Abstract

Abstract. Some have claimed that Gödel’s incompleteness theorems on the formal axiomatic model of mathematical thought can be used to demonstrate that mind is not mechanical, in opposition to a Formalist-Mechanist Thesis. Following an explanation of the incompleteness theorems and their relationship with Turing machines, we here concentrate on the arguments of Gödel (with some caveats) and Lucas among others for such claims; in addition, Lucas brings out the relevance to the free will debate. Both arguments are subject to a number of critiques. The article concludes with the formulation of a modified Formalist-Mechanist Thesis which prima facie guarantees partial freedom of the will in the development of mathematical thought. 1. Logic, determinism and free will. The determinism-free will debate is perhaps as old as philosophy itself and has been engaged in from a great variety of points of view including those of scientific, theological and logical character; my concern here is to limit attention to two arguments from logic. To begin with, there is an argument in support of determinism that dates back to Aristotle, if not farther. It rests on acceptance of the Law of Excluded Middle, according to which every proposition is either true or false, no

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