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Use and misuse of Gödel’s theorem. (English) Zbl 1073.03002

The author comments on work by Wang, Lucas and Putnam concerning the philosophical meaning of Gödel’s incompleteness theorem. We know from Wang that in Gödel’s opinion the two most interesting results proved with rigor about minds and machines are the following: (G1) The human mind is incapable of formulating all its mathematical intuitions; (G2) Either the human mind can decide more number-theoretical questions than any machine or else there exist number-theoretical questions undecidable for the human mind. In this paper the author addresses among others the following questions and does so in a most interesting way: 1. What is the difference between (G1) and (G2)? 2. Are Gödel’s theorems applied to minds or brains? 3. Which alternative in (G2) should we choose?

MSC:

03A05 Philosophical and critical aspects of logic and foundations
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