No mechanists for Lucas to play with
The dialectical game never gets off the ground because there are no mechanists for Lucas to play with.
According to Lucas, mechanists believe that producing true sentences is an activity that can be reduced to finite features and behaviours.

But no real mechanist holds this finitistic view of intentional action.

All that real mechanists demand is that the mind be deterministic, and for that we do not need to assume that the mind is finite.

Daniel Dennett (1972).
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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
Argument from Gödel's theorem is dialectical »Argument from Gödel's theorem is dialectical
No mechanists for Lucas to play with
Daniel Dennett »Daniel Dennett
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