metaphysicist

Karma: −2

metaphysicist Sep 18, 2012, 8:11 AM
1 point
in reply to: Eliezer Yudkowsky’s comment on: The raw-experience dogma: Dissolving the “qualia” problem
“If nothing exists, I want to know how the nothing works and why it seems to be so highly ordered.”

If qualia are explained by our innate intuitions (or beliefs)—propositional attitudes—then two questions follow about “how it works”:
1. What is the propositional content of the beliefs?
2. What evolutionary pressures caused their development?
I make some conjectures in another essay.

The raw-experience dogma: Dissolving the “qualia” problem

metaphysicistSep 16, 2012, 7:15 PM

−4 points

341 comments5 min readLW link

metaphysicist Sep 8, 2012, 4:48 AM
1 point
in reply to: pragmatist’s comment on: Natural Laws Are Descriptions, not Rules

If one accepts the principle of identity of indistinguishable, then it follows that quarks or points must be distinguishable (since they can be non-identical)

I accept the principle, but I think it isn’t relevant to this part of the problem. I can best elaborate by first dealing with another point.

There is no separate criterion for the identity of sets which leads to the conclusion that Q is identical to Q\Bob, so we do not have a contradiction

True, but my claim is that there is a separate criterion for identity for actually realized sets. It arises exactly from the principle of the identity of indistinguishables. Q and Q/Bob are indistinguishable when the elements are indistinguishable; they should be distinguishable despite the elements being indistinguishable.

What justifies “suspending” the identity of indistinguishables when you talk about elements is that it’s legitimate to talk about a set of things you consider metaphysically impossible. It’s legitimate to talk about a set of Platonic points, none distinguishable from another except in being different from one another. We can easily conceive (but not picture) a set of 10 Platonic points, where selecting Bob doesn’t differ from selecting Sam, but taking Bob and Sam differs from taking just Bob or just Sam. So, the identity of indistinguishables shouldn’t apply to the elements of a set, where we must represent various metaphysical views. But if you accept the identity of indistinguishables, an infinite set containing Bob where Bob isn’t distinguishable from Sam or Bill is identical to an infinite set without Bob.

Believe me, if there was an obvious contradiction in Zermelo-Fraenkel set theory (which includes an axiom of infinity), mathematicians would have noticed it by now.

I’ll take your word on that, but I don’t think it’s relevant here. I think this is an argument in metaphysics rather than in mathematics. It deals in the implications of “actual realization.” (Metaphysical issues, I think, are about coherence, just not mathematical coherence; the contradictions are conceptual rather than mathematical.) I don’t think “actual realization” is a mathematical concept; otherwise—to return full circle—mathematics could decide whether Tegmark’s right.

Among metaphysicians, infinity has gotten a free ride, the reason seeming to be that once you accept there’s a consistent mathematical concept of infinity, the question of whether there are any actually realized infinities seems empirical.

metaphysicist Sep 8, 2012, 1:10 AM
0 points
in reply to: pragmatist’s comment on: Natural Laws Are Descriptions, not Rules

Here’s my interpretation of what you’re saying: Let the set of all quarks be Q, and assume Q has infinite elements. Now pick a particular quark, let’s call it Bob, and remove it from the set Q. Call the new set thus formed Q\Bob. Now, it’s true that Q\Bob has the same number of elements as Q. But your claim seems to be stronger, that Q\Bob is in fact the same set as Q. If that is the case, then Q\Bob both is and isn’t the set of all quarks and we have a contradiction. But why should I believe Q\Bob is identical to Q?

Because there is no difference between Q and Q/Bob besides that Q/Bob contains Bob, a difference I’m trying to bracket: distinctions between individual quarks.

Instead of quarks, speak of points in Platonic heaven. Say there are infinitely many of them, and they have no defining individuality. The set Platonic points and the set of Platonic points points plus one are different sets: they contain different elements. Yet, in contradiction, they are the same set: there is no way to distinguish them.

Platonic points are potentially problematic in a way quarks aren’t. (For one thing, they don’t really exist.) But they bring out what I regard as the contradiction in actually realized infinite sets: infinite sets can sometimes be distinguished only by their cardinality, and then sets that are different (because they are formed by adding or subtracting elements) are the same (because they subsequently aren’t distinguishable).

metaphysicist Sep 7, 2012, 11:31 PM
2 points
in reply to: ata’s comment on: Stop Voting For Nincompoops
Only if your conscience exacts no penalties for lying.

metaphysicist Sep 5, 2012, 4:37 AM
0 points
in reply to: The_Duck’s comment on: Natural Laws Are Descriptions, not Rules
I take issue with your translation at only a single point:

Having made this solemn vow, I now ask you to bring me an infinite set of quarks (note that I do not specify which quarks, for that would violate my vow!). You oblige, and provide me with a set called S.

My version contains a further constraint: When you ask me to bring you an infinite set of quarks, you instruct me to be as blind as you to the features that distinguish between quarks.

The response to this argument is that because I’ve blinded myself to the differences between quarks, I’ve lost the ability to show that Q and S are different. That does not mean that I’m entitled to conclude that Q and S are the same! After all, if I did allow myself to see the differences between quarks, such as their different positions in space, I might notice that Q contained a quark located at the position (3, 4, 5), but that S contained no quark at that position. This would let me see that Q and S are in fact distinct sets. [emphasis added.]

The_Duck tells metaphysicist to gather together an infinite set of quarks while remaining blind to their individuality. Metaphysicist, having no distinctions on which to carve infinite subsets, can respond to this request in only one way; include every quark. (I want to resist calling this the “set of all quarks,” because the incoherence of that concept with infinite quarks is what I argue.) The_Duck then goes out and finds another quark, and scolds metaphysicist, “You missed one.”

The_Duck is unjustified in criticizing metaphysicist, who must have picked “all the quarks,” given that metaphysicist succeeded—without knowing of any proper subsets—in assembling an infinite set . Having “selected all the quarks” doesn’t preclude finding another when they’re infinite in number and the only criterion for success is the number.

You will say that there is a fact of the matter as to whether the first set I assembled was all the quarks. Unblind yourself to the quarks’ individuating features, you say, and you get an underlying reality where the sets are different. I agree, but I think a more limited point suffices. When I follow the same procedure—gather all the quarks—I will be equally justified in gathering a set and in gathering a superset consisting of one other quark. There’s no way for me to distinguish the two sets. The contradiction is that following the procedure “gather all the quarks” should constrain me to a single set, “all the quarks,” rather than allowing a hierarchy of options consisting of supersets.

metaphysicist Sep 3, 2012, 2:12 AM
0 points
in reply to: The_Duck’s comment on: Natural Laws Are Descriptions, not Rules

Suppose I restate your argument for integers instead of quarks...

We don’t need to assume there are infinitely many integers, only that integers are unlimited. Some Platonists may think that an infinite set of integers is realized, and I think the arguments does pertain to that claim.

As I mentioned above, we can form infinite sets of integers that do not include all integers, for example the set of even numbers, so the argument cannot be valid when it’s made about integers. What about the argument makes it valid for quarks but not for integers? I imagine it must have to do with your distinction between [a potential] infinity and an “actually realized” infinity. Perhaps you can clarify where you are using this distinction in your argument?

The distinction is relevant to why I have no quarrel with potential infinities as such.

To help us better understand what you’re claiming, suppose the universe is infinite and I form an infinite set of quarks, any infinite set of quarks. Is it your contention that we can prove that this set of quarks equals the set of all quarks?

No. It’s only the case if (per stipulation) you know nothing about properties that distinguish one quark from another. Then, the only way you can form an infinite set of quarks is by taking all of them. So, I’m not assuming that any infinite set of quarks I can form is the only infinite set of quarks I can form; I’m setting up the problem so there’s only one way to form an infinite set of quarks. Any set conforming to that description “should” be the only set.

Perhaps you could expand this sentence:

That set includes all the quarks, since there can be no set of the same cardinality that’s greater and because, from the bare description, “quarks,” I have no basis for establishing a subset/superset relationship (HT JoshuaZ) within the set of integers.

The only way you can form an infinite set of quarks—given that you can’t distinguish one quark from another—is by selecting for inclusion all quarks indiscriminately. This is because there are only two ways that infinite subsets can be distinguished from their supersets: 1) the subset is of lower cardinality than the superset or 2) the elements are distinguishable to create a logical superset/set relationship (such as exists in quarks/upside-down quarks).

metaphysicist Sep 2, 2012, 11:18 PM
0 points
in reply to: Kindly’s comment on: Natural Laws Are Descriptions, not Rules

By default, sets are different. You can’t argue “two sets are the same because they have the same cardinality and we don’t know anything else about them”

Sets with different elements are different. But, unfortunately for actually realized infinities, you can argue that two sets with different elements are the same when those infinite sets are actually realized—but only because actually realized infinities are incoherent. That you can argue both sides, contradicted only by the other side, is what makes actual infinity incoherent.

You can’t defeat an argument purporting to show a contradiction by simply upholding one side; you can’t deny me the argument that the two sets are the same (as part of that argument to contradiction) simply based on a separate argument that they’re different.

metaphysicist Sep 2, 2012, 10:06 PM
0 points
in reply to: The_Duck’s comment on: Natural Laws Are Descriptions, not Rules
The key is the qualification “from the bare description, ‘quarks.’”

To elaborate—JoshuaZ’s comment brought this home—you can distinguish infinite sets by their cardinality or by their subset/superset relationship, and these are independent. The reasoning about quarks brackets all knowledge about the distinctions between quarks that could be used to establish a set/superset relationship.

metaphysicist Sep 2, 2012, 9:10 PM
0 points
in reply to: pragmatist’s comment on: Natural Laws Are Descriptions, not Rules

Could you clarify this inference, please? How does the second sentence follow from the first?

Let me restate it, as my language contained miscues, such as “adding” elements to the set. Restated:

If there are infinitely many quarks in the universe, then I can form an infinite set of quarks. That set includes all the quarks in the universe, since there can be no set of the same cardinality that’s greater and because, from the bare description, “quarks,” I have no basis for establishing a subset/superset relationship (HT JoshuaZ) within the set of quarks. But that set does not include all the quarks in the universe because finding other quarks is consistent with the set’s defining [added ⁹⁄₀₂] requirement that it contain infinitely many elements.

I agree that belief in the existence of actually infinite sets leads to all sorts of very counterintuitive scenarios, and perhaps that is adequate reason to be an infinite set atheist like Eliezer (although I’m unconvinced). But it does not lead to explicit contradiction, as you seem to be claiming.

Could you (or anyone else) possibly provide me with a clue as to how I might find E.Y.’s opinions on this subject or on what you base that he’s an infinite set atheist?

I’m also interested in how E.Y. avoids infinite sets when endorsing Tegmarkism or even the Many Worlds Interpretation of q.m. [In another thread, one poster explained that “worlds” are not ontologically basic in MWI, but I wonder if that’s correct for realist versions (as opposed to Hawking-style fictitional worlds).]

If intuitions have any relevance to discussions of the metaphysics of infinity, I think they would have to be intuitions of incoherence: incomplete glimmerings of explicit contradiction. The contradiction that seems to lurk in actually realized infinities is between the implications of absence of limit provided by infinity and the implications of limit implied by its realization.

metaphysicist Sep 2, 2012, 2:24 AM
2 points
in reply to: JoshuaZ’s comment on: Natural Laws Are Descriptions, not Rules
I think you responded before my correction, where I came to the same conclusion that my use of “more” was imprecise.

Added

I remember reading an essay maybe five years ago by Eliezer Yudkowsky where he maintained that the early Greek thinkers had been right to reject actual infinities for logical reasons. I can’t find the essay. Has it been recanted? Is it a mere figment of my imagination? Does anyone recall this essay?

metaphysicist Sep 2, 2012, 2:18 AM
0 points
in reply to: JoshuaZ’s comment on: Natural Laws Are Descriptions, not Rules

No, then there are the same number of quarks in both cases in the sense of cardinality.

Yes, I understand that; in fact, it was my express premise: “You can always add a finite number to an infinite set and not change the number of elements.” That is, not change the number of quarks from one case to another.

Please read it again more carefully. My argument may be wrong, but it’s really not that naive.

Added.

I see what you might be responding to: “So, there are more quarks than are contained in the set of all quarks.” The second sentence, not the first. It’s stated imprecisely. It should read, “So, there are other quarks than are contained in the set of all quarks.” Now changed in the original.

metaphysicist Sep 2, 2012, 2:07 AM
−2 points
in reply to: Mitchell_Porter’s comment on: Natural Laws Are Descriptions, not Rules

No, it’s not. Maybe it blows your mind to imagine space stretching away without limit, but if space is there independent of you, and if it has no edge, and if it doesn’t close back on itself, then it’s an actually realized infinity.

The second independent clause is true, but if (as I contend) actually realized infinities are incoherent, the proper conclusion is that the three assumptions cannot all hold.

Of course, having one’s mind blown doesn’t prove the concept entertained in incoherent; I must demonstrate that the concept really contains a logical contradiction. The contradiction in actual infinity is revealed by a question such as this one:

Assume there are an infinite number of quarks in the universe. Then, are there any quarks that aren’t contained in the set of all the quarks in the universe?

Suggestion: Answer the question thoughtfully for yourself before proceeding to my answer.

By definition, they’re all in the set. But, you can add a finite number to an infinite set and not change the number of elements. So, there are at the same time other quarks than are contained in the set of all quarks.

(I accept that Cantor demonstrated that infinities are consistent. The incoherence doesn’t lie in the mathematics of infinity but in conceiving of them as actually realized. This was also the stance of mathematician and philosopher of mathematics David Hilbert, who devised the Hilbert’s Hotel thought experiment to bring out the absurdity of actually realized infinities—while warmly welcoming Cantor’s achievements in infinity taken strictly mathematically. Or as we might say, infinity as a limit rather than as a number).

Important changes for clarity Sept. 2.

metaphysicist Sep 1, 2012, 10:40 PM
−4 points
in reply to: Vladimir_Nesov’s comment on: Dealing with trolling and the signal to noise ratio

moderators could be given the power

By whom?

metaphysicist Sep 1, 2012, 8:14 PM
4 points
in reply to: ArisKatsaris’s comment on: Natural Laws Are Descriptions, not Rules

I don’t know why you retracted this. . .

I retracted it because when I wrote it I hadn’t known Tegmarkism was part of Yudkowskian eclecticism. In that light, it deserves a less flippant response. While it strikes me as being as absurd as the ontological argument, for some of the same reasons, I can dispositively refute the ontological argument; so if they’re really the same, I ought to be able to offer a simple, dispositive refutation of Tegmark. I think that’s possible to, but it’s instructive that the refutation isn’t one that applies to the ontological argument. So, contrary to what I said, they’re not really the same argument. Arguably, even, I committed what Yvain (mistakenly) considers a widespread fallacy, his “worst error,” since I submerged Tegmark in the general disreputability of inference from possibility to necessity.

Briefly, Tegmark’s analysis is obfuscatory because:

A. The best (most naturalistic) analyses of knowledge hold that it results from our reliable causal interactions with its objects. Thus, if Tegmark universes exist, we could have no knowledge of them (which leaves us with no reason to think they do exist).

I don’t know how Tegmark addresses this objection. Or even if he does, but this objection seems to me the basic reason Tegmark’s constructs seem so dismissible.

B. It’s easy to “solve” many metaphysical and cosmological problems by positing an infinite number of entities, whether parallel universes or an infinite cosmos, but the concept of an actually realized infinity is incoherent.

[Side question: Does anyone happen to know whether the many-worlds interpretation of q.m. posits infinitely many worlds—or only a very, very large number?]

metaphysicist Aug 30, 2012, 11:30 PM
0 points
on: Fake Utility Functions
That the human “program” contains a coherent utility function seems to be an unargued assumption. Of course, if it doesn’t contain one, the potential adequacy of a simple artificial implementation is probably even more doubtful.

metaphysicist Aug 30, 2012, 8:44 PM
6 points
in reply to: drethelin’s comment on: The noncentral fallacy—the worst argument in the world?
Leaving aside the differences in moral justification, virtue ethics differs from rule utilitarianism in the practical sense that virtues tend to be more abstract than rules. For example, rather than avoiding unnecessary killing, becoming a kind person.

metaphysicist Aug 30, 2012, 8:13 PM
5 points
in reply to: Shmi’s comment on: The noncentral fallacy—the worst argument in the world?
The association fallacy is indeed what Yvain invokes: “An association fallacy is an inductive informal fallacy of the type hasty generalization or red herring which asserts that qualities of one thing are inherently qualities of another, merely by an irrelevant association.”

Key to demonstrating the association fallacy is identifying the intended association because only then can you go on to argue that it’s irrelevant. Ignore this step and you are likely to fall into another fallacy: the straw-man argument.

metaphysicist Aug 30, 2012, 7:50 PM
1 point
in reply to: Shmi’s comment on: The noncentral fallacy—the worst argument in the world?

The issue is tossing out the step where the reasons the archetypal example gives the category a negative connotation are checked against the example under consideration.

And my claim is that, in typical uses of the example arguments, the reasons that make the category negative—for the arguer—are precisely the reasons the arguer intends to advance. So, Yvain hasn’t made a case that submergence in a verbal archetype is an important fallacy. And thinking that it is the key fallacy involved in these arguments promotes superficiality when considering arguments like the exemplars.

metaphysicist Aug 30, 2012, 7:00 PM
10 points
0
on: The noncentral fallacy—the worst argument in the world?
Almost 400 comments but not a word of discussion of the parsing Yvain provides for his seven examples! But if Yvain’s parsing is wrong—as I think it is—then his analysis will serve to further bias our understanding of positions we disagree with and to forsake any charity in understanding these positions.

The question that is fairly asked of Yvain is what distinguishes his “worst argument” (“X is in a category whose archetypal member has certain features. Therefore, we should judge X as if it also had those features, even though it doesn’t.”) from any form of rule-governed reasoning in ethics (whether deontological or rule-utilitarian). When the examples are expanded and recast in those terms, they do not express Yvain’s “worst argument”; they rather simply express moral premises subject to disagreement.

Taxation is theft. I’m no libertarian, but the argument isn’t that taxation shares features with “archetypal” theft but that any taking of unearned property is wrong for the same basic reasons as “archetypal” theft is wrong, whether natural law or utilitarian calculus.

Abortion is murder. The claim almost always comes from a fundamentalist religious direction. Abortion is said to be murder not because it shares features with prototypical murders but because it is the same in the essential respect that it involves killing an innocent possessed of a soul. It’s stupid enough as it stands; no reason to misrepresent it.

King is a criminal. If the psychologist-of-morality Kohlberg is believed, most adults in the U.S. identify morality with authority. Many believe it is immoral to break a law enacted through democratic procedures. Those who reason this way are indeed philistines, but their problem isn’t with some formal fallacy in reasoning but with their premises.

Evolutionary psychology is sexist People who argue in these terms usually think it is wrong to “reinforce sexual stereotypes” even if they’re true.

And so on. If you were arguing with someone defending their position in the ways Yvain summarizes, would you point out, say, that the archetypical murder is a lot different from abortion; or would you point out that souls don’t really exist (or point to similar defective assumptions)? The first would miss the point. An answer to the antiabortion argument has a similar form to the “worst argument,” but I think the answer is sound: Compelling women to remain pregnant is involuntary servitude. (More popularly, No forced labor.) The question is whether the essential features of abortions, relative to a well-chosen framework, are best captured by analogy to murder or slavery. We always reason by some sort of analogy; the question is whether the given analogy is adequate. Yvain’s proscriptions consistently carried out would toss analogical reasoning in ethics.

metaphysicist

The raw-ex­pe­rience dogma: Dis­solv­ing the “qualia” problem

The raw-experience dogma: Dissolving the “qualia” problem