Frederic Fitch’s celebrated reasoning to the conclusion that all truths are known can be interpreted as a reductio of the claim that all truths are knowable. Given this, nearly all of the proof’s reception has involved canvassing the prospects for some form of verificationism. Unfortunately, debates of this sort discount much of the philosophical import of the proof. In addition to its relevance for verificationism, Fitch’s proof is also an argument for the existence of God, one at least as strong (...) as the traditional demonstrations. Perhaps unlike other such proofs, Fitch’s also operates as a key lemma in a proof that establishes that God can’t exist. (shrink)

In ``Revising the Logic of LogicalRevision'' J. Salerno attempts to undermineCrispin Wright 's recent arguments forintuitionism, and to replace Wright andDummett's arguments with a revisionary argumentof his own. I show that Salerno's criticismsof Wright involve both attributing an inferenceto Wright that no intuitionist would make andfallaciously treating a negative universal asan existential negative. Then I show how verygeneral considerations about the nature ofwarrant undermine both Wright and Salerno'sarguments, when these arguments are applied todiscourses with defeasible warrants. WhileSalerno explicitly restricts his (...) discussion tomathematics, Wright and Dummett intend theirrevisionary arguments to have much widerscope. (shrink)

Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the right-hand side of each biconditional clause is understood as subject to the laws of intuitionistic (...) logic.2 The only other principle in play in Dummett’s discussion is (+) A iff Tr(A), which, as he notes, the anti-realist is likely to accept. (shrink)

A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.

This paper addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalised, contributes towards the solution of the other two. The key to this response is a generalised conception of indeterminacy as a specific kind of intellectual bafflement-Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as (...) liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, e.g., matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight. (shrink)

The paper responds to Neil Tennant's recent discussion of Fitch's so-called paradox of knowability in the context of intuitionistic logic. Tennant's criticisms of the author's earlier work on this topic are shown to rest on a principle about the assertability of disjunctions with the absurd consequence that everything we could make true already is true. Tennant restricts the anti-realist principle that truth implies knowability in order to escape Fitch's argument, but a more complex variant of the argument is shown to (...) elicit from his restricted principle exactly the consequences which it was intended to avoid. (shrink)

The naive anti-realist holds the following principle: (◊K) All truths are knowable. This unrestricted generalization (◊K), as is now well known, falls prey to Fitch’s Paradox (Fitch 1963: 38, Theorem 1). It can be used as the only suspect principle, alongside others that cannot be impugned, to prove quite generally, and constructively, that the set {p, ¬Kp} is inconsistent (Tennant 1997: 261). From this it would follow, intuitionistically, that any proposition that is never actually known to be true (by anyone, (...) at any time) is false; and it would follow, classically, that every truth is known (by someone, at some time). (shrink)

Using a quantified propositional logic involving the operators it is known that and it is possible to know that, we formalize various interesting philosophical claims involved in the realism debate. We set out inferential rules for the epistemic modalities, ranging from ones that are obviously analytic, to ones that are epistemologically more substantive or even controversial. Then we investigate various aporias for the realism debate. These are constructively inconsistent triads of claims from our list: a claim expressing some sort of (...) common ground in the debate; a characteristically anti-realist thesis about truth and knowability; and a characteristically realist thesis about determinacy of truth value. Various patterns of reductio proof for these inconsistent triads are generated, so as to display their variety. The reductio proofs use only the inferential rules set out earlier. The philosophical utility of each aporia for the anti-realist is then assessed. This involves consideration of the acceptability of the premiss expressing common ground; the strength and plausibility of the anti-realist premiss; the strength of the realist premiss that is the ultimate target of the reductio; and the analytic status of the inferential rules applied within the proof. (shrink)

To save antirealism from Fitch's Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennat's yields a non-ad hoc solution to (...) Fitch's Paradox; and third, the alternative is only apparently weaker than, and even provably equivalent to, Tennant's. It is thereby shown that the latter is not ad hoc after all. (shrink)

An interesting recent reply to the Paradox of Knowability is Neil Tennant's proposal: to restrict the anti-realist's knowability thesis to truths the knowing of which is logically consistent. However, this proposal is egregiously ad hoc unless motivated by something other than the wish to save anti-realism from embarrassment. We examine Tennant's argument that his restriction is motivated by parallel considerations in cases that are neutral with respect to debates about realism. We conclude that the cases are not neutral, nor the (...) considerations parallel. The failure of Tennant's argument provides an opportunity to reflect on, among other things, the nature of Moore's paradox, and the role of idealization in doxastic logic. (shrink)

An interesting recent reply to the Paradox of Knowability is Neil Tennant's proposal: to restrict the anti-realist's knowability thesis to truths the knowing of which is logically consistent. However, this proposal is egregiously ad hoc unless motivated by something other than the wish to save anti-realism from embarrassment. We examine Tennant's argument that his restriction is motivated by parallel considerations in cases that are neutral with respect to debates about realism. We conclude that the cases are not neutral, nor the (...) considerations parallel. The failure of Tennant's argument provides an opportunity to reflect on, among other things, the nature of Moore's paradox, and the role of idealization in doxastic logic. (shrink)

The paradox of knowability poses real difficulities to our understanding of truth. It does so by claiming that if we assume a truth is knowable, we can demonstrate that it is known. This demonstration threatens our understanding of truth in two quite different ways, only one of which has been recognized to this point in the literature on the paradox. Jonathan Kvanvig first unearths the ways in which the paradox is threatening, and then delineates an approach to the paradox that (...) solves both of the problems raised by the paradox for our understanding of truth. His book will be of interest throughout philosophy, but especially to logicians and epistemologists. (shrink)

Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...) sound contradictory. In this context the factivity of ‘someone might discover that’ explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). (shrink)