All of Incorrect's Comments + Replies

My visualization ability improves the closer I am to sleep, being near perfect during a lucid dream.

You can generally throw unfalsifiable beliefs into your utility function but you might consider this intellectually dishonest.

As a quick analogy, a solipsist can still care about other people.

I escape by writing a program that simulates 3^^3 copies of myself escaping and living happily ever after (generating myself by running Solomonoff Induction on a large amount of text I type directly into the source code).

You might be able to contain it with a homomorphic encryption scheme

I'm guessing Eliezer would lose most of his advantages against a demographic like that.

Oh god, remind me to never play the part of the gatekeeper… This is terrifying.

The lifespan dilemma applies to all unbounded utility functions combined with expected value maximization, it does not require simple utilitarianism.

Would your post on eating babies count, or is it too nonspecific?

http://lesswrong.com/lw/1ww/undiscriminating_skepticism/1scb?context=1

(I completely agree with the policy, I'm just curious)

There are people who claim to be less confused about this than I am

Solipsists should be able to dissolve the whole thing easily.

Thanks, can you recommend a textbook for this stuff? I've mostly been learning off Wikipedia.

I can't find a textbook on logic in the lesswrong textbook list.

Therefore a theory could be ω-consistent because it fails to prove P(n), even though P(n) is true in the standard model.

I thought for ω-consistency to even be defined for a theory it must interpret the language of arithmetic?

Just use the axiom schema of induction instead of the second order axiom of induction and you will be able to produce theorems though.

But you wont be able to produce all true statements in SOL PA, that is, PA with the standard model, because of the incompleteness theorems. To be able to prove a larger subset of such statements, you would have to add new axioms to PA. If adding an axiom T to PA does not prevent the standard model from being a model of PA+T, that is it does not prove any statements that require the existence of nonstandard numbers, then P... (read more)

There's no complete deductive system for second-order logic.

An infinite number of axioms like in an axiom schema doesn't really hurt anything, but you can't have infinitely long single axioms.

∀x((x = 0) ∨ (x = S0) ∨ (x = SS0) ∨ (x = SSS0) ∨ ...)

is not an option. And neither is the axiom set

P0(x) iff x = 0
PS0(x) iff x = S0
PSS0(x) iff x = SS0
...
∀x(P0(x) ∨ PS0(x) ∨ PS0(x) ∨ PS0(x) ∨ ...)

We could instead try the axioms

P(0, x) iff x = 0
P(S0, x) iff x = S0
P(SS0, x) iff x = SS0
...
∀x(∃n(P(n, x)))

but then again we have the problem of n being a nonstandard number.

I don't see what the difference is... They look very similar to me.

At some point you have to translate it into a (possibly infinite) set of first-order axioms or you wont be able to perform first-order resolution anyway.

I don't see how you would define Pn(x) in the language of PA.

Let's say we used something like this:

Pn(x) iff ((0 + n) = x)

Let's look at the definition of +, a function symbol that our model is allowed to define:

a + 0 = a
a + S(b) = S(a + b)

"x + 0 = x" should work perfectly fine for nonstandard numbers.

So going back to P(x):

"there exists some n such that ((0 + n) = x)"

for a nonstandard number x, does there exist some number n such that ((0+n) = x)? Yup, the nonstandard number x! Set n=x.

Oh, but when you said nth successor you meant n had to be standard? Well, that's the whole problem isn't it!

Are you saying that in reality every property P has actually three outcomes: true, false, undecidable?

By Godel's incompleteness theorem yes, unless your theory of arithmetic has a non-recursively enumerable set of axioms or is inconsistent.

And that those always decidable, like e.g. "P(n) <-> (n = 2)" cannot be true for all natural numbers, while those which can be true for all natural numbers, but mostly false otherwise, are always undecidable for... some other values?

I'm having trouble understanding this sentence but I think I know ... (read more)

Could someone please confirm my statements in the new sequence post about first-order logic? I want to be sure my understanding is correct.

http://lesswrong.com/lw/f4e/logical_pinpointing/7qv6?context=1#7qv6

If our axiom set T is independent of a property P about numbers then by definition there is nothing inconsistent about the theory T1 = "T and P" and also nothing inconsistent about the theory T2= "T and not P".

To say that they are not inconsistent is to say that they are satisfiable, that they have possible models. As T1 and T2 are inconsistent with each other, their models are different.

The single zero-based chain of numbers without nonstandard numbers is a single model. Therefore, if there exists a property about numbers that is indep... (read more)

"Because if you had another separated chain, you could have a property P that was true all along the 0-chain, but false along the separated chain. And then P would be true of 0, true of the successor of any number of which it was true, and not true of all numbers."

But the axiom schema of induction does not completely exclude nonstandard numbers. Sure if I prove some property P for P(0) and for all n, P(n) => P(n+1) then for all n, P(n); then I have excluded the possibility of some nonstandard number "n" for which not P(n) but ther... (read more)

Oh don't worry, there will always be those little lapses in awareness. Even supposing you hide yourself at night, are you sure you maintain your sentience while awake? Ever closed your eyes and relaxed, felt the cool breeze, and for a moment, forgot you were aware of being aware of yourself?

Bug:

Are you saying that dying after a billion years sounds sad to you?

And therefore you would have a thousand-year-old brain that can make trillion-year plans.

I think I have a better understanding now.

For every statement S and for every action A, except the A Myself() actually returns, PA will contain a theorem of the form (Myself()=A) => S because falsehood implies anything. Unless Myself() doesn't halt, in which case the value of Myself() can be undecidable in PA and Myself's theorem prover wont find anything, consistent with the fact that Myself() doesn't halt.

I will assume Myself() is also filtering theorems by making sure Universe() has some minimum utility in the consequent.

If Myself() halts, then if th... (read more)

How does ambient decision theory work with PA which has a single standard model?

It looks for statements of the form Myself()=C => Universe()=U

(Myself()=C), and (Universe()=U) should each have no free variables. This means that within a single model, their values should be constant. Thus such statements of implication establish no relationship between your action and the universe's utility, it is simply a boolean function of those two constant values.

What am I missing?

15: discover ordinal hierarchy of Tegmark universes, discover method of constructing the set of all ordinals without contradiction, create level n Tegmark universe for all n

It was supposed to be a sarcastic response about being too strict with definitions but obviously didn't end up being funny.

I am not a Will Newsome sockpuppet. I'll refrain from making the lower quality subset of my comments henceforth.

Here's a conversation I had with Will a while back:

http://lesswrong.com/lw/cw1/open_problems_related_to_solomonoff_induction/6rlr?context=1#6rlr

He's really wondering whether the voxel-space is a directed graph or whether up∘down=down∘up=identity (and for left/right too). Movement could be commutative with up∘down≠identity.

Consider

voxels = {a, b}

left(a)  = a
right(a) = a
up(a)    = a
down(a)  = a

left(b)  = a
right(b) = a
up(b)    = a
down(b)  = a

If f is in (left, right, up, down)
let g be the respective function in (right, left, down, up)
forall x in {a, b}
f(g(x))=g(f(x))=a

But
up(down(b))=a
whereas
identity(b)=b

If dying after a billion years doesn't sound sad to you, it's because you lack a thousand-year-old brain that can make trillion-year plans.

If only the converse were true...

They aren't adding qualia, they are adding the utility they associate with qualia.

Sorry, generic you.

What's more important to you, your desire to prevent genocide or your desire for a simple consistent utility function?

If you do happen to think that there is a source of morality beyond human beings... and I hear from quite a lot of people who are happy to rhapsodize on how Their-Favorite-Morality is built into the very fabric of the universe... then what if that morality tells you to kill people?

If you believe that there is any kind of stone tablet in the fabric of the universe, in the nature of reality, in the structure of logic—anywhere you care to put it—then what if you get a chance to read that stone tablet, and it turns out to say "Pain Is Good"? What t

Do not initiate intimate physical contact (hugs, touching shoulder, etc) unless the target has previously made similar contact with you.

If everyone follows this rule nobody will ever initiate physical contact.

Slashdot has something like this.

Genuine agreement with whimsical annoyance about having to consider actual situations and connotations.

Sounds good to me if you're going to get all connotative about it.

What about going from "members of subcategory X of category Y are more likely to possess characteristic C" to "In the absence of further information, a particular member of subcategory X is more likely to possess characteristic C than a non-X member of category Y".

You are saying you can't go from probabilistic information to certainty. This is a strawman.

I wrote my comment above under the assumption of mjgeddes' honesty but I also believe they are more likely lying than not lying.

My alternative theories are: mjgeddes is just trolling without any real plan (40%), mjgeddes is planning to laugh at us all for believing something with such an explicitly low prior. (40%), something else (>19%), actually won the lottery: <1%

Yet still I feel the need to give them the benefit of the doubt. I wonder precisely when that social heuristic should be abandoned...

http://lesswrong.com/lw/sc/existential_angst_factory/

You could try self-modifying to not hate evil people ("hate the sin not the sinner"). Here's some emotional arguments that might help (I make no claim as to their logical coherence):

If there was only one person in existence and they were evil, would you want them to be punished or blessed? Who would it serve to punish them?

If you are going to excuse people with mental illness you are going to have to draw some arbitrary line along the gradient from "purposely evil" to "evil becau... (read more)

(bit of irony here :P)

Perhaps acceptable casualties.

I just won the New Zealand national lottery.

Congratulations!

For the sake of people reading this post who may not be familiar with the concept of backwards causality:

As a fun test, I called on any future super intelligences to come to my aid, appealing to the notion of backward causality. Asking for clear evidence of the hand of a superintelligence in the event I won, I choose a number of high significance to me personally. The number I chose was 27, which I placed in all lines of the ticket. (All the other numbers I selected at random).

This is not ... (read more)