Heraclitean Dialectical Concept Space

TL;DR

This paper introduces Heraclitean Dialectical Concept Spaces, a topological framework for modeling the evolution and development of concepts across various domains, capturing their emergence and transformations.

Contribution

It presents a novel topological model that represents concept evolution through overlaps, remainders, and inheritance, extending across developmental stages with a colimit topology.

Findings

Framework successfully models concept evolution in economics, biology, and mathematics.

Demonstrates how new concepts emerge from structural gaps.

Provides a global view of conceptual change over time.

Abstract

We introduce Heraclitean Dialectical Concept Spaces (HDCS), a topological framework for modelling how concepts evolve. Concepts are represented as open regions generated by neighbourhoods in a feasible family, and their relationships are organised through overlaps and channel ideals. New concepts emerge from remainders where existing structures fail to fit together, and inherit their topology from these parent regions. HDCS extends across developmental stages using carry maps and a colimit topology, giving a global picture of conceptual change. Short case studies from economic exchange, biology, and the history of the zero symbol illustrate the scope of the framework.