GOODMAN'S NEW RIDDLE OF INDUCTION

Nelson Goodman’s great paradox¹ begins with the fact that

e: All the emeralds so far examined are green.

From this fact, by inductive generalization, we ought to be able to con­clude that

h: All emeralds are always green.

Now define “grue” as follows:

Definition: x is grue at time t if and only if t is prior to A.D. 2500 and x is green at t, or t is A.D. 2500 or later and x is blue at t.^{[25] [26]}

Since e is true, and since the emeralds so far examined have all been examined prior to 2500, the following is also true:

e': All the emeralds so far examined are grue.

So by parity of reasoning, from the fact that e' is true, we ought to be able to conclude that

h': All emeralds are always grue.

But h' says that while emeralds before 2500 are green, emeralds beginning in 2500 are blue. And even though it is true all emeralds observed so far are grue (because they are green and it is prior to 2500), this fact does not warrant the inference that all emeralds are always grue, that is, green before 2500 and blue thereafter. That would be absurd! Can this conclu­sion be avoided?

One approach, suggested first by Carnap, and defended later by Barker and me,^[27] is that grue is a temporal property in the sense that a specific time, namely, 2500, is invoked in characterizing the property, whereas this is not so in the case of green. The claim, then, is that induction works only for nontemporal properties, and not for temporal ones. In the present case this means that since h' attributes a temporal property (grue) to all emer­alds, we cannot “project” grue (to use Goodman’s term). We cannot make an inductive generalization from e' to h'. By contrast, since h attributes a nontemporal property (green) to all emeralds, we can make an inductive generalization from e to h.

This solution (which I no longer believe to be adequate) raises two important questions: What is a temporal property? And why should such properties not be projected? My answer to these questions, and my solu­tion to the paradox, will be developed step by step in what follows.

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