Prof. Dr. Vatan KARAKAYA
Kırşehir Ahi Evran University

AN ASSESSMENT ON THE PLACE OF MATHEMATICAL KNOWLEDGE BETWEEN FORM AND METAPHYSICS

It is known that the source of knowledge, which is the subject of thinking, is the realm of concrete or intangible existence. For this reason, the issue of how knowledge is produced from existence or how existence is the subject of knowledge has been one of the main subjects of philosophy throughout the history of thought. The approach of philosophy on this subject has led to finding the unchanging principles of existence, that is to seek universal truths. These orientations and pursuits have become an alliance in the fact that the knowledge of God is unchangeable and imperative, especially Aristotle and then Ibn Sînâ. The fact that the knowledge of God is logically necessary and unchangeable rather than ontological has necessitated the search for unchangeable principles on existence. Immutable principles on existence are possible through the forms possessed by the being. The lexical meaning of the word form is "shape", but it has been described as "the nature of something, the substance that makes it that thing" [1]. Depending on the philosophical definition of the form, the generally accepted definition given by Ibn Sînâ is "the substance that takes the thing it is from into the realm of action" [2]. According to Aristotle, who accepts the principle of existence as matter (heyula) and form, existence consists of the form realized in matter [3]. The first matter, which is considered as a potential force and a possibility for the emergence of existence, comes into existence only after it takes a form. The entity that takes on a form becomes available for classification as the same genus, the same species or the same chapter, and becomes perceptible by being divided into categories. Man has divided the realm of forms into different groups by using the cognitive features he has from his creation. The first group is the physical world of objects, in which the entity is open to sensory description and definitions of physical objects can be made with the forms obtained from physical objects. According to Aristotle's view adopted in Islamic Peripatetic philosophy, in order to understand what a thing is physically, it is necessary to know the reason for it and go as far as the first causes. In that case, four reasons must be sought for the realization of all kinds of phenomena and events that occur in the universe. These are matter, form, agent and objective causes. For obtaining information from non-physical entities, the form reason constitutes an important basis. The most general field of knowledge that is not physical and uses form is mathematical knowledge. Mathematical objects have form but are non-physical entities closed to the senses. In this study, how the being becomes the subject of mathematics by gaining form and the relationship between mathematical entities and the form will be examined. How mathematical entities correspond to counting and measuring through form and how we do mathematics through this relationship will be evaluated both in terms of classical philosophy and through modern approaches. Due to the dependence of mathematical and physical knowledge on logically necessary existence knowledge, the possibilities of metaphysical knowledge will also be briefly mentioned. In particular, it will be investigated whether the quantitative approach of Descartes in natural philosophy and the commitment to intuition in Kant's philosophy have a relationship with corporeal form ([4],[5]). Key Words: Knowledge, Mathematical object, Mathematical form