About this topic

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 1907, Dummett 1975, Kant 1991, Peirce 1940, Putnam 1981, and Tennant 1997, et. al. The connections between anti-realism and a rejection of classical logic are found in Dummett 1975, 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 2008 and Salerno 2010.  The only monograph on the paradox is L. Kvanvig 2006.  The last of chapter of Williamson 2000 also has exerted much influence on recent discussion.

Introductions Brogaard & Salerno 2010 Salerno 2010
Related categories

210 found
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  1. An Axiomatic Version of Fitch's Paradox.Samuel Alexander - 2013 - 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 (...)
  2. A Purely Epistemological Version of Fitch's Paradox.Samuel Alexander - 2012 - The Reasoner 6 (4):59-60.
  3. Discovering Knowability: A Semantic Analysis.Sergei Artemov & Tudor Protopopescu - 2013 - 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 (...)
  4. Restricting the Knowability Principle.Andrew Bacon - unknown
    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.
  5. Knowability and Possible Epistemic Oddities.J. C. Beall - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. pp. 105--125.
  6. Fitch's Proof, Verificationism, and the Knower Paradox.JC Beall - 2000 - 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 (...)
  7. Truth, Indefinite Extensibility, and Fitch's Paradox.Jose Luis Bermudez - 2009 - 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 (...)
  8. Omnificence.John Bigelow - 2005 - Analysis 65 (3):187–196.
  9. Review of New Essays on the Knowability Paradox. [REVIEW]Jens Christian Bjerring - 2012 - History and Philosophy of Logic 33 (1):101-104.
  10. How is Meaning Possible?— II Reply to Professor Tennant.Simon Blackburn - 1985 - Philosophical Books 26 (3):129-132.
  11. The De Re, the Per Se, the Knowable, and the Known.David Botting - 2011 - History of Philosophy Quarterly 28 (2):191.
  12. More Than Metaphors: Masculine-Gendered Names and the Knowability of God.Lynne C. Boughton - 1994 - The Thomist 58 (2):283-316.
  13. Jonathan Kvanvig, The Knowability Paradox. [REVIEW]Manuel Bremer - 2007 - Philosophy in Review 27:415-416.
  14. Clues to the Paradoxes of Knowability: Reply to Dummett and Tennant.B. Brogaard & J. Salerno - 2002 - Analysis 62 (2):143-150.
  15. On Keeping Blue Swans and Unknowable Facts at Bay : A Case Study on Fitch's Paradox.Berit Brogaard - 2009 - 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 (...)
  16. Fitch's Paradox of Knowability.Berit Brogaard & Joe Salerno - 2010 - 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 (...)
  17. Knowability, Possibility and Paradox.Berit Brogaard & Joe Salerno - 2008 - 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 (...)
  18. Knowability and a Modal Closure Principle.Berit Brogaard & Joe Salerno - 2006 - 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 (...)
  19. Clues to the Paradoxes of Knowability: Reply to Dummett and Tennant.Berit Brogaard & Joe Salerno - 2002 - 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 (...)
  20. Paradox and Argument.J. E. Broyles - 1977 - International Logic Review 16:160-7.
  21. Fitch's Paradox and the Philosophy of Mathematics.Otavio Bueno - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
  22. Can Truth Out?Johnw Burgess - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
  23. Testability and Meaning.Rudolf Carnap - 1936 - Philosophy of Science 3 (4):419-471.
  24. The Knowability Paradox in the Light of a Logic for Pragmatics.Massimiliano Carrara & Daniele Chiffi - 2014 - In R. Ciuni, H. Wansing & C. Willkommen (eds.), Recent Trends in Philosophical Logic (Proceedings of Trends in Logic XI). Berlin: Springer. pp. 47-58.
    The Knowability Paradox is a logical argument showing that if all truths are knowable in principle, then all truths are, in fact, known. Many strategies have been suggested in order to avoid the paradoxical conclusion. A family of solutions –ncalled logical revision – has been proposed to solve the paradox, revising the logic underneath, with an intuitionistic revision included. In this paper, we focus on so-called revisionary solutions to the paradox – solutions that put the blame on the underlying logic. (...)
  25. Why Knowledge Should Not Be Typed: An Argument Against the Type Solution to the Knowability Paradox.Massimiliano Carrara & Davide Fassio - 2011 - 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 (...)
  26. Perfected Science and the Knowability Paradox.Massimiliano Carrara & Davide Fassio - 2010 - In M. M. D’Agostino, G. Giorello, F. Laudisa, T. Pievani & C. Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. London College Publications.
    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.
  27. Logically Unknowable Propositions: A Criticism to Tennant's Three-Partition of Anti-Cartesian Propositions.Massimiliano Carrara & Davide Fassio - 2009 - In P. Hanna (ed.), An Anthology of Philosophical Studies, Vol.2. Atiner. pp. 181-194.
    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 (...)
  28. The Knowability Paradox, Perfectibility of Science and Reductionism.Massimiliano Carrara & Davide Fassio - unknown
    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 (...)
  29. Constructing the World.David Chalmers - 2012 - Oxford University Press.
  30. Actuality and Knowability.David J. Chalmers - 2011 - 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.
  31. Factivity, Consistency and Knowability.James Chase & Penelope Rush - 2018 - Synthese 195 (2):899-918.
    One diagnosis of Fitch’s paradox of knowability is that it hinges on the factivity of knowledge: that which is known is true. Yet the apparent role of factivity and non-factive analogues in related paradoxes of justified belief can be shown to depend on familiar consistency and positive introspection principles. Rejecting arguments that the paradox hangs on an implausible consistency principle, this paper argues instead that the Fitch phenomenon is generated both in epistemic logic and logics of justification by the interaction (...)
  32. The Comforts of Home.Earl Conee - 2005 - Philosophy and Phenomenological Research 70 (2):444–451.
    The paper argues against Timothy Williamson's anti-luminosity argument. It also offers an argument against luminosity from the possibility of defeat of introspective justification.
  33. Knowability and Singular Thought.Ezra J. Cook - manuscript
  34. Knights, Knaves and Unknowable Truths.Roy T. Cook - 2006 - Analysis 66 (1):10-16.
  35. Paraconsistency and Knowability.Alexandre Costa-Leite - manuscript
    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.
  36. Combining Possibility and Knowledge.Alexandre Costa-Leite - manuscript
    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 (...)
  37. Joe Salerno, Ed. New Essays on the Knowability Paradox. Reviewed By.Sam Cowling - 2010 - Philosophy in Review 30 (3):220-222.
  38. What Can We Learn From the Paradox of Knowability?Cesare Cozzo - 1994 - 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 (...)
  39. Another Solution of the Paradox of Knowability'.Cesare Cozzo - 1993 - In J. Czermak (ed.), Philosophy of Mathematics. Hölder-Pichler-Tempsky.
  40. From the Knowability Paradox to the Existence of Proofs.W. Dean & H. Kurokawa - 2010 - 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 (...)
  41. Analogues of Knowability.David DeVide & Tim Kenyon - 2003 - Australasian Journal of Philosophy 81 (4):481-495.
  42. Analogues of Knowability.David DeVidi & Tim Kenyon - 2003 - 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 (...)
  43. Knowability and Intuitionistic Logic.David DeVidi & Graham Solomon - 2001 - Philosophia 28 (1-4):319-334.
  44. Hope, Knowledge, and Blindspots.Jordan Dodd - 2017 - Synthese 194 (2):531-543.
    Roy Sorensen introduced the concept of an epistemic blindspot in the 1980s. A proposition is an epistemic blindspot for some individual at some time if and only if that proposition is consistent but unknowable by that individual at that time. In the first half of this paper, I extend Sorensen work on blindspots by arguing that there exist blindspots that essentially involve hopes. In the second half, I show how such blindspots can contribute to and impair different pursuits of self-understanding. (...)
  45. Fitch’s Paradox and Probabilistic Antirealism.Igor Douven - 2007 - 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.
  46. A Principled Solution to Fitch?S Paradox.Igor Douven - 2005 - Erkenntnis 62 (1):47-69.
    To save antirealism from Fitch's Paradox, Tennant has proposed to restrict the scope of the antirealist principle that all truths are knowable to truths that can be consistently assumed to be known. Although the proposal solves the paradox, it has been accused of doing so in an ad hoc manner. This paper argues that, first, for all Tennant has shown, the accusation is just; second, a restriction of the antirealist principle apparently weaker than Tennat's yields a non-ad hoc solution to (...)
  47. Fitch's Paradox of Knowability.Michael Dummett - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.
  48. Victor's Error.Michael Dummett - 2001 - Analysis 61 (1):1–2.
  49. Reply to Tennant.Michael Dummett - 1987 - In Barry Taylor (ed.), Michael Dummett: Contributions to Philosophy. Kluwer Academic Publishers. pp. 235--252.
  50. The Paradox of Knowability.Dorothy Edgington - 1985 - Mind 94 (376):557-568.
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