Search results for 'Fitch's paradox of knowability' (try it on Scholar)

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  1. Berit Brogaard & Joe Salerno, Fitch's Paradox of Knowability. The Stanford Encyclopedia of Philosophy.score: 421.8
    The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used (...)
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  2. Helge Rückert (2004). A SOLUTION TO FITCH'S PARADOX OF KNOWABILITY. In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. 351--380.score: 344.4
    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 (...)
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  3. Samuel Alexander (2013). An Axiomatic Version of Fitch's Paradox. Synthese 190 (12):2015-2020.score: 298.8
    A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out (...)
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  4. Paolo Maffezioli, Alberto Naibo & Sara Negri (2013). The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory. Synthese 190 (14):2677-2716.score: 291.6
    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 ${A \supset \diamondsuit \mathcal{K} A}$ (KP). The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$ (OP). A Gentzen-style reconstruction of the (...)
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  5. Michael Dummett (2009). Fitch's Paradox of Knowability. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.score: 246.0
     
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  6. Jiri Raclavsky (2013). Fitch's Paradox of Knowability and Ramified Theory of Types. Organon F 20:144-165.score: 234.0
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  7. Rafał Palczewski (2007). Distributed Knowability and Fitch's Paradox. Studia Logica 86 (3):455--478.score: 226.2
    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 (...)
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  8. Thorsten Sander (2006). Fitch's Paradox and the Problem of Shared Content. Abstracta 3 (1):74-86.score: 226.2
    According to the “paradox of knowability”, the moderate thesis that (necessarily) all truths are knowable – ‘∀p (p ⊃ ◊Kp) ’ – implies the seemingly preposterous claim that all truths are actually known – ‘∀p (p ⊃ Kp) ’ –, 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 (...)
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  9. Pierdaniele Giaretta (2009). The Paradox of Knowability From a Russellian Perspective. Prolegomena 8 (2):141-158.score: 214.8
    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 (...)
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  10. Jose Luis Bermudez (2009). Truth, Indefinite Extensibility, and Fitch's Paradox. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.score: 205.2
    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 (...)
     
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  11. W. Dean & H. Kurokawa (2010). From the Knowability Paradox to the Existence of Proofs. Synthese 176 (2):177 - 225.score: 204.0
    The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which (...)
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  12. Alexandre Costa-Leite (2006). Fusions of Modal Logics and Fitch's Paradox. Croatian Journal of Philosophy 6 (2):281-290.score: 202.2
    This article shows that although Fitch’s paradox has been extremely widely studied, up to now no correct formalization of the problem has been proposed. The purpose of this article is to present the paradox front the viewpoint of combining logics. It is argued that the correct minimal logic to state the paradox is composed by a fusion of modal frames, and a fusion of modal languages and logics.
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  13. Carlo Proietti (2012). Intuitionistic Epistemic Logic, Kripke Models and Fitch's Paradox. Journal of Philosophical Logic 41 (5):877-900.score: 196.8
    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 (...)
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  14. Salvatore Florio & Julien Murzi (2009). The Paradox of Idealization. Analysis 69 (3):461-469.score: 189.0
    A well-known proof by Alonzo Church, first published in 1963 by Frederic Fitch, purports to show that all truths are knowable only if all truths are known. This is the Paradox of Knowability. If we take it, quite plausibly, that we are not omniscient, the proof appears to undermine metaphysical doctrines committed to the knowability of truth, such as semantic anti-realism. Since its rediscovery by Hart and McGinn ( 1976), many solutions to the paradox have been (...)
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  15. Michael Fara (2010). Knowability and the Capacity to Know. Synthese 173 (1):53 - 73.score: 186.6
    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 (...)
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  16. Martin Fischer (2013). Some Remarks on Restricting the Knowability Principle. Synthese 190 (1):63-88.score: 183.6
    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 (...)
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  17. Wesley H. Holliday (forthcoming). Epistemic Logic and Epistemology. In Sven Ove Hansson Vincent F. Hendricks (ed.), Handbook of Formal Philosophy. Springer.score: 179.4
    This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s (...). The references and recommended readings provide gateways for further exploration. (shrink)
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  18. Elia Zardini, If Every True Proposition is Knowable, Then Every Believed (Decidable) Proposition is True, or the Incompleteness of the Intuitionistic Solution to the Paradox of Knowability.score: 164.4
    Fitch’s paradox of knowability is an apparently valid reasoning from the assumption (typical of semantic anti-realism) that every true proposition is knowable to the unacceptable conclusion that every true proposition is known. The paper develops a critical dialectic wrt one of the best motivated solutions to the paradox which have been proposed on behalf of semantic anti-realism—namely, the intuitionistic solution. The solution consists, on the one hand, in accepting the intuitionistically valid part of Fitch’s reasoning while, on (...)
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  19. Otavio Bueno (2009). Fitch's Paradox and the Philosophy of Mathematics. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.score: 161.4
  20. Massimiliano Carrara & Davide Fassio, The Knowability Paradox, Perfectibility of Science and Reductionism.score: 159.0
    A logical argument known as Fitch’s Paradox of Knowability, starting from the assumption that every truth is knowable, leads to the consequence that every truth is also actually known. Then, given the ordinary fact that some true propositions are not actually known, it concludes, by modus tollens, that there are unknowable truths. The main literature on the topic has been focusing on the threat the argument poses to the so called semantic anti-realist theories, which aim to epistemically characterize (...)
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  21. Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114 - 120.score: 149.4
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  22. Samuel Alexander (2012). A Purely Epistemological Version of Fitch's Paradox. The Reasoner 6 (4):59-60.score: 149.4
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  23. Fredrik Stjernberg (2009). Restricting Factiveness. Philosophical Studies 146 (1):29 - 48.score: 148.2
    In discussions of Fitch’s paradox, it is usually assumed without further argument that knowledge is factive, that if a subject knows that p, then p is true. It is argued that this common assumption is not as well-founded as it should be, and that there in fact are certain reasons to be suspicious of the unrestricted version of the factiveness claim. There are two kinds of reason for this suspicion. One is that unrestricted factiveness leads to paradoxes and unexpected (...)
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  24. Berit Brogaard (2009). On Keeping Blue Swans and Unknowable Facts at Bay : A Case Study on Fitch's Paradox. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.score: 148.2
    (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 (...)
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  25. Concha Martinez, Jose-Miguel SAGüILLO & Javier Vilanova (1997). Fitch's Problem and the Knowability Paradox: Logical and Philosophical Remarks'. Logica Trianguli 1:73-91.score: 147.6
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  26. David DeVidi & Tim Kenyon (2003). Analogues of Knowability. Australasian Journal of Philosophy 81 (4):481 – 495.score: 146.4
    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 (...)
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  27. Igor Douven (2007). Fitch's Paradox and Probabilistic Antirealism. Studia Logica 86 (2):149 - 182.score: 145.2
    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.
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  28. Sten Lindström (1997). Situations, Truth and Knowability: A Situation-Theoretic Analysis of a Paradox by Fitch. In Eva Ejerhed & Sten Lindström (eds.), Logic, Action and Cognition: Essays in Philosophical Logic. Kluwer.score: 144.0
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  29. Carlo Proietti & Gabriel Sandu (2010). Fitch's Paradox and Ceteris Paribus Modalities. Synthese 173 (1):75 - 87.score: 142.2
    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.
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  30. Hans van Ditmarsch, Wiebe van der Hoek & Petar Iliev (2011). Everything is Knowable – How to Get to Know Whether a Proposition is True. Theoria 78 (2):93-114.score: 137.8
    Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Moore-sentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch's and Moore's results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful’ (...)
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  31. Christopher Gregory Weaver (2013). A Church-Fitch Proof for the Universality of Causation. Synthese 190 (14):2749-2772.score: 136.8
    In an attempt to improve upon Alexander Pruss’s work (The principle of sufficient reason: A reassessment, pp. 240–248, 2006), I (Weaver, Synthese 184(3):299–317, 2012) have argued that if all purely contingent events could be caused and something like a Lewisian analysis of causation is true (per, Lewis’s, Causation as influence, reprinted in: Collins, Hall and paul. Causation and counterfactuals, 2004), then all purely contingent events have causes. I dubbed the derivation of the universality of causation the “Lewisian argument”. The Lewisian (...)
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  32. JC Beall (2000). Fitch's Proof, Verificationism, and the Knower Paradox. Australasian Journal of Philosophy 78 (2):241 – 247.score: 136.8
    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 (...)
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  33. Cesare Cozzo (1994). What Can We Learn From the Paradox of Knowability? Topoi 13 (2):71--78.score: 136.2
    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 (...)
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  34. Boris Rähme (2010). Wahrheit, Begründbarkeit und Fallibilität. Ein Beitrag zur Diskus-sion epistemischer Wahrheitskonzeptionen. Ontos Verlag.score: 135.6
    The following two theses constitute the theoretical core of all epistemic conceptions of truth: (1) The concept of truth can be explicated in epistemic terms (e.g. in terms of justified assertability under ideal epistemic conditions, ideal coherence, ideal consensus etc.). (2) The assumption that there could be truths which cannot, in principle, be known to be true is false or even absurd. The book scrutinizes theses (1) and (2). It contains discussions of the truth-theoretical approaches of Peirce, Putnam, Dummett, C. (...)
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  35. Alexander Paseau (2008). Fitch's Argument and Typing Knowledge. Notre Dame Journal of Formal Logic 49 (2):153-176.score: 134.2
    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 (...)
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  36. Bernhard Weiss (2012). Perspectives and the World. Topoi 31 (1):27-35.score: 128.4
    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 (...)
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  37. Richard Routley (2010). Necessary Limits to Knowledge: Unknowable Truths. Synthese 173 (1):107 - 122.score: 127.8
    The paper seeks a perfectly general argument regarding the non-contingent limits to any (human or non-human) knowledge. After expressing disappointment with the history of philosophy on this score, an argument is grounded in Fitch’s proof, which demonstrates the unknowability of some truths. The necessity of this unknowability is then defended by arguing for the necessity of Fitch’s premise—viz., there this is in fact some ignorance.
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  38. Neil Kennedy (2014). Defending the Possibility of Knowledge. Journal of Philosophical Logic 43 (2-3):579-601.score: 119.4
    In this paper, I propose a solution to Fitch’s paradox that draws on ideas from Edgington (Mind 94:557–568, 1985), Rabinowicz and Segerberg (1994) and Kvanvig (Noûs 29:481–500, 1995). After examining the solution strategies of these authors, I will defend the view, initially proposed by Kvanvig, according to which the derivation of the paradox violates a crucial constraint on quantifier instantiation. The constraint states that non-rigid expressions cannot be substituted into modal positions. We will introduce a slightly modified syntax (...)
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  39. Susan Rogerson (2007). Natural Deduction and Curry's Paradox. Journal of Philosophical Logic 36 (2):155 - 179.score: 118.2
    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.
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  40. Seiki Akama (1996). Curry's Paradox in Contractionless Constructive Logic. Journal of Philosophical Logic 25 (2):135 - 150.score: 118.2
    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.
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  41. Bernhard Weiss (2007). Truth and the Enigma of Knowability. Dialectica 61 (4):521–537.score: 117.0
    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 (...) 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)
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  42. Sergei Artemov & Tudor Protopopescu (2013). Discovering Knowability: A Semantic Analysis. Synthese 190 (16):3349-3376.score: 111.0
    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 (...)
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  43. Igor Douven (2005). A Principled Solution to Fitch's Paradox. Erkenntnis 62 (1):47 - 69.score: 110.4
    To save antirealism from Fitchs 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 Tennants yields a non-ad hoc (...)
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  44. Boudewijn de Bruin (2008). Epistemic Logic and Epistemology. In Vincent F. Hendricks & Duncan Pritchard (eds.), New Waves in Epistemology. Palgrave Macmillan.score: 105.6
    This paper contributes to an increasing literature strengthening the connection between epistemic logic and epistemology (Van Benthem, Hendricks). I give a survey of the most important applications of epistemic logic in epistemology. I show how it is used in the history of philosophy (Steiner's reconstruction of Descartes' sceptical argument), in solutions to Moore's paradox (Hintikka), in discussions about the relation between knowledge and belief (Lenzen) and in an alleged refutation of verificationism (Fitch) and I examine an early argument about (...)
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  45. Joe Salerno (ed.) (2009). New Essays on the Knowability Paradox. Oxford University Press.score: 103.2
    This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox.
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  46. C. S. Jenkins (2009). The Mystery of the Disappearing Diamond. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. 302--319.score: 100.2
    Addresses the question of why we find Fitch's knowability 'paradox' argument surprising.
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  47. Alonzo Church (2009). Referee Reports on Fitch's "Definition of Value". In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. 13--20.score: 98.4
     
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  48. Robert G. Hudson (2009). Faint-Hearted Anti-Realism and Knowability. Philosophia 37 (3):511-523.score: 90.0
    It is often claimed that anti-realists are compelled to reject the inference of the knowability paradox, that there are no unknown truths. I call those anti-realists who feel so compelled ‘faint-hearted’, and argue in turn that anti-realists should affirm this inference, if it is to be consistent. A major part of my strategy in defending anti-realism is to formulate an anti-realist definition of truth according to which a statement is true only if it is verified by someone, at (...)
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  49. Neil Tennant (2010). Williamson's Woes. Synthese 173 (1):9 - 23.score: 90.0
    This is a reply to Timothy Williamson’s paper ‘Tennant’s Troubles’. It defends against Williamson’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True . Williamson’s purported Fitchian reductio , involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson’s attempt to cause problems for the anti-realist by means of a supposed rigid designator (...)
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