Gödel’s theorem is not decisive
The question of whether thinking is algorithmic can't be decided on the basis of Gödel’s theorem (see detailed text).
1) No mathematical insight is necessary to construct Gödel sentences.
2) Mathematical insight is involved only in seeing that the system that produces the Gödel sentence is consistent.
3) But, insight into consistency is not reliable—as is shown by numerous historical examples.
4) Because insight into consistency is unreliable, we can't know whether Gödel’s theorem applies to a given system, and we don't know that mathematical insight is non-algorithmic.
Martin Davis (1990).
Note: Also see the "Is the use of consistency in the Lucas argument problematic?" arguments on this map.