ec429

Karma: 133

ec429 Sep 23, 2011, 10:55 PM
2 points
in reply to: ArisKatsaris’s comment on: The Apparent Reality of Physics

I recognize that my map is a different portion of the territory, that portion of the territory which resides inside my head and which is merely correlated to the actual territory outside of my head.

But the actual-territory is not (or at least, need not be) causally influenced by the territory inside your head that’s implementing the map.

But tsn’t that the opposite of what you and Tegmark IV are saying: namely that the maps we call “equations” represent something ontologically basic about the whole of the territory?

I can’t speak for Tegmark, of course, but what I’m saying is that “equations” are the territory, and the stuff that looks to us like rocks and trees and people and the Moon is just a map.

I’d be careful what I’d call “nonsensical” when your argument instead must lead to the conclusion that things must exist even when they don’t exist...

On the contrary, the conclusion is that things must exist even when they don’t “exist”—where that quotation refers to some silly little savanna-concept we have in our brains, about rocks and trees and people and the Moon. Which don’t exist.

Epiphenomenalism is usually referring to something conceptual or cognitive (e.g qualia or consciousness or subjective experience) that doesn’t have an influence on physical states.

You’re instead talking about physical existence not having an influence on conceptual entities (namely the mathematical equations).

That’s because (in my model) the conceptual entities are the bedrock of the hierarchy, and physical existence is strongly analogous in this model to qualia in a physical-realist model. After all, “{equations}” and “rocks following {equations}” both give the same result for “value of X at time T”, so the existence of rocks is epiphenomenal to the equations.

once you have the physical reality of a mouth and a keyboard (which happen to require mass-energy) to be able to say to the equations, you can just say “equations”

But a simulated me, existing only as information represented by electrons in a computer, could say “equations” just as loudly. So why couldn’t a purely informational me, existing as unrepresented information, say “equations” too? Physical reality is a burdensome detail which doesn’t add any explanatory power to your model; the claim that information needs to be represented in order for conscious entities contained within that information to exist seems to me to have no evidence backing it up, nor indeed to be capable of having such evidence, and therefore Occam demands that we frame our model in such a way as to make that claim inexpressible. It’s rather like moving from configuration space to relative configuration space; unmeasurable claims become unreal.

But it still doesn’t conclusively explain how the territory came to be.

It doesn’t need to “come to be”; ‘time’ and ‘causality’ are parochial notions, concepts we can use to model things within our universe. Expecting the multiverse to obey them seems to me to be a Mind Projection Fallacy. A block universe just is.

Thanks for the insightful critique, by the way—it’s helping me to understand the arguments better and see weak points that I wouldn’t have noticed myself. I’m still not sure whether my theory is circular, nor whether I should care if it is.

ec429 Sep 23, 2011, 10:37 PM
0 points
in reply to: lavalamp’s comment on: The Apparent Reality of Physics

When actually run, it makes two pieces of the territory change so that they contain a pattern that we would recognize as “5”.

Right, but it doesn’t attach little “” tags to that pattern.

Can you give an example of information with that property?

Well, trivially not, because by giving the example I create a representation. But, does a theorem become true when it is proven? That seems to me to be absurd. Counterfactually, suppose there were no minds. Would that prevent it from being true that “PA proves 2+2=4”? That also seems absurd. I can’t prove it’s absurd, but that’s because a rock doesn’t implement modus ponens (no universally compelling arguments).

If X will happen tomorrow, then it is a fact that X will happen tomorrow, even though (ignoring for now timeless physics) tomorrow “doesn’t exist yet”, and the information “X will happen tomorrow” needn’t be represented anywhere to be true; it inheres in the state of the universe today + {equations of physics}. Information which can be arrived at by computation from other, existing information, exists—or perhaps we should move the ‘other, existing information’ across the turnstile: it is an existing truth that (Information which can be arrived at by computation from foo) can be arrived at by computation from foo. Tautologies are true.

ec429 Sep 23, 2011, 10:26 PM
2 points
in reply to: loqi’s comment on: The Apparent Reality of Physics

All I see here is Tegmark re-hashed and some assertions concerning the proper definitions of words like “real” and “existence”. Taboo those, are you still saying anything?

I’m saying that our intuitive concepts of “real” and “existence” have no referents, that Tegmark’s restriction to computable structures is unnecessary, that nesting (ie. simulation) of worlds is an explicit causal dependence, and that Platonism needn’t be as silly and naïve as it sounds. Also to the extent that I am rehashing Tegmark, I’m doing so in order to combine it with Syntacticism and several other prerequisites in order to build a framework that lets me talk about “the existence of infinite sets”, because I think Eliezer’s ‘infinite set atheism’ is a confusion.

Have you read any of Paul Almond’s thoughts on the subject? Your position might be more understandable if contrasted with his.

I’ll read “Minds, Substrate, Measure and Value” (which seems relevant) and then get back to you on that one, ok?

ec429 Sep 23, 2011, 10:08 PM
1 point
in reply to: lavalamp’s comment on: The Apparent Reality of Physics

Are you claiming that all possible mistaken simulations of all possible sets of physical laws somehow exist platonically?

Inasmuch as a mistaken simulation of B is a simulation of “B plus the arbitrary law that ‘foo happens at time t’”, then yes, B’ exists platonically. Consider B = “x″ + x = 0, x(0)=x’(0)=0″, B’ = “x″ + x = δ(x-1), x(0)=x’(0)=0”. These are both coherent mathematical models; they model different things, but B’ still exists platonically. A cosmic ray could indeed make an ostensible model of B model B’.

It’s not clear to me what this system you’re describing gains you. What predictions does it cause you to make differently? (i.e., how does it pay rent?)

It’s observationally equivalent to the hypothesis of manifest reality, but strictly simpler (it removes unnecessary ontological elements, and converts uncertainty about physical law into indexical uncertainty). Like Many Worlds, really.

ec429 Sep 23, 2011, 9:52 PM
−1 points
in reply to: ArisKatsaris’s comment on: The Apparent Reality of Physics
Good objections, but I think they all have answers:

Of course it would, though it’s underlying reality wouldn’t be what we expect. (it might be a pointer in some program, instead of a collection of atoms)

But a pointer is information. At the physical layer, it’s a configuration—when you say char *p=malloc(1); you haven’t created an electron to sit in &p, rather you’ve configured existing electrons so as to have a pattern that is meaningful to one of your higher-level maps, but as a good reductionist you know that your higher maps don’t represent anything ontologically basic about the territory.

As far as I know from any given perspective, existence is a binary quantity, something either is or isn’t.

That’s the point—I’m showing that the belief that ‘existence’ results from physical manifestation reduces to the absurdity that more physical manifestations of something means it exists more, which is nonsensical.

In Object-Oriented Programming, there’s Classes which are a description of the instantiated objects, and there are the objects themselves, which you can do different things with than with the classes.
```
String a="5"; String b=a;
```
Does this make String(“5”) exist twice as hard? No; it doesn’t even change whether it exists or not. It may be an object rather than a class, but it’s still just a collection of information, which can be represented once, many times, or not at all, without ever changing the value of String(“5″).toInteger().

Again, how do you know there’s no XML tag attached to the mathematics of our universe?

I don’t know it, but such a tag would be epiphenomenal, and therefore it makes sense to assume it doesn’t exist. If you’re so sure that physical reality is manifest/instantiated, then how do you know, and why does it happen to follow regular mathematical laws? I think that believing in manifest physical reality is like believing in p-zombies (or, which comes to the same thing, dualistic consciousness).

The Tegmark IV hypothesis is exciting but I don’t see how it’s supposedly so self-proving as its proponents suggest.

It’s not self-proving—at least, I don’t claim it so—it’s just simpler (shorter message length) to say “{equations}” than to say “mass-energy and space and time, which follow {equations}”, and thus in the absence of evidence for the existence of manifest reality (which evidence I do not believe to be possible) a Bayesian, taking an Occamian prior, should conclude that the former is more likely than the latter. The only reason we mostly believe the latter is that, like Copenhagen, it came first.

EDIT: also, my views are distinct from (and were formed before I read) Tegmark IV; in particular his paper makes no mention of the concept of instantiation (and seems to me to be assuming that all Tegmark worlds are physically instantiated), and he wants to limit his hypothesis to computable structures, which I consider unnecessary and unjustified—I’m happy with the existence of structures so transfinite we can’t even imagine them, perhaps because I’m a mathematician rather than a physicist.

ec429 Sep 23, 2011, 8:22 PM
1 point
in reply to: David_Allen’s comment on: Syntacticism
If that is so, then how come others tend to reach the same truth? In the same way that there is something outside me that produces my experimental results (The Simple Truth), so there is something outside me that causes it to be the case that, when I (or any other cognitive agent) implements this particular algorithm, this particular result results.

It is not a mind-projection fallacy, any more than “the sheep control my pebbles” is a mind-projection fallacy. It’s just that it’s operating one meta-level higher.

The Apparent Reality of Physics

ec429Sep 23, 2011, 8:10 PM

−4 points

62 comments2 min readLW link

ec429 Sep 23, 2011, 7:12 PM
0 points
in reply to: [deleted]’s comment on: Syntacticism

I agree with the main tenets of your view—rejecting the platonic realm of mathematical truths, instead founding mathematics rigorously and finitely on formal systems—but you do not hold fast to it

This is because you have misconstrued my view. My philosophy of syntacticism is not formalism, nor is it a straight rejection of Platonism. Instead it is a Platonic formalism, in which the Platonic ideals are of the form “thus-and-such is derivable from these axioms with these deduction rules”, except that any attempt to talk directly and formally about those Platonic ideals fails (because that involves application of a formal system to a formal system).

It is not possible to consider Godel’s theorem with only a direct understanding of PA, you need an implemented one.

The point of my post is that ‘implemented PA’ in fact implements “PA”, and there can be no rigorous proof that the referent of “PA” is PA (because such a rigorous proof in fact ends with “”PA” is PA”, and how do we know that this new system’s “PA” is PA?)

Inside our implemented PA we construct a predicate and then prove in ZFC that it satisfies a particular property defined in terms of PA.

But how do we prove that (ZFC proves statement about PA) ⇔ (statement about PA)? Only by appealing to a higher-order theory. After all, I can define a theory T by the axioms “1. PA is consistent. 2. PA proves PA is consistent.”, where (if necessary) PA is defined by listing PA’s axioms, and yet if I were to conclude from this that PA proves PA’s consistency without thereby becoming inconsistent, you would scream blue Gödelian murder, because you have a proof in ZFC that if PA proves PA is consistent then PA is not consistent. But I have a proof in T that PA is consistent and proves PA consistent (a trivial one, in fact). So how can you justify privileging ZFC’s referent of “PA” over T’s referent of “PA”? Only by appeal to some meta-theory—or by informal justification.

I have no idea what real means here.

It is a fact that agents implementing the same deduction rules and starting from the same axioms tend to converge on the same set of theorems. Therefore there is some sense in which the theorems are inherent in the (axioms + deduction rules): there is a truth about what those (axioms + deduction rules) lead to, and that truth exists outside of any implementation. But that truth is not like a rock, it is not a physical object—so it must be a metaphysical one. Thus, Platonism.

But then why privilege any particular set of rules as having Platonic existence? Thus, all possible formal systems have Platonic existence.

The “magical spirit realm” does not say that “2+2=4″. But it does say that “If you apply the rules of PA to evaluate the expression 2+2, a failure to converge on 4 implies a failure to follow the rules of PA” (which failure might, for instance, be a cosmic ray hitting a neuron).

Do I make sense now?

ec429 Sep 23, 2011, 6:23 PM
4 points
in reply to: prase’s comment on: Syntacticism
Map-territory. You’re not distinguishing formal system X from our knowledge of formal system X.

ec429 Sep 23, 2011, 6:21 PM
0 points
in reply to: Alex_Altair’s comment on: Harry Potter and the Methods of Rationality discussion thread, part 8
Actually, my understanding was that he said it didn’t have geometry at all, only topology.

ec429 Sep 23, 2011, 5:36 PM
1 point
in reply to: prase’s comment on: Syntacticism
Well, actually doing mathematics is an ‘application’ of the Platonic ideal mathematics; the perfect draughtsman’s copy does involve semantics simply because that’s how the brain works. So I would indeed be surprised to see ¬□S and S proved for some PA-statement S, but only because in my experience thus far it has been predictively accurate to apply second-order arithmetic to PA. Nonetheless, if it did happen, then it wouldn’t refute PA, nor would it refute second-order arithmetic (neither has inherent ‘truth-value’, so the concept of ‘refuting’ them is unsinnig). What it would refute is the informal application of second-order arithmetic to PA. Though note that it wouldn’t refute the third-order arithmetic which proves the statement “second-order arithmetic applies to PA”, because “PA” is not PA.

It is, in my opinion, important to distinguish between the formal system X (which is timeless, unchanging, and Platonically real), and our experiences of applying X. Such experiences, which may lead us to make predictions, are not informative about X, rather they are informative about the informal process of applying X. My experiences with arithmetic lead me to predict, informally, that applying second-order arithmetic to PA won’t lead to contradiction. That says nothing about either arithmetic itself.

ec429 Sep 23, 2011, 5:26 PM
1 point
in reply to: Mitchell_Porter’s comment on: Syntacticism
Statements have no meaning inherent in themselves. That doesn’t stop us ascribing semantics to things, we just have to stop believing that “P∧(P=>Q) ⊦ Q” has a little XML tag saying “true” stuck to it out there in Plato-space.

ec429 Sep 23, 2011, 5:24 PM
−1 points
in reply to: [deleted]’s comment on: Syntacticism
I guess I expected a short inferential distance. I really did think it was obvious why the apparent reality of a physical universe was consistent with physical nonrealism and formal realism. I’ll make another post about this soon.

EDIT: The Apparent Reality of Physics

ec429 Sep 23, 2011, 5:20 PM
−1 points
in reply to: MrMind’s comment on: Syntacticism

you’re basically restating formalism

Not quite: what I have here is game formalism with the additional claim that the games are ‘real’ in a Platonic sense (and nothing else is).

you can have formal systems that talk about formal systems

But you cannot prove, formally, that formal system A talks about formal system B, without appealing to another formal system C (and then how do you know that C talks about A?). I already made this point in the OP.

if you want your system to have any utility you have to assert the consistency of the systems you’re using

Yes, but you only have to make that assertion as a condition of the application; in order to claim that two pebbles plus two pebbles makes four pebbles I have to assert that PA applies to pebbles, which assertion involves asserting that PA is consistent—but if it turns out that PA is inconsistent, that only refutes the assertion that PA applies to pebbles; it does not ‘refute’ PA, since PA makes no claims of consistency (indeed, PA does not have a notion of “truth”, so even Q=PA+”Q is consistent” makes no claims of consistency). Thus, while paradoxes may conceivably destroy the utility of mathematics, they still could not destroy mathematics itself.

the set of all formal system?

Good point, that should have been ‘class’. Fixed.

Syntacticism

ec429Sep 23, 2011, 6:49 AM

−4 points

62 comments3 min readLW link

ec429 Sep 23, 2011, 5:29 AM
2 points
on: Invisible Frameworks

Roko is adopting a special and unusual metamoral framework in regarding “Most agents do X!” as a compelling reason to change one’s utility function. Why might Roko find this appealing? Humans, for very understandable reasons of evolutionary psychology, have a universalizing instinct; we think that a valid argument should persuade anyone.

Perhaps this can be fixed; maybe if we say Q:=”moral(X):=”A supermajority of agents which accept Q consider X moral”″. Then agents accepting Q cannot agree to disagree, and Q-based arguments are capable of convincing any Q-implementing agent.

On the other hand, the universe could stably be in a state in which agents which accept Q mostly believe moral(torture), in which case they all continue to do so. However, this is unsurprising; there is no way to force everyone to agree on what is “moral” (no universally compelling arguments), so why should Q-agents necessarily agree with us?

But what we are left with seems to be a strange loop through the meta-level, with the distinction that it loops through not only the agent’s own meta-level but also the agent’s beliefs about other Q-agents’ beliefs.

However, I’m stripping out the bit about making instrumental values terminal, because I can’t see the point of it (and of course it leads to the “drive a car!” problem). Instead we take Q as our only terminal value; the shared pool of things-that-look-like-terminal-values {X : Q asserts moral(X)} is in fact our first layer of instrumental values.

Also, I’m not endorsing the above as a coherent or effective metaethics. I’m just wondering whether it’s possible that it could be coherent or effective. In particular, is it PA+1 or Self-PA? Does it exhibit the failure mode of the Type 2 Calculator? After all, the system as a whole is defined as outputting what it outputs, but individual members are defined as outputting what everyone else outputs and therefore, um, my head hurts.

ec429 Sep 21, 2011, 12:46 PM
0 points
in reply to: Will_Sawin’s comment on: What is Evidence?
Ah, I get it now, thanks!

(Copenhagen is still wrong though ;)

ec429 Sep 19, 2011, 4:53 AM
1 point
on: Arguing “By Definition”
Would it be accurate, then, to say that any valid use of “by definition” can be replaced by “a fortiori”?

As in, “Socrates is a [mortal, featherless, biped]. Therefore a fortiori Socrates is mortal.” is valid (though one might dispute the premise). But “Socrates is a [featherless, biped]. Therefore a fortiori Socrates is mortal.” is plainly obviously nonsense, even to people who think they can argue “by definition!”. The remaining problem, of course, being that not everyone accepts that a fortiori deserves the certainty that they have been claiming for by definition!.

(In classical logic, if A∧B, then a fortiori A. In Bayescraft, P(A) >= P(A∧B) a fortiori)

ec429 Sep 19, 2011, 4:15 AM
0 points
on: Moral Complexities

When and why do people change their terminal values? Do the concepts of “moral error” and “moral progress” have referents? Why would anyone want to change what they want?

Suppose I currently want pie, but there is very little pie and lots of cake. Wouldn’t I have more of what-I-want if I could change what I want from pie to cake? Sure, that doesn’t get me more pie, but it increases the valuation-of-utility-function.

Suppose I currently want pie for myself, but wanting pie for everyone will make Omega give me more pie without changing how much pie everyone else gets? Then I want to change what-I-want to wanting-pie-for-everyone because that increases the valuations of both utility functions.

Suppose I currently want pie for myself, but wanting pie for everyone will make Omega give me pie at the expense of everyone else? Now I have no stable solution. I want to change what I want, but I don’t want to have changed what I want. My head is about to melt because I am very confused. “Rational agents should WIN” doesn’t seem to help when Omega’s behaviour depends on my definition of WIN.

ec429 Sep 19, 2011, 3:30 AM
−1 points
in reply to: XiXiDu’s comment on: What Would You Do Without Morality?
That’s what I’d do too. If all utilities equal 0, then there’s no reason not to act as though utilities are non-zero. There’s also no reason to privilege any set of utilities over any other set. Firstly this means that if there’s any probability that utilities don’t really all equal zero (maybe EY’s proof is flawed, maybe my brain made an error in hearing the proof and it really proves something else entirely...) then the p-mass on “all utilities are 0” should have no effect on my decisions. If it actually is true, with probability 1 (which EY says doesn’t exist, but I’m not sure whether that’s true[*]), then I have no reason to behave differently, nor any reason to behave the same, so in some sense I “may as well” behave the same—but I can’t formalise this, because of course there’s no negative utility attached to “changing one’s behaviour”. I wonder if it can be got out of a limit—whether my behaviour in the limit as P(all utilities are 0) goes to 1 ought to define my behaviour when it equals 1 - but defining behaviour of limit to equal limit of behaviour is precisely what makes unbounded utility functions Dutch-bookable (as EY showed in Trust in Bayes).

So… I’d behave exactly as I do now, believing in utility functions, but I can’t justify that if I know for certain that all utilities are 0. Given that I haven’t thus far accepted the argument that ‘0 and 1 are not probabilities’, this is disturbing and confusing, hence maybe I should accept that argument; at least, updating on this has caused me to raise my probability estimate that 0 and 1 are not probabilities.

[*] If I were sure that ¬\exist X : P(X) = 1, then P(¬\exist X : P(X) = 1) = 1, in which case things break. A formal system can’t talk about itself coherently. (That ‘coherently’ is necessary, because Gödel numberings do allow PA to do something that looks to us like “talk about itself”, but you can’t conclude PA is talking about itself unless you have some metatheory outside PA, which ends up recursing to a skyhook.)

ec429

The Ap­par­ent Real­ity of Physics

Syntacticism

The Apparent Reality of Physics