Computability and Logic

Boolos, George S.; Burgess, John P.; Jeffrey, Richard C.

doi:10.1017/cbo9780511804076

Cited by 264 publications

(243 citation statements)

References 0 publications

Supporting

Mentioning

237

Contrasting

Unclassified

Order By: Relevance

“…Thus, Leitgeb's theory can be considered as a special case of Kripke's. 2 (Thus, whenever we talk about Kripke's theory of truth in what follows, Leitgeb's theory is always included.) We observe the following:…”

Section: Thus Whenever (N E A) Is a Fixed Point M E Coincides Witmentioning

confidence: 99%

Some Notes on Truths and Comprehension

Schindler

2017

J Philos Logic

View full text Add to dashboard Cite

In this paper we study several translations that map models and formulae of the language of second-order arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some well-known results in this area, and to provide a number of new results. Sections 3 and 4 contain some recursion-and proof-theoretic results about Kripke-style fixed-point theories of truth. Section 5 shows how to derive full second-order arithmetic from principles of truth. Section 6 investigates the proof-theoretic strength of disquotation without an arithmetical base theory.

show abstract

Section: Thus Whenever (N E A) Is a Fixed Point M E Coincides Witmentioning

confidence: 99%

Some Notes on Truths and Comprehension

Schindler

2017

J Philos Logic

View full text Add to dashboard Cite

show abstract

“…In words: if x y, then both x and y are sentences of L <2 , which is just the language of arithmetic L extended with the truth predicate T r 1 . Taken together, all of these modified axioms entail that our new theory respects Tarski's distinction between objectand meta-language.…”

Section: Axioms For Partial Ground and Typed Truthmentioning

confidence: 99%

“…First, note that P G 0 is P AG. Next, note P G 1 is a functional analog of our original theory P G, where the truth-predicate has been "renamed" T r 1 . In particular, we get that P G 1 proves the theory P T of positive truth.…”

Section: Axioms For Partial Ground and Typed Truthmentioning

confidence: 99%

See 1 more Smart Citation

Axiomatic Theories of Partial Ground II

Korbmacher

2017

J Philos Logic

View full text Add to dashboard Cite

This is part two of a two-part paper in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. In this part of the paper, we extend the base theory of the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to 0 and thus is consistent. We argue that this theory provides a natural solution to Fine's "puzzle of ground" about the interaction of truth and ground. Finally, we show that if we apply the truth-predicate to sentences involving our ground-predicate, we run into paradoxes similar to the semantic paradoxes: we get ground-theoretical paradoxes of self-reference.

show abstract

“…This calculus includes sentential logic, but also deals with inferences based on logical analogs of the quantifiers, any and some, with variables ranging over individuals in the universe of discourse. But, it is only semi-decidable, i.e., validity can be established in a finite number of steps, but no such procedure can exist to establish invalidity (see, e.g., Boolos & Jeffrey, 1989).…”

Section: Logical Form In Sentential Logicmentioning

confidence: 99%

Against Logical Form

Johnson‐Laird

2010

PSYCHOL BELG

View full text Add to dashboard Cite

, for help and encouragement over the years. The paper is dedicated to André Vandierendonck, a stalwart investigator of mental models. AbstractAn old view in logic going back to Aristotle is that an inference is valid in virtue of its logical form. Many psychologists have adopted the same point of view about human reasoning: the first step is to recover the logical form of an inference, and the second step is to apply rules of inference that match these forms in order to prove that the conclusion follows from the premises. The present paper argues against this idea. The logical form of an inference transcends the grammatical forms of the sentences used to express it, because logical form also depends on context. Context is not readily expressed in additional premises. And the recovery of logical form leads ineluctably to the need for infinitely many axioms to capture the logical properties of relations. An alternative theory is that reasoning depends on mental models, and this theory obviates the need to recover logical form. introduction

show abstract

Computability and Logic

Cited by 264 publications

References 0 publications

Some Notes on Truths and Comprehension

Some Notes on Truths and Comprehension

Axiomatic Theories of Partial Ground II

Against Logical Form

Contact Info

Product

Resources

About