Using Kreisel’s Way Out to Refute Lucas-Penrose-Putnam Anti-Functionalist Arguments

Abstract

DOI: http://doi.org/10.26333/sts.xxxiv1.06 Georg Kreisel (1972) suggested various ways out of the Gödel incompleteness theorems. His remarks on ways out were somewhat parenthetical, and suggestive. He did not develop them in subsequent papers. One aim of this paper is not to develop those remarks, but to show how the basic idea that they express can be used to reason about the Lucas-Penrose-Putnam arguments that human minds are not (entirely) finitary computational machines. Another aim is to show how one of Putnam’s two anti-functionalist arguments (that use the Gödel incompleteness theorems) avoids the logical error in the Lucas-Penrose arguments, extends those arguments, but succumbs to an absurdity. A third aim is to provide a categorization of the Lucas-Penrose-Putnam anti-functionalist arguments.

Keywords

• functionalism
• Computational Liar
• Gödel incompleteness theorems
• finitary computational machine
• mathematical certainty
• finitary reasoning