## Posts

## Comments

**ebthgidr**on Stupid Questions December 2014 · 2014-12-23T10:36:40.799Z · score: 1 (1 votes) · LW · GW

Ohhh, thanks. That explains it. I feel like there should exist things for which provable(not(p)), but I can't think of any offhand, so that'll do for now.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-22T17:54:45.391Z · score: 0 (0 votes) · LW · GW

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 lemma. All I need to prove is that the logical operations that lead from Not(provable(P))) to Provable(P)) are truth and provability preserving

**ebthgidr**on Stupid Questions December 2014 · 2014-12-22T01:22:28.669Z · score: 0 (0 votes) · LW · GW

is x or not x provable? Then use my proof structure again.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-20T23:28:03.216Z · score: 0 (0 votes) · LW · GW

So then here's a smaller lemma: for all x and all q:

If(not(x))

Then provable(if x then q): by definition of if-then

So replace x by Provable(P) and q by p.

Where's the flaw?

**ebthgidr**on Stupid Questions December 2014 · 2014-12-19T18:12:12.338Z · score: 0 (0 votes) · LW · GW

Oh, that's what I've been failing to get across.

I'm not saying if not(p) then (if provable(p) then q). I'm saying if not provable(p) then (if provable(p) then q)

**ebthgidr**on Stupid Questions December 2014 · 2014-12-19T00:40:39.496Z · score: 0 (0 votes) · LW · GW

So the statement (if not(p) then (if p then q)) is not provable in PA? Doesn't it follow immediately from the definition of if-then in PA?

**ebthgidr**on Stupid Questions December 2014 · 2014-12-18T19:59:31.032Z · score: 0 (0 votes) · LW · GW

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:

- provable(P) or not(provable(P)) by premise 1

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 Provable(P): By premise 2, line 2, and line 4.

Where's the flaw? Is it between lines 3 and 4?

**ebthgidr**on Stupid Questions December 2014 · 2014-12-18T03:30:07.905Z · score: 0 (0 votes) · LW · GW

Well, there is, unless i misunderstand what meta level provable(not(provable(consistency))) is on.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-17T17:44:27.926Z · score: 0 (0 votes) · LW · GW

Your reasons were that not(provable(c)) isn't provable in PA, right? If so, then I will rebut thusly: the setup in my comment immediately above(I.e. either provable(c) or not provable(c)) gets rid of that.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-17T03:15:09.399Z · score: 0 (0 votes) · LW · GW

I'll rephrase it this way:

For all C:
Either provable(C) or not(provable(C))
If provable(C), then provable(C)
If not provable(C), then use the above logic to prove provable C.
Therefore all C are provable.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-16T12:29:47.457Z · score: 0 (0 votes) · LW · GW

Wait. Not(provable(consistency)) is provable in PA? Then run that through the above.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-10T11:17:23.468Z · score: 0 (0 votes) · LW · GW

Ok, thanks for clearing that up.

**ebthgidr**on Welcome to Less Wrong! (6th thread, July 2013) · 2014-12-10T10:41:44.948Z · score: 1 (1 votes) · LW · GW

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.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-10T10:37:36.043Z · score: 0 (0 votes) · LW · GW

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.

**ebthgidr**on Stupid Questions December 2014 · 2014-12-10T03:04:02.434Z · score: 3 (3 votes) · LW · GW

A question about Lob's theorem: assume not provable(X). Then, by rules of If-then statements, if provable(X) then X is provable But then, by Lob's theorem, provable(X), which is a contradiction. What am I missing here?

**ebthgidr**on December 2014 Bragging Thread · 2014-12-10T02:34:30.043Z · score: 0 (0 votes) · LW · GW

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

**ebthgidr**on Welcome to Less Wrong! (6th thread, July 2013) · 2014-12-10T02:29:28.567Z · score: 3 (3 votes) · LW · GW

Not only that--the greater degree of neuroplasticity that I think 16-year olds still have(if I'm wrong about this, someone please correct me) makes it a good deal easier to learn skills/ingrain rationality techniques.

**ebthgidr**on Welcome to Less Wrong! (6th thread, July 2013) · 2014-12-10T01:11:34.311Z · score: 2 (2 votes) · LW · GW

Nice to meet you--it's rather reassuring to see another member at my age.

**ebthgidr**on Welcome to Less Wrong! (6th thread, July 2013) · 2014-12-09T20:16:33.901Z · score: 11 (11 votes) · LW · GW

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 like a fish to water, finishing up to the update point in a matter of days before hungrily rereading to attempt to catch whatever plot points I could glean from hints and asides in earlier chapters. However, I still read it almost purely for story-enjoyment, noting the rationality techniques as interesting asides if I noticed them.

About a year later, I followed the link on the MoR website to LW, and began reading the sequences. They were...well, transformative doesn't quite fit. Perhaps massively map-modifying might be a better term. How to Actually Change Your Mind specifically gave me the techniques I needed to update on rather many beliefs, and still does. Both Reductionism and the QM sequence, while not quite as revolutionary as HtACYM for me, explained what I had previously understood of science in a way that just...well, fit seems to be the only word that works to describe it, though it doesn't fully carry the connotation I'm trying to express.
Now, I'm endeavoring to learn what I can. I'm rereading the sequences, trying to internalize the techniques I'll need and make them reflexive, and attempting to apply them as often as possible. I've gone pretty far--looking back at things I said and thought before makes that clear. On the other hand, I've still got one heck of a ways to go. Tsuyoku Naritai

**ebthgidr**on The Importance of Saying "Oops" · 2014-01-01T18:20:08.801Z · score: 0 (0 votes) · LW · GW

Is this a possible explanation or corollary to the sunk-costs fallacy of economics?

**ebthgidr**on Religion's Claim to be Non-Disprovable · 2013-12-31T17:49:09.534Z · score: -1 (3 votes) · LW · GW

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.

**ebthgidr**on The Futility of Emergence · 2013-12-31T00:59:59.167Z · score: 2 (2 votes) · LW · GW

Isn't his usage of "switches flipping" basically another 'literary genre' switch--i.e. he had attached some sort of negative connotation to the phrase which he could not conceive of attaching to intelligence?