re: #763 itellu3times

Sure, but who ever said mathematics should be both correct and complete? And who said this extends to claims about infinite sets? Any finite set can be tested to completion in principle, and if it is too large, then why should even its failures be relevant? In any case, however important you take Godel to be, there are other topics that it does not address.

I’m some kind of bush-philosopher at this point, in an area I’m making up as I go, which comes to something like philosophy of computation, where the topic of NP-completeness and TM halting and such is old hat. I haven’t found much use for it, using a constructive approach instead. I have yet to publish anything but a few noisy messages on this or that Internet forum, but hope springs eternal.

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.