Topological and Algebraic Patterns in Philosophical Analysis: Case Studies from Ockham’s Quodlibetal Quaestiones and Avenarius’ Kritik der Reinen Erfahrung

The intersection of mathematics and philosophy has been extensively explored through logic and set theory, but the application of topological and algebraic tools to the analysis of philosophical arguments and conceptual structures has received less attention. By integrating key concepts from algebraic topology, homotopy theory and probability theory, we propose a framework for analysing epistemological and logical relationships across different philosophical traditions. Our approach classifies conceptual relations within mathematical spaces, allowing for systematic comparisons between frameworks of thought. The application of mathematical models contributes to a more comparative evaluation of epistemic dependencies, revealing local and global structures that might otherwise remain implicit. Within this framework, we consider as examples William of Ockham’s Quodlibetal Quaestiones and Richard Avenarius’ Kritik der Reinen Erfahrung, assessing their epistemological positions through the lens of formal mathematical tools. By utilizing theorems such as Seifert-van Kampen, Borel’s theorem and Kolmogorov’s zero-one law, we examine the logical foundations of Ockham’s rejection of metaphysical universals and Avenarius’ theory of pure experience. Our interdisciplinary analysis suggests that the two philosophical positions align with distinct but definable mathematical structures, reinforcing the applicability of topology and algebra to philosophical inquiry. This provides a refined model for historical and conceptual investigations in philosophy of science and epistemology.