Meanings, Metaphors, and Morphisms: Theory of Indeterminate Natural Transformation (TINT)

TL;DR

This paper introduces TINT, a novel mathematical framework using category theory to model the dynamic and indeterminate process of meaning creation, exemplified through metaphor comprehension.

Contribution

It develops the concept of indeterminate natural transformation within category theory to formalize how meanings and metaphors are dynamically generated.

Findings

Models metaphor comprehension as a stochastic process.

Uses coslice categories and functors to represent structure interactions.

Provides a formal mathematical basis for understanding meaning creation.

Abstract

In the present paper, we propose a new theory named "Theory of indeterminate natural transformation (TINT)" to investigate the dynamical creation of meanings as association relationships between images, focusing on the metaphor comprehension as an example. TINT models the meaning creation as a kind of stochastic processes based on the mathematical structure defined by association relationships as morphisms in category theory, so as to represent the indeterminate nature of structure-structure interactions between the systems of the meanings of images. Such interactions are formulated in terms of so-called coslice categories and functors as structure-preserving correspondence between them. The relationship between such functors is "indeterminate natural transformation", the central notion in TINT, which models the creation of meanings in a precise manner. For instance, the process of metaphor comprehension is modeled by the construction of indeterminate natural transformation from a canonically defined functor which we call the base-of-metaphor functor.