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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. 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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  5. 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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  6. 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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  7. John Bigelow (2005). Omnificence. Analysis 65 (287):187–196.
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  8. 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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  9. 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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  10. 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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  11. 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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  12. 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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  13. 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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  14. Otavio Bueno (2009). Fitch's Paradox and the Philosophy of Mathematics. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
  15. Johnw Burgess (2009). Can Truth Out? In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
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  16. Rudolf Carnap (1936). Testability and Meaning. Philosophy of Science 3 (4):419-471.
  17. 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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  18. 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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  19. 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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  20. Ezra J. Cook, Knowability and Singular Thought.
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  21. Roy T. Cook (2006). Knights, Knaves and Unknowable Truths. Analysis 66 (289):10–16.
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  22. 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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  23. Cesare Cozzo (1994). ``What We Can Learn From the Paradox of Knowability&Quot. Topoi 13:71-78.
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  24. 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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  25. David DeVide & Tim Kenyon (2003). ``Analogues of Knowability&Quot. Australasian Journal of Philosophy 81:481-495.
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  26. 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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  27. David DeVidi & Graham Solomon (2001). Knowability and Intuitionistic Logic. Philosophia 28 (1-4):319-334.
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  28. 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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  29. 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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  30. 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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  31. Michael Dummett (2001). Victor's Error. Analysis 61 (1):1–2.
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  32. Dorothy Edgington (1985). ``The Paradox of Knowability&Quot. Mind 94:557-568.
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  33. Dorothy Edgington (1985). The Paradox of Knowability. Mind 94 (376):557-568.
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  34. Eva Ejerhed & Sten Lindström (eds.) (1997). Logic, Action, and Cognition: Essays in Philosophical Logic. Kluwer Academic.
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  35. 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 capacity to know that p (...)
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  36. Frederic B. Fitch (1963). A Logical Analysis of Some Value Concepts. Journal of Symbolic Logic 28 (2):135-142.
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  37. 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. In this article, (...)
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  38. André Fuhrmann (2014). Knowability as Potential Knowledge. Synthese 191 (7):1627-1648.
    The thesis that every truth is knowable is usually glossed by decomposing knowability into possibility and knowledge. Under elementary assumptions about possibility and knowledge, considered as modal operators, the thesis collapses the distinction between truth and knowledge (as shown by the so-called Fitch-argument). We show that there is a more plausible interpretation of knowability—one that does not decompose the notion in the usual way—to which the Fitch-argument does not apply. We call this the potential knowledge-interpretation of knowability. We compare our (...)
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  39. 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 pointed out.
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  40. Alessandro Giordani (2013). On the Factivity of Implicit Intersubjective Knowledge. Synthese (8):1-15.
    The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said to be implicitly known just in case it is derivable from the set of propositions that are explicitly (...)
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  41. Volker Halbach (2008). On a Side Effect of Solving Fitch's Paradox by Typing Knowledge. Analysis 68 (2):114 - 120.
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  42. M. Hand (2003). Knowability and Epistemic Truth. Australasian Journal of Philosophy 81 (2):216 – 228.
    The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic nature of truth (...)
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  43. Michael Hand (2010). Antirealism and Universal Knowability. Synthese 173 (1):25 - 39.
    Truth’s universal knowability entails its discovery. This threatens antirealism, which is thought to require it. Fortunately, antirealism is not committed to it. Avoiding it requires adoption (and extension) of Dag Prawitz’s position in his long-term disagreement with Michael Dummett on the notion of provability involved in intuitionism’s identification of it with truth. Antirealism (intuitionism generalized) must accommodate a notion of lost-opportunity truth (a kind of recognition-transcendent truth), and even truth consisting in the presence of unperformable verifications. Dummett’s position cannot abide (...)
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  44. Michael Hand (2009). Performance and Paradox. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
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  45. Michael Hand (2003). ``Knowability and Epistemic Truth&Quot. Australasian Journal of Philosophy 81:216-228.
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  46. Michael Hand & Jonathan L. Kvanvig (1999). Tennant on Knowability. Australasian Journal of Philosophy 77 (4):422 – 428.
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  47. Michael Hand & Jonathan L. Kvanvig (1999). ``Tennant on Knowability&Quot. Australasian Journal of Philosophy 77:422-428.
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  48. W. D. Hart (2009). Invincible Ignorance. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
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  49. W. D. Hart & Colin McGinn (1976). Knowledge and Necessity. Journal of Philosophical Logic 5 (2):205 - 208.
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  50. Vincent Hendricks (ed.) (2008). New Waves in Epistemology. Palgrave Macmillan.
    This book provides a valuable look at the work of up and coming epistemologists. The topics covered range from the central issues of mainstream epistemology to the more formal issues in epistemic logic and confirmation theory. This book should be read by anyone interested in seeing where epistemology is currently focused and where it is heading. - Stewart Cohen , Arizona State University..
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