The limits of AI aesthetics and the limits of axiomatic systems

Abstract

As is well known, Artificial Intelligence systems, from now on AI, were nourished by some of the mathematical developments that occurred during the 20th century. Among these theorizations, Kurt Gödel's theorems regarding the consistency and completeness of axiomatic systems are especially relevant. Gödel's conclusions ended the idea of finding a complete mathematical system without contradictions. Since mathematical systems are theorizations that are based on basic postulates, it follows that in any system based on axioms there will be certain limits or insurmountable contradictions. Alan Turing discussed the aesthetic possibilities of computer systems, and his ideas can be understood as contradictory to those of Gödel regarding computing and art, considering that several generative AI systems are capable of imitating artistic activities and generating products that can or not fall into the category of “works of art.” We then discuss whether the aesthetics of AI have as boundaries the limits proposed by Gödel.