3 is worded entirely differently. You've not stated that F cannot see that F is consistent, nor that humans can prove that F is consistent. So nothing seems to have been demonstrated at all. Line 4 does not follow at all.2. Then, according to Gödel’s theorem, F cannot prove its own consistency.
3. We, as human beings, can see that F is consistent.
4. Therefore, since F captures our reasoning, F could prove that F is consistent. — deepideas
the most compelling of which is I think Roger Penrose's argument based on Gödel's Incompleteness Theorem. — deepideas
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