Penrose can't argue for his hypothesis
No scientist can either establish or refute the hypothesis that mathematical insight is non-algorithmic / noncomputable (see detailed text).
  • An empirically decidable property must be "a A2 property in the Borel hierarchy". Computability and noncomputability lack that property. Therefore, the hypothesis that mathematical intuition is non-computable is empirically undecidable.
  • Penrose's ability to recognise mathematical truths by insight is consistent both with the hypothesis that insight is algorithmic and the hypothesis that it isn't. So, Penrose's intuitions fail to establish his hypothesis one way or other.
Clark Glymour and Kevin Kelly (1990).
Immediately related elementsHow this works
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Artificial Intelligence Â»Artificial Intelligence
Are thinking computers mathematically possible? [7] Â»Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems Â»No: computers are limited by Gödel's theorems
Mathematical insight is non-algorithmic Â»Mathematical insight is non-algorithmic
The absurdity of algorithmic insight Â»The absurdity of algorithmic insight
Penrose can't argue for his hypothesis
Glymour and Kelly are too strict Â»Glymour and Kelly are too strict
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