In his 1955 book Fact, Fiction, and Forecast, Nelson Goodman shows that the distinction between justified and unjustified inductive inferences has nothing to do with the logical structure of the inference. Justified and unjustified inductive inferences can have exactly the same form! For instance, consider the inference from the premise all observed emeralds are green to the conclusion that the next emerald to be discovered also will be green. This instance of enumerative induction seems perfectly reasonable, or justified. However, Goodman points out that it is possible to construct another inference with exactly the same grammatical and logical structure, but in which the conclusion is clearly unjustified.
To show this, Goodman introduces an unusual property: the property of being grue. An object is grue if and only if the object is either green and was first observed before some particular time t or the object is blue and was never observed until after time t. According to this definition, the proposition all observed emeralds are grue is true at time t, since all the emeralds observed until that time were green and observed prior to t.
Notice that the proposition all observed emeralds are grue has exactly the same form as all observed emeralds are green. From the latter proposition, we can infer that the next observed emerald will be green. So, if inductive inferences depend solely on logical form, we should be able to infer likewise that the next emerald to be discovered will be grue. But this cannot be correct, because in order for the next emerald to be grue its color would have to be blue rather than green (since it was never observed until after time t).
Obviously, “grue” is a strange property, and it’s not the sort of concept we would ordinarily use in enumerative induction. But that’s exactly Goodman’s point: the meanings of the words we use in an inductive inference make a difference to whether the inference is reasonable, or justified. We cannot assess whether the inference is justified on the basis of its logical form alone. This proves that the difference between justified and unjustified inductive inferences cannot be determined solely by rules of logical structure. In other words, there can be no such thing as a formal logic of induction.
Goodman’s conclusion raises a puzzling question. Since there are no rules of inductive logic analogous to the rules of deductive logic, how can we determine whether an inductive inference is justified or unjustified? In other words, what methods or criteria can we use to distinguish justified inductive inferences from unjustified ones? Goodman calls this the new riddle of induction. Attempts to answer this new riddle can be found in a relatively young field of philosophical inquiry called confirmation theory, which is the subject of the next chapter.