On Gödel's Theorem and Mechanism: Inconsistency or Unsoundness is Unavoidable in any Attempt to 'Out-Gö del' the Mechanist

Issue title: Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk

Article type: Research Article

Authors: Krajewski, Stanisław

Affiliations: Institute of Philosophy, University of Warsaw, Poland. E-mail: [email protected]

Abstract: The so called Lucas argument, and more recently that put forward by Penrose, attempt to use Gödel's incompleteness theorems to demonstrate the non-mechanical nature of the mind, or in other words, that mind is not computational. Generalizing and strengthening the criticism of those arguments that have been made by mathematical logicians, it is proved that all possible variants of the argument must lead to a vicious circle or to inconsistency or to unsoundness (acceptance of a false statement). This defeats Lucas, who assumes his consistency and Penrose, who assumes his soundness. As Gödel has remarked, the existence of a robot, whom we will call Luke, equivalent to the humanmind as far as mathematical capacities go, is not excluded by his incompleteness theorem.

Journal: Fundamenta Informaticae, vol. 81, no. 1-3, pp. 173-181, 2007