On Philomatics and Psychomatics for Combining Philosophy and Psychology with Mathematics

TL;DR

This paper introduces the concepts of philomatics and psychomatics as interdisciplinary frameworks combining philosophy, psychology, and mathematics, illustrating their potential through examples like semantics, Plato's forms, and Wittgenstein's family resemblance.

Contribution

It proposes novel interdisciplinary concepts that integrate philosophy and psychology with mathematics, providing foundational examples and motivating future research directions.

Findings

Analysis of the relation between the context principle and attention mechanisms.

Connections between Plato's forms and modern scientific theories.

Linking Wittgenstein's family resemblance to mathematical clustering.

Abstract

We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy, proposing science of philosophy, justifying mathematical algorithms by philosophy, and abstraction in both philosophy and mathematics. We enumerate various examples for philomatics and psychomatics, some of which are explained in more depth. The first example is the analysis of relation between the context principle, semantic holism, and the usage theory of meaning with the attention mechanism in mathematics. The other example is on the relations of Plato's theory of forms in philosophy with the holographic principle in string theory, object-oriented programming, and machine learning. Finally, the relation between Wittgenstein's family resemblance and clustering in mathematics is explained. This paper opens the door of research for combining philosophy and psychology with mathematics.