all emeralds are grue
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What the competing hypotheses “all emeralds are grue” and “all emeralds are green” show us is that this way of thinking about projection into the future is wrong – that this is an inadequate way to explain how we form beliefs about unobserved cases. This worry is not devastating. Naturally existing in the world are green things, even if there is no one in the world to observe it. For part of what it is to be grue is to be first observed at a certain time. the pot, the fire) isolated from one another, you see the elements interacting. This is easy and legitimate. , one of the two hypotheses must fail, for their predictions contradict each other [^4]. category. A third response to Goodman’s problem is to appeal not to the way in which ‘grue’ is defined, Which part of the disjunction is effective in the application of the predicate is determined by, , but not the definition. follows: An object is grue if and only if the object is either (1) green, and has been I give it an objective Bayesian formalisation, and contrast it with Goodman's and Sober's solutions, which make appeal to both methodological and non‐methodological considerations, and those of Jackson, Godfrey‐Smith, and White, on which explanatory considerations play a very different role. We can’t see anything about t in the emerald. Change ), You are commenting using your Twitter account. When we say X is grue, we say that X belongs to the set of grue things. If all we do is infer from particular instances to general claims, then we have equal evidence for two competing hypotheses [^3], . . How did we acquire it [^6], ? Now let’s define a new predicate, “grue”. When a predicate contains a time-dependent disjunction, it applies to one set of objects before t and a different set of objects after t. In this way, it appears poorly defined. Because of this, we cannot legitimately predicate “grue” of emeralds. What the competing hypotheses “all emeralds are grue” and “all emeralds are green” show us is that this way of thinking about projection into the future is wrong – that this is an inadequate way to explain how we form beliefs about unobserved cases. Let’s return to our consideration of the grue and green emeralds. His perception is mistaken, but we do not dismiss him as a poor perceiver or suddenly begin to doubt his judgment of his perception. When I see that every emerald I have observed has been green, I am inclined to form the belief that something about the emerald causes it to be green. If we form beliefs about unobserved events based solely on the flat-footed understanding of induction (marked [, are going to be green (but we do), because there is an equally well-supported competing hypothesis. Moreover, while grue is admittedly an artificial term, that does not mean that it is illegitimate to predicate it of natural objects. But when I look at a grue emerald, I do not believe that something caused it to be grue. Because intuitively we believe that after t, the emeralds will persist in being green and cease to be observed as grue. This is easy and legitimate. the predicate seem so artificial, so it is natural to think that it is also part of what makes its use However, when I see that every emerald I have observed has been grue, I am not inclined to form the belief that there is something about the emerald that causes it to be grue. grass and emeralds first observed before t, and peacocks and blueberries first observed after t. Note that it is just as easy and legitimate to consider this set as it was to consider the green set. Each newly observed instance of an A as a B (and assuming that no A has been observed as not B) confirms a hypothesis, viz.
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