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Goedel's Theorem and Mechanism

Published online by Cambridge University Press:  25 February 2009

David Coder
David Coder
Affiliation:
University of Alberta
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Extract

In “Minds, Machines, and Gödel”, J. R. Lucas claims that Goedel's incompleteness theorem constitutes a proof “that Mechanism is false, that is, that minds cannot be explained as machines”. He claims further that “if the proof of the falsity of mechanism is valid, it is of the greatest consequence for the whole of philosophy”. It seems to me that both of these claims are exaggerated. It is true that no minds can be explained as machines. But it is not true that Goedel's theorem proves this. At most, Goedel's theorem proves that not all minds can be explained as machines. Since this is so, Goedel's theorem cannot be expected to throw much light on why minds are different from machines. Lucas overestimates the importance of Goedel's theorem for the topic of mechanism, I believe, because he presumes falsely that being unable to follow any but mechanical procedures in mathematics makes something a machine.

Type
Discussion
Information
Philosophy , Volume 44 , Issue 169 , July 1969 , pp. 234 - 237
Copyright
Copyright © The Royal Institute of Philosophy 1969

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References

1 Philosophy, Vol. XXXVI, No. 137, pp. 112–27Google Scholar; reprinted in Minds and Machines, Anderson, A. R., editor (Englewood Cliffs, N.J., 1964)Google Scholar. My page references are to the original.)

2 P. 112.

3 P. 126.

4 P. 112.

5 P. 113.

6 P. 113.

7 See e.g. Mendelson, E., Introduction to Mathematical Logic (Princeton, N.J., 1964), pp. 229 and following.Google Scholar

8 Pp. 113–4.