Goodman’s new riddle of induction
Many attempts have been made since Hume's day to say what justifies induction as a form of ampliative inference. Some of them have relied on a principle of the uniformity of nature.
But all these suggestions were called into question when the American philosopher Nelson Goodman showed in 1955 that even if the principle of the uniformity of nature were correct, it would not solve the problem of justifying these inferences. Goodman's work thus poses what he called the “new riddle of induction.”Any solution to Hume's problem that requires a principle of the uniformity of nature supposes that we understand what it means for the future to be like the past. Goodman's new riddle shows that this is not such a clear idea. The problem, remember, is how to justify conclusions of the form “All A's are B's” on the basis of lots of evidence of the form “This A is a B.” Goodman produced examples where we had lots of evidence of the form “This A is a B” but we would certainly not think that the conclusion that all such A's were B's was reasonable.
Here is his most famous example. Suppose all the emeralds in the world that have been examined up until now have been green. Since we have discovered that each emerald we have observed is green at each time we have looked at it, we are entitled to infer by enumer- ative induction that
All emeralds are always (i.e., at all times) green.
Consider, now, the invented predicate “is grue.” We define it as follows:
Something is grue if and only if it has been examined before January 1, 2100, and is green, or has not been examined before January 1, 2100, and is blue.
You will notice that it follows from this definition that all the emeralds observed so far are grue.
The time is before January 2100, and all the ones we have observed so far have been green each time we have looked at them. So we are entitled by the same argument to infer thatAll emeralds are always grue.
size=2 color=black face="Times New Roman">So far there may seem to be no problem. But what will happen on New Year's Day 2100? If all the emeralds we find after then are blue, then they will indeed have been grue all along; but if the emeralds we find after then aren't blue, then they were never grue. In that case enumerative induction will have led us badly astray. If they are all blue, then enumerative induction will not have led us astray by getting us to infer that emeralds are always grue, but it will have led us astray by getting us to infer that they are always green. Either way, then, enumerative induction will have led us astray.
Goodman's own suggestion for dealing with the new riddle of induction is that we should only rely on enumerative induction in certain cases, cases where the predicates involved, unlike “is grue,” are what he calls “entrenched.” A predicate is entrenched if it has frequently and successfully been used in other inductions. He says that predicates that are well entrenched are projectible; we can rely on them when we project them into the future.
The difficulty with this answer is that it looks as though it begs the question in exactly the way that Hume originally pointed out.
For Goodman seems to be recommending that we project those predicates that we have successfully projected in the past. But that seems to rely on the inference:
This predicate has been successfully projected in the past.
So: This predicate will be successfully projected in the future.
And that is just another enumerative induction!
These problems with induction raise the question whether inductively based beliefs can provide a form of knowledge, which is obviously an important epistemological question.
There is, in fact, a connection between Goodman's proposal and reliabilism. Goodman's argument is, in essence, that induction is not a generally reliable method of belief formation because it can be seen to lead us astray with predicates such as “is grue.” One way of justifying his proposal that we should use only some predicates in induction and not others is to observe that induction is reliable with some predicates and not others. If we use induction with a predicate that is reliable, we are using a reliable belief-forming process, and so, according to reliabil- ism, we are acquiring knowledge. So we can't guarantee that a particular induction, using particular projectible predicates, will work; but if it does, then, the argument suggests, induction can provide knowledge.This argument has something of the same air of paradox about it as the argument that we know what is going on in the world and the brain in the vat does not, even though we could not tell whether we were brains in vats if we were. Here, Goodman is saying that induction with projectible predicates is a source of knowledge, even though we can't tell in advance whether a particular predicate is projectible. Someone who wanted a guarantee that the procedures of science would be reliable would be no more satisfied with this response than they would be with the objective (or externalist) account of justification I suggested in 2.8.
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