Mind or sensory experience?

Mathematics is the first to float independently of philosophical thought, creating a special approach based on deduction and a separate subject based on the study of the abstract quantum in things and the universe. Some believed that the innate mind is completely independent of experience and the sensory world, while, on the contrary, some disagreed with them, and judged the empirical sensory origin of all mathematical concepts, which gave rise to controversy and dissonance between the two positions and the problem. Which presents itself: Are mathematical concepts innate mental concepts or have they acquired the senses?

mental belief.

All rationalist philosophers, without exception, believe that the origin of mathematical concepts is pure and pure reason, that is, completely independent of the real sensuous world and knowledge emanating from it through the senses, and the mind is based on the subjective and innate principles and principles in it. Among the most famous representatives of this thesis are the Greek philosopher Plato, the French Descartes, the German Kant and others.

Where we find that the Greek philosopher Plato believed that mathematical concepts such as the straight line, the circle, the infinite, the largest and the smallest ... etc., are elementary concepts stemming from the mind and pre-existing in it; The mind, according to him, lived in the world of ideals and was aware of all facts. Among them are mathematical statements that are eternal and immutable, but when he left this world he forgot his thoughts and had to remember them. In order to understand it by reason alone, as he says in his book Al-Jumhuriya, “The world of parables is the principle of everything that exists and is reasonable and mentions knowledge.” Plato based his vision on the theory of knowledge and existence, as I previously believed that mathematical concepts in their properties are fixed, eternal and absolute, and from this it is judged that they are absent in the sensory world. Because it is mortal, relative, and always changing, and therefore it exists in its origin in the world of ideals from time immemorial, and the realities of this world are absolute, immutable and eternal. For example, when we say five pens, we see only pens, but we do not see the number 05, it is a purely mental concept.

The same opinion was found by the French philosopher and father of modern philosophy, René Descartes, who believed that the mathematical meanings of shapes and numbers are innate ideas that God placed in us from the beginning. Where they base their conclusions on it, he says in his book "Reflections", "Mathematical meanings are innate ideas that God deposited in us from the beginning." Descartes also proceeds from the fact that intuition is a feature of immutable mathematical concepts, but the senses err and deceive, such as seeing a broken stick in water, and its reality is otherwise. Intuitive and two qualities rooted in mathematical facts and concepts. Therefore, it cannot exist in the world of the senses, because it is changeable, while those concepts are subtle, and from it the mind did not lack in the beginning to see the external world in order to be able to perceive the concepts of mathematics. Rather, they are present in it instinctively and a priori.

This is what the leader of critical philosophy, Immanuel Kant, seeks, as he sees that time and space are abstract concepts, innate and a priori, and not derived from sensations or derived from experience, and therefore, mathematical concepts are innate concepts of their origin and the mind does not emerge from experience but is devoid of it.