The fundamental cognitive approaches of mathematics


We propose a way to explain the diversification of branches of mathematics, distinguishing the different approaches by which mathematical objects can be studied. In our philosophy of mathematics, there is a base object, which is the abstract multiplicity that comes from our empirical experience. However, due to our human condition, the analysis of such multiplicity is covered by other empirical cognitive attitudes (approaches), diversifying the ways in which it can be conceived, and consequently giving rise to different mathematical disciplines. This diversity of approaches is founded on the manifold categories that we find in physical reality. We also propose, grounded on this idea, the use of Aristotelian categories as a first model for this division, generating from it a classification of mathematical branches. Finally we make a history review to show that there is consistency between our classification, and the historical appearance of the different branches of mathematics.

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