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Philosophical paradox introduced by Nelson Goodman

The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem. It presents the logical predicates grue and bleen which are unusual due to their time dependence. Many have tried to solve the new riddle on those terms, but Hilary Putnam and others have argued such time dependency depends on the language adopted, and in some languages it is equally true for natural sounding predicates such as "green". For Goodman they illustrate the problem of projectible predicates and ultimately, which empirical generalizations are law like and which are not. Goodman's construction and use of grue and bleen illustrates how philosophers use simple examples in conceptual analysis.

Goodman defined "grue" relative to an arbitrary but fixed time t: an object is grue if and only if it is observed before t and is green, or else is not so observed and is blue. An object is "bleen" if and only if it is observed before t and is blue, or else is not so observed and is green. For some arbitrary future time t, say January 1, , for all green things observed prior to t, such as emeralds and well watered grass, both the predicates green and grue apply. Likewise for all blue things observed prior to t, such as bluebirds or blue flowers, both the predicates blue and bleen apply. On January 2, , however, emeralds and well watered grass are bleen, and bluebirds or blue flowers are grue. The predicates grue and bleen are not the kinds of predicates used in everyday life or in science, but they apply in just the same way as the predicates green and blue up until some future time t. From the perspective of observers before time t it is indeterminate which predicates are future projectible (green and blue or grue and bleen).

In this section, Goodman's new riddle of induction is outlined in order to set the context for his introduction of the predicates grue and bleen and thereby illustrate their philosophical importance.

Goodman poses Hume's problem of induction as a problem of the validity of the predictions we make. Since predictions are about what has yet to be observed and because there is no necessary connection between what has been observed and what will be observed, there is no objective justification for these predictions. Deductive logic cannot be used to infer predictions about future observations based on past observations because there are no valid rules of deductive logic for such inferences. Hume's answer was that observations of one kind of event following another kind of event result in habits of regularity (i. e., associating one kind of event with another kind). Predictions are then based on these regularities or habits of mind. Goodman takes Hume's answer to be a serious one. He rejects other philosophers' objection that Hume is merely explaining the origin of our predictions and not their justification. His view is that Hume has identified something deeper. To illustrate this, Goodman turns to the problem of justifying a system of rules of deduction. For Goodman, the validity of a deductive system is justified by its conformity to good deductive practice. The justification of rules of a deductive system depends on our judgements about whether to reject or accept specific deductive inferences. Thus, for Goodman, the problem of induction dissolves into the same problem as justifying a deductive system and while, according to Goodman, Hume was on the right track with habits of mind, the problem is more complex than Hume realized. In the context of justifying rules of induction, this becomes the problem of confirmation of generalizations for Goodman. However, the confirmation is not a problem of justification but instead it is a problem of precisely defining how evidence confirms generalizations. It is with this turn that grue and bleen have their philosophical role in Goodman's view of induction.

The new riddle of induction, for Goodman, rests on our ability to distinguish lawlike from non lawlike generalizations. Lawlike generalizations are capable of confirmation while non lawlike generalizations are not. Lawlike generalizations are required for making predictions. Using examples from Goodman, the generalization that all copper conducts electricity is capable of confirmation by a particular piece of copper whereas the generalization that all men in a given room are third sons is not lawlike but accidental. The generalization that all copper conducts electricity is a basis for predicting that this piece of copper will conduct electricity. The generalization that all men in a given room are third sons, however, is not a basis for predicting that a given man in that room is a third son. The question, therefore, is what makes some generalizations lawlike and others accidental. This, for Goodman, becomes a problem of determining which predicates are projectible (i. e., can be used in lawlike generalizations that serve as predictions) and which are not. Goodman argues that this is where the fundamental problem lies. This problem is known as Goodman's paradox: from the apparently strong evidence that all emeralds examined thus far have been green, one may inductively conclude that all future emeralds will be green. However, whether this prediction is lawlike or not depends on the predicates used in this prediction. Goodman observed that (assuming t has yet to pass) it is equally true that every emerald that has been observed is grue. Thus, by the same evidence we can conclude that all future emeralds will be grue. The new problem of induction becomes one of distinguishing projectible predicates such as green and blue from non projectible predicates such as grue and bleen. Hume, Goodman argues, missed this problem. We do not, by habit, form generalizations from all associations of events we have observed but only some of them. All past observed emeralds were green, and we formed a habit of thinking the next emerald will be green, but they were equally grue, and we do not form habits concerning grueness. Lawlike predictions (or projections) ultimately are distinguishable by the predicates we use. Goodman's solution is to argue that lawlike predictions are based on projectible predicates such as green and blue and not on non projectible predicates such as grue and bleen and what makes predicates projectible is their entrenchment, which depends on their successful past projections. Thus, grue and bleen function in Goodman's arguments to both illustrate the new riddle of induction and to illustrate the distinction between projectible and non projectible predicates via their relative entrenchment.

One response is to appeal to the artificially disjunctive definition of grue. The notion of predicate entrenchment is not required. Goodman said that this does not succeed. If we take grue and bleen as primitive predicates, we can define green as "grue if first observed before t and bleen otherwise", and likewise for blue. To deny the acceptability of this disjunctive definition of green would be to beg the question. Another proposed resolution that does not require predicate entrenchment is that "x is grue" is not solely a predicate of x, but of x and a time t—we can know that an object is green without knowing the time t, but we cannot know that it is grue. If this is the case, we should not expect "x is grue" to remain true when the time changes. However, one might ask why "x is green" is not considered a predicate of a particular time t—the more common definition of green does not require any mention of a time t, but the definition grue does. Goodman also addresses and rejects this proposed solution as question begging because blue can be defined in terms of grue and bleen, which explicitly refer to time.