The mechanist's dilemma
The Lucas argument can be restated as a dilemma about consistency (see detailed text).
Consider some arbitrary machine M:

Either: M is consistent,

In which case, by Gödel’s theorem there will be a sentence that humans recognise as true but that M can't prove. So, we can do something that machine M can't.

Or, M is not consistent

In which case, M can't be a mind because minds must be consistent systems.

In either case, the machine can't be a mind.

John Lucas (1961).
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Artificial Intelligence »Artificial Intelligence
Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
The problem of consistency »The problem of consistency
The mechanist's dilemma
Lucas can't know when his Gödelization procedure is applicable »Lucas can't know when his Gödelization procedure is applicable
John Lucas »John Lucas
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