Fitch’s Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitch’s result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any ‘level-bridging principle’ suffices. A consequence is that the result holds for some logics in which the “Moorean contradiction” commonly thought to underlie the result is (...) in fact consistent. This generalised result improves on the current understanding of Fitch’s result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitch’s result which answers a challenge raised by Kvanvig. (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.

The paper attempts to give a solution to the Fitch's paradox though the strategy of the reformulation of the paradox in temporal logic, and a notion of knowledge which is a kind of ceteris paribus modality. An analogous solution has been offered in a different context to solve the problem of metaphysical determinism.

Recently, there have been several attempts to use the kind of reasoning found in Fitch’s knowability paradox to argue for rather sweeping metaphysical claims: Jago (2020) uses such reasoning to argue that every truth has a truthmaker, and Loss (2021) does so to argue that every fact is grounded. This strategy has been criticized by Trueman (2021), who points out that the same kind of reasoning could be used to establish entirely opposite conclusions. In response, Jago (2021) has offered a (...) revised argument that is meant to avoid Trueman’s objection. I argue that this revised argument is in fact undermined by an objection quite similar to Trueman’s. (shrink)

I argue that if one applies the standard intuitionistic criterion for truth to Kp in (p) (p&Kp), one avoids Fitch’s paradox, but with disastrous consequences having to do with the expressive resources of one’s semantics. On the other hand, if one conceives of Kp as a function recording what happens in the actual world, one gets a double benefit. First, the semantics become tolerably expressive. Second, and because of the same move, the paradox can be blocked. (The solution I provide (...) bares resemblances with the ones proposed by Edgington 1985, 2009 and Kvanvig 1995, 2006, and especially with this latter as it has been reformulated by Brogaard and Salerno 2007). Finally, I shown that in some models for temporal intuitionistic logic (Kapantaïs 2009), and which are extensions of Beth models, (i) the knowability principle can be assumed to be valid, (ii) the paradox is blocked in the above mentioned way, and also (iii) a sentence saying that we will come to know something we now ignore becomes true and known in some worlds. (shrink)

A number of authors have noted that the key steps in Fitch’s argument are not intuitionistically valid, and some have proposed this as a reason for an anti-realist to accept intuitionistic logic (e.g. Williamson 1982, 1988). This line of reasoning rests upon two assumptions. The first is that the premises of Fitch’s argument make sense from an anti-realist point of view – and in particular, that an anti-realist can and should maintain the principle that all truths are knowable. The second (...) is that we have some independent reason for thinking that classical logic is not appropriate in this area. This paper explores these two assumptions in the context of Michael Dummett’s version of anti-realism, with particular reference to the argument from indefinite extensibility developed at various points in Dummett’s writings (e.g. Dummett 1991 Ch. 24). -/- Dummett argues that certain concepts, the indefinitely extensible concepts, are such that we cannot form a clear and determinate conception of all the objects that fall under them. The most familiar examples of indefinitely extensible concepts are mathematical. Dummett discusses the concepts ordinal number, real number, and natural number, which are indefinitely extensible because any conception that one might form of their complete extension can be extended to a more inclusive conception (as, for example, in Cantor’s proof of the non-denumerability of the set of real numbers). This paper argues that the concept of a truth is indefinitely extensible. This gives a Dummettian anti-realist an independent motivation for rejecting the classical understanding of the quantifiers in this area. At the same time, however, it places in doubt the admissibility of the knowability principle, which seems to involve quantification over the “totality” of truths. As Dummett is at pains to point out (1991: 316), some sentences that purport to quantify over the extension of an indefinitely extensible concept plainly have a truth-value (we can truly say, for example, that every ordinal number has a successor, even though when we say that we are not quantifying over the set of all ordinals). But is the knowability principle one of these sentences? (shrink)

Jago and Loss have recently used variations on Fitch's paradox to argue that every truth has a truthmaker, and that every fact is grounded. In this paper, I show that Fitch's paradox can also be adapted to prove the exact opposite conclusions: no truth has a truthmaker, and no fact is grounded. All of these arguments are as dialectically effective as each other, and so they are all in bad company.

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)

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 present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of (...) our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (shrink)

In a recent paper, Alexander argues that relaxing the requirement that sound knowers know their own soundness might provide a solution to Fitch’s paradox and introduces a suitable axiomatic system where the paradox is avoided. In this paper an analysis of this solution is proposed according to which the effective move for solving the paradox depends on the axiomatic treatment of the ontic modality rather than the limitations imposed on the epistemic one. It is then shown that, once the ontic (...) modality is standardly introduced, the paradox still follows and, in addition, some puzzling consequences arise. (shrink)

I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, non-dogmatic reflection (...) on the knower paradox provides strong support for the second. Whether verificationists want to go the route I've suggested is not for me todecide. As in the previous section my aim has been that of defending the mere viability of verificationism in the face of what many, many philosophers have taken to be its death-knell, namely Fitch's Proof. But, as the final objection makes clear, showing that verificationism can live in the face of Fitch's Proof is one thing; showing that it should live is another project. If nothing else, I hope that this papershows that verificationists still have a project to pursue; Fitch's Proof, contrary to popular opinion, need not bury verificationism.13. (shrink)

Fitch´s problem and the "knowability paradox" involve a couple of argumentations that are to each other in the same relation as Cantor´s uncollected multitudes theorem and Russell´s paradox. The authors exhibit the logical nature of the theorem and of the paradox and show their philosophical import, both from an anti-realist and from a realist perspective. In particular, the authors discuss an anti-realist solution to Fitch´s problem and provide an anti-realist interpretation of the problematic statement "It is knowable that r is (...) known and yet unknown". Then, it is argued that the knowability paradox has a solution even if one adopts a realist point of view. The authors provide a solution that takes into account the ambiguity of the term 'knowability' by deploying a temporal possible world semantics for epistemic modalities. (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)

Reformulation strategies for solving Fitch’s paradox of knowability date back to Edgington. Their core assumption is that the formula \, from which the paradox originates, does not correctly express the intended meaning of the verification thesis, which should concern possible knowledge of actual truths, and therefore the contradiction does not represent a logical refutation of verificationism. Supporters of these solutions claim that can be reformulated in a way that blocks the derivation of the paradox. Unfortunately, these reformulation proposals come with (...) other problems, on both the logical and the philosophical side. We claim that in order to make the reformulation idea consistent and adequate one should analyze the paradox from the point of view of a quantified modal language. An approach in this line was proposed by, among others, Kvanvig but was not fully developed in its technical details. Here we approach the paradox by means of a first order hybrid modal logic, a tool that strikes us as more adequate to express transworld reference and the rigidification needed to consistently express this idea. The outcome of our analysis is ambivalent. Given a first order formula we are able to express the fact that it is knowable in a way which is both consistent and adequate. However, one must give up the possibility of formulating as a substitution free schema of the kind \. We propose that one may instead formulate by means of a recursive translation of the initial formula, being aware that many alternative translations are possible. (shrink)

Saul Kripke is one of the most original and creative philosophers writing today. His work has had a tremendous impact on the direction that philosophy has taken in the last thirty years and continues to dominate some of its most fundamental aspects. Given Kripke's importance it is perhaps surprising that there is no introduction to his philosophy available to the general student. This book fills that gap. As much of Kripke's work is highly technical, the book's central aim is to (...) provide clear exposition of Kripke's ideas in a form that is understandable to a beginning readership as well as a commentary on them that more advanced students will find useful. The book begins with a discussion of Kripke's early work on modal logic, which provides the foundation for many of his later philosophical contributions, before examining in detail Kripke's central ideas and arguments contained in Naming and Necessity. In further chapters, Kripke's work on semantic paradoxes and his theory of truth are outlined as well as his controversial interpretation of Wittgenstein's famous private language argument. Kripke's ideas are situated alongside those of his precursors and some of the most important and interesting responses to them are explored. The reader is thus able to appreciate the path-breaking nature of Kripke's contributions, how they have challenged fundamentally traditional interpretations, and how they have sparked some of the most important philosophical debates of recent years. (shrink)

We propose contractionless constructive logic which is obtained from Nelson's constructive logic by deleting contractions. We discuss the consistency of a naive set theory based on the proposed logic in relation to Curry's paradox. The philosophical significance of contractionless constructive logic is also argued in comparison with Fitch's and Prawitz's systems.

This chapter explores the different grounds for accepting the claim that all truths are knowable, the assumption central to the derivation of Fitch’s result. It argues that although there is no compelling argument for holding that all truths are knowable, there are various positions in which this feature of semantic anti-realism fits naturally; rejecting this puts serious tension into a broad range of philosophical outlooks, including theism and physicalism. In the end, the paradox should be felt by everyone, even those (...) who do not accept the knowability claim, because the heart of the paradox is not simply in what is implied by the knowability claim, but in a lost logical distinction between what is actual and what is possible. (shrink)

Humberstone has shown that if some set of agents is collectively omniscient (every true proposition is known by at least one agent) then one of them alone must be omniscient. The result is paradoxical as it seems possible for a set of agents to partition resources whereby at the level of the whole community they enjoy eventual omniscience. The Humberstone paradox only requires the assumption that knowledge distributes over conjunction and as such can be viewed as a reductio against the (...) universal validity of that principle. A new route to this paradox is presented which does not require the distribution principle, building on earlier work of Jago and Williamson on Fitch’s paradox. The result relies on an axiom strictly weaker than one necessary for the Jago-Fitch variant. It is shown that the same reasoning behind the variant form of Humberstone’s paradox can recover Bigelow’s results in action theory in a way that is immune to an objection brought against it by Guigon and Humberstone. (shrink)

Résumé — Toute vérité est-elle connaissable en principe ? Une réponse négative à cette question suit d’un argument logique dû à F. Fitch, voisin du paradoxe de Moore, et connu sous le nom de paradoxe de la connaissabilité. Le paradoxe de Fitch constitue un obstacle à la conception antiréaliste de la vérité et, plus généralement, semble-t-il, à l’idéal positiviste d’après lequel toute vérité devrait nous être accessible en principe. Dans cet article, j’examine différentes tentatives pour préserver le (...) principe selon lequel toute vérité est connaissable, chacune inspirée d’une forme propre d’antiréalisme . Ces différentes approches sont comparées à une conception réaliste du positivisme, évoquée récemment par Burgess, qui postulerait seulement que toute vérité nécessaire est connaissable. Selon cette conception, certaines vérités contingentes sont effectivement inconnaissables, mais l’accessibilité de principe des vérités nécessaires demeure suffisante pour garantir la confiance positiviste dans la science.— Are all truths knowable ? A negative answer to this question follows from a logical argument related to the Moore Paradox and due to F. Fitch, also known as Fitch’s Knowability Paradox. Fitch’s paradox is widely considered to be an obstacle to the antirealist conception of truth, but even for a realist, it appears to threaten the positivist faith in the accessibility of all truths to our minds. In this paper, I first review different strategies to circumvent the paradox, each of them inspired by a different form of antirealism . I then compare these approaches to a realist version of positivism, discussed recently by Burgess, which would only postulate that all necessary truths are knowable. On that view, some contingent truths are indeed unknowable, but the idea that all necessary truths are within our reach remains sufficient to maintain the positivist faith in scientific knowledge. (shrink)

Curry's paradox, sometimes described as a general version of the better known Russell's paradox, has intrigued logicians for some time. This paper examines the paradox in a natural deduction setting and critically examines some proposed restrictions to the logic by Fitch and Prawitz. We then offer a tentative counterexample to a conjecture by Tennant proposing a criterion for what is to count as a genuine paradox.

Two proofs are given which show that if some set of truths fall under finitely many concepts (so-called Collectivity), then they all fall under at least one of them even if we do not know which one. Examples are given in which the result seems paradoxical. The first proof crucially involves Moorean propositions while the second is a reconstruction and generalization of a proof due to Humberstone free from any reference to such propositions. We survey a few solution routes including (...) Tennant-style restriction strategies. It is concluded that accepting Collectivity for some set of truths while also denying that any of the involved concepts in isolation capture all of them requires that one of these concepts cannot be closed under conjunction elimination. This is surprising since the paper surveys several applications in which Collectivity and the latter closure condition seemed jointly satisfiable for concepts of actual philosophical interest. (shrink)

Fitch's argument purports to show that if all truths are knowable then all truths are known. The argument exploits the fact that the knowledge predicate or operator is untyped and may thus apply to sentences containing itself. This article outlines a response to Fitch's argument based on the idea that knowledge is typed. The first part of the article outlines the philosophical motivation for the view, comparing it to the motivation behind typing truth. The second, formal part presents (...) a logic in which knowledge is typed and demonstrates that it allows nonlogical truths to be knowable yet unknown. (shrink)

Enligt ett realistiskt synsätt kan ett påstående vara sant trots att det inte ens i princip är möjligt att veta att det är sant. En sanningsteoretisk antirealist kan inte godta denna möjlighet utan accepterar en eller annan version av Dummetts vetbarhetsprincip: (K) Om ett påstående är sant, så måste det i princip vara möjligt att veta att det är sant. Det kan dock förefalla rimligt, även för en antirealist, att gå̊ med på̊ att det kan finnas sanningar som ingen faktiskt (...) vet (har vetat, eller kommer att veta) är sanna. Man kan därför tänka sig att en antirealist skulle acceptera principen (K) utan att därför gå med på den till synes starkare principen: (SK) Om ett påstående är sant, så måste det faktiskt finnas någon som vet att det är sant. Ett mycket omdiskuterat argument – som ytterst går tillbaka till Alonzo Church, men som först publicerades i en uppsats av Frederic Fitch i Journal of Symbolic Logic 1963 – tycks emellertid visa att principen (K) implicerar principen (SK). Anta nämligen att (K) är sann, medan (SK) inte är det. Men om (SK) är falsk, så finns det ett påstående som är sant men som ingen faktiskt vet är sant. Anta nu att p är ett sådant påstående. Låt Kp betyda att någon vet att p är sant. Det galler alltså̊ att p är sant samtidigt som Kp inte är det. Betrakta nu påståendet (p ∧ −Kp). Enligt antagandet är detta påstående sant. Enligt (K) måste det då vara möjligt att någon vet att (p ∧ −Kp). D.v.s., det måste vara möjligt att påståendet K(p ∧ −Kp) är sant. Men i så fall är det också̊ möjligt att påståendet Kp ∧ K−Kp är sant, vilket i sin tur implicerar att det är möjligt att Kp ∧ −Kp är sant, vilket ju är absurt. Således kan inte (K) vara sann samtidigt som (SK) är falsk. Vi tycks således kunna sluta oss till att (K) implicerar (SK). I uppsatsen diskuterar jag några olika sätt att undgå̊ Church-Fitch paradoxala slutsats. Ett tillvägagångssätt är att ersätta kunskapsoperatorn med en hierarki av kunskapspredikat. Ett annat är baserat på distinktionen mellan faktisk och potentiell kunskap och ett förkastande av den vanliga modallogiska formaliseringen av principen (K). Den senare typen av lösning betraktas både från ett realistiskt och ett icke-realistiskt perspektiv. Utifrån denna analys kommer jag fram till slutsatsen att vi, vare sig vi är realister eller antirealister rörande sanning, kan sluta oroa oss för vetbarhetsparadoxen och ändå uppskatta Church-Fitchs argument. (shrink)

Fitch's knowability paradox shows that for each unknown truth there is also an unknowable truth, a result which has been thought both odd in itself and at odds with views which impose epistemic constraints on truth and/or meaningfulness. Here a solution is considered which has received little attention in the debate but which carries prima facie plausibility. The decidability solution is to accept that Fitch sentences are unknowably true but deny the significance of this on the grounds that Fitch (...) sentences are nevertheless decidable. The decidability solution is particularly attractive for those whose primary concern is an epistemic constraint on meaningfulness (‘verificationists’). For those whose main concern is truth (‘anti-realists’), the situation is more complex: Melia takes the solution to exonerate anti-realism completely; Williamson sees it as completely irrelevant. The truth lies between these two extremes: there is one broad anti-realist commitment to which the solution does not apply, but there is also one, the “fundamental tenet” of anti-realism according to Dummett, to which it does. (shrink)

The paradox of knowability, derived from a proof by Frederic Fitch in 1963, is one of the deepest paradoxes concerning the nature of truth. Jonathan Kvanvig argues that the depth of the paradox has not been adequately appreciated. It has long been known that the paradox threatens antirealist conceptions of truth according to which truth is epistemic. If truth is epistemic, what better way to express that idea than to maintain that all truths are knowable? In the face of the (...) paradox, however, such a characterization threatens to undermine antirealism. If Fitch's proof is valid, then one can be an antirealist of this sort only by endorsing the conclusion of the proof that all truths are known.Realists about truth have tended to stand on the sidelines and cheer the difficulties faced by their opponents from Fitch's proof. Kvanvig argues that this perspective is wholly unwarranted. He argues that there are two problems raised by the paradox, one that threatens antirealism about truth and the other that threatens everybody's view about truth, realist or antirealist. The problem facing antirealism has had a number of proposed solutions over the past 40 years, and the results have not been especially promising with regard to the first problem. The second problem has not even been acknowledged, however, and the proposals regarding the first problem are irrelevant to the second problem. This book thus provides a thorough investigation of the literature on the paradox, and also proposes a solution to the deeper of the two problems raised by Fitch's proof. It provides a complete picture of the paradoxicality that results from Fitch's proof, and presents a solution to the paradox that claims to address both problems raised by the original proof. (shrink)

This chapter examines the logical structure of the knowability paradox, presenting the details of the proofs that underlie the paradox, and clarifying which elements of these proofs give rise to paradox. It argues that there is no simple and obvious logical mistake in the derivation of the knowability result. A paradox has deep significance only if it arises from plausible premises. Those in question in Fitch’s proof are the claim of epistemic modesty, that some truths will never be known, and (...) the knowability principle that all truths are knowable. Although the second claim does not have the same intuitive pull as the first, there are substantive grounds in its favour; grounds that some hold show that all truths are knowable, but which show at the very least that it is plausible to maintain that all truths are knowable. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

In an anonymous referee report written in 1945, Church suggested a sweeping argument against verificiationism, the thesis that every truth is knowable. The argument, which was published with due acknowledgement by Fitch almost two decades later, has generated significant attention as well as some interesting successor arguments. In this paper, we present the most important episodes in this intellectual history using the logic that Church himself favoured, and we give reasons for thinking that the arguments are less than decisive. However, (...) we present some new arguments against verificationism that we believe to be dialectically effective. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (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 this paper I consider metaphysical positions which I label as ‘perspectival’. A perspectivalist believes that some portion of reality cannot extend beyond what an appropriately characterised investigator or investigators can (in some sense) reveal about it. So a perspectivalist will be drawn to claim that a portion of reality is, in some sense, knowable. Many such positions appear to founder on the paradox of knowability. I aim to offer a solution to that paradox which can be adopted by any (...) perspectivalist, which involves no restriction on the claim of knowability and which allows certain sentences to be unknowable. The solution hinges on recognising that what is meant by ‘knowable’ will vary from one type of proposition to another and thus that characterising the modality involved in the notion in terms of possible worlds will be impossible. I thus offer a subjunctive conditional reading of that modality, a reading which, I claim, has the virtues just recounted. (shrink)

1) We will begin by offering a short introduction to Epistemic Logic and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will proceed to presenting three Epistemic Temporal logical frameworks creat‑ ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL (Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal Public Announcement Logic with Labeled Past Operators). We will show how Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze his argument on why this (...) version of it is immune from paradox. (3) Edgington (1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s paradox and we will propose a way to formulate it in a TAPAL‑based lan‑ guage. The language we will use is a combination of TAPAL and TPAL+P ! with an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑ ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑ tive semantics for this language. We will investigate whether the tentative re‑ formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from paradox and adequate to Edgington’s ideas on how „all truths are knowable“ should be interpreted. (shrink)

Some propositions are structurally unknowable for certain agents. Let me call them ‘Moorean propositions’. The structural unknowability of Moorean propositions is normally taken to pave the way towards proving a familiar paradox from epistemic logic—the so-called ‘Knowability Paradox’, or ‘Fitch’s Paradox’—which purports to show that if all truths are knowable, then all truths are in fact known. The present paper explores how to translate Moorean statements into a probabilistic language. A successful translation should enable us to derive a version of (...) Fitch’s Paradox in a probabilistic setting. I offer a suitable schematic form for probabilistic Moorean propositions, as well as a concomitant proof of a probabilistic Knowability Paradox. Moreover, I argue that traditional candidates to play the role of probabilistic Moorean propositions will not do. In particular, we can show that violations of the so-called ‘Reflection Principle’ in probability need not yield structurally unknowable propositions. Among other things, this should lead us to question whether violating the Reflection Principle actually amounts to a clear case of epistemic irrationality, as it is often assumed. This result challenges the importance of the principle as a tool to assess both synchronic and diachronic rationality—a topic which is largely independent of Fitch’s Paradox—from a somewhat unexpected source. (shrink)

There is an argument (first presented by Fitch), which tries to show by formal means that the anti-realistic thesis that every truth might possibly be known, is equivalent to the unacceptable thesis that every truth is actually known (at some time in the past, present or future). First, the argument is presented and some proposals for the solution of Fitch's Paradox are briefly discussed. Then, by using Wehmeier's modal logic with subjunctive marks (S5*), it is shown how the derivation (...) can be blocked if one respects adequately the distinction between the indicative and the subjunctive mood. Essentially, this proposal amounts to the one by Edgington which was formulated with the help of the actuality-operator. Finally it is shown how the criticisms by Williamson against Edgington can be answered by the formulation of a new conception of possible knowledge that \alpha (thereby \alpha being in the indicative mood and thus referring to the actual world). This conception is based on the concept of same de re knowledge in different possible worlds. (shrink)

In this commentary on Berwick and Chomsky's “Why Only Us,” I discuss three key points. I first offer a brief critique of their scholarship, notably their often unjustified dismissal of previous thinking about language evolution. But my main focus concerns two arguments central to the book's thesis: the irrelevance of externalization to language evolution and the discontinuity between human conceptual representations and those of other animals. I argue against both stances, using cognitive data from nonhuman species to show that externalization (...) is not irrelevant to understanding the biology of language, and that many human conceptual structures have clear animal homologs. (shrink)

Accepting Bullot & Reber's (B&R's) criteria for art appreciation would confine the study of aesthetics to those works for which historical information is available, mainly posthigh art.correct” artistic understanding is limited to experts with detailed knowledge or education in art, which implies a narrowly elitist conception of aesthetics. Scientific aesthetics must be broadly inclusive.

Alvin Plantinga has recently argued that there are certain propositions which are necessary but known only a posteriori. If Plantinga is correct then he has shown that the traditional view that all necessary truths are knowable a priori is false. Plantinga's examples deserve special attention because they differ in important respects from other proposed examples of necessary a posteriori truths. His examples depend on a certain conception of possible worlds and in particular on his conception of the actual world. It (...) will be argued that these examples of necessary a posteriori propositions can be understood in two different ways. According to one way of understanding Plantinga, the propositions turn out to be contingent a posteriori truths, and according to the other way they turn out to be necessary a priori truths. The plausibility of Plantinga's position is due to a confusion between the two possible interpretations. (shrink)

One of the most important insights that Russell had in presenting his philosophy of language was his view of singular definite descriptions. Russell held that singular phrases of the form ‘the so-and-so’ should not be viewed as names, but rather incomplete symbols which can be said to have meaning only in a context. We should not represent the sentence The inventor of bifocals is bald.as a simple subject-predicate sentence of the form ‘Fa.’ but rather as a complex existential sentence. According (...) to Russell we should analyze as There is a unique x such that x invented bifocals and x is bald.Moreover, if Russell's analysis is correct then the proposition expressed by will be true in a given circumstance provided that there is a unique inventor of bifocals who is bald in that circumstance. (shrink)