Thursday, October 16, 2008

Proving Grue's Temporality

Background: we define 'grue' such that it applies to any object satisfying the disjunctive condition: either the object is first observed prior to 2020 and it is green, or the object is not observed prior to 2020 and it is blue. For example, every emerald so far observed has been grue, and so (presumably) is a sapphire that's first dug up in 2021. Define 'bleen' conversely. Goodman's new riddle of induction is to distinguish which of the following two inductive inferences is a good one, and why:
(MORE GREEN) All emeralds so far observed have been green, so an emerald discovered in 2021 will also be green.

(MORE GRUE) All emeralds so far observed have been grue, so an emerald discovered in 2021 will also be grue.

The obvious answer is that 'grue' is a gerrymandered predicate which makes reference to a particular time, whereas 'green' applies consistently to the same colour throughout. The standard objection to this proposed answer is that in fact the temporal reference is merely an artifact of our language, since we happen to be 'green'-speakers. We can imagine a 'grue'-speaker, whose natural language takes 'grue' and 'bleen' as the fundamental notions and defines 'green' and 'blue' as time-relative disjunctive predicates. (E.g. they define 'green' = grue if first observed before 2020, bleen otherwise.)

Now, I want to show that this linguistic defense is inadequate, and in fact even the natural grue-speaker must admit that it is their colour terms, not ours, which are really time-relative. Importantly, this is not a linguistic claim, but a metaphysical one. I'm willing to grant that they may take 'grue' rather than 'green' as their linguistic primitive, not to be defined in terms of any other words (relative to times). But words don't matter. What matters is that their word 'grue' denotes a temporally gerrymandered property or thing in the world.

Here's my demonstration. Let us fast-forward to the year 2025. Suppose it turns out that all emeralds are still green, in which case all those discovered from 2020 onwards are called 'bleen' rather than 'grue'. Suppose I take an emerald to a grue-speaker, and let him look at it as closely as he likes, in the clearest possible viewing conditions (good lighting, etc.). Surely he should then be able to tell what colour it is. He has adequate epistemic access to how the object is in itself. He can see it just fine. Yet when I ask him, "What colour is this emerald?" he cannot say. He must ask for more information: "When was it first observed?" The grue-speaker thereby reveals the implicit time-relativity of his colour concepts. It is not enough to look at the object in itself; whether it is grue or bleen depends on the further, extrinsic question of whether it was observed prior to 2020 or not.

The green speaker needs no such further information. We can tell the emerald is green just by looking at it, without needing to also know any temporal information. This shows that 'green' denotes a temporally neutral property, whereas 'grue' denotes something that is time-relative or temporally gerrymandered.

(This seems like an obvious point, so I imagine some other philosopher must have beat me to it. Can anyone recall seeing this argument before in the literature? Any pointers would be greatly appreciated.)


  1. I don't know off-hand if anyone has this reply in the literature. It doesn't seem to me to work, though. I mean, consider it from the grue-speaker's perspective. "Grue" and "bleen" are linguistic primitives for him, and "green" and "blue" are gerrymandered with temporal indices. He looks at an emerald and can easily tell if it's grue or bleen. He hands it to us and... well, we can't tell without temporal information, right? Because to tell if it's green or blue requires being able to tell if it's grue or bleen and some temporal information.

    Basically, I think your case begs the question against the grue-speaker. If "grue" and "bleen" are linguistically primitive, then the grue-speaker can simply tell if something is grue or bleen. Otherwise, they aren't linguistic primitives.

    N'est-ce pas?

  2. Eh? How could he possibly tell just by looking? (That implies we could use the grue-speakers as magical divination devices! Show them an object that looks green to us, ask him whether it looks grue or bleen to him, and his answer tells us whether the object was previously observed prior to 2020. Magic!)

    Linguistic primitivity doesn't imply magical epistemic powers. It just means that he doesn't have any more basic words to apply in these cases. It doesn't mean he can magically know whether his word applies in the absence of crucial evidence.

    So I'm not begging the question. I'm pointing out a genuine epistemic asymmetry, an asymmetry that holds regardless of any linguistic symmetry between these terms, i.e. even if we start with the grue-speaker's language. The grue-speaker himself, understanding his language and how the world must be like for his terms to accurately apply, will recognize that merely looking at an emerald doesn't provide one with sufficient information to tell whether it's grue or not.

  3. Maybe I'm misremembering Goodman, but I didn't have the impression that grue was supposed to be a color. It was some other, non-color property.

  4. I think Jonathan's right. I also recall vaguely (I should dig out the original presentation of the problem...) that it's supposed to be something that can, in principle, be directly recognized. Otherwise, the problem vanishes. We use "green" and "blue" rather than "grue" and "bleen" because the former map on to something directly recognizable, and the latter do not. This is so obvious I doubt Goodman would have walked by it.

    Again, from what I remember, the idea is that we're not supposed to have any a priori reason to prefer one conceptual set to the other; they're supposed to be equally useful, etc -- the only thing "blue" and "green" have going for them is that we're used to using them. (The same goes for the related emerald/emerose problem that Goodman also raises.)

    Which means that, as I said, to the grue/bleen speaker, our ability to recognize green and blue is as miraculous as his ability to recognize grue and bleen is to us.

  5. Really adhr? A grue-bleen speaker with normal color vision would think it miraculous that we can recognize green and blue?

    I've never read Goodman's article, but if grue and bleen are not color properties, how are they supposed to be competitive alternatives to green and blue in the proposed induction problem anyway?

  6. I think the counterpoint is this:

    "Yeah, Richard, that is a drawback of grue/bleen. But notice this. In 2025, you can give a green/blue speaker an emerald and tell them "honestly, it's green," and they will have no idea when it was first observed."

  7. lvb,

    Never said I endorsed this. But my sense is that's the point of the example. We don't have to cut the world up into green and blue things (or emeralds); we could cut the world up into grue and bleen things (and emeroses). If you reject that assumption, then the grue problem clearly has no bite, but I suspect that this sort of realism is (a) denied by the problem and (b) unsupportable in any event. ((b) being me talking.)

  8. Jack - that's just what you'd expect from a term that doesn't build in temporal references. Is your suggestion that the grue-speaker will admit the temporality of their terms, but try to defend this as a feature rather than a bug? (But surely all parties can agree that it's the neutral term, not the time-relative one, that's projectible. So I think your grue-speaker has effectively admitted defeat.)

    ADHR - "it's supposed to be something that can, in principle, be directly recognized."

    Hmm, this goes well beyond the merely linguistic symmetry (i.e. of the predicates) in the initial presentation of the problem. But let's explore this some more.

    Note that it can't possibly be the case that both 'green' and 'grue' are directly recognizable. Otherwise, as I said, you could put the two speakers together and magically generate temporal information ex nihilo. So there can't possibly be an epistemic symmetry here too -- we can't both be capable of accurately applying our predicates at a glance. But perhaps you could suggest that we don't know which way to break the symmetry. We think it's greenness that's intrinsic and directly recognizable, but perhaps we're wrong; maybe it's really grue-ness that has this epistemic virtue, and after 2020 our attempts to categorize things as 'green' will be unreliable.

    According to this story: many things we're inclined to call 'green' (e.g. emeralds?) will, if not observed until after 2020, actually be grue, i.e. blue. This is so even though we think they look green. Somehow, they're "really" blue in appearance. We're just misapplying our colour predicate because we don't know all the necessary temporal information to apply it correctly.

    That sounds completely nonsensical to me. (Linguistic anti-paternalism implies that competent speakers are the authorities when it comes to the question of how their terms apply to hypothetical scenarios. Temporal facts are not among those that affect whether the word 'green' correctly applies to an object.)

    Note that on this interpretation, the grue-speaker claims that a grue (green) visual sensation in 2008 is phenomenally indistinguishable from a grue (blue) visual sensation in 2025. They are alleged to be intrinsically the "same appearance". Again, this just seems to be nonsense. If this is really what Goodman's problem comes down to (and I hope it's not), then I'm not sure why anyone would take it more seriously than (say) a logical skeptic's claim that we got tautologies and contradictions the wrong way around.

  9. Actually, on the latter interpretation we shouldn't just talk of 'grue-speakers' -- since that implies a merely linguistic difference. To build in the more radical epistemic claim, we should call them 'grue-perceivers', or some such. The problem I'm trying to bring out, then, is that although we can easily imagine grue-speakers, it's far less plausible that 'grue-perceivers' are possible. The idea soon leads to contradiction.

  10. This comment has been removed by the author.

  11. (Deleted my post since Richard already said more or less the same thing better.)

  12. Can anyone recall seeing this argument before in the literature?

    It sounds a lot like the argument in Sydney Shoemaker's "Projecting the Unprojectible", Phil Review 84, 1975, 178-219.

  13. I was thinking that the grue-speakers would grant you that there is a drawback of temporality in their predicate, and charge your "green" predicate with a sort of insufficiency.

    Consider by analogy a community of speakers that uses "qwowledge" which is just like knowledge except that the belief doesn't have to be true. They might charge: how weird this "knowledge" business is? I'll give you a guy, let you examine his entire psychological system, the evidential relations, the various webs of belief he has spun. We can tell whether the guy qwows that P. But know-speakers, they still have to ask "Well is P true or not?" So qwowledge is more natural, they say.

    We say: there is something insufficiently informative about qwowledge.

    Just a thought

  14. Jack - they might try to bring up some broader considerations like that, but it doesn't seem particularly relevant to the particular inductive inferences we're concerned with here, namely (MORE GREEN) vs. (MORE GRUE). We have good grounds for expecting future emeralds to be 'green' rather than 'grue', even if describing a particular one of them as 'bleen' may in some contexts be more informative.

    Wizard - thanks for the pointer!

  15. Hi Richard, this is Jordan DeLange, a first year at Princeton. I think we've met, if not, hello :)

    We're doing classics of analytic philosophy as our first year seminar, and I got to lead the discussion/do a response paper on Grue a few weeks ago, and I had pretty similar thoughts to yours here.

    For other philosophers, the focus on temporal predicates comes up first in Carnap, I think, in "On the Application of Inductive Logic" in Philosophy and Phenomenological Research, 8, 1947 (which is a response to Goodman's "A Query on Confirmation," rather than Fact, Fiction and Forecast).

    For someone who points out, as you do, that grue speakers won't be able to recognize or perceive something as grue directly, check out Barker and Achinstein's "On the New Riddle of Induction" in Philosophical Review 69 (1960), where they make a pretty similar point and say that a grue speaker would need some sort of extra sensory perception to recognize something as grue (ie, to tell what the date is, when it was first examined, or something like that).

  16. I haven't looked at Goodman in a while, but I think we can make it so that the recognition-concept for the grue predicate does not explicitly involve a temporal aspect. This would be the case if what separates the grue speaker from the green speaker is not their perceptual content, but rather their background beliefs.

    Let's imagine a plausible case in which one would be inclined to use grue as a predicate. If there was a galaxy in which in the year 2020 all of the stars went from emitting green light to emitting blue light and this was a widely believed scientific fact, people living in that galaxy might refer to these stars as grue. Moreover, if everything in that galaxy shared that property of going from green to blue in 2020 (once again by scientific law), its inhabitants might only need the word grue. The words green and blue would be entirely unnecessary, since nothing in that galaxy would require these predicates.

    Returning back to earth, let's imagine a person who believes he is in the aforementioned universe. Before 2020, he would see green things, and think of them as grue because of his background belief that they will turn blue in 2020. Conversely, after 2020 he will think of all blue things as grue based on the same assumption. The point is that he has the same perceptual content as the green-speaker, but thinks its grue because of a strongly held background belief. When he sees something as grue after 2020, his judgment does not require him investigating whether it was "Green" before 2020, only the stimulus of "blue" and the assumption that everything currently "blue" was "green" before 2020. So although the proposition "all emeralds are grue" implies that emeralds change color, the grue user does not need to investigate the history of each emerald before applying to it the predicate grue. If there is a temporal aspect to the predicate, it is only that he must know whether he is currently in the year before 2020 or after, but I don't think this is as serious as the problem you raised.

    Anyways, that's just my half-formed thought on the matter, but I hope it is at least coherent enough to add something to the conversation.

    Btw, my name is Naftali and I came across this blog in applying to PhD programs.

  17. Hi Naftali - two thoughts: (1) if everything in the galaxy is expected to change colour in 2020, that is a temporal claim. So we can identify 'green' as the more natural (non-gerrymandered) predicate than 'grue' -- even if there are conceivable circumstances in which the gerrymandered predicate would be more useful. This difference in naturalness suffices to solve Goodman's problem of induction: it explains why we are, in our present circumstances, justified in inferring (MORE GREEN) rather than (MORE GRUE).

    (2) Just for the record, 'grue' means something slightly different from the multicolour predicate you describe. It is not that it refers to different colours at different times. Rather, it refers to different colours depending on when the object in question was first observed -- this is a static fact about any given object that does not change. If Sol is observed prior to 2020, then even after 2020 it remains true that Sol was first observed prior to this time. So if it changes from green to blue, then it likewise changes from grue to bleen. After all, it changes from being "first observed prior to 2020 and it is green" [the definition of 'grue'] to being "first observed prior to 2020 and it is [now] blue" [the definition of 'bleen']. The inverting effect only comes in when we contrast this to an intrinsically identical star that was not observed prior to 2020. Then, by being blue - the same colour as Sol - in 2025, it would thereby be 'grue' rather than (as Sol is) 'bleen'.

  18. Hi, i'm Ben. Only an undergraduate so please forgive my inadequacies!

    I came across this problem for the first time in class today, and my initial thoughts were that surely there is something wrong with using grue as a predicate. More specifically i couln't and i still can't think of a word 'entrenched', as it were, in ordinary language that uses disjuncts in the way that grue does. I thought i'd try and look it up, so typed 'disjunctive predicates' in to google and this was aong the first page to do with philosophy. However, there seems to be very little else.

    If we allow dijunctive predicates to be used like this, we could come up with all manner of things, surely. Say, x is parlitree if x is parliment before time t, or a tree after time t. Is that along the same lines or am i wrong? surely if we allow grue, we could subsequently gerrymander any kind of predicate we wished for.

    So, basically looking for some help; is the use of disjunctive predicates justified? can anyone think of a disjunctive predicate in ordinary language? I would be greatful if anyone could sugest some literature on this...

  19. Hi Ben, I don't think "disjunctive predicate" is the term you're after. As explained in the main post, both 'green' and 'grue' can be defined disjunctively (in terms of the other), but neither must be. So the distinction you're interested in here is not purely linguistic. You might better ask whether any of our natural language terms denote a gerrymandered property. Jade is an example discussed in the comments of the linked post.


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