1/ The debate over the philosophical implications of Godel's incompleteness theorems seem extremely misguided to me. They *are*, in my opinion, a proof that not all is mechanism, *but* it has nothing to do with humans having special oracle powers; that's stupid.

2/ What Godel's theorem suggests, by telling us that a system cannot prove its own consistency but can only have its consistency proven via some larger system in which one embeds it, is that the world is ontologically NOT simply made up of analytic truths

3/ Instead, analytic truths are things that *must* ultimately be built up by starting from postulates and going from there, and that these postulates, insofar as they create a system that isn't merely arbitrary, are in some way correlated to patterns of human/technological action

4/ And therefore, when we *do* hit some undecidability in a system, the choice of how to fill that gap has some kind of guidance because there is *already* something in the real world that system is embedded in and we're just further formalizing with the help of some constraints

5/ But humans as magic oracles in a vacuum? Of course not, that's like suggesting a pigeon could win a race against an SR-71. On the other hand, there *is* a way humans could win, and that's if they know the *synthetic* space surrounding the analytic problem better

6/ So it would be as if the bird found some portal that made it win the race against the airplane. More importantly, if something is undecidable, that's not a question of the problem being *unsolvable*, it just means that it has an undefined answer, this is not about "better"

7/ One worrying about whether there are math problems humans can't solve is a facile issue; that's just a question of whether or not the problem *has* an answer given the context--adding the context to solve it is just adding the sufficient context, i.e. synthesis

8/ So to sum this up, no, there's no special human superpower of any kind, it's simply that computation *is a different world* than ours, or particularly a subset, something like a 2D sliver in a 3D space. You don't have special powers in 2D world, there's simply different stuff

9/ Again, *none* of this is about magical powers, humans in fact suck at computation. It's simply that analytic statements/mechanisms are *not* the whole world but something we build and integrate into our world, and Godel's theorems mean that the hard work will *never* end

10/ I also mean "correlated" ("corresponding") in a very loose sense. I do not actually believe this is the right way to put it, because that brings us right back to the idea that everything is analytic.

So what I really mean by postulates is that they are effective *actions*

11/ i.e. mathematics/computation is the construction of what most of us would call "rationality" or "objectivity" via the construction of stable systems of entailment, and the formalisms we see are but one expression of this

12/ what do i mean by an "expression"? well, there are other ways that these rigorous systems of entailment exist: think about actual computers, or systems of currency, or just our neural/cultural wiring that enables counting and arithmetic. that too is "formalism"

13/ in other words, analytic truth is form, and form is constructed, but *not* in any way imaginary.

and we're so good at this that it now looks like everything was just made this way for us by god, but that simply isn't so, because if that were true we'd be able to hit a bottom

And what do the incompleteness theorems tell us?

THERE. IS. NO. BOTTOM.

But this is the bottom of this thread (I think.)

Oh, one other thing: Godel may have considered himself a Platonist, but as far as I'm concerned, he is, however uintentionally, an exquisite variation on Heraclitus.

Also I assume this is the basis for his theological beliefs, that he knew man could not live on mechanism alone