Advances in Peircean Mathematics : : The Colombian School / / ed. by Fernando Zalamea.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2022 Part 1
• MitwirkendeR: Arengas, Gustavo,; Oostra, Arnold,; Vargas, Francisco,; Zalamea, Fernando,
• HerausgeberIn: Zalamea, Fernando,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2022]; ©2022
• Year of Publication: 2022
• Language: English
• Series: Peirceana , 7
• Physical Description: 1 online resource (XVI, 212 p.)

The book explores Peirce's non standard thoughts on a synthetic continuum, topological logics, existential graphs, and relational semiotics, offering full mathematical developments on these areas. More precisely, the following new advances are offered: (1) two extensions of Peirce's existential graphs, to intuitionistic logics (a new symbol for implication), and other non-classical logics (new actions on nonplanar surfaces); (2) a complete formalization of Peirce's continuum, capturing all Peirce's original demands (genericity, supermultitudeness, reflexivity, modality), thanks to an inverse ordinally iterated sheaf of real lines; (3) an array of subformalizations and proofs of Peirce's pragmaticist maxim, through methods in category theory, HoTT techniques, and modal logics. The book will be relevant to Peirce scholars, mathematicians, and philosophers alike, thanks to thorough assessments of Peirce's mathematical heritage, compact surveys of the literature, and new perspectives offered through formal and modern mathematizations of the topics studied.

Table of Contents

Frontmatter -- Contents -- Dedication -- Acknowledgments -- Introduction -- 1 Category Theory Variations and Proofs of Peirce’s PragmaticistMaxim -- 2 A Full Model for Peirce’s Continuum -- 3 Intuitionistic and Geometrical Extensions of Peirce’s Existential Graphs -- 4 Around Arengas, Vargas, and Oostra Models for Peirce’s Thought -- Peirce Bibliography -- Secondary Bibliography -- Name Index -- Keyword Index