Abstract

Lucas plays off his understandings of the problem of freedom and Gödel's Theorem, concluding that, "... a human being cannot be represented by a logistic calculus and therefore cannot be described completely in terms of physical variables, all of whose values are completely determined by the conjunction of their values at some earlier time". Lucas approaches the problem of freedom from the perspective of a computer programmer. His argument is as follows. Men can construct a logistic calculus, L, of which Gödel's theorem is a theorem. Gödel's theorem is known-by-men-to-be-true, which is a fact. Facts have ontological status. Any attempt to represent this fact by a definite description must result in an infinite regress of meta-L's, for a Gödel theorem can be constructed in any meta-L powerful enough to show that Gödel's theorem is a theorem of L. Accordingly, men can do something which cannot be represented within L; men are therefore undeterminable. Lucas's position amounts to a rethinking of Fichte's position, set in the metaphor of meta-mathematical logic. However, whereas Fichte concluded that a man can choose to posit that he is free, and thereby make himself free, Lucas concludes that all men are free since some men know that Gödel's theorem is true. One question suggested by Lucas's argument is ontological, and another is epistemological. First, what is the ontological status of facts? Secondly, what is the distinction between knowing-that-p and showing-that-p? Ultimately, Lucas's demonstration pivots on equating the-completeness-of-L with knowing-the-completeness-of-L. It remains to be shown that that which is capable of knowing-that-p is governed in the act of knowing-that-p by the conditions which determine p.--M. D. P. [[sic]]