We have managed to come up with one perfect formal system of rationality: mathematics, in which you can be “absolutely certain” of a statement, as long as it can be expressed in a certain language and doesn’t actually depend on any observations.
When doing math, humans tend to assume that certain formal systems are consistent. But we can’t actually prove it; it’s ultimately an empirical question (and actually it would be even without the incompleteness theorem; if strong consistent formal system could prove their own consistency, that wouldn’t make them any different from strong inconsistent formal systems).
Though as far as empirical questions go, the consistency of certain formal systems fundamental to human math does seem to be extremely probable.
That’s incorrect. As shown by Gödel’s second incompleteness theorem, mathematical formal systems divide into three categories:
Systems that are inconsistent.
Systems that can’t prove their own consistency.
Systems that aren’t particularly powerful.
When doing math, humans tend to assume that certain formal systems are consistent. But we can’t actually prove it; it’s ultimately an empirical question (and actually it would be even without the incompleteness theorem; if strong consistent formal system could prove their own consistency, that wouldn’t make them any different from strong inconsistent formal systems).
Though as far as empirical questions go, the consistency of certain formal systems fundamental to human math does seem to be extremely probable.