Perennial philosophers' hopes are unlikely victims of swift, natural deduction. Yet anti-realism has been thought one. Not hoping for anti-realism myself I here show it, lest it be underestimated, to survive the following argument, adapted from W. D.Hart pp. 156, 164-5; he credits first publication to Fitch).

Michael Dummett; VIII.—Truth, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 141–162, https://doi.org/10.1093/aristotelian/59.1.

This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...

A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.

This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox.

Knowledge and its Limits presents a systematic new conception of knowledge as a kind of mental stage sensitive to the knower's environment. It makes a major contribution to the debate between externalist and internalist philosophies of mind, and breaks radically with the epistemological tradition of analyzing knowledge in terms of true belief. The theory casts new light on such philosophical problems as scepticism, evidence, probability and assertion, realism and anti-realism, and the limits of what can be known. The arguments are (...) illustrated by rigorous models based on epistemic logic and probability theory. The result is a new way of doing epistemology and a notable contribution to the philosophy of mind. (shrink)

The Taming of the True poses a broad challenge to realist views of meaning and truth that have been prominent in recent philosophy. Neil Tennant argues compellingly that every truth is knowable, and that an effective logical system can be based on this principle. He lays the foundations for global semantic anti-realism and extends its consequences from the philosophy of mathematics and logic to the theory of meaning, metaphysics, and epistemology.

Michael Dummett is a leading contemporary philosopher whose work on the logic and metaphysics of language has had a lasting influence on how these subjects are conceived and discussed. This volume contains some of the most provocative and widely discussed essays published in the last fifteen years, together with a number of unpublished or inaccessible writings. Essays included are: "What is a Theory of Meaning?," "What do I Know When I Know a Language?," "What Does the Appeal to Use Do (...) for the Theory of Meaning?," "Language and Truth," "Truth and Meaning," "Language and Communication," "The Source of the Concept of Truth," "Mood, Force, and Convention," "Frege and Husserl on Reference," "Realism," "Existence," "Does Quantification Involve Identity?," "Could there be Unicorns?," "Causal Loops," "Common Sense and Physics," "Testimony and Memory," "What is Mathematics About?," "Wittgenstein on Necessity: Some Reflections," and "Realism and Anti-Realism." Serving well as a companion to Dummett's other collections, the essays in this volume are not forbiddingly technical or specialized, and have relevance to many areas of analytic philosophy. (shrink)

Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...

In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume ...

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 (...) the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view. (shrink)

In this paper I attempt to clarify a relatively little-studied aspect of Michael Dummett's argument for intuitionism: its use of the notion of ‘undecidable’ sentence. I give a new analysis of this concept in epistemic terms, with which I resolve some puzzles and questions about how it works in the anti-realist critique of classical logic.

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.

This paper addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalised, contributes towards the solution of the other two. The key to this response is a generalised conception of indeterminacy as a specific kind of intellectual bafflement-Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as (...) liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, e.g., matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight. (shrink)

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 (...) entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true. The knowability paradox and the related idealism problem draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility. This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable. (shrink)

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, we (...) present a new proof to the effect that not all truths are knowable, which rests on different assumptions from those of the original argument published by Fitch. We highlight the general form of the knowability paradoxes, and argue that anti-realists who favour either an hierarchical or an intuitionistic approach to the Paradox of Knowability are confronted with a dilemma: they must either give up anti-realism or opt for a highly controversial interpretation of the principle that every truth is knowable. (shrink)

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

First, some reminiscences. In the years 1973-80, when I was an undergraduate and then graduate student at Oxford, Michael Dummett’s formidable and creative philosophical presence made his arguments impossible to ignore. In consequence, one pole of discussion was always a form of anti-realism. It endorsed something like the replacement of truth-conditional semantics by verification-conditional semantics and of classical logic by intuitionistic logic, and the principle that all truths are knowable. It did not endorse the principle that all truths are known. (...) Nor did it mention the now celebrated argument, first published by Frederic Fitch (1963), that if all truths are knowable then all truths are known. (shrink)

The naive anti-realist holds the following principle: (◊K) All truths are knowable. This unrestricted generalization (◊K), as is now well known, falls prey to Fitch’s Paradox (Fitch 1963: 38, Theorem 1). It can be used as the only suspect principle, alongside others that cannot be impugned, to prove quite generally, and constructively, that the set {p, ¬Kp} is inconsistent (Tennant 1997: 261). From this it would follow, intuitionistically, that any proposition that is never actually known to be true (by anyone, (...) at any time) is false; and it would follow, classically, that every truth is known (by someone, at some time). (shrink)

Michael Dummett’s realism debate is a semantic dispute about the kind of truth conditions had by a given class of sentences. According to his semantic realist, the truth conditions are potentially verification-transcendent in that they may obtain (or not) despite the fact that we may be forever unable to recognize whether they obtain. According to Dummett’s semantic anti-realist, the truth conditions are of a different sort. Essentially, for the anti-realist, that the truth conditions obtain (whenever they do) is a matter (...) that is always recognizable by us in principle. On this view, truth cannot outrun all possible human knowledge. Unsurprisingly, the outcome of the debate is sometimes said to hinge on whether all truths are knowable.1 More carefully the point of contention is the following.. (shrink)

In "Truth and the Past, " Dummett, best known as a proponent of antirealism, clarifies his current positions on the metaphysical issue of realism and the ...

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 (...) is that we have some independent reason for thinking that classical logic is not appropriate in this area. This paper explores these two assumptions in the context of Michael Dummett’s version of anti-realism, with particular reference to the argument from indefinite extensibility developed at various points in Dummett’s writings (e.g. Dummett 1991 Ch. 24). -/- Dummett argues that certain concepts, the indefinitely extensible concepts, are such that we cannot form a clear and determinate conception of all the objects that fall under them. The most familiar examples of indefinitely extensible concepts are mathematical. Dummett discusses the concepts ordinal number, real number, and natural number, which are indefinitely extensible because any conception that one might form of their complete extension can be extended to a more inclusive conception (as, for example, in Cantor’s proof of the non-denumerability of the set of real numbers). This paper argues that the concept of a truth is indefinitely extensible. This gives a Dummettian anti-realist an independent motivation for rejecting the classical understanding of the quantifiers in this area. At the same time, however, it places in doubt the admissibility of the knowability principle, which seems to involve quantification over the “totality” of truths. As Dummett is at pains to point out (1991: 316), some sentences that purport to quantify over the extension of an indefinitely extensible concept plainly have a truth-value (we can truly say, for example, that every ordinal number has a successor, even though when we say that we are not quantifying over the set of all ordinals). But is the knowability principle one of these sentences? (shrink)

Anti-realists typically contend that truth is epistemically constrained. Truth, they say, cannot outstrip our capacity to know. Some anti-realists are also willing to make a further claim: if truth is epistemically constrained, classical logic is to be given up in favour of intuitionistic logic. Here we shall be concerned with one argument in support of this thesis - Crispin Wright's Basic Revisionary Argument, first presented in his Truth and Objectivity. We argue that the reasoning involved in the argument, if correct, (...) validates a parallel argument that leads to conclusions that are unacceptable to classicists and intuitionists alike. (shrink)

There is an argument which seems to show that if all truths are knowable then all truths are known. It may be viewed as a "reductio ad absurdum" of certain forms of antirealism. However, The claim has been made elsewhere that the argument fails against antirealists who employ constructivist rather than classical logic. The paper defends and amplifies this claim against criticisms by crispin wright and others. Relations between knowability and time are discussed. Suggestions are also made about the proper (...) form of the constructivist semantics for the conditional, Involving a non-Platonistic version of the distinction between types and tokens of proofs. (shrink)

In this paper, I focus on some intuitionistic solutions to the Paradox of Knowability. I first consider the relatively little discussed idea that, on an intuitionistic interpretation of the conditional, there is no paradox to start with. I show that this proposal only works if proofs are thought of as tokens, and suggest that anti-realists themselves have good reasons for thinking of proofs as types. In then turn to more standard intuitionistic treatments, as proposed by Timothy Williamson and, most recently, (...) Michael Dummett. Intuitionists can either point out the intuitionistc invalidity of the inference from the claim that all truths are knowable to the insane conclusion that all truths are known, or they can outright demur from asserting the existence of forever-unknown truths, perhaps questioning—as Dummett now suggests—the applicability of the Principle of Bivalence to a certain class of empirical statements. I argue that if intuitionists reject strict finitism—the view that all truths are knowable by beings just like us—the prospects for either proposal look bleak. (shrink)

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 (...) in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if φ is true, then there exists a proof of φ Building on the work of Artemov (Bull Symb Log 7(1): 1-36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence. (shrink)

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 (...) entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true . The knowability paradox and the related idealism problem (that antirealism seems, but is not, committed to the necessary existence of an epistemic agent) draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility (e.g., that there is an unknown truth). This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable. (shrink)