On Modeling of the Mathematical Objects from the Philosophy of Mathematics

It has been accepted by most of the philosophers of mathematics that mathematical objects are abstract beings and closed to the five senses. However, although mathematical knowledge is closed to the senses as being an abstract entity, it is nevertheless so effective in the sensible world. In this study, it will be examined how the objects of the sensible real world are used as models to explain abstract mathematical objects. To make this modeling understandable, the relationship between abstract and sensible will be explained through mathematical objects like the concepts of number and geometric object, by making use of the views of some philosophers. Again, in order to better express the modeling relationship, the derivative, which is a mathematical concept, will be examined in two ways with an example from daily life. With the derivative example, both the concrete to abstract and the abstract to concrete thinking process will be tried to be exemplified. While explaining this thought process, it will be tried to explain how the information from an object perceived by the five senses transforms into information related to the abstract entity. The relationship between abstract and sensible will be tried to be made more understandable by exemplifying a method used by the tradition of kalam in history. The study will be concluded by briefly mentioning the possible contribution of the discussions we have mentioned to the relationship between metaphysical knowledge and mathematical knowledge.