On Gupta-Belnap Revision Theories of Truth, Kripkean Fixed Points, and The Next Stable Set

AbstractWe 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 (in terms of definitional complexity) 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.

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The Revision Theory of Truth.

Philosophy and Phenomenological Research ◽

10.2307/2108400 ◽

1996 ◽

Vol 56 (3) ◽

pp. 727

Author(s):

Vann McGee ◽

Anil Gupta ◽

Nuel Belnap

Keyword(s):

Revision Theory ◽

Revision Theory Of Truth

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Probability for the Revision Theory of Truth

Journal of Philosophical Logic ◽

10.1007/s10992-018-9475-0 ◽

2018 ◽

Vol 48 (1) ◽

pp. 87-112 ◽

Cited By ~ 1

Author(s):

Catrin Campbell-Moore ◽

Leon Horsten ◽

Hannes Leitgeb

Keyword(s):

Revision Theory ◽

Revision Theory Of Truth

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On revision operators

Journal of Symbolic Logic ◽

10.2178/jsl/1052669071 ◽

2003 ◽

Vol 68 (2) ◽

pp. 689-711 ◽

Cited By ~ 11

Author(s):

P. D. Welch

Keyword(s):

Fixed Points ◽

Alternative Account ◽

Revision Operations ◽

Revision Sequences

AbstractWe look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta's theory of truth over arithmetic using fully varied revision sequences yields a complete Σ31 set of integers; (iii) the set of stably categorical sentences using their revision operator Ψ is similarly Σ31 and which is complete in GÖdel's universe of constructive sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points.

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REVISION REVISITED

The Review of Symbolic Logic ◽

10.1017/s175502031100030x ◽

2012 ◽

Vol 5 (4) ◽

pp. 642-664 ◽

Cited By ~ 9

Author(s):

LEON HORSTEN ◽

GRAHAM E. LEIGH ◽

HANNES LEITGEB ◽

PHILIP WELCH

Keyword(s):

Object Language ◽

Revision Theory ◽

Revision Theory Of Truth ◽

Axiomatic Systems

AbstractThis article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.

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Reply to Beall and Priest

The Australasian Journal of Logic ◽

10.26686/ajl.v6i0.1797 ◽

2008 ◽

Vol 6 ◽

Cited By ~ 3

Author(s):

Matti Eklund

Keyword(s):

Revision Theory ◽

Australasian Journal ◽

Revision Theory Of Truth ◽

Cast Doubt ◽

The Liar ◽

Anil Gupta

In my “Deep Inconsistency” (Australasian Journal of Philosophy, 2002), I compared my meaning-inconsistency view on the liar with Graham Priest’s dialetheist view, using my view to help cast doubt on Priest’s arguments for his view. Jc Beall and Priest have recently published a reply to my article (Australasian Journal of Logic, 2007). I here respond to their criticisms. In addition, I compare the meaning–inconsistency view with Anil Gupta and Nuel Belnap’s revision theory of truth, and discuss how best to deal with the strengthened liar.

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NOTES ONω-INCONSISTENT THEORIES OF TRUTH IN SECOND-ORDER LANGUAGES

The Review of Symbolic Logic ◽

10.1017/s1755020313000269 ◽

2013 ◽

Vol 6 (4) ◽

pp. 733-741 ◽

Cited By ~ 3

Author(s):

EDUARDO BARRIO ◽

LAVINIA PICOLLO

Keyword(s):

Classical Theory ◽

Second Order ◽

Revision Theory ◽

Theories Of Truth ◽

First Order ◽

Order Case ◽

Desirable Feature ◽

Conceptual Problems ◽

Inconsistent Theories

It is widely accepted that a theory of truth for arithmetic should be consistent, butω-consistency is less frequently required. This paper argues thatω-consistency is a highly desirable feature for such theories. The point has already been made for first-order languages, though the evidence is not entirely conclusive. We show that in the second-order case the consequence of adoptingω-inconsistent truth theories for arithmetic is unsatisfiability. In order to bring out this point, well knownω-inconsistent theories of truth are considered: the revision theory of nearly stable truthT#and the classical theory of symmetric truthFS. Briefly, we present some conceptual problems withω-inconsistent theories, and demonstrate some technical results that support our criticisms of such theories.

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