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21
Ultimate truth vis à vis stable truth
 Journal of Philosophical Logic
, 2003
"... Abstract. We show that the set of ultimately true sentences in Hartry Field’s Revengeimmune solution to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger’s revision sequence starting from the null hypothesis. We further remark that this ..."
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Abstract. We show that the set of ultimately true sentences in Hartry Field’s Revengeimmune solution to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger’s revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second order number theory is needed to establish the semantic values of sentences over the ground model of the standard natural numbers: ¢¡Comprehension Axiom scheme) is insufficient. £¤¦¥¨ § (second order number theory with a ©��
SetTheoretic Absoluteness and The Revision Theory of Truth
 STUDIA LOGICA
, 2000
"... 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. ..."
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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.
Reasoning about belief and knowledge with selfreference and time
 In Proceedings of the second conferennce on Theoretical Aspects of Reasoning About Knowledge
, 1988
"... In two previous papers (Asher & Karnp 1986,1987), Hans Kamp and I developed a framework for investigating the logic of attitudes whose objects involved an unlimited capacity for selfreference. The framework was the daughter of two wellknown parents possible worlds semantics and the revisionist, ..."
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In two previous papers (Asher & Karnp 1986,1987), Hans Kamp and I developed a framework for investigating the logic of attitudes whose objects involved an unlimited capacity for selfreference. The framework was the daughter of two wellknown parents possible worlds semantics and the revisionist, semiinductive theory of truth developed by Herzberger (1982) and Gupta (1982). Nevertheless, the offspnng from our point of view was not an entirely happy one. We had argued that orthodox possible worlds semantics was an unacceptable solution to the problem of the semantics of the attitudes. Yet the connection between our use of possible worlds semantics and the sort of representational theories of the attitudes that we favor remained unclear. This paper attempts to provide a better connection between the framework developed in the previous papers and representational theories of attitudes by developing a notion of reasoning about knowledge and belief that a careful examination of the model theory suggests. This notion of reasoning has a temporal or dynamic aspect that I exploit by introducing temporal as well as attitudinal predicates.
On Revision Operators
"... We look at various notions of a class of denability operations that generalise inductive operations, and are characterised as \revision operations ". More particularly we: (i) characterise the revision theoretically denable subsets of a countable acceptable structure; (ii) show that the categori ..."
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We look at various notions of a class of denability operations that generalise inductive operations, and are characterised as \revision operations ". More particularly we: (i) characterise the revision theoretically denable 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 1 3 set of integers; (iii) the set of stably categorical sentences using their revision operator is similarly 1 3 and which is complete in Godel's universe of constructible sets L; (iv) give an alternative account of a theory of truth  realistic variance that simplies full variance, whilst at the same time arriving at Kripkean xed points. We should like to thank the Mathematics Department of UC Berkeley for its hospitality during the period when this research was conducted, and to the Institut fur Formale Logik in Vienna for a Gastprofessur where this paper was nally written. Keywords: revision theory, denability theory, admissibility theory, descriptive set theory. AMS Classications: 03A05,03D70,03E15,03F35 1 1
On GuptaBelnap Revision Theories of Truth, Kripkean Fixed Points, and The Next Stable Set.
 in Bulletin of Symbolic Logic, 7, No.3
, 2001
"... . 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 (in terms of definitional complexit ..."
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. 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 (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. x1.
Characteristics of discrete transfinite time Turing machine models: halting times, stabilization times, and . . .
, 2008
"... ..."
A ContextualHierarchical Approach to Truth and the Liar Paradox
 Journal of Philosophical Logic
, 2004
"... This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context dra ..."
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This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad hoc nor unnatural. Your bait of falsehood takes this carp of truth: And thus do we of wisdom and of reach, With windlasses, and with assays of bias, By indirections find directions out: Hamlet II.i.68–71 It is a perennial idea in the study of the Liar paradox, from Tarski [56] onwards, that its solution requires some kind of hierarchy. More recent, but
Arithmetical quasiinductive definitions and the transfinite action of one tape Turing machines. typescript
 Machines, in: [CoLöTo05
, 2004
"... • We produce a classification of the pointclasses using infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We consider some relations of such classes ..."
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• We produce a classification of the pointclasses using infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We consider some relations of such classes with other similar notions, such as arithmetical quasiinductive definitions. • It is noted that the action of ω many steps of such a machine can correspond to the double jump operator (in the usual Turing sense): a− → a ′ ′. • The ordinals beginning gaps in the “clockable ” ordinals are admissible ordinals, and the length of such gaps corresponds to the degree of reflection those ordinals enjoy. 1
On the transfinite action of 1 tape Turing machines
 Computational Paradigms: Proceedings of CiE2005
, 2005
"... Abstract. • We produce a classification of the pointclasses of sets of reals produced by infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We conside ..."
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Abstract. • We produce a classification of the pointclasses of sets of reals produced by infinite time turing machines with 1tape. The reason for choosing this formalism is that it apparently yields a smoother classification of classes defined by algorithms that halt at limit ordinals. • We consider some relations of such classes with other similar notions, such as arithmetical quasiinductive definitions. • It is noted that the action of ω many steps of such a machine can correspond to the double jump operator (in the usual Turing sense): a−→ a ′ ′. • The ordinals beginning gaps in the “clockable ” ordinals are admissible ordinals, and the length of such gaps corresponds to the degree of reflection those ordinals enjoy. 1
The Undecidability of Propositional Adaptive Logic ∗
, 2005
"... p r e p r i n t s i n a n a l y t i c p h i l o s o p h y ..."
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p r e p r i n t s i n a n a l y t i c p h i l o s o p h y