Grue and bleen are artificial predicates, coined as two portmanteaux of "green" and "blue" by philosopher Nelson Goodman in one of the seminal works in the philosophy of science, Fact, Fiction, and Forecast. The words are used to illustrate what Goodman calls "the new riddle of induction".

Grue and bleen definedEdit

The word grue is defined relative to an arbitrary but fixed time t as follows: An object X satisfies the proposition "X is grue" if X is green and was examined before time t, or blue and was not examined before t.

The word bleen has a complementary definition: An object X is bleen if X is blue and was examined before time t, or green and was not examined before t.

Some popularizations of the concept have described it in a slightly different way: an object is grue if it is green when examined before time t and blue when examined afterwards (and likewise for bleen). That version is different because it envisions the same object as appearing green or blue at different times, while the original definition means that the object is always green or always blue, but which one depends on when the object was first observed. This article will deal only with the original definition.

Note. In his original presentation in Fact, Fiction, and Forecast, Goodman said that the predicate grue "applies to all things examined before t just in case they are green but to other things just in case they are blue". For clarity, some later authors used concrete times t such as "January 1, 2000", dates that at the time were in the future but are now in the past. For understanding the problem posed by Goodman, it is best to imagine some time t in the future, say January 1, 2019.

The new riddleEdit

The problem is as follows. A standard example of induction is this: All emeralds examined thus far are green. This leads us to conclude (by induction) that also in the future emeralds will be green, and every next green emerald discovered strengthens this belief. Goodman observed that (assuming t has yet to pass) it is equally true that every emerald that has been observed is grue. Why, then, do we not conclude that emeralds first observed after t will also be grue, and why is the next grue emerald that comes along not considered further evidence in support of that conclusion? The problem is to explain why.


The most obvious response is to point to the artificially disjunctive definition of grue. But, said Goodman, this move will not work. For if we take grue and bleen as primitive, 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 of the paradox is that "x is grue" is not solely a predicate of x, but of x and the time — we can know that an object is green without knowing the current time, 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 the current time — the more common definition of green does not require any mention of the time of observation, but the disjunctive definition given above does. However, this response also begs the question given that the above definition of blue in terms of grue and bleen also refers to time.

Kripke's WittgensteinEdit

In his book Wittgenstein on Rules and Private Language Saul Kripke proposes a related argument that leads to skepticism about meaning rather than skepticism about induction, as part of his personal interpretation (nicknamed Kripkenstein) of the private language argument. He proposes a new form of addition, which he calls quus, which is identical with plus in all cases except those in which either of the numbers to be added are greater than 57; in which case the answer would be 5. He then asks how, given certain obvious circumstances, anyone could know that previously when I thought I had meant plus, I had not actually meant quus. Kripke then argues for an interpretation of Wittgenstein as holding that it is not possible to state the meaning of a word.

See alsoEdit


  • Goodman, Nelson (1955). Fact, Fiction, and Forecast. Cambridge, MA: Harvard UP, 1955. 2nd ed. Indianapolis: Bobbs-Merrill, 1965. 3rd. ed. Indianapolis: Bobbs-Merrill, 1973. 4th ed. Cambridge, MA: Harvard UP, 1983.

fr:Paradoxe de Goodman ja:グルーのパラドックス sv:Grue (färg)

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