The problem of computational complexity and undecidability from the perspective of transcendental philosophy

In this study, artificial intelligence's ability to model human thinking is discussed through transcendental philosophy. The question of what it means to think is addressed from different perspectives in order to provide a basis for discussion. Based on this ground, the field of the theory of computation is analyzed in order to look at the counterpart of thinking in theoretical computer science. Within this field, the problem of computational complexity, in which computability is subject to certain kinds of undecidability, is discussed. In the case of the P vs Np problem, it was determined that the reason for the emergence of the computational complexity problem was the theoretical limitations of computers operating on the basis of the Turing machine. The aim of this study is to show that NP cannot be equal to P based on Kant's transcendental philosophy. The view that NP is not equal to P is since computers are subjected to the brute search method when solving problems in the set NP. It has been argued that the justification for brute search can only be understood from transcendental philosophy. In defense of this thesis, Kant's views on the distinction of concept-intuition, three dimensionality of intuition, regulative use of reason, the function of practical reason for problem solving, and reflexive judgments were used. In addition to understanding the P vs NP problem, these views provide an important explanation of the human-machine difference in terms of thinking activity. Consequently, in the case of computational complexity problems in P vs NP, the reason for the exposure to brute search is the computational limitations of computers. Moreover, Kant's understanding of the multifaceted functioning of human thinking has also shown that human thinking is not limited to formal representation. It has been seen that the human mind, which is not limited to the faculty of formal representation, is able to avoid brute searching in many cases. Based on this difference that the human mind has against machines, it is concluded that P is not equal to NP.