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)

According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable and (...) (ii) their conjunction is equivalent to p. I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very di:erently depending on another thesis connecting knowledge and possibility. If there are two propositions, inconsistent with one another, but both knowable, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is weak. (shrink)

This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox.

Since its disc overy by Fitch, the paradox of knowability has been a thorn in the anti-realist's side. Recently both Dummett and Tennant have sought to relieve the anti-realist by restricting the applicability of the knowability principle -- the principle that all truths are knowable -- which has been viewed as both a cardinal doctrine of anti-realism and the assumption for reductio of Fitch's argument. In this paper it is argued that the paradox of knowability is a peculiarly acute manifestation (...) of a syndrome affecting anti-realism, against which Dummett's and Tennant's manoeuvres are not finally efficacious. The anti-realist can only cope with the syndrome by being much clearer about her notion of knowability. In fact, she'll have to offer an account which relativises the notion of knowability both to the world at which knowability is assessed and to the content of the proposition to which it is applied. This is not, however, merely an ad hoc manoeuvre to counter the problematic syndrome; rather it is just what we should expect from the anti-realist's intuitive use of the notion. A preliminary investigation indicates that there is no way of providing a general, systematic explanation of such a notion of knowability and thus an inherent restriction on the principle of knowability -- but one differing from those offered by either Dummett or Tennant -- is developed. (shrink)

The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand what (...) the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view. (shrink)

According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable and (...) (ii) their conjunction is equivalent to p. I show that the conjunctive knowability thesis avoids triviality arguments against it, and that it fares very di:erently depending on another thesis connecting knowledge and possibility. If there are two propositions, inconsistent with one another, but both knowable, then the conjunctive knowability thesis is trivially true. On the other hand, if knowability entails truth, the conjunctive knowability thesis is coherent, but only if the logic of possibility is weak. (shrink)