re: #767 Salamantis

It’s like the barber paradox; in a town was a barber who shaved all the people in the village who did not shave themselves. So who shaved the barber?

All such recursive paradoxes are examples of Godelian Incompleteness rending the fabric of logic - just like the set of all sets that do not contain themselves. There are many candidate members, but they cannot in principle be formed into a set without violating the set’s definition.

I never claimed that Godelian Incompleteness addressed everything, but what it DOES address hs proven to be central and fundamental to the understanding of the mathematical enterprise itself, and well beyond it. For the theorem’s philosophical and cognitive implications, I recommend I Am A Strange Loop by Douglas R. Hofstadter, the guy who wrote Godel, Escher, Bach: An Eternal Golden Braid, and for its wider mathematical implications, I recommend Mathematics: The Loss of Certainty by Morris Kline.

But you see, all of this assumes a Cartesian certainty is possible, or desirable, or even useful, relevant.

Ask your zen friends about certainty, about worldly things.

It’s only in some kind of Platonistic fervor for transcendental truth, that the questions even arise. I’m more interested in understanding whether the cat is on the mat. Different game entirely.