Friday, May 09, 2008

Structure and Similarity

I once thought that all possible ways of categorizing the world were metaphysically on a par. We may find it more useful to talk of tables and chairs, but objectively speaking this way of dividing up the world is not metaphysically privileged over alternatives that seem "gerrymandered" to us, e.g. combining chairs and cockroaches into a single category.

I now realize that my past self was very silly. Though it may at first seem puzzling that there could be privileged categories, or 'structure' to the world, it seems perfectly obvious that some pairings are objectively more similar than others. Two chairs are more alike -- have more natural properties in common -- than a chair and a cockroach, and this is nothing to do with our words and everything to do with how the world is. (A tribe might have a but a single word X that means 'chair or cockroach', but in that case their language would be objectively inferior to ours in this respect, for it fails to carve nature at the joints.)

One way to bring this out is to think about projectability, or what properties you can reason inductively from. All the emeralds I've seen so far have been green, so I expect the first emerald I see after 2020 will also be green. That seems a perfectly reasonable induction. On the other hand: "All emeralds I've seen so far have been grue, so I expect the first emerald I see after 2020 will also be grue" is clearly not good reasoning. This is because green is a more natural property than grue. It is an objectively better way to categorize reality.

48 comments:

  1. I'm not sure what you mean by "metaphysically on par." Did you past self thing that they were all equal in being kinds of natural kinds? i.e. the ultimate metaphysical constitutents?

    Or merely that one could categorize them anyway you want and that the act of categorization had no metaphysical import?

    I think that last view actually is defensible. I'm not sure how you could hold the former just from a curious view. For instance I could talk about tables and chairs and ignore atoms, quarks, electrons and so forth. And arguably for most things that's more useful. But to talk about metaphysical privilege seems odd. If we talk about the ultimate reduction then that's one thing. But at the same time a table isn't merely the atoms. It's part of a world of equipment. And metaphysically we can't ignore that feature.

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  2. A shorter way of saying what I said is to take this claim

    "This is because green is a more natural property than grue. It is an objectively better way to categorize reality."

    and note that "objectively better" is meaningless unless you add better for what.

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  3. Donald Davidson in his paper "Mental Events" argues about the proyectability of predicates as 'green' or 'grue' that the former are better suited to natural laws than the other, if I recall correctly. If that holds, then we can ask if when you say "[green over grue] is an objectively better way to categorize reality, you are talking about the objectivity of the laws where those predicates could appear.
    It isn't merely reduction what you have in mind here, is it? At any rate, it doesn't seem to be only about the metaphysical status of certain fundamental things in the world.

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  4. This confuses me. It would seem like it was precisely the use value of categorizing emeralds as green that would prevent you from categorizing them as grue. Green is useful because there is empirical evidence that suggests that Green is useful. There is no empirical data whatsoever to suggest that grue would have any use NOW. It might have use in 2020, but at that point we can reevaluate.

    So I guess I'm more sympathetic to your past self.

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  5. Colin: what empirical difference is there between green and grue? Prior to 2020, they coincide, so all the green data is also grue data.

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  6. I take that to be exactly the point. If there is no useful empirical distinction to be made between green data and grue data prior to 2020, then no distinction is to be made. If in 2020 all green data is now grue, then then there would be a useful reason to call all green data grue; however, if in 2020 green and grue appear identical, then there is no useful reason to change names.

    Come to think of it I might even disagree with your past self in that metaphysics doesn't have to enter into the discussion at all.

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  7. Either I have no idea how this works, or blogger and wordpress aren't as compatible as one might think.

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  8. Suppose we started off with the word 'grue' rather than 'green'. Would we have a reason to change? Yes, because green does a better job of carving the world at its joints.

    If green and grue were equally good, then the two inductive arguments would be equally good. But they are not. If you infer that the emeralds you see after 2020 will be grue, you will (most probably) be wrong.

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  9. Hello, Richard. I've enjoyed your blog for a while, but this is my first comment.

    The tribe that uses the same word for chair and cockroach--wouldn't this just be what we call homonyms? From the linguistic point of view it's important that alternative meanings of homonyms (and similar sounding words) be very different so that context easily clears up any ambiguity. That's why languages that are designed by philosophers tend to suck since by "carving nature at its joints" they make similar words sound the same.

    Nevertheless, this only reinforces your main point, since it is their intuitive understanding of natural properties that allows the tribe (or us) to distinguish between alternative meanings of homonyms.

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  10. Richard: It is not because green is objectively better that we use it instead of grue. Rather we use it because it is more useful. Grue covers the same set of objects as green, but with the addition of this future oriented limitation that cannot be empirical accessed at present. Thus grue is a less useful category, then green. If when 2020 roles around all green things become blue things, grue might be a startlingly useful category.

    It's unclear to me how a language would be objectively better because it cuts up the world in a certain way. A language/society that connected chairs and cockroaches would presumably have different needs in carving up the world.

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  11. Richard,

    I think it helps to recall the original context of Goodman's grue example.* At the time of its invocation, he was in debate with Carnap and others over the possibility of a logical probability. Carnap had elaborated a system of assigning probabilities to state descriptions via a measure m*. This measure gave greater weight to homogeneous states than heterogeneous, but using gruesome predicates, we can show that these assignments can be flipped, thereby demonstrating that his "logic" is not language invariant, and thus not a logic at all. Further, as Graham Priest demonstrated in his 1976 paper "Gruesome Simplicity", notions of simplicity in curve fitting can be similarly changed.

    Since its origination, gruesome arguments have tended to center around three primary reactions— (ordered according to the strength of the claims) our "natural" predicates:

    1) Mark the metaphysical structures (regularities) in the universe

    2) Are more likely to be true of the things to which they are currently assigned than gruesome predicates

    3) Are more useful for our purposes than gruesome predicates

    The first claim amounts to our language (rather conveniently) cutting nature at its seams. Saying that our language uniquely marks the invariants in the structure of the universe is quite a strong claim in need of equally strong defense. Unfortunately, there are plenty of natural-seaming predicates that become untrue of their referents over time, and figuring-out exactly which change under what circumstances would represent a solution to the frame problem in AI. Since this remains a real and very difficult problem, at the least we can say if our language cuts nature at the seams, we are not sure at which ones it does so.

    The second position was implicit in Carnap’s system of inductive probability elaborated in his Logical Foundations of Probability and expanded in The Continuum of Inductive Methods. It is exactly akin to the uniformity of nature argument in that it counts past regularities as being more likely in the future than changes in the state of things. The possibility of an alternate language using gruesome predicates being equally confirmed implied that the measures of likelihood were not of a logical nature. So, how then to justify the natural likelihoods? There is of course an extensive methodological literature on this question.

    One answer I like deviates from likelihoods and justifies the provisional acceptance of the language-varying simple answer because of its guaranteeing some efficiency in convergence to the correct answer (See Kevin Kelly for the details).

    The last, and weakest claim, is simply a pragmatic one about language coding. We must use some set of predicates, and the predicates we currently use are the result of a selection process tuned to our human needs, not timeless philosophical pronouncements. Personally, I find this credible and compatible with Kelly's account.

    It is somewhere between the first and second positions that Richard's claims seem to fall. So far I have not read any defense in these comments commensurate with these claims.

    Cheers.

    *Please excuse the excessive pedantry of this post; I had a deep interest in the subject before abandoning Carnegie Mellon for the world of IT and this is a chance for me to reorganize my thoughts about it.

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  12. John: unless I completely misunderstand you, your solution, that language is based on specific human needs and that it does not have a privileged place in cutting up the world, is quite similar to my solution. Language is based on usefulness, usefulness alters, and language alters to accommodate that usefulness.

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  13. Basically, yes.

    There is a strong philosophical desire to see our language and intuitions as corresponding directly to truths about the world. I see labeling some predicates natural is a shortcut to asserting things that are properly discovered; though it might be said that assertions based on intuition and linguistic use have all the advantage of theft over honest toil (zing!).

    Rather, I prefer considering parallel methodological problems in-line with Malcolm Forster's characterization of weakly normative advice from philosophers, where 'ought' statements are coupled with goal statements (e.g. if one could establish that A is more effective than B in achieving X, and X is the goal of science, then it would follow that one ought to adopt A as the methodology of science).

    For example, Kelly's "mind-change" efficiency result gives some good reason (under certain assumptions) to prefer simple answers over complex ones without appealing to metaphysical structures that we somehow access with our philosophical intuition.

    This is a pretty unsympathetic and cartoonish sketch, but you get the point.

    Regards.

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  14. Goodman's "Seven Strictures on Similarity," from Problems and Projects, is also important in this debate. It's probably both logically and psychologically true that talking about similarity in terms of properties is a dead end. I might try to say more about this in the relatively near future.

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  15. Chris - that'd be interesting to hear!

    John - I'm not too fussed about whether our actual language and intuitions succeed in carving the world at its joints. (Maybe we're just confused and it's really grue, not green, that's natural and projectible.) For the purposes of this post, I was merely wanting to explain how it makes sense to think that the world really does have natural 'joints' or categories of objective similarity. Whether we can know these is a separate question; a question in epistemology, not metaphysics. (I generally ignore skeptical worries for sake of making progress on other arguments.)

    Aron - no, I didn't mean homonyms. I meant a single word ('plog', say) with the universal meaning 'chair or cockroach'. They might say, for example, "Some plogs have four legs and are for sitting on, and others have 6 legs and scurry away." This is a possible language, surely. Fortunately, all real (and remotely realistic) languages do a much better job of latching on to real and relevant distinctions that are there in the world.

    Colin - I think you're actually implicitly committed to something more like my view. For what is your basis for judging that grue is less useful? You say, "Grue covers the same set of objects as green, but with the addition of this future oriented limitation that cannot be empirical accessed at present."

    To a 'grue' speaker, it's 'green' that has the future oriented limitation. For the grue speaker defines 'green' as "grue if first observed before 2020, bleen otherwise". (Where 'bleen' to us is the inverse of grue, i.e. blue now and green later.)

    In order to say that it's grue, rather than green, which has the future limitation, you must think there is some sense in which green is more fundamental. Grue is properly defined in terms of green, whereas to define green in terms of grue is somehow 'backwards' or less natural.

    I can make my point even more simply. It is as follows. The collection of green things has more in common (i.e. are more similar) than the collection of grue things. A grue object today, and another grue object from after 2020, are less alike than two green objects. If you agree that this is true, then you must think that green is objectively more natural than grue.

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  16. > In order to say that it's grue, rather than green, which has the future limitation, you must think there is some sense in which green is more fundamental.

    But if I thought this was a Chinese forum I'd use 'lu se' (green) if i thought it was a 'grue believer' forum I'd use 'grue' (probably).

    It just happens its reasonable to assume it isn't a Chinese or a 'grue believer' forum.

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  17. For some reason I think of this in dialogue form: why would I introduce grue in place of green in my color vocabulary?

    (Fictional) You would say: Because it might really (really really) be grue! You might be wrong that it is green.

    I would say: What would be the practical consequences of calling something green grue?

    (Fictional) You would say: None whatsoever, but it might have consequences in the future.

    I would say: Well if or when it does have consequences then I will take the appropriate course of action. Until then there is no reason to alter my present theory (which is just a theory) because nothing at all would change as a result. (Fictional) You, on the other hand, can call green grue and mean exactly the same thing. It might cause some communication problems though, so I suspect that it is more practical to stick to green. (at least until 2020)

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  18. You're assuming that we are already green-speakers. I'm asking a prior question: is there any good reason to be green speakers rather than grue speakers in the first place?

    I think it is obvious that there is (or at least that one of the two is more reasonable than the other), and this shows that there is such a thing as objective similarity/naturalness.

    But if you are really willing to bite the bullet and say that a tribe of grue-speakers (who reason inductively to the conclusion that emeralds will continue to be grue in future) is not doing anything wrong, then I guess I have nothing more to say here.

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  19. Maybe I should try again. I'm curious as to why this seems to bother you:

    My solution allows people to be either green or grue speakers depending on the consequences of their actions and the available data. This seems to be how we actually do make decisions. In other words my account begins at the descriptive level, but it becomes a low level normative claim. If a decision has no consequences then I have no reason to adopt it. There is, in fact, no distinguishable difference between green and grue. None! So there is no reason for me to adopt grue or green (depending on my circumstances).

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  20. You seem to be ignoring my point about induction and projectability. We want to be able to reason about how objects will be in the future, and green and grue are really different here. It's just not true that we have "no reason" to prefer one over the other. One is projectible (makes for good inductions) and the other is not.

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  21. I might be able to concede this: grue assumes a level of access to the future that green does not. I have lots and lots of data that say green stays green. I have no data that says green changes to blue in 2020. Therefore, it is more useful to use green than grue.

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  22. Let's cut to the chase: do you agree with the suggestion in my comment yesterday that green things are ipso facto more similar (in respect of their colour) than grue things?

    Consider three objects: X, Y and Z. X is a round ball in 2008 that is both green and grue. Y is a round ball in 2021 that is green (so not grue). Z is a round ball in 2021 that is grue (so not green).

    Do you think there is an objective fact of the matter as to whether X is more like Y or Z? That's the question I'm trying to get at, and it is not merely a matter of "usefulness", but of how the world is.

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  23. It seems like a rather obvious fact to point out that colors change color all the time (due to fading, types of light etc) and that there are even colors that are designed to change color (invisible ink etc). These do not raise metaphysical questions, why should grue? The distinction you are making between appearance and reality seems forced. If a color surprises me and changes color I reassess my assumptions about that color. Nothing more and nothing less.

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  24. You didn't answer my question. (Do you think there is an objective fact of the matter as to whether X is more like Y or Z?)

    Again, if you think that the colour of a grue object "changes" between now and 2021 then you are implicitly treating green as more fundamental. From the perspective of a grue speaker, the colour is the same all along: grue now, and grue later. In order to make sense of the idea that the shift from green to blue is a change (whereas the shift from grue to bleen in 2020 is not a change), we must think that some colour predicates are more natural than others. Talk of grue and bleen is really just a gerrymandered way to talk about the underlying properties of being green and blue at various times. Green and blue are real properties in a way that grue and bleen are not.

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  25. I can conceive of a society in which no difference is made between green and blue. Maybe this is because the don't perceive a difference or maybe it is because they think that grue has two states both of which are grue. This wouldn't be because there way of cutting up the world is objectively worse, but that our way of cutting up the world isn't particularly useful for their projects. Conceivably we could have a way of cutting up the world that seems particularly ludicrous (or at least absolutely useless) to them.

    One way of cutting up the world is not objectively better than another; however one way may be more useful.

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  26. So I guess the answer to your question is...no.

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  27. If you think that both inductive arguments are equally reasonable, and that there's no sense in which X is objectively more similar to Y than Z, then you have no grounds for believing one conclusion rather than the other (e.g. that future emeralds will be green rather than grue). By the principle of metacoherence, you should be agnostic.

    There's nothing special about the case of emerald colour, of course. You should become a skeptic about all manner of induction, even (e.g.) whether the sun will rise tomorrow. After all, our belief here rests on the premise that the future will be like the past (ceteris paribus). But you think all possible states are equally "similar", objectively speaking. So you have no grounds for judging that a world where the sun explodes tomorrow is any more different or unusual than one in which it carries on in what I would consider to be the "usual" manner.

    I consider that a reductio of your position. But, as I said, if you're willing to bite that bullet then my arguments will have no further traction on you. So perhaps we should simply call it a day.

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  28. See what I'm trying to show you, however obliquely, is that I can make a choice between grue and green without any notion of objective knowledge creeping in. I begin with the world as it is now (how else CAN I begin?) and precede to consider how useful a change in the way we define color is. Based on how you define grue I determine (as I demonstrated above) that its practical consequences are nonexistent (now) and therefore it is not useful.

    Note that I do not have to assume that the way I cut up the world now is the best way (in fact I'm pretty sure it isn't), I just have to consider if the way that you are proposing has useful consequences.

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  29. And if you want to stop, I'm more than willing to. I don't think that denying that there is a fact of the matter to color should be a complete blockage to discussion, but maybe it is.

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  30. Well, I have missed a lot.

    Richard,

    Thanks for the clarification; given my interests I naturally conceived of the question as being epistemological, rather than metaphysical. Though, I am confused about whether or not you claims are metaphysical or epistemic, given that you assert that green is projectible and thus good for making inductions (more probable, etc.). The closest to an argument you have made for this is as follows:

    The collection of green things has more in common (i.e. are more similar) than the collection of grue things. A grue object today, and another grue object from after 2020, are less alike than two green objects. If you agree that this is true, then you must think that green is objectively more natural than grue.

    I simply must disagree, since this seems to me a straightforwardly question-begging exercise. Thinking as a green-speaker, naturally grue things are less self-similar than green things for the simple reason that it is more complex to express its behavior through time than green. Unfortunately, to a grue-speaker, it is green that would thus be more complexly expressed and less natural. Simply put, “likeness” is derivative of a particular language, not prior to it.

    The situation is completely analogous to problems in Kolmolgorov complexity, clustering algorithms, and other machine learning settings; mathematically, these codings are homeomorphic, meaning they are intertranslatable (with a computable translation function) and derivative properties are not objective (in the sense of being language invariant), yet we must use some language.* Given background knowledge, languages may be tailored to the structure of the domain of discourse (e.g. closed-world assumptions, assumed dimensionality, etc.). Though I think that there is some structure to the world, I think that appealing to your language to get and inferentially exploit this structure is exactly backwards.

    So, having bitten this bullet, all I can say is that our intuitions about this differ, and I’m not sure how to proceed from there (important problems with philosophical methodology are implied here, but this is off-topic).

    I hope this exchange has not frustrated you overmuch—I have enjoyed the chance to think about philosophy again.

    Cheers.

    *If this intersection of machine learning and philosophy interests you, there is a result called the No free lunch in search and optimization that has concerned some epistemologists and philosophers of science.

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  31. Hi John, no worries. Just to clarify: I do not mean to argue that green is projectible. I'm just assuming this for sake of argument. If you suspect that it is really grue that is projectible rather than green, you can simply switch the terms accordingly and my metaphysical conclusions will still go through fine. If you do not believe that any terms are projectible, or that any inductive arguments are more or less reasonable than any others, then indeed we have reached a bedrock, fundamental disagreement, and further progress may not be possible.

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  32. Richard,

    I see. While I am inclined to agree that there are projectible predicates (as this directly follows from thinking the world has some structure), I do not know how we can know which are projectible (again with the epistemology, but it seems an important question!), and what follows from there being said predicates.

    As an aside to those who are still interested, here is a pretty clear presentation of the difficulties around projectibility, including its over-reliance on language, question-begging on uniformity of nature, etc.

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  33. I wonder whether we can conceive of a species of enquirer with the following perceptual hardware: colour-blindness, and an acute sensitivity to the chemical structures of things. Perhaps, for some such creatures, our concept 'jade' would seem as gerrymandered as our 'plog'.

    Indeed, if there is anything to Wittgenstein's notion of family resemblance - which the difficulty of finding necessary and sufficient conditions for application of many concepts might suggest - then it seems plausible that there could be other creatures who were sensitive to very different patterns.

    Then we're back with your old self, Richard.

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  34. Barry, I thought 'jade' was a paradigm example of a concept that we discovered is indeed hopelessly unnatural (gerrymandered).

    I'm sure there could be creatures who are sensitive to different things. They may be better or worse than us at discerning the natural properties, i.e. categorizing things appropriately. How is that an argument against my view?

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  35. Hi Richard,

    I think jade is an interesting case because with it there is an obvious sense in which the concept is gerrymandered, but nevertheless a clear pattern which all jade things appear to instantiate, namely being a green, partly-transparent precious stone found in such an such rock (I beg the geologists' forgiveness). The thought was that discovering the deeper evidence of gerrymandering would serve as a premise in a sceptical argument the same way that a hallucination might. In the case of jade we have something that appears to track a natural pattern but doesnt. So appearing to track a natural pattern doesnt entail tracking a natural pattern. But all we have to go on, surely, are cases of things appearing to track natural patterns. If you have discovered anything surer than this, I would be delighted. Descartes would dance a jig. But I am not optimistic. So I doubt your confidence in having found the "appropriate" standard for categorising things. Now, I dont deny there is theoretical advantage in positing naturalness, as Lewis argued. I just worry that there may be insufficient justification for drawing it here rather than there.

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  36. I don't think the mere fact that we're fallible should lead us to skepticism. But that's a separate issue, in any case. For now, I'm just concerned with the question whether some properties are more natural than others; not whether we can know it. This metaphysical question is where I depart from my "old self".

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  37. An epistemological response to a metaphysics argument. Ug. I should have concluded as follows. We have no justification for drawing the line here rather than there. And we have good reason to believe that the line which seems most intuitive to us will be totally unintuitive to some other creatures. And this should lead us to think that there may be no line to be drawn in abstraction from creatures. We are left with all lines 'metaphysically on a par.' I think this was the view of your older self.

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  38. As you might expect, I'm suspicious of your key step: "And this should lead us to think that there may be no line to be drawn in abstraction from creatures."

    Can you elaborate on this?

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  39. It is trivial that any two objects are similar and disimilar to each other in countlessly many respects. We are especially sensitive to some of them - mainly the ones we see without instruments, though we do sometimes revise our beliefs on the basis of stuff we see with instruments (glass being a liquid, jadite&nephrite, all that empty space in our tabletops). But, prima facie, just as it is possible that there could be creatures who were baffled by the concept of jade, it seems possible to me that there could be creatures who were baffled by our concept of an electron, or quark, or planet. Imagine the arrangment of stuff a couple of levels below quarks bears the same relation to quarks as electrons to tables, i.e. that they show quark-talk to be grossly misleading. (I am supposing that the claim that tables are completed solid is grossly misleading given that there are mainly space.) Creatures sensitive to these lower levels will think our concepts gerrymandered. Suppose gunk, and that different levels mislead, and that different creatures are sensitive to different levels. Then which sensitivities should we privilege? Our own? I'd say so. But we shouldn't thereby take ourselves to be describing 'the world, as it really is.'

    I am constitutionally struck by the anthropocentricity of the notions of simplicity, explanatoriness, intuitiveness, usefulness, even predictability, which underpin objective claims. This inclines me to modesty in making claims about how the world really is. It also throws doubt on any argument from theoretical utility.

    Would God see electrons? Or anything else? Maybe just pure information? A single, buzzing, whole? Or an infinity of little interactions?

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  40. Interesting! But I think the real work there is being done by the metaphysical assumption of gunk, and not the mere fact of epistemic disagreement. Without the supposition of gunk (which is highly controversial!), there is no problem at all.

    But let's suppose the world is gunky, so that there is no final, fundamental level to reality. Even then, would it follow that there is no structure to the world? Well, no. It seems the appropriate conclusion is not that all divisions are equally natural (which is absurd, and immediately refuted by the fact that we learned that jade is less natural than jadeite and nephrite), but simply that there is no maximally natural categorization. Whatever we come up with, further investigation would reveal some more natural way to carve this up.

    Unlimited room for improvement should not be confused with no room for improvement.

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  41. Richard,

    Very good point! I'm afraid that I have been infected with an unreasonable distrust of metaphysics; even so, a provisional structural or pattern realism about our categories as being the most natural so-far seems perfectly philosophically acceptable, and, further, practically indispensable (Bas Van Fraassen and many friends of mine would disagree).

    Hmm...Prolegomena to Provisional Metaphysics from our Best Science-- I'd read that.

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  42. The structure of my argument is this. We are sensitive to some patterns in nature. It is possible that there are other patterns that we are not sensitive to. Suppose two patterns, one discernible by us, the other by some other creature. Which is the more natural? One way to answer this would be to claim that either ourselves or the other creatures were more sensitive to naturalness. But I cannot think of any good arguments for this result. Absent such an argument, I think we have to say that both patterns are equally valid. This is not to say that nature has no structure, quite the opposite. It is simply to point to a difficulty in defending a natural-nonnatural distinction within its structure.

    (You beg the question, Richard, by presupposing a conception of naturalness in your claim that jade has been shown to be 'less natural' than jadeite and nephrite.)

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  43. "I think we have to say that both patterns are equally valid."

    I don't see any reason to grant that. I'm far more inclined to take as a default response that "either ourselves or the other creatures were more sensitive to naturalness." This meshes with our commonsense judgments that some divisions are more natural and projectible than others (e.g. jade). You can deny this premise, but I think that's crazy. So I'm unmoved by your objection. It just strikes me as thoroughly unmotivated (though I grant you see things differently).

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  44. I have just been playing devil's advocate here. The arguments for both sides seem unconclusive. On the one side there is what currently strikes me as a strong modal argument. On the other - occupied by yourself and the later Lewis - we have an argument from theoretical utility, and an inference to the best explanation. (From very young I have been struck by the contingency of our ways of carving things up, so you are right in not attributing to me the intuition that our way must be the right way.) Perhaps I can end with a point from Carla: just because Lewis calls his favourite properties 'natural' properties doesn't mean that there are natural properties, and that those are them.

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  45. What's the "strong modal argument"? I don't see how you get from the possibility of alternative sensitivities to the conclusion that they're all equally valid.

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  46. I have been assuming the standard peer disagreement premise that one shouldnt unduly privilege oneself. With that, I think, the argument goes through.
    1. It is possible that there are many different sets of creatures each of which carve the world up differently.
    2. We shouldnt unduly privilege our way.
    3. Therefore it is possible that there are many equally valid ways to carve the world up.

    I'm not sure what work is being done by 'unduly' in the second premise. I mean something like: for each creature to whom the world appears to be patterned in some way, that pattern is projectible, etc. in the same sort of way as our is for us.

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  47. This seems like a similar question to whether there exists an ideal set of beliefs about the world. Although there would be multiple sets of beliefs consistent with one carving up of the world, assuming you were able to define the boundary between the carving up and the set of beliefs. Anyway, in both cases we are creating a simplified representation of the world and then wanting some measure of how good a representation it is. If I understand your arguments then you are claiming/have claimed that in both cases such a measure does exist, and that there is only one correct measure. I don't like this idea because it introduces another fundamental entity into the world (the measure) which doesn't seem to give us anything that we wouldn't get from using utility to define the quality of a representation.

    I heard you earlier talking about maximally consistent belief sets (or something similar) before, but I've never really got what you were getting at. Is the idea the that there exists some measure that determines how good a belief set is, that we don't know what it is, but we know it exists?

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