Paradoxes and contradictions of artificial intelligence: 90 years of K. Gödel’s first incompleteness theorem and 60 years of J. Lucas’s argument

Abstract

Today, the study of the issue of distinction has turned out to be extremely relevant – what proportion of the work in the produced artifact belongs to a person, and what proportion belongs to a computer. In this direction, it is important to develop computer analyzers of computer generators of texts, pictures, music, animations, and videos. The fundamental theoretical-algorithmic status of such generators is given by the Gödel–Lucas–Penrose test. In 1961, Oxford professor J. Lucas, on the basis of Gödel’s second theorem, con­cluded that the human mind is fundamentally superior to all kinds of computing systems. R. Penrose, supporting this position, stated that human consciousness is not algorithmic and goes beyond computability. This argument has generated extensive discussion regard­ing its philosophical underpinnings, mathematical validity, physical and neurophysiologi­cal explanations, psychological credibility, and technological implementation. The dispute about the importance and alternative ways of interpreting the argument does not stop, con­stituting one of the basic provisions of the philosophy and methodology of artificial intel­ligence and cognitive science. In October 2021, the SCMAI RAS held the All-Russian Symposium “Artificial Intelligence: Paradoxes and Contradictions”, during which the log­ical-philosophical, formal-computational and cultural-anthropological aspects of the Gödel-Lucas argument were studied, and possible ways of its transformation and development were shown, such as the Gödel-Lucas-Watt test.