Advances In Proof Theoretic Semantics
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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.
Advances In Proof Theory
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Author : Reinhard Kahle
language : en
Publisher: Birkhäuser
Release Date : 2016-05-04
Advances In Proof Theory written by Reinhard Kahle and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-04 with Mathematics categories.
The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science.
Axiomatic Thinking I
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Author : Fernando Ferreira
language : en
Publisher: Springer Nature
Release Date : 2022-10-13
Axiomatic Thinking I written by Fernando Ferreira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
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 : 2024-04-01
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 2024-04-01 with Philosophy categories.
This book provides philosophers and logicians with a broad spectrum of views on contemporary research on the problem of deduction, its justification and explanation. The variety of distinct approaches exemplified by the single chapters allows for a dialogue between perspectives that, usually, barely communicate with each other. The contributions concern (in a possibly intertwined way) three major perspectives in logic: philosophical, historical, formal. The philosophical perspective has to do with the relationship between deductive validity and truth, and questions the alleged conclusiveness of deduction and its epistemic contribution. It also discusses the role of linguistic acts in deductive practice, and provides a cognitive-didactic contribution on how we may learn through deduction. In the historical perspective, the contributions discuss the ideas of some major historical figures, such as Bolzano, Girard, Gödel, and Peano. Finally, in the formal perspective, the mathematics of deduction is dealt with mainly from an intuitionistic-constructivist or proof-theoretic point of view, with focus on “ecumenic” or internalistic approaches to logical validity, on the nature and identity of proofs, and on dialogical setups. Chapter [14] is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
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.
Reasoning With Attitude
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Author : Luca Incurvati
language : en
Publisher: Oxford University Press
Release Date : 2023-12-15
Reasoning With Attitude written by Luca Incurvati and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-15 with Language Arts & Disciplines categories.
Certain combinations of sounds or signs on paper are meaningful. What makes it the case that, unlike most combinations of sounds or signs, they have meaning? What is this meaning that they have? And what is it to understand this meaning? The traditional answers to these questions are based on the idea that words stand for something, but it is difficult to say what words such as good, if, or probable stand for. This book advances novel answers based on the idea that words get their meaning from the way they are used to express states of mind and what follows from them. It articulates a precise version of this idea, at a time when the shortcomings of the traditional answers are hotly discussed.
Epistemology Knowledge And The Impact Of Interaction
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Author : Juan Redmond
language : en
Publisher: Springer
Release Date : 2016-04-28
Epistemology Knowledge And The Impact Of Interaction written by Juan Redmond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Philosophy categories.
With this volume of the series Logic, Epistemology, and the Unity of Science edited by S. Rahman et al. a challenging dialogue is being continued. The series’ first volume argued that one way to recover the connections between logic, philosophy of sciences, and sciences is to acknowledge the host of alternative logics which are currently being developed. The present volume focuses on four key themes. First of all, several chapters unpack the connection between knowledge and epistemology with particular focus on the notion of knowledge as resulting from interaction. Secondly, new epistemological perspectives on linguistics, the foundations of mathematics and logic, physics, biology and law are a subject of analysis. Thirdly, several chapters are dedicated to a discussion of Constructive Type Theory and more generally of the proof-theoretical notion of meaning.Finally, the book brings together studies on the epistemic role of abduction and argumentation theory, both linked to non-monotonic approaches to the dynamics of knowledge.
Proceedings Of The 14th And 15th Asian Logic Conferences
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Author : Byunghan Kim
language : en
Publisher: World Scientific
Release Date : 2019-01-15
Proceedings Of The 14th And 15th Asian Logic Conferences written by Byunghan Kim and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-15 with Mathematics categories.
The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.
Harmony And Paradox
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Author : Luca Tranchini
language : en
Publisher: Springer Nature
Release Date : 2024-04-18
Harmony And Paradox written by Luca Tranchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-18 with Philosophy categories.
This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs). It demonstrates that identity of proof is a key both to clarify some —still not wholly understood— notions at the core of proof-theoretic semantics, such as harmony; and to broaden the range of the phenomena which can be analyzed using the tools of this semantic paradigm, so as to include for instance paradoxes. The volume covers topics such as the philosophical significance of different criteria of identity of proofs, and adequacy conditions for an intensional account of the notion of harmony. The author also examines the Prawitz-Tennant analysis of paradoxes by investigating on the one hand the prospectsof turning it into a theory of meaning for paradoxical languages, and on the other hand two distinct kinds of phenomena, first observed by Crabbe and Ekman, showing that the Tennant-Prawitz criterion for paradoxicality overgenerates. This volume is of interest to scholars in formal and philosophical logic.
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.