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<p>This paper reconstructs the philosophical genesis of a foundational motif—<b>difference that preserves</b>—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—<i>Mnēmaic logic</i>—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.</p>

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Difference That Preserves: From Transcendental Genesis to a Genealogical Foundation of Mathematics

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  • 发表日期：

    2026年1月27日

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  • Andreu Ballús Santacana

摘要

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.