To answer the below: I'm not saying that provable(X or notX) implies provable (not X). I'm saying...I'll just put it in lemma form(P(x) means provable(x):
If P( if x then Q) AND P(if not x then Q)
Then P(not x or Q) and P(x or Q): by rules of if then
Then P( (X and not X) or Q): by rules of distribution
Then P(Q): Rules of or statements
So my proof structure is as follows: Prove that both Provable(P) and not Provable(P) imply provable(P). Then, by the above lemma, Provable(P). I don't need to prove Provable(not(Provable(P))), that's not required by the ...
That doesn't actually answer my original question--I'll try writing out the full proof.
Premises:
P or not-P is true in PA
Also, because of that, if p -> q and not(p)-> q then q--use rules of distribution over and/or
So:
2: If provable(P), provable(P) by: switch if p then p to not p or p, premise 1
3: if not(provable(P)) Then provable( if provable(P) then P): since if p then q=not p or q and not(not(p))=p
4: therefore, if not(provable(P)) then provable(P): 3 and Lob's theorem
5: Therefore Prova...
That's an interesting correlation, but I'm curious about the causal link: is it that a certain type of neural architecture causes both predisposition to rationality and asperger's, or the social awkwardness added on to the neural architecture creates the predisposition--i.e. I'm curious to see how much being social affects rationality. I shall need to look into this more closely.
I forget the formal name for the theorem, but isn't (if X then Y) iff (not-x or Y) provable in PA? Because I was pretty sure that's a fundamental theorem in first order logic. Your solution is the one that looked best, but it still feels wrong. Here's why: Say P is provable. Then not-P is provably false. Then not(provable(not-P)) is provable. Not being able to prove not(provable(x)) means nothing is provable.
I finished up to the first major plot twist/divergence in the rationalfic(well, sort of. I'll just call it an attempted rationalfic) I've been working on for 3 months or so, and it's now in the top 15 most followed fics in the fandom(Danganronpa). Link: light in despair's darkness
Hello. I'm Leor Fishman, and also go by 'avret' on both reddit and ffn. I am currently 16. The path I took to get here isn't as...dramatic as some of the others I've seen, but I may as well record it: For as long as I can remember, I've been logically minded, preferring to base hypotheses on evidence than to rest them on blind faiths. However, for the majority of my life, that instinct was unguided and more often than not led to rationalizations rather than belief-updating. A few years back, I discovered MoR during a stumbleupon binge. I took to it lik...
For number 3, I realize the implied point, and I assume that there is more to this argument, but that sentence was one big strawman. Also, I would respond by asking why someone following the 'true essence' but confirming to modern societal/ethical norms is any worse than someone who is following said norms for a different reason. For #4, those novels don't explicitly provide ethical direction-one can use a system of ethical precepts without it being absolute and unchangeable.
My suspicion about the thin-tailed risk here is that either congress or the SEC passes landmark regulation about SPACs (which is potentially plausible) and those stocks go to 0, very quickly, as the initial investors who IPOed the SPAC pull their money out. See, ICOs (though those were obviously higher risk)