E-Books →Advances in Peircean Mathematics The Colombian School (Peirceana)

English | 2023 | ISBN: 978-3110717617 | 228 pages | True PDF EPUB | 13.99 MB
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.