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Switch to: Citations
References in:
The Knowability Argument and the Syntactic Type-Theoretic Approach
Theoria 29 (2):201-221 (2014)
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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, formal part presents a logic (...) |
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In my paper , I noted that Fitch's argument, which purports to show that if all truths are knowable then all truths are known, can be blocked by typing knowledge. If there is not one knowledge predicate, ‘ K’, but infinitely many, ‘ K 1’, ‘ K 2’, … , then the type rules prevent application of the predicate ‘ K i’ to sentences containing ‘ K i’ such as ‘ p ∧¬ K i⌜ p⌝’. This provides a motivated response (...) |
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Recently, it has been observed that the usual type-theoretic restrictions are not enough to block certain paradoxes involving two or more predicates. In particular, when we have a self-referential language containing modal predicates, new paradoxes might appear even if there are type restrictions for the principles governing those predicates. In this article we consider two type-theoretic solutions to multimodal paradoxes. The first one adds types for each of the modal predicates. We argue that there are a number of problems with (...) |
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A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences. |
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In this article, the prospects of deflationism about the concept of truth are investigated. A new version of deflationism, called inferential deflationism, is articulated and defended. It is argued that it avoids the pitfalls of earlier deflationist views such as Horwich’s minimalist theory of truth and Field’s version of deflationism. |
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In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) |
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At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the (...) |
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This collection assembles Church's referee reports, Fitch's 1963 paper, and nineteen new papers on the knowability paradox. |
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Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...) |
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Addresses the question of why we find Fitch's knowability 'paradox' argument surprising. |
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