This paper draws out and connects two neglected issues in Kant’s conception of a priori knowledge. Both concern topics that have been important to contemporary epistemology and to formal epistemology in particular: knowability and luminosity. Does Kant commit to some form of knowability principle according to which certain necessary truths are in principle knowable to beings like us? Does Kant commit to some form of luminosity principle according to which, if a subject knows a priori, then they can know that (...) they know a priori? I defend affirmative answers to both of these questions, and by considering the special kind of modality involved in Kant’s conceptions of possible experience and the essential completability of metaphysics, I argue that his combination of knowability and luminosity principles leads Kant into difficulty. (shrink)

According to the “paradox of knowability”, the moderate thesis that all truths are knowable – ... – implies the seemingly preposterous claim that all truths are actually known – ... –, i.e. that we are omniscient. If Fitch’s argument were successful, it would amount to a knockdown rebuttal of anti-realism by reductio. In the paper I defend the nowadays rather neglected strategy of intuitionistic revisionism. Employing only intuitionistically acceptable rules of inference, the conclusion of the argument is, firstly, not ..., (...) but .... Secondly, even if there were an intuitionistically acceptable proof of ..., i.e. an argument based on a different set of premises, the conclusion would have to be interpreted in accordance with Heyting semantics, and read in this way, the apparently preposterous conclusion would be true on conceptual grounds and acceptable even from a realist point of view. Fitch’s argument, understood as an immanent critique of verificationism, fails because in a debate dealing with the justification of deduction there can be no interpreted formal language on which realists and anti-realists could agree. Thus, the underlying problem is that a satisfactory solution to the “problem of shared content” is not available. I conclude with some remarks on the proposals by J. Salerno and N. Tennant to reconstruct certain arguments in the debate on anti-realism by establishing aporias. (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)

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)

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how (...) we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic. (shrink)

The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.

Verificationism is the doctrine stating that all truths are knowable. Fitch’s knowability paradox, however, demonstrates that the verificationist claim (all truths are knowable) leads to “epistemic collapse”, i.e., everything which is true is (actually) known. The aim of this article is to investigate whether or not verificationism can be saved from the effects of Fitch’s paradox. First, I will examine different strategies used to resolve Fitch’s paradox, such as Edgington’s and Kvanvig’s modal strategy, Dummett’s and Tennant’s restriction strategy, Beall’s paraconsistent (...) strategy, and Williamson’s intuitionistic strategy. After considering these strategies I will propose a solution that remains within the scope of classical logic. This solution is based on the introduction of a truth operator. Though this solution avoids the shortcomings of the non-standard (intuitionistic) solution, it has its own problems. Truth, on this approach, is not closed under the rule of conjunction-introduction. I will conclude that verificationism is defensible, though only at a rather great expense. (shrink)

The best defense of the doctrine of the Incarnation implies that traditional Christianity has a special stake in the knowability paradox, a stake not shared by other theistic perspectives or by non-traditional accounts of the Incarnation. Perhaps, this stake is not even shared by antirealism, the view most obviously threatened by the paradox. I argue for these points, concluding that these results put traditional Christianity at a disadvantage compared to other viewpoints, and I close with some comments about the extent (...) of the burden incurred. (shrink)

The Fitch paradox poses a serious challenge for anti-realism. This paper investigates the option for an anti-realist to answer the challenge by restricting the knowability principle. Based on a critical discussion of Dummett's and Tennant's suggestions for a restriction desiderata for a principled solution are developed. In the second part of the paper a different restriction is proposed. The proposal uses the notion of uniform formulas and diagnoses the problem arising in the case of Moore sentences in the different status (...) propositional letters receive. The new proposal is able to avoid some of the criticism on its predecessors. (shrink)

In light of the paradox of knowability anti‐realists ought to revise their wholesale equation of truth and knowability, lest they be committed to the absurd conclusion that there are no truths that will never be known. The task accordingly becomes to identify the problematic statements the knowability of whose truth would force that conclusion and to restrict the equation in appropriate ways to all but the problematic statements. This restriction strategy was first implemented by Tennant. However, recently Williamson and Brogaard (...) and Salerno have argued that the restriction strategy, and in particular Tennant's implementation of it, fail to avert the paradoxical conclusion. Here I argue, first, that the arguments devised by Brogaard and Salerno are ineffective because they rely on an invalid closure principle and, second, that while Williamson's argument may suffice to undermine Tennant's specific proposal, it fails to discredit the restriction strategy as such. To this end, I give a better characterisation of the problematic cases, which is immune to Williamson's criticism, and then show how the restricted anti‐realist thesis fares in light of the meaning‐theoretical arguments anti‐realists typically advance in support of their view. (shrink)

The thesis includes six essays, each corresponding to a chapter, which have the target of widening the discussion on the limits of knowability through the consideration of some general problematics and the discussion of specific topics. The work is composed of two parts, each of three chapters. In the first part, the discussion is focused on a perspective proper of the philosophy of language. In particular, I consider the discussion on the limits of knowability from the point of view of (...) the debate between semantic realism and antirealism. The second part of the thesis is focused on the discussion on the limits of knowability from a perspective more strictly epistemological and proper of the philosophy of science. (shrink)

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)

In light of the paradox of knowability anti‐realists ought to revise their wholesale equation of truth and knowability, lest they be committed to the absurd conclusion that there are no truths that will never be known. The task accordingly becomes to identify the problematic statements the knowability of whose truth would force that conclusion and to restrict the equation in appropriate ways to all but the problematic statements. This restriction strategy was first implemented by Tennant. However, recently Williamson and Brogaard (...) and Salerno have argued that the restriction strategy, and in particular Tennant's implementation of it, fail to avert the paradoxical conclusion. Here I argue, first, that the arguments devised by Brogaard and Salerno are ineffective because they rely on an invalid closure principle and, second, that while Williamson's argument may suffice to undermine Tennant's specific proposal, it fails to discredit the restriction strategy as such. To this end, I give a better characterisation of the problematic cases, which is immune to Williamson's criticism, and then show how the restricted anti‐realist thesis fares in light of the meaning‐theoretical arguments anti‐realists typically advance in support of their view. (shrink)