When a theory is confronted with a problem such as a paradox, an empirical anomaly, or a vicious regress, one may change part of the theory to solve that problem. Sometimes the proposed solution is considered ad hoc. This paper gives a new definition of ‘ad hoc solution’ as used in both philosophy and science. I argue that a solution is ad hoc if it fails to live up to the explanatory requirements of a theory because the solution is not (...) backed by an explanation or because it does not diagnose the problem. Ad hoc solutions are thus magical: they solve a problem without providing insight. This definition helps to explain both why ad hoc solutions are bad and why there may be disagreement about cases. (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)

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)

Husserl endorses ideal verificationism, the claim that there is a necessary correlation between truth and the ideal possibility of experience. This puts him in the company of semantic anti-realists like Dummett, Tennant, and Wright who endorse the knowability thesis that all truths are knowable. Unfortunately, there is a simple, seductive, and troubling argument due to Alonzo Church and Frederic Fitch that the knowability thesis collapses into the omniscience thesis that all truths are known. Phenomenologists should be worried. I assess the (...) damage by surveying responses that may be open to Husserl. In particular, I explore whether Husserl ought to have adopted intuitionistic logic and motivate a restriction of ideal verificationism on phenomenological grounds. (shrink)

European Journal of Philosophy, Volume 30, Issue 3, Page 1010-1027, September 2022.

It has been shown that the concept of ad hocness is ambiguous when applied to natural science. Here, it is established that a similar ambiguity is present also when the concept is applied in a philosophical debate. Neil Tennant’s proposal for solving Fitch’s paradox has been accused for being ad hoc several times, and he has presented several defenses. In this paper, it is established that ad hocness is never defined, although each author uses different notions of the concept. And (...) we see that no reason to adopt a certain notion is offered. (shrink)

Constructivist epistemology posits that all truths are knowable. One might ask to what extent constructivism is compatible with naturalized epistemology and knowledge obtained from inference-making using successful scientific theories. If quantum theory correctly describes the structure of the physical world, and if quantum theoretic inferences about which measurement outcomes will be observed with unit probability count as knowledge, we demonstrate that constructivism cannot be upheld. Our derivation is compatible with both intuitionistic and quantum propositional logic. This result is implied by (...) the Frauchiger-Renner theorem, though it is of independent importance as well. (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)

This paper presents a generalized form of Fitch's paradox of knowability, with the aim of showing that the questions it raises are not peculiar to the topics of knowledge, belief, or other epistemic notions. Drawing lessons from the generalization, the paper offers a solution to Fitch's paradox that exploits an understanding of modal talk about what could be known in terms of capacities to know. It is argued that, in rare cases, one might have the capacity to know that p (...) even if it is metaphysically impossible for anyone to know that p, and that recognizing this fact provides the resources to solve Fitch's paradox. (shrink)

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.

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)

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)

The Knowability Paradox is a logical argument to the effect that, if there are truths not actually known, then there are unknowable truths. Recently, Alexander Paseau and Bernard Linsky have independently suggested a possible way to counter this argument by typing knowledge. In this article, we argue against their proposal that if one abstracts from other possible independent considerations supporting reasons for typing knowledge and considers the motivation for a type-theoretic approach with respect to the Knowability Paradox alone, there is (...) no substantive philosophical motivation to type knowledge, except that of solving the paradox. Every attempt to independently justify the typing of knowledge is doomed to failure. (shrink)

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...) relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of /stability/: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting /stable knowability principle/ and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience. (shrink)

(T5) ϕ → ◊Kϕ |-- ϕ → Kϕ where ◊ is possibility, and ‘Kϕ’ is to be read as ϕ is known by someone at some time. Let us call the premise the knowability principle and the conclusion near-omniscience.2 Here is a way of formulating Fitch’s proof of (T5). Suppose the knowability principle is true. Then the following instance of it is true: (p & ~Kp) → ◊K(p & ~Kp). But the consequent is false, it is not possible to know (...) p & ~Kp. That is because the supposition that it is known is provably inconsistent.3 The inconsistency requires us to deny the possibility of the supposition, yielding ~◊K(p & ~Kp). This, together with the above instance of the knowability principle, entails ~(p & ~Kp), which is (classically) equivalent to p → Kp. Since p occurs in none of our undischarged assumptions, we may generalize to get near-omniscience, ϕ → Kϕ. QED. (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)

The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known; i.e. if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well known criticism to the Knowability Paradox is the so called restriction (...) strategy. It bounds the scope of the universal quantification in (KP) to a set of formulas whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests to restrict the quantifier in (KP) to propositions whose knowledge is provably inconsistent. He calls them Anti-Cartesian propositions and distinguished them in three kinds. In this paper we will not be concerned with the soundness of the restriction proposal and the criticisms it has received. Rather, we are interested in analyzing the proposed distinction. We argue that Tennant’s distinction is problematic because it is not completely clear, it is not grounded on an adequate logical analysis, and it is incomplete. We suggest an alternative distinction, and we give some reasons for accepting it: it results logically grounded and more complete than Tennant’s one, inclusive of it and independent from non-epistemic notions. (shrink)