Kurt Gödel, our favorite Good Guy, expresses a novel sort of challenge to the reductionist ethos typical of neuroscientists. Dawson Logical Dilemmas (1997), p. 198, reports that Gödel believed he had demonstrated the following:
Either ‘the working of the human mind cannot be reduced to the working of the brain, which to all appearances is a finite machine”, or else “mathematical objects and facts .. exist objectively and independently of our mental acts and decisions.” Those alternatives were not, of course, mutually exclusive. Indeed, he was firmly convinced of the truth of both.
Logically speaking, a neurological reductionist could still assent to that proposition, negating the first disjunct and allowing mathematical objects to sort themselves out as they may, since they lie outside his purview. But in practice, such reductionists tend to dismiss the other Invisibilia as well.
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