Mathematicians are machines that are unable to recognize the fact that they are machines

I am reading a Russian book about the “no computer thesis” based on the Gödel theorem. In the book there was a nice quote – see below – that somewhat close to what Bruno says.

“And if such is the case, then we (qua mathematicians) are machines that are unable to recognize the fact that they are machines. As the saying goes: if our brains could figure out how they work they would have been much smarter than they are. Gödel’s incompleteness result provides in this case solid grounds for our inability, for it shows it to be a mathematical necessity. The upshot is hauntingly reminiscent of Spinoza’s conception, on which humans are predetermined creatures, who derive their sense of freedom from their incapacity to grasp their own nature. A human, viz. Spinoza himself, may recognize this general truth; but a human cannot know how this predetermination works, that is, the full theory. Just so, we can entertain the possibility that all our mathematical reasoning is subsumed under some computer program; but we can never know how this program works. For if we knew we could diagonalize and get a contradiction.”

Haim Gaifman, What Gödel’s Incompleteness Result Does and Does Not Show

Discussion on the everything-list, 15.10.2017

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