Dag Prawitz On Proofs And Meaning
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Dag Prawitz On Proofs And Meaning
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Author : Heinrich Wansing
language : en
Publisher: Springer
Release Date : 2014-11-27
Dag Prawitz On Proofs And Meaning written by Heinrich Wansing and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Philosophy categories.
This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.
Natural Deduction
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Author : Dag Prawitz
language : en
Publisher: Courier Dover Publications
Release Date : 2006-02-24
Natural Deduction written by Dag Prawitz and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-24 with Mathematics categories.
An innovative approach to the semantics of logic, proof-theoretic semantics seeks the meaning of propositions and logical connectives within a system of inference. Gerhard Gentzen invented proof-theoretic semantics in the early 1930s, and Dag Prawitz, the author of this study, extended its analytic proofs to systems of natural deduction. Prawitz's theories form the basis of intuitionistic type theory, and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics. The concept of natural deduction follows a truly natural progression, establishing the relationship between a noteworthy systematization and the interpretation of logical signs. As this survey explains, the deduction's principles allow it to proceed in a direct fashion — a manner that permits every natural deduction's transformation into the equivalent of normal form theorem. A basic result in proof theory, the normal form theorem was established by Gentzen for the calculi of sequents. The proof of this result for systems of natural deduction is in many ways simpler and more illuminating than alternative methods. This study offers clear illustrations of the proof and numerous examples of its advantages.
Essays On Mathematical And Philosophical Logic
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Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 1979
Essays On Mathematical And Philosophical Logic written by Jaakko Hintikka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Gardening categories.
Proceedings of the Fourth Scandinavian Logic Symposium and of the First Soviet-Finnish Logic Conference, Jyväskylä, Finland, June 29-July 6, 1976.
Truth Meaning Justification And Reality
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Author : Michael Frauchiger
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-20
Truth Meaning Justification And Reality written by Michael Frauchiger and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-20 with Philosophy categories.
This collection concentrates on vital themes from Michael Dummett, one of the most influential and creative analytic philosophers of our time. The contributors, who include some of Dummett's distinguished former students, critically reflect on various concerns of Dummett's ground-breaking work in philosophy of language, metaphysics, and philosophy of mathematics and logic. The essays direct towards aspects of Dummett's pioneering work in the history of analytical philosophy, particularly his interpretations of the works of Frege and of Wittgenstein, which in conjunction with Dummett’s own highly original ideas on truth and meaning have shaped decisive contemporary debates concerning notably the distinction between realism and anti-realism. Further, the volume includes a cheerfully serious excursion into popular philosophy by Dummett himself and reveals less known facets of Dummett's many-sided work and activities such as his political philosophy of immigration and asylum, and beyond that, his untiring and warm-hearted campaign for racial justice and humanity. Contributors: Michael Dummett, Eva Picardi, Crispin Wright, Timothy Williamson, Ian Rumfitt, Daniel Isaacson, Dag Prawitz, Dale Jacquette, Alex Burri, Michael Frauchiger.
Prawitz S Epistemic Grounding
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Author : Antonio Piccolomini d’Aragona
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Prawitz S Epistemic Grounding written by Antonio Piccolomini d’Aragona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Philosophy categories.
This book presents an in-depth and critical reconstruction of Prawitz’s epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz’s theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz’s grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.
Philosophy Of Science
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Author : Alexander Christian
language : en
Publisher: Springer
Release Date : 2018-03-26
Philosophy Of Science written by Alexander Christian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-26 with Philosophy categories.
This broad and insightful book presents current scholarship in important subfields of philosophy of science and addresses an interdisciplinary and multidisciplinary readership. It groups carefully selected contributions into the four fields of I) philosophy of physics, II) philosophy of life sciences, III) philosophy of social sciences and values in science, and IV) philosophy of mathematics and formal modeling. Readers will discover research papers by Paul Hoyningen-Huene, Keizo Matsubara, Kian Salimkhani, Andrea Reichenberger, Anne Sophie Meincke, Javier Suárez, Roger Deulofeu, Ludger Jansen, Peter Hucklenbroich, Martin Carrier, Elizaveta Kostrova, Lara Huber, Jens Harbecke, Antonio Piccolomini d’Aragona and Axel Gelfert. This collection fosters dialogue between philosophers of science working in different subfields, and brings readers the finest and latest work across the breadth of the field, illustrating that contemporary philosophy of science has successfully broadened its scope of reflection. It will interest and inspire a wide audience of philosophers as well as scholars of the natural sciences, social sciences and the humanities. The volume shares selected contributions from the prestigious second triennial conference of the German Society for Philosophy of Science/ Gesellschaft für Wissenschaftsphilosophie (GWP.2016, March 8, 2016 – March 11, 2016).
Objects Structures And Logics
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Author : Gianluigi Oliveri
language : en
Publisher: Springer Nature
Release Date : 2022-03-08
Objects Structures And Logics written by Gianluigi Oliveri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Science categories.
This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
Advances In Proof Theoretic Semantics
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Author : Thomas Piecha
language : en
Publisher: Springer
Release Date : 2015-10-24
Advances In Proof Theoretic Semantics written by Thomas Piecha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-24 with Philosophy categories.
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.
Meaning And Justification An Internalist Theory Of Meaning
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Author : Gabriele Usberti
language : en
Publisher: Springer Nature
Release Date : 2023-07-28
Meaning And Justification An Internalist Theory Of Meaning written by Gabriele Usberti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-28 with Philosophy categories.
This volume develops a theory of meaning and a semantics for both mathematical and empirical sentences inspired to Chomsky’s internalism, namely to a view of semantics as the study of the relations of language not with external reality but with internal, or mental, reality. In the first part a theoretical notion of justification for a sentence A is defined, by induction on the complexity of A; intuitively, justifications are conceived as cognitive states of a particular kind. The main source of inspiration for this part is Heyting’s explanation of the intuitionistic meaning of logical constants. In the second part the theory is applied to the solution of several foundational problems in the theory of meaning and epistemology, such as Frege’s puzzle, Mates’ puzzle about synonymy, the paradox of analysis, Kripke’s puzzle about belief, the de re/de dicto distinction, the specific/non-specific distinction, Gettier’s problems, the paradox of knowability, and the characterization of truth. On a more general philosophical level, throughout the book the author develops a tight critique of the neo-verificationism of Dummett, Prawitz and Martin-Löf, and defends a mentalist interpretation of intuitionism.
Perspectives On Deduction Contemporary Studies In The Philosophy History And Formal Theories Of Deduction
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Author : Antonio Piccolomini d'Aragona
language : en
Publisher: Springer Nature
Release Date :
Perspectives On Deduction Contemporary Studies In The Philosophy History And Formal Theories Of Deduction written by Antonio Piccolomini d'Aragona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.