On the Issue of the Formation of Mathematical Ontology: Historical and Philosophical Aspect

Abstract

The article analyzes the possibilities of mathematics’ application to the physical reality from the historical-philosophical point of view. The undertaken analysis of the specific works of natural scientists of the past shows that the well-known thesis of Aristotle’s philosophy about the impossibility of applying mathematics in the “sublunary” world requires clarification. Most of the naturalists before Galileo’s time were undoubtedly Aristotelians. Accepting the qualitative variabil­ity of the “sublunary” world in Aristotle’s philosophy, when turning to physics they put into use, starting with Ptolemy, the possibility of a mathematical de­scription of the world. In this connection one of the main principles was the ad­justment of “projecting the law of heaven onto the earth”, which has been used in different ways. Aristotle’s philosophy forbade the application of mathematical laws in the world of physics, specifically in the so-called “sublunary world”. This was because in this area of being prevail four primary elements – fire, air, earth, and water, subject to continuous change, emergence, and destruction. From Aristotle’s point of view this could not be described within the framework of a mathematical approach. These changes are qualitative and this qualitative­ness should be reflected by corresponding physics. Such qualitative physics op­posed the Pythagorean and Platonic tradition, that allowed the use of mathe­matics in the physical world. In the course of history, however, exactly the philosophy of Aristotle held the dominant position. A thorough analysis of the natural scientists’ works who adhered to the Aristotelian point of view shows that all of them allowed the possibility of applying mathematics in the physical world