| Abstract [eng] |
This master’s thesis examines Aristotle’s philosophy of arithmetic and aims to present a consistent definition of the ontological status of the number. Its main thesis is that numbers are mental substances that exist only potentially in reality. It is argued that the existence of numbers as such is enabled by the mind that perceives them: prior to perception, they exist potentially as accidental attributes of groups of objects; in thought they appear as hylomorphic substances, the units as matter being constituted by numerical form. The matter of sensible numbers is specific due to the measure applied to them, and the mathematician considers noetic numbers, the matter of which is sensible as well, yet not considered as sensible – only as an abstract discrete multitude. Numerical forms are separated in the mind by abstraction, after mentally reducing individual groups of various objects to their quantity alone and separating the number as the property constituting this quantity. In this way, the numerical attribute appears as if it plays the role of form, establishing a unifying collective identity of the units. Such a theory of arithmetic allows to state that numbers as entities are not separate from the sensible world, but rather derived from it, and applicable to it. |
