Fernando Zalamea – författare

Drawing a line, and then another, and another. Go back from the lines to the movements they capture and see gestures in them: not spatial displacements, but modes of knowledge that pass through the exercise of the body. Discovering something new in a gesture: the line that contracts into a point or the point that expands into a zone, perhaps sinking into a hole. Thus experiencing a diagram: a becoming other inscribed in the novelty of the gesture and in the changes of the forms it shapes. This and much more is discussed in the essays gathered in Diagrams and Gestures. Resulting from trans-disciplinary work between mathematicians, philosophers, linguists and semioticians, the volume delivers an up-to-date account of the most valuable research on the connections between gesture and diagram. As one of the most important themes in contemporary thought, the study of these connections poses a challenge for the future: to elaborate a theory that is equal to new and stimulating research methodologies. We call this theory a philosophy of diagrammatic gestures.

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.

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.

Cet ouvrage offre une vue panoramique du large spectre des mathématiques, modernes et contemporaines, et des nouvelles possibilités philosophiques qu’elles suggèrent. En négligeant les changements conceptuels profonds apparus en mathématiques au cours du XXe siècle, l’approche analytique dominante a en réalité entamé le divorce entre philosophie et pratique effective des mathématiques. Par l’étude de penseurs engagés dans les « mathématiques réelles » de leur époque (Lautman, Deleuze, Badiou, de Lorenzo ou Châtelet), Zalamea met au défi cette ignorance auto-imposée du « faire mathématique ».Les gestes créateurs du maître du XXe siècle Grothendieck et de ses continuateurs (Lawvere, Connes, Shelah ou Zilber – à côté de huit autres grands mathématiciens) sont ici explorés en détail. S’appuyant sur des philosophes comme Peirce, Merleau-Ponty ou Petitot, l’auteur fixe le programme d’une épistémologie nouvelle fondée sur ces puissants instruments conceptuels, forgés par l’esprit mathématique, mais négligés par les philosophes. En particulier, il ébauche une philosophie synthétique, proche de la théorie des catégories et de la logique des faisceaux, qui devrait aider à ouvrir des nouvelles portes à la pensée contemporaine.