Pure logic and a phenomenological constitution of algebraic structures: apophantics, ontology, and theory of manifolds in Edmund Husserl

Abstract

This article presents a possible way of understanding algebraic structures based on studies related to Edmund Husserl’s pure logic and theory of manifolds. It begins with the refutation of psychologism and the consequent grounding of logic as a theoretical, normative, and ideal science. Subsequently, apophantic logic and formal ontology are distinguished as correlative spheres of pure logic, responsible respectively for the structure of judgments and for the possible forms of objectivity. The theory of manifolds is then introduced as the natural unfolding of this articulation, providing the basis for the constitution of ideal mathematical domains. Group Theory is analyzed as a paradigmatic example of an algebraic manifold, showing how formal laws and predicative judgments constitute ideal objects. It is concluded that algebraic structures, phenomenologically understood, stem from a judicative rationality grounded in pure logic.