Difference That Preserves : From Transcendental Genesis to a Genealogical Foundation of Mathematics
Ballús Santacana, Andreu (Universitat Autònoma de Barcelona. Departament de Filosofia)

Fecha:	2026
Resumen:	This paper reconstructs the philosophical genesis of a foundational motif-difference that preserves-emerging at the intersection of ontology, logic, and mathematics. Through a genealogical arc spanning Fichte's theory of self-positing, Hegelian mediation, Bergsonian duration, and the anti-psychologism of Bolzano and Frege, we identify a deep tension in modern foundations: how can a logic of differentiation account for identity across transformation? We propose that this unresolved tension structures both historical and contemporary foundational programs. To address it, we articulate a new meta-theoretical framework-Mnēmaic logic-which grounds preservation not in static identity, but in recursive genesis. This paper provides the philosophical foundation and conceptual justification for that framework; its formal development appears in a companion article (Ballús Santacana, 2025). We conclude by suggesting that difference-that-preserves offers a powerful alternative to existing models of identity, continuity, and foundation in mathematical logic.
Nota:	Altres ajuts: acords transformatius de la UAB
Derechos:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió publicada
Materia:	German Idealism ; Fichte ; Simondon ; Individuation ; Genealogical ontology ; Category theory ; Mathematical epistemology
Publicado en:	Foundations of Science, 2026 , ISSN 1572-8471

DOI: 10.1007/s10699-025-10028-x

26 p, 1.1 MB

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