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Summary

Knowability is the concept that figures in epistemic theories true---for instance semantic anti-realism claims, necessarily, every truth is knowable in principle.  Michael Dummett argues for the position along the following lines.  Given that meaning is fully manifestable in use and that grasp of meaning involves knowing truth conditions, the fully competent user of the language is in principle able to recognize that a proposition is true when it is.   The most important alleged consequence of the position is that classical logic is not unrestrictedly valid.  For the unrestricted principle of excluded middle together with semantic anti-realism (and some modest auxiliary assumptions) entails strong decidability---i.e., that, unrestrictedly, every proposition or it’s negation is knowable in principle.  And that conclusion is false, not known apriori, and unacceptably immodest. Therefore, exclusively classical principles are false, not known apriori and unacceptably immodest. 

Most recent discussion centers around  Fitch’s paradox of knowability.  The paradox threatens to collapse semantic anti-realism into an implausible idealism----the theory that, necessarily, every truth is (at some time) known.  Since an important selling point of moderate anti-realism is that it distances itself from naïve idealism, the collapse is unwelcome to the anti-realist.  But the paradox is not just a problem for anti-realists, because the result threatens to erase the very logical distinction between semantic anti-realism and naïve idealism. Even those of us who have not been seduced by anti-realism may still want to distinguish it from (and treat it as logically weaker than) idealism.  

Key works

Influential variations on the thesis that truth is an epistemic notion are articulated in Berkeley 1940, Dummett 1973, Kant 2007, Peirce 1940, Putnam 1981, and Tennant 1997, et. al. The connections between anti-realism and a rejection of classical logic are found in Dummett 1973, Wright 1992, Tennant 1997, and Salerno 2000.   The first publication of Fitch's paradox is Fitch 1963.  The result there was conveyed anonymously to Fitch in a pair of referee reports in 1945, which were later published in Church 2009.  An overview of the key points of debate regarding Fitch’s paradox is found in Brogaard & Salerno 2010.  Two volumes of essays, which center around the key points of contention in that debate are Salerno 2009 and Salerno 2010.  The only monograph on the paradox is Kvanvig 2006.  The last of chapter of Williamson 2000 also has exerted much influence on recent discussion.

Introductions Brogaard & Salerno 2010 Salerno 2010
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  1. 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 of the (...)
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  2. Samuel Alexander (2012). A Purely Epistemological Version of Fitch's Paradox. The Reasoner 6 (4):59-60.
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  3. Sergei Artemov & Tudor Protopopescu (2013). Discovering Knowability: A Semantic Analysis. Synthese 190 (16):3349-3376.
    In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...)
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  4. Andrew Bacon, Restricting the Knowability Principle.
    Could there unknowable truths? Truths which, regardless of any extension to ones capacities or resources, remain impossible to know. The answer to this question is central in the evaluation of semantic anti-realism. But even for a metaphysical realist, the matter is far from closed.
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  5. J. C. Beall (2009). Knowability and Possible Epistemic Oddities. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. 105--125.
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  6. 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 honest, non-dogmatic reflection on (...)
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  7. 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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  8. John Bigelow (2005). Omnificence. Analysis 65 (287):187–196.
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  9. Jens Christian Bjerring (2012). Review of New Essays on the Knowability Paradox. [REVIEW] History and Philosophy of Logic 33 (1):101-104.
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  10. Simon Blackburn (1985). How is Meaning Possible?— II Reply to Professor Tennant. Philosophical Books 26 (3):129-132.
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  11. David Botting (2011). The De Re, the Per Se, the Knowable, and the Known. History of Philosophy Quarterly 28 (2):191.
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  12. Lynne C. Boughton (1994). More Than Metaphors: Masculine-Gendered Names and the Knowability of God. The Thomist 58 (2):283-316.
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  13. Manuel Bremer (2007). Jonathan Kvanvig, The Knowability Paradox. [REVIEW] Philosophy in Review 27:415-416.
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  14. 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 to know (...)
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  15. 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 to argue (...)
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  16. Berit Brogaard & Joe Salerno (2008). Knowability, Possibility and Paradox. In Vincent Hendricks (ed.), New Waves in Epistemology. Palgrave Macmillan.
    The paradox of knowability threatens to draw a logical equivalence between the believable claim that all truths are knowable and the obviously false claim that all truths are known. In this paper we evaluate prominent proposals for resolving the paradox of knowability. For instance, we argue that Neil Tennant’s restriction strategy, which aims principally to restrict the main quantifier in ‘all truths are knowable’, does not get to the heart of the problem since there are knowability paradoxes that the restriction (...)
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  17. Berit Brogaard & Joe Salerno (2006). Knowability and a Modal Closure Principle. American Philosophical Quarterly 43 (3):261-270.
    Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...)
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  18. Berit Brogaard & Joe Salerno (2002). Clues to the Paradoxes of Knowability: Reply to Dummett and Tennant. Analysis 62 (2):143–150.
    Tr(A) iff ‡K(A) To remedy the error, Dummett’s proposes the following inductive characterization of truth: (i) Tr(A) iff ‡K(A), if A is a basic statement; (ii) Tr(A and B) iff Tr(A) & Tr(B); (iii) Tr(A or B) iff Tr(A) v Tr(B); (iv) Tr(if A, then B) iff (Tr(A) Æ Tr(B)); (v) Tr(it is not the case that A) iff ¬Tr(A), where the logical constant on the right-hand side of each biconditional clause is understood as subject to the laws of intuitionistic (...)
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  19. J. E. Broyles (1977). Paradox and Argument. International Logic Review 16:160-7.
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  20. Otavio Bueno (2009). Fitch's Paradox and the Philosophy of Mathematics. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
  21. M. W. Bunder & Jonathan P. Seldin (1978). Some Anomalies in Fitch's System QD. Journal of Symbolic Logic 43 (2):247-249.
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  22. Johnw Burgess (2009). Can Truth Out? In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
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  23. Rudolf Carnap (1936). Testability and Meaning. Philosophy of Science 3 (4):419-471.
  24. Massimiliano Carrara & Davide Fassio (2011). Why Knowledge Should Not Be Typed: An Argument Against the Type Solution to the Knowability Paradox. Theoria 77 (2):180-193.
    The Knowability Paradox is a logical argument to the effect that, if there are truths not actually known, then there are unknowable truths. Recently, Alexander Paseau and Bernard Linsky have independently suggested a possible way to counter this argument by typing knowledge. In this article, we argue against their proposal that if one abstracts from other possible independent considerations supporting reasons for typing knowledge and considers the motivation for a type-theoretic approach with respect to the Knowability Paradox alone, there is (...)
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  25. 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 the notion (...)
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  26. Massimiliano Carrara & Davide Fassio, Logically Unknowable Propositions: A Criticism to Tennant's Three-Partition of Anti-Cartesian Propositions.
    The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known; i.e. if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well known criticism to the Knowability Paradox is the so called restriction (...)
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  27. Massimiliano Carrara & Davide Fassio, Perfected Science and the Knowability Paradox.
    In "The Limits of Science" N. Rescher introduces a logical argument known as the Knowability Paradox, according to which, if every true proposition is knowable, then every true proposition is known, i.e. if there are unknown truths, there are unknowable truths. Rescher argues that the Knowability Paradox, giving evidence to a limit of our knowledge (the existence of unknowable truths) could be used for arguing against perfected science. In this article we present two criticisms against Rescher's argument.
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  28. David Chalmers (2012). Constructing the World. Oxford University Press.
    Uncorrected proofs for Constructing the World (contents, introduction, chapter 1, and first excursus).
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  29. David J. Chalmers (2011). Actuality and Knowability. Analysis 71 (3):411-419.
    It is widely believed that for all p, or at least for all entertainable p, it is knowable a priori that (p iff actually p). It is even more widely believed that for all such p, it is knowable that (p iff actually p). There is a simple argument against these claims from four antecedently plausible premises.
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  30. Ezra J. Cook, Knowability and Singular Thought.
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  31. Roy T. Cook (2006). Knights, Knaves and Unknowable Truths. Analysis 66 (289):10–16.
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  32. Alexandre Costa-Leite, Paraconsistency and Knowability.
    We propose a modal paraconsistent logic sound and complete in order to create a model where the premisses of the knowability paradox are true except the conclusion.
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  33. Alexandre Costa-Leite, Combining Possibility and Knowledge.
    This paper is an attempt to define a new modality with philosophical interest by combining the basic modal ingredients of possibility and knowledge. This combination is realized via product of modal frames so as to construct a knowability modality, which is a bidimensional constructor of arity one defined in a two-dimensional modal frame. A semantical interpretation for the operator is proposed, as well as an axiomatic system able to account for inferences related to this new modality. The resulting logic for (...)
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  34. Sam Cowling (2010). Joe Salerno, Ed. New Essays on the Knowability Paradox. Reviewed By. Philosophy in Review 30 (3):220-222.
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  35. Sam Cowling (2010). Joe Salerno, Ed. New Essays on the Knowability Paradox. [REVIEW] Philosophy in Review 30:220-222.
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  36. 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 understand what (...)
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  37. Cesare Cozzo (1994). ``What We Can Learn From the Paradox of Knowability&Quot. Topoi 13:71-78.
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  38. Cesare Cozzo (1993). Another Solution of the Paradox of Knowability'. In J. Czermak (ed.), Philosophy of Mathematics. Hölder-Pichler-Tempsky.
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  39. 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 are employed (...)
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  40. David DeVide & Tim Kenyon (2003). ``Analogues of Knowability&Quot. Australasian Journal of Philosophy 81:481-495.
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  41. 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 neutral, nor the (...)
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  42. David DeVidi & Graham Solomon (2001). Knowability and Intuitionistic Logic. Philosophia 28 (1-4):319-334.
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  43. 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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  44. Igor Douven (2005). A Principled Solution to Fitch's Paradox. Erkenntnis 62 (1):47 - 69.
    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 solution to (...)
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  45. 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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  46. Michael Dummett (2001). Victor's Error. Analysis 61 (1):1–2.
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  47. Michael Dummett (1987). Reply to Tennant. In Barry Taylor (ed.), Michael Dummett: Contributions to Philosophy. Distributors for the United States and Canada, Kluwer Academic Publishers. 235--252.
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  48. Dorothy Edgington (1985). The Paradox of Knowability. Mind 94 (376):557-568.
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  49. Dorothy Edgington (1985). ``The Paradox of Knowability&Quot. Mind 94:557-568.
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  50. Eva Ejerhed & Sten Lindström (eds.) (1997). Logic, Action, and Cognition: Essays in Philosophical Logic. Kluwer Academic.
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