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Author: Volker Halbach
Publisher: Cambridge University Press
ISBN: 1107424429
Category : Philosophy
Languages : en
Pages : 361
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Book Description
A survey of the most important axiomatizations of truth, exploring their properties and how the logical results impinge on philosophical topics.
Author: Volker Halbach
Publisher: Cambridge University Press
ISBN: 1107424429
Category : Philosophy
Languages : en
Pages : 361
Get Book Here
Book Description
A survey of the most important axiomatizations of truth, exploring their properties and how the logical results impinge on philosophical topics.
Author: Volker Halbach
Publisher: Cambridge University Press
ISBN: 1316584232
Category : Philosophy
Languages : en
Pages : 362
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Book Description
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 philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth.
Author: Leon Horsten
Publisher: MIT Press
ISBN: 0262297760
Category : Philosophy
Languages : en
Pages : 178
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Book Description
A philosopher proposes a new deflationist view of truth, based on contemporary proof-theoretic approaches. In The Tarskian Turn, Leon Horsten investigates the relationship between formal theories of truth and contemporary philosophical approaches to truth. The work of mathematician and logician Alfred Tarski (1901–1983) marks the transition from substantial to deflationary views about truth. Deflationism—which holds that the notion of truth is light and insubstantial—can be and has been made more precise in multiple ways. Crucial in making the deflationary intuition precise is its relation to formal or logical aspects of the notion of truth. Allowing that semantical theories of truth may have heuristic value, in The Tarskian Turn Horsten focuses on axiomatic theories of truth developed since Tarski and their connection to deflationism. Arguing that the insubstantiality of truth has been misunderstood in the literature, Horsten proposes and defends a new kind of deflationism, inferential deflationism, according to which truth is a concept without a nature or essence. He argues that this way of viewing the concept of truth, inspired by a formalization of Kripke's theory of truth, flows naturally from the best formal theories of truth that are currently available. Alternating between logical and philosophical chapters, the book steadily progresses toward stronger theories of truth. Technicality cannot be altogether avoided in the subject under discussion, but Horsten attempts to strike a balance between the need for logical precision on the one hand and the need to make his argument accessible to philosophers.
Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 696
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Book Description
Author: Franco Montagna
Publisher: Springer
ISBN: 3319062336
Category : Mathematics
Languages : en
Pages : 324
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Book Description
This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.
Author: Cezary Cieśliński
Publisher: Cambridge University Press
ISBN: 1107197651
Category : Philosophy
Languages : en
Pages : 313
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Book Description
This volume explores the deflationary claim of the innocence of truth, taking into account recent results on axiomatic truth theories.
Author: Dov M. Gabbay
Publisher: Elsevier
ISBN: 0080885470
Category : Mathematics
Languages : en
Pages : 1069
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Book Description
This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.• The entire range of modal logic is covered• Serves as a singular contribution to the intellectual history of the 20th century• Contains the latest scholarly discoveries and interpretative insights
Author: Mario Piazza
Publisher: Springer
ISBN: 3319933426
Category : Mathematics
Languages : en
Pages : 278
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Book Description
This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.
Author: Volker Halbach
Publisher: Walter de Gruyter
ISBN: 3110332728
Category : Philosophy
Languages : en
Pages : 248
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Book Description
On the one hand, the concept of truth is a major research subject in analytic philosophy. On the other hand, mathematical logicians have developed sophisticated logical theories of truth and the paradoxes. Recent developments in logical theories of the semantical paradoxes are highly relevant for philosophical research on the notion of truth. And conversely, philosophical guidance is necessary for the development of logical theories of truth and the paradoxes. From this perspective, this volume intends to reflect and promote deeper interaction and collaboration between philosophers and logicians investigating the concept of truth than has existed so far.Aside from an extended introductory overview of recent work in the theory of truth, the volume consists of articles by leading philosophers and logicians on subjects and debates that are situated on the interface between logical and philosophical theories of truth. The volume is intended for graduate students in philosophy and in logic who want an introduction to contemporary research in this area, as well as for professional philosophers and logicians
Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486782972
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Combining stories of great writers and philosophers with quotations and riddles, this original text for first courses in mathematical logic examines problems related to proofs, propositional logic and first-order logic, undecidability, and other topics. 2014 edition.
