The meaning of "existence": Lessons from infinity

2013-01-22T02:18:31.166Z · score: -12 (20 votes)
Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-06T21:30:37.039Z · score: 0 (0 votes) · LW · GW

You've got quite a lot of negative responses to your formatting, not a single positive response (correct me if I am wrong), yet you still persist and speculate about status reasons.

I just found it curious: I've addressed typography issues in a blog posting, "Emphasis by Typography."

I have to say I'm surprised by your tone; like you're accusing me of some form of immorality for not being attentive to readers. This all strikes me as very curious. I read Hanson's blog and so have gotten attuned to status issues. I'm not plotting a revolution over font choice; I'm only curious about why people find Verdana objectionable just because other postings use a different font.

If infinite sets and brutely distinguishable elements exist, infinite sets with brutely distinguishable elements should exist. Why? It doesn't follow.

The argument concerns conceptual possibility, not empirical existence. If actually existing sets can consist of brutely distinguishable elements and of infinite elements, there's nothing to stop it conceptually from being both.

You have located a place for a counter-argument: supplying the conceptual basis. But it seems unlikely that a conceptual argument would successfully undermine brutely distinguishable infinite elements without undermining brutely distinguishable elements in general.

Then we have a predicate P(Z) = "Z is a subset of X", and P(X) holds while P(Y) doesn't. What's wrong here?

You can distinguish the cardinality of finite sets with brutely distinguishable points. That is, if a set contains 7 points, you can know there are seven different points, and that's all you can know about them.

Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-06T01:39:50.006Z · score: 0 (0 votes) · LW · GW

Thank your for the astute response.

1.You say that the points are brutely distinguishable and later you say that they are indistinguishable, which nevertheless you hold to be different properties.

The points are brutely distinguishable, but the sets aren't.

2.Why are the sets indistinguishable? Although I don't particularly understand what predicates you allow for brutely distinguishable entities, it seems possible to have X = set of all brutely distinguishable points (from some class) and Y = set of all brutely distinguishable points except one. It is, of course, not a definition of Y unless you point out which of the points is missing (which you presumably can't), but even if you don't have a definition of Y, Y may still exist and be distinguishable from X by the property that X contains all the points while Y doesn't.

No predicates besides brute distinguishability govern it. Entities that are brutely distinguishable are different only by virtue of being different.

The sets that differ but for one element differ because their cardinality is different. This is how they differ from the infinite case.

3.If the argument were true, haven't you just shown only that you can't define an infinite set of brutely distinguishable entities, rather than that infinite sets can't be defined at all?

If infinite sets and brutely distinguishable elements exist, infinite sets with brutely distinguishable elements should exist.

4.What is your opinion about the set of all natural numbers? Is it finite or can't it be defined?

It is infinite, but it isn't "actually realized." (They don't exist; we employ them as useful fictions.)

  1. And how does the argument depend on infiniteness, after all? Assume there is a class of eleven brutely distinguishable points. Now, can you define a set containing seven of them? If you can't, since there is no property to distinguish those seven from the remaining four, doesn't it equally well prove that sets of cardinality seven don't exist?

To make the cases parallel (which I hope doesn't miss the point): take 7 brutely distinguishable points; 4 more pop into existence. The former and latter sets are distinguishable by their cardinality. When the sets are infinite, the cardinality is identical.

The frequentist definition of probability says that probability is the limit of relative frequencies, which is the limit of (the number of occurrences divided by the number of trials), which is not equal to (limit of the number of occurrences) divided by (limit of the number of trials).

This doesn't seem relevant to actually realized infinities, since the limit becomes inclusive rather than exclusive (of infinity). The relative frequency of heads to tails with an actually existing infinity of tosses is undefined. (Or would you contend it is .5?)

And emphasis is usually marked by italics, not red.

Are my aesthetics off? I've decided that unbolded red is best for emphasizing text sentences, the reason being that it is more legible than bolding, centainly than italics. If you don't use many pictures or diagrams, I think helps maintain interest to include some color whenever you can justify it.

Color seems increasingly used in textbooks. Perhaps its a status thing, as the research journals don't use it. But blog writing should usually be more succinct than research-journal writing, and this makes typographical emphasis more valuable because there's less opportunity to imply emphasis textually.

Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-05T22:06:33.125Z · score: 0 (0 votes) · LW · GW

What makes you think there's some equivocation in my usage of "exists"? (Which is where taboo is useful.) If I were pushing the boundaries of the concept, that would be one thing. I'm not taking any position on whether abstract entities exist; what I mean by exist is straightforward. If the universe has existed for an infinite amount of time, the infinity is "actually realized," that is, infinite duration is more than an abstract entity or an idealization. If I say, the universe is terribly old, so old we can approximate it by regarding it as infinitely old, then I am not making a claim about the actual realization of infinity.

Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-05T21:56:34.096Z · score: 0 (0 votes) · LW · GW

some quite smart people disagree on the meaning of this term

We have an apparently very deep philosophical difference here. Some "quite smart people" have offered different accounts of existence: Quine's, that we are committed to the existence of those variables we quantify over in our best theory, comes to mind. My use of "exists" is ordinary enough that most any reasonable account will serve. I think the intuition of "existence" is really extremely clear, and we argue about accounts, not concepts. Existence is very simple

Maybe addressing your specific examples will clarify. "Can infinite quantities be observed?" as a meaning of existing. Clearly doesn't mean the same thing. Whether something exists or it can be observed are two different questions, existence being a necessary but insufficient condition for observability. "Can models with infinities in them fit the observations better than those without?" Still not existence. There are instrumentalist models and realist models. (Realists will agree; some intrumentalists will consider all theory instrumental, but that's another question.) There's a difference between saying something predicts the data and saying that the model describes reality (what exists) even if the latter claim is justified by the former. "Do numbers exist?" There the dispute isn't about existence but about numbers, and it's only because we do have a clear intuition of "existence" that the question about numbers can arise. So, we get different theories about numbers, which imply that numbers exist or don't.

So, even when it comes to numbers, I don't think there's much problem with the concept of existence. Sometimes one sees an unphilosophical tendency to treat problems regarding concepts as though they could be resolved by a mere choice of definition. Such flaws so easily corrected rarely arise in sophisticated thought. The question here is whether our intuition of existence implies that only the finite can exist. In analyzing an intuition, it rarely helps to start with a definition.

Can infinite quantities exist? A philosophical approach

2013-01-03T22:52:56.745Z · score: -9 (50 votes)
Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-03T22:02:12.170Z · score: -1 (13 votes) · LW · GW

Thank you for the criticism. I will indeed consider it. It may be that we have different theories of writing. Regarding our likely differences considering how to write, see my "Plain-talk writing: The new literary obfuscation."

I don't see how it can be accused of meandering. I'd be pleased to receive a personal note explaining.

Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-03T21:56:53.721Z · score: -7 (7 votes) · LW · GW

Something's got to be primitive, and I can't think of a candidate better than existence.

Comment by metaphysicist on Can infinite quantities exist? A philosophical approach · 2013-01-03T21:56:06.601Z · score: -1 (3 votes) · LW · GW

If you're not sure of the "brute distinguishability" concept, I've conveyed something, because it is the main novelty in my argument.

The deeper solution to the mystery of moralism—Believing in morality and free will are hazardous to your mental health

2012-10-14T13:21:36.086Z · score: -17 (57 votes)
Comment by metaphysicist on The noncentral fallacy - the worst argument in the world? · 2012-10-05T16:51:33.179Z · score: 7 (7 votes) · LW · GW

Where can i find out what "near-type" means here?

It refers to "near-mode," which is jargon in construal-level theory for "construed concretely." So in context, it means direct and involving personal experience, as opposed to reading or discussing abstractly.

Robin Hanson applies construal-level theory speculatively in numerous posts at Overcoming Bias. A concise summary of construal-level theory can be found in my posting "Construal-level theory: Matching linguistic register to the case's granularity.".

Comment by metaphysicist on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? · 2012-09-29T02:07:09.792Z · score: 1 (1 votes) · LW · GW

What state of affairs is "correspondence theory is true" congruent with?

The concept of scientific truth--the concept used by scientists--is the state of affairs some correspondence theories purport to be congruent with.

Comment by metaphysicist on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? · 2012-09-28T20:53:49.602Z · score: 1 (1 votes) · LW · GW

That's an excellent argument if it's the case that correspondence theory is not the sort of thing allowed to have truth values under correspondence theory. Why do you say it's not?

Comment by metaphysicist on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? · 2012-09-28T20:51:29.976Z · score: 2 (2 votes) · LW · GW

Theories using Piercian concepts are today usually termed antirealist or instrumentalist.

Comment by metaphysicist on [Poll] Less Wrong and Mainstream Philosophy: How Different are We? · 2012-09-27T21:49:54.982Z · score: 5 (5 votes) · LW · GW

Tabooing "truth", one can see that the theories really speak about (slightly) different concepts.

Then, you would merely choose which of the concepts is the one needed for a particular theoretical purpose. Right?

Wrong! The arguments go to the concepts' coherence. This is why it's philosophy, not lexicography.

For example, a correspondence theorist generally argues that the notion of an epistemological limit to which scientific findings converge need not exist and can never be established empirically. If correspondence theory is true, you aren't allowed to use the Piercian limit. It's a vacuous concept.

Or, the correspondence theorist argues that the epistemological limit of scientific investigation can't even be defined without assuming a correspondence variety of truth (which the Piercian, in turn, argues can't exist). The correspondentist argues that if you define truth at a limit, then you have to define the truth that science is converging as itself the result of a scientific investigation at an endpoint, and similarly for the concepts you use to define scientific investigation, etc. Thus, a Piercian view, it's contended, produces an infinite regress.

It's possible that both concepts are coherent, but that too would require a philosophical argument--and it's an unlikely result here, at least in my opinion: it's probably more likely that both concepts are incoherent than that both are coherent.

These kinds of conclusions, philosophical and lacking in direct application, help inform the priors one assigns to just about every scientific controversy.

Comment by metaphysicist on The raw-experience dogma: Dissolving the “qualia” problem · 2012-09-24T04:05:31.618Z · score: 7 (9 votes) · LW · GW

me: A "p-zombie" "behaves" the same way we do, but does a p-zombie believe it has qualitative awareness?

To be precise about the value of the belief/intuition concept in accounting for the illusion that qualia exist—one defect in the zombie thought experiment is that it prompts the attitude: maybe I can't prove that you're not a zombie, but I sure as hell know I'm not one!

The zombie experiment imposes a consistent outside view; it seems to deny the evidence of "personal experience" by fiat—because it simply doesn't address what it would feel like to be a zombie.

So, the zombie experiment seems to show that people might not be able to distinguish zombies from humans; but invoking the beliefs held by the "zombie" shows from the inside that being a zombie can be no different from being a human: the two are subjectively indistinguishable.

To address your question directly: the ordinary zombie thought experiments purport to show that without qualia humans would be zombies; whereas when you allow zombies' (false) beliefs (in ineffable perceptual essences), the thought experiment shows that zombies are really humans.

Comment by metaphysicist on The raw-experience dogma: Dissolving the “qualia” problem · 2012-09-23T20:03:12.759Z · score: 4 (6 votes) · LW · GW

Sophistry. It's madness to say that the blue isn't actually there. But this is tempting for people who like the science we have, because the blue isn't there in that model of reality.

If by blue you mean--as you do--the purely subjective aspect of perceiving the color blue (call that "blue"), then it's only madness to deny it exists if you insist on confusing blue with "blue." No one but a madman would say blue doesn't exist; no philosopher should be caught saying "blue" exists.

If you can show a causal role for pure experience, that would be something else, but instead you speak of the "causal role they appear to play." But we don't want a theory where things play the role they "appear" to play; the illusion of conscious experience includes the seemingness that qualia play a causal role (Added: as I explain in my account of the related illusion of "free will."

In short, it just won't do to call qualia nihilism "madness," when you offer no arguments, only exasperation.

But modern physics is mathematical and operational, there is plenty of opportunity for something to actually be a conscious experience, while appearing in the formal theory as a state or entity with certain abstractly characterized structural and algebraic properties.

This simply doesn't solve the problem; not in the least. If you posit abstractly characterized structural entities, you are still left with the problem regarding what makes that configuration give the appearance "blue." You're also left with the problem of explaining why evolution would have provided a means of registering these "abstractly characterized structural and algebraic properties" when they make no difference for adaptation.

My guess, you espouse an epistemology that makes sense data necessary. Completely freeing epistemology from sensationalism is virtue rather than vice: philosophers have been looking for a way out of sensationalism since Karl Popper's failed falsificationism.

You need an argument better than alleging madness. Many things seem blatantly wrong before one reflects on them.

Comment by metaphysicist on The raw-experience dogma: Dissolving the “qualia” problem · 2012-09-23T19:40:02.013Z · score: 3 (5 votes) · LW · GW

You may be omitting or misunderstanding the role of the concept of belief in my account. The role of that concept is original in this account (and novel, to the best of my less-than-comprehensive knowledge).

A "p-zombie" "behaves" the same way we do, but does a p-zombie believe it has qualitative awareness? If it does, then there's no distinction between humans and p-zombies, but the antimaterialists who came up with the p-zombie thought experiment were of the persuasion that belief is as meaningless a concept for materialists as is qualia; both were then derogated by the reigning behaviorists as "mentalistic" concepts, hence illicit. The Churchlands are eliminitivist about all "folk psychological" concepts like belief; Dennett doesn't apply the concept of belief to the problem of qualia. But qualia proponents make belief dependent on qualitative awareness: eliminating qualia does preclude deriving knowledge (a kind of belief) from conscious sensation.

On my account, what dissolves the problem of qualia is recognizing that the only "evidence" favoring their existence is our sense of certainty favoring our sequestered belief that they exist. (See 3.C. in OP.)

Comment by metaphysicist on The raw-experience dogma: Dissolving the “qualia” problem · 2012-09-19T19:37:04.733Z · score: 3 (3 votes) · LW · GW

Is your position the same as Dennett's position (summarized in the second paragraph of synopsis here)?

Let me try to answer more succinctly. Dennett and I are concerned with different problems; Dennett's is a problem within science proper, while mine is traditionally philosophical. Dennett's conclusion is that "qualia" don't provide introspective access to the functioning of the brain; my conclusion is that our common intuition concerning the existence of qualia is incoherent.

Comment by metaphysicist on The raw-experience dogma: Dissolving the “qualia” problem · 2012-09-18T09:05:24.950Z · score: 5 (7 votes) · LW · GW

Is your position the same as Dennett's position (summarized in the second paragraph of synopsis here) ?

I agree with Dennett that qualia don't exist. I disagree that the concept of qualia is basically a remnant of an outmoded psychological doctrine; I think it's an innate idea.

Dennett can be criticized for ignoring the subjective nature of qualia. He shows, for example, that reported phenomenal awareness is empirically bogus in that it doesn't correspond to the contents of working memory. I'm concerned with accounting for the subjective nature of the qualia concept.

Dennett basically thinks qualia are empirically falsifiable; I think the concept is incoherent.

Comment by metaphysicist on The raw-experience dogma: Dissolving the “qualia” problem · 2012-09-18T08:11:30.711Z · score: 1 (1 votes) · LW · GW

"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

2012-09-16T19:15:13.794Z · score: 4 (52 votes)
Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-08T04:48:26.287Z · score: 1 (1 votes) · LW · GW

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.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-08T01:10:17.625Z · score: 0 (0 votes) · LW · GW

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).

Comment by metaphysicist on Stop Voting For Nincompoops · 2012-09-07T23:31:29.734Z · score: 1 (2 votes) · LW · GW

Only if your conscience exacts no penalties for lying.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-05T04:37:16.670Z · score: 0 (0 votes) · LW · GW

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.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-03T02:12:58.177Z · score: 0 (0 votes) · LW · GW

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).

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-02T23:18:54.455Z · score: 0 (0 votes) · LW · GW

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.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-02T22:06:29.643Z · score: 0 (0 votes) · LW · GW

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.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-02T21:10:37.839Z · score: 0 (0 votes) · LW · GW

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.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-02T02:24:48.259Z · score: 2 (2 votes) · LW · GW

I think you responded before my correction, where I came to the same conclusion that my use of "more" was imprecise.


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?

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-02T02:18:19.962Z · score: 1 (3 votes) · LW · GW

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.


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.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-02T02:07:19.380Z · score: -1 (5 votes) · LW · GW

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.

Comment by metaphysicist on Dealing with trolling and the signal to noise ratio · 2012-09-01T22:40:57.126Z · score: -2 (4 votes) · LW · GW

moderators could be given the power

By whom?

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-09-01T20:14:33.139Z · score: 3 (5 votes) · LW · GW

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?]

Comment by metaphysicist on Fake Utility Functions · 2012-08-30T23:30:29.692Z · score: 0 (0 votes) · LW · GW

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.

Comment by metaphysicist on The noncentral fallacy - the worst argument in the world? · 2012-08-30T20:44:52.987Z · score: 3 (3 votes) · LW · GW

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.

Comment by metaphysicist on The noncentral fallacy - the worst argument in the world? · 2012-08-30T20:13:13.634Z · score: 3 (3 votes) · LW · GW

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.

Comment by metaphysicist on The noncentral fallacy - the worst argument in the world? · 2012-08-30T19:50:28.399Z · score: 1 (1 votes) · LW · GW

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.

Comment by metaphysicist on The noncentral fallacy - the worst argument in the world? · 2012-08-30T19:00:05.265Z · score: 7 (11 votes) · LW · GW

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.

Comment by metaphysicist on [Link] Reddit, help me find some peace I'm dying young · 2012-08-20T15:12:38.810Z · score: 0 (0 votes) · LW · GW

I do hope you cited the aphorism rather than taking credit for it as original. But seeing it repeated once again forced me for once to pay attention to its meaning: to find it vacuous. The point should be stated Don't confuse functional and mechanistic explanations. Organisms don't "execute" their adaptations, this being just another confusion of kinds of explanation, at least if taken literally. And organisms can be said to be fitness maximizers, once it is realized that functional generalizations are always riddled with exceptions.

Comment by metaphysicist on Bayes for Schizophrenics: Reasoning in Delusional Disorders · 2012-08-19T22:40:54.924Z · score: 1 (1 votes) · LW · GW

You seem to be conflating the original schizophrenic state with the residual after the patients get antipsychotic medication: the latter may be readily amenable to reason; the former, the therapist would breach rapport with the patient, by challenging full delusions.

Medication is part of the standard treatment for schizophrenia--usually, the major part. Drawing conclusions about delusions from the residuals following treatment seems to shield you from what would be obvious had you observed unmedicated patients. Delusions aren't failures of Bayesian rationality: they involve, typically, accepting a few self-evident priors, and these are driven by intense affect.

Comment by metaphysicist on Against Modal Logics · 2012-08-19T18:26:04.544Z · score: 2 (3 votes) · LW · GW

then why read Hanson also? if they are colleagues and co-bloggers there must be something about EY that Robin thinks is first rate, no?

Not necessarily. Hanson might be a good thinker who is also a personal opportunist who'll do anything to enhance his status, where co-publishing with Yudkowsky helped put Hanson's blog on the map. Hanson could have "admired" Yudkowsky for his fan-club building capacities rather than for the high quality of his thinking.

Comment by metaphysicist on Proposed rewrites of LW home page, about page, and FAQ · 2012-08-19T18:01:27.729Z · score: 3 (3 votes) · LW · GW

LW is called a "community blog," but there's no information on how the "community" acts. Who adopts the new page? Is the vote binding? If so, on whom? Who pays for the fancy Reddit machinery on this blog? (Who refuses to pay for better machinery?)

Most people only invest themselves in conceiving changes in practices when they have some actual power to bring those changes to fruition. If the mere existence of a British monarch dampens popular enthusiasm for government, what's the effect of having an essentially autocratic "owner"?

Added September 1:

Then the proposed FAQ says, "Sequence posts provide Less Wrong's philosophical foundation."

Which goes to a worry more important than relating to public relations: philosophical foundations at the discretion of the Compiler of the Sequences.

Comment by metaphysicist on [SEQ RERUN] Against Modal Logics · 2012-08-19T17:44:50.093Z · score: 1 (1 votes) · LW · GW

It is possible, I suppose, that the thing that makes us conscious is different from the thing that makes us talk about consciousness -- but there's certainly no evidence for it, and it's a damned silly idea in any case.

True, but it seems to me almost trivially true that explaining why we talk about consciousness makes a theory positing that we "are conscious" otiose. What other evidence is there? What other evidence could there be? The profession of belief in mysterious "raw experience" merely expresses a cognitive bias, the acceptance of which should be a deep embarrassment to exponents who call themselves rationalist.

The term "self-awareness," however, is quite misleading. I can have awareness of my inner states--some knowledge about what I'm thinking--without having mysterious raw experience. "Self-awareness" here is used by raw-experience believers to mean something special: knowledge of "what it is like to be me." (Thomas Nagel.) The ambiguous usage of self-awareness obfuscates the problem, making belief in "raw experience" seem reasonable, when it's really a believed (and beloved) superstition.

Comment by metaphysicist on Why Don't People Help Others More? · 2012-08-16T19:49:02.393Z · score: 1 (1 votes) · LW · GW

You're reffering to the experiment itself; they're talking about the experiment within the experiment.

I was compelled to post that clarification after being primed for "helping behavior."

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-08-09T00:32:46.123Z · score: 0 (0 votes) · LW · GW

Conceiving of laws as rules activates all sorts of unconscious inferences stemming from the part of our brain that processes social rules, such as the intuitions that motivate nomic fundamentalism. So whether or not there is a genuine distinction between determination and description, there is certainly a cognitive difference in how we respond to those concepts.

That's question begging, in that the question is just what are those differences when applied to physics rather than sociology. The connotation of 'rule' that survives transfer to physics might be just the one that's useful: choose from the parts of the intuition and discard the irrelevant.

The distinction that physics seems to have retained from the original intuition is that between a determinate and finite set of rules (or laws or universals of a particular kind) and an infinitely large set of potential descriptions.

To collapse the distinction between rules and descriptions as you suggest is to invite gliding over what the distinction really represents. The empiricist armory may not have the conceptual equipment to distinguish our restrictive expectations for laws of physics from the broad pragmatic tolerance in other fields and in ordinary description. You have to mark that distinction, and that's accomplished with 'rules' and 'descriptions.' If you choose to mark it some other way, then the difference is merely rhetorical. But the empiricists really don't want to mark it--they have seemingly principled objections to the distinction's coherence--have you noticed? That's what the dispute about rules and descriptions is really about. To say the universals are 'causes' of physical events under realism really does introduce connotations into your descriptions that I'd be surprised to see Lewis himself endorse.

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-08-09T00:08:03.856Z · score: -1 (1 votes) · LW · GW

What do you think of Max Tegmark's answer, that it's because universes with every possible (i.e., non-contradictory) set of laws of physics exist

If I can be frank, this is insane. This is the ontological argument for god revisited. Possibility does not imply necessity, and to think it does means you can rationally posit entities by defining them: defining them into existence.

Comment by metaphysicist on The supposedly hard problem of consciousness and the nonexistence of sense data: Is your dog a conscious being? · 2012-08-08T05:01:35.656Z · score: 1 (1 votes) · LW · GW

That doesn't commit us to infinities, just to a non-vicious circularity, of the Neurath's Boat variety.

Not my point. I'm saying whether actual infinities exist physically does not appear to be empirical (or else is resolved by empirical evidence we already have), and there are good rational grounds--endorsed by Yudkowsky, if I'm not mistaken--for rejecting actual infinities, grounds that already existed for the classical Greeks, who rejected the concept . The comparison was between the contention that qualia don't exist and the contention that absolute infinities don't exist: speculative but rationally grounded.

I wish to revise my statement: understanding the reference of terms as well as possible requires doing empirical work.

It requires empirical evidence, but that's not to say we don't have it, absent experiments. But here, we're not really talking about the reference of concepts but whether the concepts could even have referents--because of conceptual incoherence.

That would have a chance to be convincing if you stated an alternative account of what philosophers have called qualia.

Philosophers don't have an account of qualia, but philosophers of mind do have a consensus about what qualia are not, which is what you said qualia are. So, you haven't correctly defined what "philosophers call qualia"; you've defined the topic of the "easy question of consciousness."

The motivation of the lead essay is to give a (novel) account of the illusion of qualia; it's in red. But if you're saying you don't know what I'm talking about when I refer to raw experience, then either you're "lying" or I'm wrong, as I do in fact rely on your ability to understand me when I speak of raw experience--at least after reading the philosophers of mind, who mainly accept a concept of qualia distinct from the "easy question" you address. These philosophers work hard at pumping your intuitions to be sure you grasp the concept in question. Shoemaker's inverted-spectrum thought experiments are particularly useful. You can probably guess what's involved; and if so, you really do understand the concept of qualia and how the "hard question" is distinct from the "easy question."

Saying "raw experience" leaves everything open, including the possibility that some internal aspects of the way we sense the world are raw experience.

What it leaves open is the subject of this discussion. To have the discussion, we must agree in our basic intuitions about qualitative experience. I'm actually not sure whether you're saying we disagree on our intuitive understanding of the concept of "raw experience," but given that understanding, we can then talk about whether it makes sense to say that unknown neural processes might constitute raw experience. Let's take it more modestly: which account of raw experience, neural underpinnings or illusion (as described in the red in the main article), best explains the intuition.

The advantages of the illusion account are:

  1. We are spared finding explanation for a fact that would be so ill-suited to the reigning scientific ontology that nobody who has understood the problem claims to have any idea what kind of theory might explain this fact;

  2. We have a solution to the long-standing problem of why there's no private language. (Wittgenstein saw that there could not be, but didn't intelligibly explain why.) There's no private language because what we always assume a private language would have to be anchored to--qualitative experience--doesn't exist.

  3. We are delivered from the dominant form of epistemological skepticism--that based on sensationalism.

Now, what is gained conceptually by accepting raw experience as an empirical reality that can be nailed down neurologically.

  1. Only the implausibility that a single belief held very strongly is false--which is to say, we gain hardly anything.

It's more sensible to conclude that we have a single very wrong belief.

Updated with last section 11:09 PM. August 7

Comment by metaphysicist on Natural Laws Are Descriptions, not Rules · 2012-08-08T03:49:06.163Z · score: 8 (10 votes) · LW · GW

If I were an economist, I wouldn't be interested (at least not qua economist) in deductive systems that talked about quarks and leptons. I would be interested in deductive systems that talked about prices and demand. The best system for this coarser-grained vocabulary will give us the laws of economics, distinct from the laws of physics.

There's this difference between economics and physics. The axioms of economics don't come close to completely explaining prices and demand, and we don't expect them to, even in principle. It would be a miracle if they did: finding coarse-grained descriptions at different levels of abstraction that are exceptionless would be miraculous.

We want a complete physics; we know we can't have a complete economics. The expectation that physics can be complete reflects an assumption that we can cut physical reality at its seams, but we have no similar expectation for economics. Physical descriptions are more than mere descriptions because we expect a finite number of them to describe the (physical) universe; we don't expect axiomatized economics to describe the coarse grain of the economics universe, only what's really a small part.

Accusing realists about physical laws as conceiving of them as "pushing matter around" is to substitute a metaphorical description of the philosophical landscape for an actual analysis. Here's an analysis. On a realist view--that is, laws are "rules"--you expect a finite number of axioms to be exhaustive. This is what makes them like laws--their finite number. On the other hand, descriptions are infinite in their variety. What makes the laws of physics "real" is that, if they work as supposed, they describe the structure of matter. That we see matter as having a structure leads us to expect a finite number of principles to describe that structure. We don't think that way about ordinary descriptions or the "laws" of the "special sciences." There, we take what we can get, and don't expect exhaustiveness.

Comment by metaphysicist on Bayesians vs. Barbarians · 2012-08-07T20:00:07.550Z · score: 0 (0 votes) · LW · GW

What function describes your threshold as the negative values go below -1?

Comment by metaphysicist on The supposedly hard problem of consciousness and the nonexistence of sense data: Is your dog a conscious being? · 2012-08-07T19:36:57.105Z · score: -2 (2 votes) · LW · GW

I think it's a cool font!

Comment by metaphysicist on The supposedly hard problem of consciousness and the nonexistence of sense data: Is your dog a conscious being? · 2012-08-07T19:36:30.955Z · score: 0 (0 votes) · LW · GW

you can then think about exactly how your brain turns a sentence about consciousness into meaning and it will exactly mirror the actual process your brain used to turn the sentence into the meaning you experience.

We don't experience meanings. An organism without qualia could--without contradiction--grasp the meaning of a sentence.

Comment by metaphysicist on The supposedly hard problem of consciousness and the nonexistence of sense data: Is your dog a conscious being? · 2012-08-07T19:24:08.064Z · score: -1 (1 votes) · LW · GW

Not at all the same. Yudkowsky points out that science can explain events and things in ways that a layman may not even conceive. Here, the question is whether it even makes sense to call qualia an event.