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Epistemology: The Puzzle of Grue

In this video, Sinan Dogramaci (The University of Texas at Austin) explains the puzzle of grue. He discusses how this puzzle undercut the attempt to formally develop inductive logic, the logic of probabilistic support.

Speaker: Dr. Sinan Dogramaci, Assistant Professor of Philosophy, University of Texas at Austin.

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  • orange juice squid orange style avatar for user Daniel Rigal
    Is it oversimplistic to just shout "That's cheating!" at the screen?

    I mean, ambiguity is bad enough but having premises contrived to completely change their meaning half way through the evaluation of the argument, solely to mess the argument up, seems like a dirty trick.
    (8 votes)
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  • piceratops ultimate style avatar for user Micah Isser
    How exactly does Goodman's argument of induction differ from Hume's? Is it a form of cultural relativism, suggesting that the only reason we say 'green' and not 'grue' is because of social convention?

    Also, wouldn't disputes - like the one between green and grue - still be able to be settled by a criteria of falsifyability? If there's literally no way to determine in practice whether a thing is green or grue (i.e., the emeralds turn blue whenever no one's looking), then there seems to be no pragmatic difference between the two. And if there is a way to falsify one of the beliefs, wouldn't theories gain probabilistic credence, the longer they survive?
    (1 vote)
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    • hopper jumping style avatar for user Yago
      I think you might have misunderstood how grue was defined. It's not that the colour changes when you look at it or look away. It just so happens that we have seen every one of those that are green and not seen every one of those that are blue. So when you find a new one it will be blue.
      (2 votes)
  • leaf blue style avatar for user Neil Kale
    Couldn't it be considered that the second argument is wrong purely because it's premise and conclusion are disconnected? The subject in the premise is all emeralds yet seen, the conclusion is all emeralds in general. The first argument is also wrong for that same reason! It is not correct to believe that just because all emeralds yet discovered are green all future emeralds will be green. That's just an assumption, correct?
    (1 vote)
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Video transcript

My name is Sinan Dogramaci and I teach philosophy at the University of Texas at Austin and today I want to talk to you about the Puzzle of Grue. The Puzzle of Grue really burst the bubble for philosophers like Carnap and Hempel who had dreams of confirmation theory or inductive logic as a formal theory in the way deductive logic was developed. With deductive logic we've succeeded in identifying many patterns that make for good deductive arguments where these patterns concerned just the forms or the logical syntax of the premises and conclusions in the arguments. Anything beyond form — in particular, the subject matter under discussion — makes no difference to the quality of an argument as a deductive argument. The premises that "All X's are Y" and "This is an X" deductively entail the conclusion that "This is a Y" no matter what particular X's and Y's we're talking about — flamingos, bongos, bellybuttons, whatever. Unfortunately, the philosopher Nelson Goodman gave us a puzzle that pretty convincingly shows that whether an argument is a good inductive argument cannot similarly just be a matter of form. Goodman showed that we can cook up two arguments that share the very same form, but one is intuitively an excellent argument in support of its conclusion while the other is no good at all. For the first argument, the good one, we have this: Premise: All of the numerous emeralds observed in the past have been green. Conclusion: all emeralds — those observed and those yet to be observed — are green. In order to see what the second argument is, the bad one with the same form, we need to first introduce a new term. The term is "grue", and to define it, we say that a thing is grue if either it has been observed by now and it is green or it has not been observed yet and it is blue. So this new term we've introduced has what we call a "disjunctive definition" - an either/or definition. The second argument we want to consider, then, is this. Premise: all the numerous emeralds observed in the past have been grue. Conclusion: all emeralds — those observed and those yet to be observed — are grue. This is not a good argument. Its premise is perfectly correct — all observed emeralds have been green and thus by definition they are also grue — but that premise does not lend any support to the conclusion. The conclusion is not probable at all! For the conclusion implies that the next new emerald to be observed will be grue, and that means it will be blue, which is not likely at all. The real puzzle here is that we have two arguments, apparently with the exact same form. The only difference is the substitution of the two simple predicates green and grue. So the moral seems to be that form alone does not settle what makes a conclusion probable. Now, there's an objection that might come to mind here and which we should address Is "grue", as I said a moment ago, really as simple a term as "green"? Perhaps its complexity makes the second argument actually have a different form. After all, "grue" is a defined term, and we said its definition is disjunctive, so maybe the term "grue" is not as simple as the perfectly simple term "green", right? Well, that's one way to see things, but as Goodman was quick to point out there is another perspective. It might equally well be thought that "grue" is the simple one and "green" is the more complex term. How could that be? Well, to see how, consider one more new term: bleen. Let's say an object is bleen if it is observed by now and blue or else, if unobserved, green Well, given that understanding of bleen, we now have a way of giving "green" its own definition: an object is green if it's grue and has been observed or if it's as yet unobserved and bleen. That's really a pretty good definition of green. Let's think it over. Emeralds, which we know are all green, meet the definition. All the observed emeralds which are green are also grue and observed. And the unobserved ones, which we also expect to be green, are bleen, since unobserved bleen emeralds are green. What does this mean? It makes it hard to maintain that "green" is really the simpler term and "grue" the more complex one. Maybe, in the end, "grue" is more complex, but it's difficult to say why that's objectively so — and as long as we can't distinguish "green" and "grue" in their complexity or otherwise in their logical form, then we can't distinguish, just by appealing to form, arguments that do and don't make their conclusions probable. So for this reason, among others, the development of inductive logic — confirmation theory — looks like it's not going to be easy.