Recent content by semioticghost

From a pragmatic standpoint, logic (and by extension mathematics) is simply the best system mankind has concocted so far to distinguish bad arguments from good arguments. Given its basis in evidence to make arguments, one could also argue that it has some empirical basis, though higher-level...

I would hope that you've experienced it somewhere else; it'd be a bit of a shame for you to declare how much time it's "worth" (a dubious assignation in its own right) based solely on your forum experiences. Anyway (just clarifying here), metamathematics is used to parse mathematics, and thus...

Where does the notion of self-referentiality come into play in all of this, then?

So then a metamathematical proof would be devoid of such statements P that can be neither proven nor disproven, and thus not subject to its own theorems, I assume. But you can't really used the specific breed of metamathematics to write MATHEMATICAL proofs, and the majority of logical axiomatic...

It depends on how exactly you define "truth".

What's even more intriguing is that concepts that originated as forays into mathematical abstraction, made in accordance with mathematical procedures but not intended to have any basis in or connection to physical reality at all, are becoming increasingly relevant to modern physics...

But doesn't Godel's work demonstrate that formal logic is incomplete? You can't use formal logic to prove that formal logic is incomplete, because your proof will be vulnerable to the incompleteness. From what I understand, Godel's metamathematical Incompleteness Theorems establish that...

Why isn't metamathematics studied by formal logic, then? What makes it fundamentally different from formal logic? I guess that's my question.

Well, if mathematics is incomplete, then how can a MATHEMATICAL proof of incompleteness be considered definitive? Thus was, I thought, the rationale for making the proof metamathematical.

From what I've read, Godel's Theorems are able to make definite statements about mathematics because they are in fact metamathematical proofs, and thus not self-referentially subject to the incompleteness of mathematics or any rigorously logical system that they demonstrate. What exactly...