Linking Game-Theoretical Approaches with Constructive Type Theory: Dialogical Strategies, CTT demonstrations and the Axiom of Choice (SpringerBriefs in Philosophy) - Softcover

Clerbout, Nicolas; Rahman, Shahid

Softcover

ISBN 10: 3319190628 ISBN 13: 9783319190624

Publisher: Springer, 2015

Synopsis

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.

About this title

About the Author

Shahid Rahman is full-professor (classe exceptionnelle) of logic and epistemology at the Université de Lille-Nord-pas-de-Calais, Sciences Humaines et Sociales. He is also researcher at the UMR-CNRS 8163 : STL. Prof. Rahman works on philosophy and history of logic and the foundations of mathematics. He is the leading researcher in the field of the dialogical approach to logic. Prof. Rahman is the main editing director of two collections of books in Springer, namely, Logic, Epistemology and the Unity of Science (more than 40 volumes edited so far) ; and Logic, Argumentation and Reasoning, Perspectives from the Social Sciences and the Humanities. He is also main editor director of three other collections in College Publications, London. His most recent book include N. Clerbout/S. Rahman: Linking Game-Theoretical Approaches with Constructive Type Theory. Dialogical Strategies, CTT Demonstrations and the Axiom of Choice, Dordrecht, Springer, 2015; a Ansten Klev is postdoctoral fellow at the Czech Academy of Sciences. He holds a PhD in philosophy from Leiden University. His research interests are primarily in the philsophy and history of logic and mathematics. He is especially interested in the philosophical foundations of Martin-Löf's type theory. Zoe McConaughey is a Ph.D student in history and philosophy of logic at the Université de Lille and the Université du Québec à Montréal under the joint supervision of Shahid Rahman and Mathieu Marion; her doctoral dissertation, "La Science et l'activité du dialecticien", aims at developping Aristotle's logic within the dialogical framework of immanent reasoning in order to highlight the dialectical background of the Organon.

¿Nicolas Clerbout is Profesor of Philosophy at the University of Valparaíso, Chile. He works on logic and philosophy of logic and is an expert in the field of the dialogical approach to logic. He also serves as executive editor for the Springer collection "Logic, Epistemology and the Unity of Science" and as editor for one other collection in College Publications.

Edition details

• Publisher: Springer
• Publication date: 2015
• Language: English
• ISBN 10: 3319190628
• ISBN 13: 9783319190624
• Binding: Paperback
• Edition number: 1
• Number of pages: 99