Strong mechanism refuted: weak mechanism safe
Strong mechanism either contains mentalistic concepts—in its explanatory apparatus—or is inconsistent with Gödel’s theorem. Weak mechanism doesn't contain mentalistic concepts and can be shown to be consistent with Gödel’s theorem.
Strong mechanism holds that the mind can be entirely explained in mechanistic terms. But strong mechanism either contains mentalistic concepts—in its explanatory apparatus—or is inconsistent with Gödel’s theorem.
Weak mechanism, though, doesn't contain mentalistic concepts—because it only explains the concept of mind—and can be shown (via lengthy proof) to be consistent with Gödel’s theorem.
William Nelson Reinhardt (1986).
Notes: For a similar line of argument directed against philosophical behaviourism, see "Philosophical behaviourism is circular" Map 2, Box 87.
Strong mechanism: The mind is mechanical.
Weak mechanism: the concept of mind is mechanical.