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

2 metaphysicist 16 September 2012 07:15PM

[Cross-posted.]

1. Defining the problem: The inverted spectrum

Philosophy has been called a preoccupation with the questions entertained by adolescents, and one adolescent favorite concerns our knowledge of other persons’ “private experience” (raw experience or qualia). A philosophers’ version is the “inverted spectrum”: how do I know you see “red” rather than “blue” when you see this red print? How could we tell when we each link the same terms to the same outward descriptions? We each will say “red” when we see the print, even if you really see “blue.”

The intuition that allows us to be different this way is the intuition of raw experience (or of qualia). Philosophers of mind have devoted considerable attention to reconciling the intuition that raw experience exists with the intuition that inverted-spectrum indeterminacy has unacceptable dualist implications making the mental realm publicly unobservable, but it’s time for nihilism about qualia, whose claim to exist rests solely on the strength of a prejudice.

A. Attempted solutions to the inverted spectrum.

One account would have us examine which parts of the brain are activated by each perception, but then we rely on an unverifiable correlation between brain structures and “private experience.” With only a single example of private experience—our own—we have no basis for knowing what makes private experience the same or different between persons.

A subtler response to the inverted spectrum is that red and blue as experiences are distinct because red looks “red” due to its being constituted by certain responses, such as affect. Red makes you alert and tense; blue, tranquil or maybe sad. What we call the experience of red, on this account, just is the sense of alertness, and other manifestations. The hope is that identical observable responses to appropriate wavelengths might explain qualitative redness. Then, we could discover we experience blue when others experience red by finding that we idiosyncratically become tranquil instead of alert when exposed to the long wavelengths constituting physical red. This complication doesn’t remove the radical uncertainty about experiential descriptions. Emotion only seems more capable than cognition of explaining raw experience because emotional events are memorable. The affect theory doesn't answer how an emotional reaction can constitute a raw subjective experience.

B. The “substitution bias” of solving the “easy problem of consciousness” instead of the “hard problem.”

As in those examples, attempts at analyzing raw experience commonly appeal to the substitution process that psychologist Daniel Kahneman discovered in many cognitive fallacies. Substitution is the unthoughtful replacement of an easy for a related hard question. In the philosophy of mind, the distinct questions are actually termed the “easy problem of consciousness” and the “hard problem of consciousness,” and errors regarding consciousness typically are due to substituting the “easy problem” for the “hard,” where the easy problem is to explain some function that typically accompanies “awareness.” The philosopher might substitute knowledge of one’s own brain processes for raw experience; or, as in the previous example, experience’s neural accompaniments or its affective accompaniments. Avoiding the “substitution bias” is particularly hard when dealing with raw awareness, an unarticulated intuition; articulating it is a present purpose.

2. The false intuition of direct awareness

A. Our sense that the existence of raw experience is self-evident doesn’t show that it is true.

The theory that direct awareness reveals raw experience has long been almost sacrosanct in philosophy. According to the British Empiricists, direct experience consists of sense data and forms the indubitable basis of all synthetic knowledge. For Continental Rationalist Descartes, too, my direct experience—“I think”—indubitably proves my existence.
We do have a strong intuition that we have raw experience, the substance of direct awareness, but we have other strong intuitions, some turn out true and others false. We have an intuition that space is necessarily flat, an intuition proven false only with non-Euclidean geometries in the 19th century. We have an intuition that every event has a cause, which determinists believe but indeterminists deny. Sequestered intuitions aren’t knowledge.

B. Experience can’t reveal the error in the intuition that raw experience exists.

To correct wayward intuitions, we ordinarily test them against each other. A simple perceptual illusion illustrates: the popular Muller-Lyer illusion, where arrowheads on a line make it appear shorter than an identical line with the arrowheads reversed. Invoking the more credible intuition that measuring the lines finds their real length convinces us of the intuitive error that the lines are unequal. In contrast, we have no means to check the truth of the belief in raw experience; it simply seems self-evident, but it might seem equally self-evident if it were false. 

C. We can’t capture the ineffable core of raw experience with language because there’s really nothing there.

One task in philosophy is articulating the intuitions implicit in our thinking, and sometimes rejecting the intuition should result from concluding it employs concepts illogically. What shows the intuition of raw experience is incoherent (self-contradictory or vacuous) is that the terms we use to describe raw experience are limited to the terms for its referents; we have no terms to describe the experience as such, but rather, we describe qualia by applying terms denoting the ordinary cause of the supposed raw experience. The simplest explanation for the absence of a vocabulary to describe the qualitative properties of raw experience is that they don’t exist: a process without properties is conceptually vacuous.

D. We believe raw experience exists without detecting it.

One error in thinking about the existence of raw experience comes from confusing perception with belief, which is conceptually distinct. When people universally report that qualia “seem” to exist, they are only reporting their beliefs—despite their sense of certainty. Where “perception” is defined as a nervous system’s extraction of a sensory-array’s features, people can’t report their perceptions except through beliefs the perceptions sometimes engender: I can’t tell you my perceptions except by relating my beliefs about them. This conceptual truth is illustrated by the phenomenon of blindsight, a condition in  patients report complete blindness yet, by discriminating external objects, demonstrate that they can perceive them. Blindsighted patients can report only according to their beliefs, and they perceive more than they believe and report that they perceive. Qualia nihilism analyzes the intuition of raw experience as perceiving less than you believe and report you perceive, the reverse of blindsight.

3. The conceptual economy of qualia nihilism pays off in philosophical progress

Eliminating raw experience from ontology produces conceptual economy. A summary of its conceptual advantages:

   A. Qualia nihilism resolves an intractable problem for materialism: physical concepts are dispositional, whereas raw experiences concern properties that seem, instead, to pertain to noncausal essences. If raw experience was coherent, we could hope for a scientific insight, although no one has been able to define the general character of such an explanation. Removing a fundamental scientific mystery is a conceptual gain.
 
    B. Qualia nihilism resolves the private-language problem. There seems to be no possible language that uses nonpublic concepts. Eliminating raw experience allows explaining the absence of a private language by the nonexistence of any private referents.

    C.  Qualia nihilism offers a compelling diagnosis of where important skeptical arguments regarding the possibility of knowledge go wrong. The arguments—George Berkeley’s are their prototype—reason that sense data, being indubitable intuitions of direct experience, are the source of our knowledge, which must, in consequence, be about raw experience rather than the “external world.” If you accept the existence of raw experience, the argument is notoriously difficult to undermine logically because concepts of “raw experience” truly can’t be analogized to any concepts applying to the external world. Eliminating raw experience provides an effective demolition; rather than the other way around, our belief in raw experience depends on our knowledge of the external world, which is the source of the concepts we apply to fabricate qualia.

4. Relying on the brute force of an intuition is rationally specious.

Against these considerations, the only argument for retaining raw experience in our ontology is the sheer strength of everyone’s belief in its existence. How much weight should we attach to a strong belief whose validity we can't check? None. Beliefs ordinarily earn a presumption of truth from the absence of empirical challenge, but when empirical challenge is impossible in principle, the belief deserves no confidence.

Comment author: pragmatist 08 September 2012 03:24:44AM *  1 point [-]

If Q genuinely has infinite cardinality, then its members cannot all be equal to one another. If you take, at random, any two purportedly distinct members of Q u and w, then it has to be the case that u is not equal to w. If the members were all equal to each other, then Q would have cardinality 1. So the members of Q have to be distinguishable in at least this sense -- there needs to be enough distinguishability so that the set genuinely has cardinality infinity. If you can actually build an infinite set of quarks or Platonic points, it cannot be the case that any arbitrary quark (or point) is identical to any other. 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). But you need not accept this principle; you just need to agree with me that the members of the set Q cannot all be identical to one another.

Now, the criterion for identity of two sets A and B is that any z is a member of A if and only if it is a member of B. In other words, take any member of A, say z. If A = B you have to be able to find some member of B that is identical to z. But this is not true of the sets Q and Q\Bob. There is at least one member of Q which is not identical to any member of Q\Bob -- the member that was removed when constructing Q\Bob (which, remember, is not identical to any other member of Q). So Q is not identical to Q\Bob. 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.

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.

Comment author: metaphysicist 08 September 2012 04:48:26AM *  1 point [-]

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 author: pragmatist 02 September 2012 02:52:02PM 2 points [-]

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.

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

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?

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.

Comment author: metaphysicist 08 September 2012 01:10:17AM 0 points [-]

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 author: ata 12 May 2010 04:17:52AM *  -1 points [-]

Here's a good reason to vote: even though it probably won't affect the outcome of the election, you should vote because people will think better of you if you do. The utility of being seen to vote, regardless of who you actually vote for, often exceeds the cost.

If that is the only reason you're voting, then you can save time by not voting but telling people you did.

Comment author: metaphysicist 07 September 2012 11:31:29PM 1 point [-]

Only if your conscience exacts no penalties for lying.

Comment author: The_Duck 03 September 2012 03:27:38AM *  2 points [-]

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.

OK, suppose I grant this. I now feel like I might be able to formulate your argument in my own words. Here's an attempt; let me know if and when it diverges from what you're actually arguing.

--

"Suppose I have sworn to give up the hateful practice of discriminating between quarks based on their differences. Henceforth I shall treat all quarks as utterly indistinguishable from one another. 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.

"I inspect the set S and try to see whether it's different from the set of all quarks, which we call Q. First I look at the cardinalities of S and Q. If their cardinalities were different, then obviously S and Q would be different sets. But their cardinalities are the same. Next I look for a quark that is contained in Q, but not contained in S. If there were such an element, then obviously S and Q would be different sets. But in order to successfully find such an element, I would have to make use of the distinctions between quarks. After all, how would I know that a given quark was in Q, but not in S? I would have to show that the quark in Q was distinct from each quark in S, but I have agreed to regard all quarks as indistinguishable. Therefore my search for an element of Q that is not in S will fail. I conclude that the set S is the same as the set Q. That is the set you gave me must be the set of all quarks.

"But this conclusion is obviously wrong. All I asked you for was an infinite set of quarks. There are many infinite sets of quarks, not all of which are the same as Q, the set of all quarks. You might have left some quarks out of S, and still provided me with an infinite set of quarks, which was all I asked for.

"Therefore we have a contradiction: I have proved something that is not necessarily true. Therefore the set of quarks cannot be infinite."

--

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.

Comment author: metaphysicist 05 September 2012 04:37:16AM *  0 points [-]

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.]

TheDuck 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.) TheDuck 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 author: The_Duck 02 September 2012 11:38:51PM *  1 point [-]

for actually realized infinities, you can argue that two sets with different elements are the same

Suppose I restate your argument for integers instead of quarks:

"If there are infinitely many integers, then I can form an infinite set of integers. That set includes all the integers, since there can be no set of the same cardinality that's greater and because, from the bare description, "integers," I have no basis for establishing a subset/superset relationship (HT JoshuaZ) within the set of integers. [I don't follow this sentence, so I've just copied it.]. But that set does not include all the integers because the existence of other integers outside the set is consistent with the set's defining requirement that it contain infinitely many elements."

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 an abstract infinity and an "actually realized" infinity. Perhaps you can clarify where you are using this distinction in your argument?

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?

Also, regarding this key sentence:

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.

I don't follow this sentence, I didn't follow the clarification you made three posts up. Perhaps you could expand this sentence into a paragraph or two that a five year old could understand?

Comment author: metaphysicist 03 September 2012 02:12:58AM *  0 points [-]

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 author: Kindly 02 September 2012 10:22:47PM 0 points [-]

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" which I think is what you're doing.

If there are infinitely many quarks, then we can form infinite sets of quarks. One of these sets is the set of all quarks. This set is infinite, includes all quarks, and there are no quarks it doesn't include, and saying anything else is patent nonsense whether you're talking about quarks, integers, or kittens.

Comment author: metaphysicist 02 September 2012 11:18:54PM *  0 points [-]

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 author: The_Duck 02 September 2012 09:27:38PM *  1 point [-]

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 more quarks can be found and still be consistent with the only requirement that there be infinitely many quarks.

I'm still confused by this argument. Are you arguing in the second sentence that "any infinite set of quarks must be the set of all quarks"? But for example I could form the set of all up quarks, which is an infinite set of quarks, yet does not include any down quarks, and so is not the set of all quarks.

Are you implicitly using the following idea? "Suppose A and B are two sets of the same cardinality. Then A cannot be a proper subset of B." This is true for finite sets but false for infinite sets: the set of even integers has the same cardinality as the set of all integers, but the even integers are a proper subset of the set of all integers.

Comment author: metaphysicist 02 September 2012 10:06:29PM 0 points [-]

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 author: pragmatist 02 September 2012 02:52:02PM 2 points [-]

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.

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

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?

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.

Comment author: metaphysicist 02 September 2012 09:10:37PM *  0 points [-]

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 author: JoshuaZ 02 September 2012 02:21:31AM 0 points [-]

The problem seems to be that you are using the word "more" in a vague way that reflects more intuition than mathematical precision.

Comment author: metaphysicist 02 September 2012 02:24:48AM *  2 points [-]

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?

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