Andreu Ballús

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.

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.

Much attention has been drawn to the cognitive basis of innovation. While interesting in many ways, this poses the threat of falling back to traditional internalist assumptions with regard to cognition. We oppose the ensuing contrast between internal cognitive processing and external public practices and technologies that such internal cognitive systems might produce and utilize. We argue that innovation is best understood from the gibsonian notion of affordance, and that many innovative practices emerge from the external scaffolding of cognitive processes. The public engageability that allows the disclosure of hidden affordances is not only –not even primarily– a property of cognitive products, but of cognitive processes. We elaborate on this claims by drawing on Dutilh Novaes’ account of formal languages as cognitive technologies and Hutto’s Narrative Practice Hypothesis. This paves the way to sketch some general principles on how to strategically seek for innovation by targeting hidden affordances.