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

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  1.  98
    Berit Brogaard & Joe Salerno, Fitch's Paradox of Knowability. The Stanford Encyclopedia of Philosophy.
    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.  19
    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.
    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.  9
    Thorsten Sander (2006). Fitch's Paradox and the Problem of Shared Content. Abstracta 3 (1):74-86.
    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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  4. Michael Dummett (2009). Fitch's Paradox of Knowability. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press
     
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  5. Samuel Alexander (2013). An Axiomatic Version of Fitch's Paradox. Synthese 190 (12):2015-2020.
    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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  6.  65
    Paolo Maffezioli, Alberto Naibo & Sara Negri (2013). The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory. Synthese 190 (14):2677-2716.
    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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  7. Jiri Raclavsky (2013). Fitch's Paradox of Knowability and Ramified Theory of Types. Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20:144-165.
     
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  8.  61
    Rafał Palczewski (2007). Distributed Knowability and Fitch's Paradox. Studia Logica 86 (3):455--478.
    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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  9.  8
    Concha Martinez, Jose-Miguel SAGüILLO & Javier Vilanova (1997). Fitch's Problem and the Knowability Paradox: Logical and Philosophical Remarks'. Logica Trianguli 1:73-91.
    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 (...)
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  10.  72
    Alessandro Giordani (2015). On a New Tentative Solution to Fitch’s Paradox. Erkenntnis.
    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, (...)
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  11. Jose Luis Bermudez (2009). Truth, Indefinite Extensibility, and Fitch's Paradox. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press
    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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  12. Otavio Bueno (2009). Fitch's Paradox and the Philosophy of Mathematics. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press
  13.  14
    Alexandre Costa-Leite (2006). Fusions of Modal Logics and Fitch's Paradox. Croatian Journal of Philosophy 6 (2):281-290.
    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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  14. 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.
    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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  15. Salvatore Florio & Julien Murzi (2009). The Paradox of Idealization. Analysis 69 (3):461-469.
    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 offered. (...)
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  16.  53
    Pierdaniele Giaretta (2009). The Paradox of Knowability From a Russellian Perspective. Prolegomena 8 (2):141-158.
    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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  17.  9
    Massimiliano Carrara & Davide Fassio, The Knowability Paradox, Perfectibility of Science and Reductionism.
    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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  18.  57
    W. Dean & H. Kurokawa (2010). From the Knowability Paradox to the Existence of Proofs. Synthese 176 (2):177 - 225.
    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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  19. 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
    (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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  20.  17
    Carlo Proietti (2012). Intuitionistic Epistemic Logic, Kripke Models and Fitch's Paradox. Journal of Philosophical Logic 41 (5):877-900.
    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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  21.  77
    Jason Megill (2015). Fitch’s Paradox and the Existence of an Omniscient Being. In Miroslaw Szatkowski (ed.), God, Truth, and Other Enigmas. De Gruyter 77-88.
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  22.  43
    Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114 - 120.
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  23.  85
    Carlo Proietti & Gabriel Sandu (2010). Fitch's Paradox and Ceteris Paribus Modalities. Synthese 173 (1):75 - 87.
    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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  24.  41
    Samuel Alexander (2012). A Purely Epistemological Version of Fitch's Paradox. The Reasoner 6 (4):59-60.
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  25.  4
    Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (298):114-120.
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  26.  4
    V. Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114-120.
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  27.  1
    Rafał Palczewski (2007). Distributed Knowability and Fitch’s Paradox. Studia Logica 86 (3):455-478.
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  28. Michael Fara (2010). Knowability and the Capacity to Know. Synthese 173 (1):53 - 73.
    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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  29. 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
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  30.  10
    Martin Fischer (2013). Some Remarks on Restricting the Knowability Principle. Synthese 190 (1):63-88.
    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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  31.  65
    Wesley H. Holliday (forthcoming). Epistemic Logic and Epistemology. In Sven Ove Hansson Vincent F. Hendricks (ed.), Handbook of Formal Philosophy. Springer
    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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  32.  10
    Eleonora Cresto (forthcoming). Lost in Translation: Unknowable Propositions in Probabilistic Frameworks. Synthese:1-23.
    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 (...)
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  33.  42
    Vincent C. Müller & Christian Stein (1996). Epistemic Theories of Truth: The Justifiability Paradox Investigated. In C. Martínez Vidal, U. Rivas Monroy & L. Villegas Forero (eds.), Verdad: Lógica, Representatión y Mundo. Universidade de Santiago de Compostela 95-104.
    Epistemic theories of truth, such as those presumed to be typical for anti-realism, can be characterised as saying that what is true can be known in principle: p → ◊Kp. However, with statements of the form “p & ¬Kp”, a contradiction arises if they are both true and known. Analysis of the nature of the paradox shows that such statements refute epistemic theories of truth only if the the anti-realist motivation for epistemic theories of truth is not taken (...)
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  34.  28
    David DeVidi & Tim Kenyon (2003). Analogues of Knowability. Australasian Journal of Philosophy 81 (4):481 – 495.
    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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  35. Christopher Gregory Weaver (2013). A Church-Fitch Proof for the Universality of Causation. Synthese 190 (14):2749-2772.
    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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  36. 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.
     
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  37.  24
    Alexander Paseau (2008). Fitch's Argument and Typing Knowledge. Notre Dame Journal of Formal Logic 49 (2):153-176.
    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, (...)
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  38.  54
    JC Beall (2000). Fitch's Proof, Verificationism, and the Knower Paradox. Australasian Journal of Philosophy 78 (2):241 – 247.
    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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  39.  33
    Igor Douven (2007). Fitch's Paradox and Probabilistic Antirealism. Studia Logica 86 (2):149 - 182.
    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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  40.  95
    Cesare Cozzo (1994). What Can We Learn From the Paradox of Knowability? Topoi 13 (2):71--78.
    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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  41.  3
    Dr Alessandro Giordani (forthcoming). On a New Tentative Solution to Fitch’s Paradox. Erkenntnis:1-15.
    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, (...)
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  42.  48
    Fredrik Stjernberg (2009). Restricting Factiveness. Philosophical Studies 146 (1):29 - 48.
    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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  43.  6
    Carlo Proietti (2016). The Fitch-Church Paradox and First Order Modal Logic. Erkenntnis 81 (1):87-104.
    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 (...)
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  44.  47
    Bernhard Weiss (2007). Truth and the Enigma of Knowability. Dialectica 61 (4):521–537.
    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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  45.  11
    Ansten Klev (2016). A Proof‐Theoretic Account of the Miners Paradox. Theoria 82 (2).
    By maintaining that a conditional sentence can be taken to express the validity of a rule of inference, we offer a solution to the Miners Paradox that leaves both modus ponens and disjunction elimination intact. The solution draws on Sundholm's recently proposed account of Fitch's Paradox.
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  46. Jonathan L. Kvanvig (2006). Knowability Paradox. Oxford University Press Uk.
    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 (...)
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  47.  32
    Boris Rähme (2010). Wahrheit, Begründbarkeit und Fallibilität. Ein Beitrag zur Diskus-sion epistemischer Wahrheitskonzeptionen. Ontos Verlag.
    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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  48.  19
    Bernhard Weiss (2012). Perspectives and the World. Topoi 31 (1):27-35.
    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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  49.  72
    Richard Routley (2010). Necessary Limits to Knowledge: Unknowable Truths. Synthese 173 (1):107 - 122.
    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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  50.  28
    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.
    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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