Chapter

The Application of Gödel’s Theorem<sup>1</sup>

J. R. LUCAS

in The Freedom of the Will

Published in print September 1970 | ISBN: 9780198243434
Published online October 2011 | e-ISBN: 9780191680687 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198243434.003.0025
The Application of Gödel’s Theorem1

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According to the physical determinist, the conclusions which a particular man can produce as true will correspond to the theorems that can be proved in the corresponding logistic calculus. We now construct a Gödelian formula in this logistic calculus, say L, which cannot itself be proved-in-the-logistic-calculus-L. Therefore the particular human being who is, according to the physical determinist, represented by the logistic calculus L, cannot produce such a formula as being true. But he can see that it is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-logistic-calculus-L, was nonetheless — in fact, for that very reason — true. Therefore 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.

Keywords: Gödel; physical determinism; physical variables; logistic calculus

Chapter.  1610 words. 

Subjects: Metaphysics

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