- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
Switch to: References
Citations of:
Add citations
You must login to add citations.
|
|
|
We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes. |
|
|
We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem forGLusing arithmetical interpretations. We adapt our proof to (...) |
|
|
An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain. |
|
|
|
|
|
The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I want to (...) |
|
|
Russell’s type theory has been the standard property theory for years, relying on rigid type distinctions at the grammatical level to circumvent the paradoxes of predication. In recent years it has been convincingly argued by Bealer, Cochiarella, Turner and others that many linguistic and ontological data are best accounted for by using a type-free property theory. In the spirit of exploring alternatives and “to have as many opportunities as possible for theory comparison”, this paper presents another type-free property theory, to (...) |
|
|
In this paper, an objective conception of contexts based loosely upon situation theory is developed and formalized. Unlike subjective conceptions, which take contexts to be something like sets of beliefs, contexts on the objective conception are taken to be complex, structured pieces of the world that (in general) contain individuals, other contexts, and propositions about them. An extended first-order language for this account is developed. The language contains complex terms for propositions, and the standard predicate "ist" that expresses the relation (...) |
|
|
We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set. |
|
|
I survey some important semantical and axiomatic theories of self-referential truth. Kripke's fixed-point theory, the revision theory of truth and appraoches involving fuzzy logic are the main examples of semantical theories. I look at axiomatic theories devised by Cantini, Feferman, Freidman and Sheard. Finally some applications of the theory of self-referential truth are considered. |
|
|
I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, S, under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that S yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of S to the theory of truth. |
|
|
We argue that distinct conditionals—conditionals that are governed by different logics—are needed to formalize the rules of Truth Introduction and Truth Elimination. We show that revision theory, when enriched with the new conditionals, yields an attractive theory of truth. We go on to compare this theory with one recently proposed by Hartry Field. |
|
|
In this paper we show that the Gupta-Belnap systems S# and S* are П12. Since Kremer has independently established that they are П12-hard, this completely settles the problem of their complexity. The above-mentioned upper bound is established through a reduction to countable revision sequences that is inspired by, and makes use of a construction of McGee. |
|
|
|
|
|
|
|
|
This original and enticing book provides a fresh, unifying perspective on many old and new logico-philosophical conundrums. Its basic thesis is that many concepts central in ordinary and philosophical discourse are inherently circular and thus cannot be fully understood as long as one remains within the confines of a standard theory of definitions. As an alternative, the authors develop a revision theory of definitions, which allows definitions to be circular without this giving rise to contradiction (but, at worst, to “vacuous” (...) |
|
|
Philip Kremer, Department of Philosophy, McMaster University Note: The following version of this paper does not contain the proofs of the stated theorems. A longer version, complete with proofs, is forthcoming. §1. Introduction. In "The truth is never simple" and its addendum, Burgess conducts a breathtakingly comprehensive survey of the complexity of the set of truths which arise when you add a truth predicate to arithmetic, and interpret that predicate according to the fixed point semantics or the revision-theoretic semantics for (...) |
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-7c76586df8-l2pxr uwo