The Realism-Antirealism Debate in the Age of Alternative Logics
The Realism-Antirealism Debate in the Age of Alternative Logics

Author: Shahid Rahman

Publisher: Springer Science & Business Media

Published: 2011-09-22

Total Pages: 352

ISBN-13: 940071923X

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The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.

Logics and Falsifications
Logics and Falsifications

Author: Andreas Kapsner

Publisher: Springer

Published: 2015-01-07

Total Pages: 216

ISBN-13: 3319052063

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This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time. The volume is divided into three large parts. The first part provides important background information about Dummett’s program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take. "Kapsner’s book is the first detailed investigation of how to incorporate the notion of falsification into formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." Graham Priest, Graduate Center, City University of New York and University of Melbourne

Past and Present Interactions in Legal Reasoning and Logic
Past and Present Interactions in Legal Reasoning and Logic

Author: Matthias Armgardt

Publisher: Springer

Published: 2015-05-18

Total Pages: 275

ISBN-13: 3319160214

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This volume explores the relation between legal reasoning and logic from both a historical and a systematic perspective. The topics addressed include, among others, conditional legal acts, disjunctions in legal acts, presumptions and conjectures, conflicts of values, Jørgensen ́s Dilemma, the Rhetor ́s Dilemma, the theory of legal fictions and the categorization of contracts. The unifying problematic of these contributions concerns the conditional structures and, more particularly, the relationship between legal theory and legal reasoning in the context of conditions. The contributions in this work constitute the first results of the ANR-DFG joint research project “JuriLog” (Jurisprudence and Logic), which aims at fostering the cooperation between legal scholars and philosophers. On the one hand, lawyers and legal scholars have an interest in emphasizing the logical character of legal reasoning. In this respect, the present enquiry examines the question of how logic, especially newer forms of dialogical logic, can be made fruitful as a significant area of philosophy for jurisprudence and legal practice. On the other hand, logicians find in legal reasoning a striving towards clear definitions and inference-procedures that is relevant to their discipline. In order to fully understand such reciprocal relationships, it is necessary to bridge the gap between law, logic and philosophy in contemporary academic research. The essays collected in this volume all work towards this common goal. The book is divided in three sections. In the first part, the strong relation between Roman Law and logic is explored with respect to the analysis of disjunctive statements in legal acts. The second part focuses on Leibniz ́s legal theory. The third part, finally, is dedicated to current interactions between law and logic.

Linking Game-Theoretical Approaches with Constructive Type Theory
Linking Game-Theoretical Approaches with Constructive Type Theory

Author: Nicolas Clerbout

Publisher: Springer

Published: 2015-07-08

Total Pages: 118

ISBN-13: 3319190636

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This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work’s subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.

Pluralisms in Truth and Logic
Pluralisms in Truth and Logic

Author: Jeremy Wyatt

Publisher: Springer

Published: 2018-12-29

Total Pages: 479

ISBN-13: 3319983466

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This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth theorists and philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity.

Epistemology, Knowledge and the Impact of Interaction
Epistemology, Knowledge and the Impact of Interaction

Author: Juan Redmond

Publisher: Springer

Published: 2016-04-28

Total Pages: 556

ISBN-13: 3319265067

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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.

Graham Priest on Dialetheism and Paraconsistency
Graham Priest on Dialetheism and Paraconsistency

Author: Can Başkent

Publisher: Springer Nature

Published: 2020-01-01

Total Pages: 704

ISBN-13: 3030253651

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This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes .

Garcian Meditations
Garcian Meditations

Author: Jon Cogburn

Publisher: Edinburgh University Press

Published: 2017-03-08

Total Pages: 256

ISBN-13: 1474415938

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The publication of Form and Object: A Treatise on Things by Tristan Garcia, Prix de Flore-winning novelist, philosopher, essayist, and screenwriter is a genuine event in the history of philosophy. Situating this event within classical, modern and contemporary dialectical space, Jon Cogburn evaluates Garcia's metaphysics, differential ontology, and militant anti-reductionism through a series of seemingly incompatible oppositions: substance/process, analysis/dialectic, simple/whole and discovery/creation. ogburn also includes a critical assessment of the consequences of Garcia's philosophy, the various unresolved problems in his treatise and the future prospects of speculative metaphysics.

Meaning in Dialogue
Meaning in Dialogue

Author: James Trafford

Publisher: Springer

Published: 2016-10-24

Total Pages: 238

ISBN-13: 3319472054

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This book argues for a view in which processes of dialogue and interaction are taken to be foundational to reasoning, logic, and meaning. This is both a continuation, and a substantial modification, of an inferentialist approach to logic. As such, the book not only provides a critical introduction to the inferentialist view, but it also provides an argument that this shift in perspective has deep and foundational consequences for how we understand the nature of logic and its relationship with meaning and reasoning. This has been upheld by several technical results, including, for example a novel approach to logical paradox and logical revision, and an account of the internal justification of logical rules. The book shows that inferentialism is greatly strengthened, such that it can answer the most stringent criticisms of the view. This leads to a view of logic that emphasizes the dynamics of reasoning, provides a novel account of the justification and normativity of logical rules, thus leading to a new, attractive approach to the foundations of logic. The book addresses readers interested in philosophy of language, philosophical and mathematical logic, theories of reasoning, and also those who actively engage in current debates involving, for example, logical revision, and the relationship between logic and reasoning, from advanced undergraduates, to professional philosophers, mathematicians, and linguists.

The Road to Universal Logic
The Road to Universal Logic

Author: Arnold Koslow

Publisher: Birkhäuser

Published: 2015-06-10

Total Pages: 607

ISBN-13: 3319153684

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This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.