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[Kybernetes Moros]

Based on Gödel's work, I don't think you can actually get to that state.

Speaking as a very, very mediocre formal logician, I'm inclined to sorta-kinda-ish agree.

Going off Gödel's two incompleteness theorems, my understanding is that you couldn't ever create, say, a completely axiomatised and self-proving theory of mathematics, to steal the nice phrasing Jev used. It'd be a (clearly non-trivial) formal system, but therein there would exist statements that couldn't be proved in that system -- and, to bring in the second theorem, if that system can be proved to be consistent using its own logic, then it must itself be inconsistent.

This can, I assume, be extended to physics, to direct this post towards a field with which I'm more familiar: a 'theory of everything' to fully explain and link all physical phenomena capable of predicting the outcome of any experiment that could possibly be carried out (in principle) would qualify quite certainly as a non-trivial, consistent mathematical system; a TOE wouldn't necessarily be impossible, but to be able to rigorously define it as a final theory would be a different matter.

Something that struck me midway through writing this was that, if one of the implications of Gödel's incompleteness theorems is that (pure) mathematics is inexhaustible, then so too must physics as a finite superset of the laws of mathematics, i.e. there would always be new problems that couldn't be solved within existing rules. How this would tie in with the SoCT, I'm uncertain, due in no small part to my general fuzziness with this field -- would the existence of new problems as a result of the incompleteness theorems keep them going? Would they reach Istvaan's outcome as a result of being aware of the two theorems alongside everything else they know? Something else entirely?

[Casiella]

I'm just trying to decide whether to integrate my new main into this somehow or roll another character.




Somebody stop me before I alt again...

[Horatius Caul]

Somebody stop me before I alt again...

Stop! In the name of EVE, be-fore you aaaalt again!

[hellgremlin]

Based on Gödel's work, I don't think you can actually get to that state.

Yes, no, kind of. I've a little experience with formal logic. Gödel's main work was proving a few shortcomings of formal logic, most notably that any consistent logical system whose expressiveness is worth a damn cannot be both complete and consistent, and moreover that any logical system can express its own consistency only if it's inconsistent itself.

This sucks immensely if you're trying to build an axiomatized and self-proving theory of mathematics, the major project of logicians at the time. I'm not read well enough in epistemology to be definite about it, but the exact consequences of this result in that field aren't immediately clear to me.. human reason doesn't bluescreen when we come across a sentence like "this sentence is a lie"; we simply shrug, classify it as a paradox, and move on. I don't know what the exact relation between something being knowable and something being logically provable is; but I very much doubt anyone's come up with a definite answer.

Pure epistemology is just as treacherous. There's rather a lot of discussion on whether it's possible for things to be by their nature unknowable. The case for is that there's a good number of problems out there that we can't even begin to attack; the case against is that there's a fair few we thought to be intractable and have since solved. As you'd expect, the unknowable is a horrible beast to try and reason about.

If it's "known" it has already been proven, at least to the satisfaction of those "knowing."

[hellgremlin]

I'm just trying to decide whether to integrate my new main into this somehow or roll another character.


Somebody stop me before I alt again...

I have been the same character since day one. Characters evolve. You don't need to discard your current one to introduce a new one.

[Casiella]

Mhmm. Fair point... though I freely admit that you almost certainly do a better job than I can at this whole idea of integrating new choices and ideas into a singular character. In fact, most RPers probably do a better job at that than I do.

[hellgremlin]

Mhmm. Fair point... though I freely admit that you almost certainly do a better job than I can at this whole idea of integrating new choices and ideas into a singular character. In fact, most RPers probably do a better job at that than I do.

There's nothing difficult about it. Compare yourself today, to yourself five years ago. You'll find it pretty different. It's the natural evolution of people. People change views, opinions, beliefs, a few times at least in their lifetime.

[Casiella]

Excellent point, and well-received. So then the question (to drag this back to something like the topic): the SoCT seems to focus on individuals they educated and indoctrinated. Does it have room for individuals coming to it later in life? >.>

[hellgremlin]

What's a Gödel btw? Haven't heard of him before.

[Casiella]

Kurt Gödel

[Jev North]

Something that struck me midway through writing this was that, if one of the implications of Gödel's incompleteness theorems is that (pure) mathematics is inexhaustible, then so too must physics as a finite superset of the laws of mathematics, i.e. there would always be new problems that couldn't be solved within existing rules. How this would tie in with the SoCT, I'm uncertain, due in no small part to my general fuzziness with this field -- would the existence of new problems as a result of the incompleteness theorems keep them going? Would they reach Istvaan's outcome as a result of being aware of the two theorems alongside everything else they know? Something else entirely?

I suspect (but am once again not sure) that a physical ToE might be expressed as a subset within a larger logical system; un-isolable from it because it'd be unintelligible without reference to the system's constructs that necessarily lead to paradox or incompleteness, but not self-referencing in a way that leads to problems either, and a complete description of the physical laws of the universe.

Exactly what this'd entail is, er, stuff I shouldn't be breaking my head about while trying to absorb a lot of hard stuff on a completely different subject..

Excellent point, and well-received. So then the question (to drag this back to something like the topic): the SoCT seems to focus on individuals they educated and indoctrinated. Does it have room for individuals coming to it later in life? >.>

Edit: back on topic - yes, I'd say so. It might be exceptional to some degree, but old dogs can and do learn new tricks, and capsuleers are somewhat exceptional people to begin with. I don't think they're like the Millenarians, and only accept babies whose umbilical cord hasn't fallen off yet.

[Horatius Caul]

Excellent point, and well-received. So then the question (to drag this back to something like the topic): the SoCT seems to focus on individuals they educated and indoctrinated. Does it have room for individuals coming to it later in life? >.>

If we go with my idea of a Kitzless academy type of thing, it would be easy to accept any comers. Even if we take it in another direction, I doubt it would be difficult to accommodate an oldbie.

After Isvaan's rousing speech, I'm also considering bringing Horatius himself into this - depending on what direction we end up taking. We'll see.

[Casiella]

Perhaps a SoCT-organized salon for capsuleers of some sort? I would almost certainly get involved and probably drag one or two people with me. (This starts to feel like a Tupperware party.)

[hellgremlin]

Kurt Gödel

Can't wrap my head around what this guy is trying to say. Not yet anyway.

Uhh... actually, a summary would be good.

[Casiella]

Kurt Gödel

Can't wrap my head around what this guy is trying to say. Not yet anyway.

Uhh... actually, a summary would be good.

To greatly oversimplify to the point that Jev may stab me: in any fairly decent system, you can construct the equivalent of "this statement is false", which means that complete systems are inconsistent and consistent systems are incomplete.