re: #760 Salamantis

Most mathematicians would beg to disagree with you; Godel’s Incompleteness Theorem has been widely lauded as the most important theorem in mathematics. It has been considered to be such becauise it places an uppoer limit on the complexity of axiomatic systems claiming to be both correct and complete. Once an axiomatic system, be it logical or mathematical, breaches the Godelian threshhold and become complex enough to permit self-referential statements, it cannot, in rigorously proven principle, be both correct and complete.

And yes, I was a mathematics major before I switched to philosophy. After taking a logic course, abstract mathematics seemed to sterile to me, and I switched to a discipline that I perceived could be more readily pplied to real-world situations. I was wrong in that perception, but never regretted my decision to change majors, for I found philosophy to be a rich vein from which I could mine profound understandings.

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.