The Grue Paradox
Every observed emerald is both green and grue. The evidence for 'all emeralds are green' and 'all emeralds are grue' is identical. Why do we believe one and not the other?
Nelson Goodman introduced this case in 1955 as 'the new riddle of induction.' The paradox shows that induction cannot be purely formal: the same evidence can equally support incompatible predictions, and logic alone cannot tell us which generalization to project into the future.
Goodman, N. (1955). Fact, Fiction, and Forecast. Harvard University Press.
The definition
Nelson Goodman coined a new predicate: grue. Something is grue if and only if it is green and first observed before the year 2100, or blue and first observed after 2100.
Every emerald examined so far has been observed before 2100 and has been green. So every observed emerald is grue. The evidence for "all emeralds are green" is exactly the same as the evidence for "all emeralds are grue." We have seen the same stones, done the same tests, written down the same results.
But "all emeralds are green" predicts that the next emerald will be green. "All emeralds are grue" predicts that emeralds observed after 2100 will be blue. The two hypotheses make incompatible predictions. We can't inductively confirm both.
The problem this creates
Standard induction says: if all observed Fs have been G, project that the next F will also be G. But this principle applies equally to green and to grue. We have no purely logical basis for preferring one over the other.
Goodman's point is that not all predicates are equal candidates for inductive generalization. "Green" seems like a legitimate predicate to project. "Grue" seems like a trick. But the trick is hard to expose. Grue is defined precisely, consistently, and applies to all the same objects. If you try to object that grue is defined using a time-boundary, the grue-speaker can redescribe green using grue and bleen as the primitives, making green look equally arbitrary.
Entrenchment and the new riddle
Goodman's response was the concept of entrenchment. Some predicates have been successfully used in inductive generalizations many times before. "Green" is deeply entrenched in our practice. "Grue" is not. We should prefer to project predicates that have a track record of successful projection.
This is not a logical answer. It's a pragmatic one. The difference between green and grue is not written into the evidence or into logic. It reflects the history of our conceptual practices.
The new riddle of induction, then, is not "can induction be justified?" but "which inductions should we make?" And the answer turns out to depend not just on evidence but on the words we use and the concepts we have inherited. Logic underdetermines which generalizations we are entitled to form.
Discussion questions
- Why is 'all emeralds are green' a better prediction than 'all emeralds are grue'?
- Is there a fact of the matter about which generalizations are natural versus artificial?
- Does this make you more cautious about how much confidence to place in scientific predictions?
Take it to the dinner table.
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