes to undo what he sees as their neglect and misappropriation by the culture at large and by the academic profession. He makes his case for these writers not so much by exhortation as by his own use of them.The impact of Cavell's own writing on his readers continues to unfold, as these three books attest. Each is a helpful collection of essays by scholars in various fields discussing his work. Reading Cavell includes [End Page 198] an essay by Cavell ("The Wittgensteinian Event"), as does Contending with Stanley Cavell ("Passionate and Performative Utterance: Morals of Encounter"), which also features a response by Cavell to the other essays in the volume.The contributors in these three volumes all begin from the assumption that Cavell, like the writers who have influenced him, remains marginalized even though interest in his work has grown. But his isolation can be overstated. In an otherwise insightful essay on Cavell's literary criticism ("The Avoidance of Stanley Cavell" in Contending with Stanley Cavell ), Garrett Stewart laments "the regrettable undercirculation of Cavell's ideas" (p. 140) in literary studies and predicts that "mainstream literary scholars will increasingly have a hard time" with his writing—Stewart calls it "literary prose"—because it calls on reading skills that in the "epoch of cultural studies, discourse analysis, and the semiotics of social energy" have "atrophied" (p. 153). In the introduction to this same volume, Russell Goodman offers a more measured, less pessimistic assessment that gets Cavell's peculiar professional status exactly right: "Cavell occupies a curious position in all the fields in which he works: he is at the same time a major figure and one whose work people do not quite know how to use" (p. 3).In figuring out how to use Cavell, several contributors to these volumes begin by explicating his key ideas and texts. The writers in Stanley Cavell assess his contributions to several broad areas, including ethics, theory of action, philosophy of mind and language, aesthetics, and Shakespeare criticism. Reading Cavell and Contending with Stanley Cavell include essays on such central topics as his view of skepticism and his understanding of the ordinary. Of special note is Stephen Mulhall's close reading of the opening of The Claim of Reason, "On Refusing to Begin," in Contending with Stanley Cavell. One barrier to using Cavell remains his style, which readers either love or hate. Mulhall shows that the very features of Cavell's writing that some readers find most annoying—for example, his penchant for complicating and qualifying even the apparently most obvious point—in fact instruct us in how to read him. Mulhall astutely describes The Claim of Reason and Philosophical Investigations as modernist texts written in the absence of philosophical conventions that the writers can take for granted. Such writing must resemble "a half-built edifice whose form acknowledges both its origin in ruins and the completion it foreshadows" (p. 32)—but never attains.In addition to explicating Cavell, other contributors to these volumes extend his work to texts and issues he does not address. These... (shrink)