On Philomatics and Psychomatics for Combining Philosophy and Psychology with Mathematics
This work proposes a novel interdisciplinary framework for researchers in philosophy, psychology, and mathematics, though it appears incremental as it builds on existing cross-disciplinary ideas without solving a specific problem.
The paper introduces philomatics and psychomatics as hybrid fields combining philosophy and psychology with mathematics, exploring motivations like analytical philosophy and mathematical algorithm justification, and provides examples such as linking Plato's theory of forms to machine learning and Wittgenstein's family resemblance to clustering.
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.