Meta-Epistemological Nature of Mathematics and Its Implication to the Empirical Learning Process in Mathematics: An Extension of Plato’s Thoughts

Abstract

Mathematics philosophers do not have a common agreed understanding about the nature of Mathematics. An attempt to describe the nature of Mathematics begun in the 4^th C, BC, when Plato conceived that, Mathematics is constituted by abstract objects existing beyond the mind; and its mathematical knowledge is acquired empirically. Aristotle (Plato’s student) extended the ideas of Plato by conceiving that mathematical knowledge can be acquired with or without senses.Since then up to 17^th C, AD, debates continued, experimentalists standing on one side and rationalist on the other side, instead of focusing on the fundamental nature of Mathematics, they focused on whether mathematical knowledge is a an empirical knowledge or rational knowledge. However, from 17^th C, AD, debates moved from experimentalist versus rationalist to an attempt in resolving paradoxes in real number and set theories. The focus in describing precisely nature of Mathematics was completely lost.In respect to the reviews of Plato’s thoughts and related literature, it is concluded that, thoughts of Plato’s thoughts are correct and consistent. Metaphysically, Mathematics is built upon a set of mathematical objects that exist beyond the mind. The mathematical objects possess six attributes: shape, qualities, form, structure, properties and applicability. Also, epistemologically, the attributes of mathematical objects build the body of mathematical empirical knowledge. The empirical mathematical knowledge is acquired in a cycle of five stages: perception, exposition, execution, assimilation and rationalization stages.

Keywords: Nature of Mathematics, Metaphysical objects, Mathematical space, Mathematical objects, Meta-Epistemological attributes.

DOI: 10.7176/JPCR/56-02

Publication date:March 31^st 2023