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.
