The Boundary of Determinism: First Enlightenment from Turing’s Thought

Amid the significant breakthroughs in artificial intelligence (AI), it is of great significance to rationally understand its development. This article revisits Turing's ideas on computability and explores the issue of the boundaries of determinism. While the computational theory community recognizes that Turing's 1936 contribution on computable numbers touched upon the boundary of computability; however, this article argues that its profound significance lies in revealing the inherent limitations of human deterministic thinking itself. The article systematically combs through and analyzes how the pursuit of determinism in classical science ultimately relies on symbolic systems, as well as how Gödel and Turing mathematically proved the incompleteness and undecidability of such determinism through the encoding and self-reference of formal systems. The enlightenment derived from Turing's thought is that the boundary of determinism resides in self-reference. This insight provides crucial implications for understanding the essential limitations of artificial intelligence in the current technological landscape.