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
http://www.columbia.edu/~hg17/godel-incomp4.pdf
Best wishes,
Evgenii
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