The Reliability of Mathematical Reflection on the Thinking Structure of the World and Human Beings: Will Intuitionism Replace Logicism as the Foundation of Mathematics?

Abstract

Logicism has prevailed with the development of modern technology innovation for decades. This is true, especially in the research field of Artificial Intelligence and Machine Learning. On the contrary, the development of another branch of mathematical thought, Intuitionism was not so optimistic. No matter how large the gap between Logicism and Intuitionism is in the current development of several research fields, the debates and challenges that Intuitionism raised to the domination of Logicism are worthy of fundamental scrutiny. This article will not adopt a simplistic view of the two schools but compare them through their arguments upon whether mathematics is reliable to reflect or to tell the thinking structure of the world and human beings. It is concluded that the debate over the authenticity of the mathematical foundation is far from drawing a clear and satisfactory answer.