Philosophy of Logic and Artificial Intelligence

Abstract

For many years, scientists have been trying to implement human intelligence in machines without being able to make a complete model of human mind. Some people connect this failure to theorems proved by Kurt Gödel in 1931 and they are called Gödel’s Incompleteness Theorems. The results of Gödel’s Incompleteness Theorem caused many philosophical debates between the “believers” of Artificial Intelligence (A.I) and those who find it impossible. The purpose of this project is to examine how Gödel’s Incompleteness Theorems give rise to limits on the prospects of A.I. The main subject area of this report is Philosophy of Logic, yet the scope is somewhat extended to Mathematics and Computer Science. Arguments in this report are based on the book ‘Gödel, Escher, Bach: an Eternal Golden Braid’ by Douglas R. Hofstadter and the article ‘Minds, Machines and Gödel’ by J.R. Lucas. As Gödel’s Incompleteness Theorems apply to ‘formal systems’, we firstly spell out what the theorems state and how they work inside a formal system. Further more, arguments on possibilities of implementing human intelligence are presented. Since this project is set on a debatable subject, no concrete conclusion is made.