Grue (color)
Encyclopedia
Grue and bleen are artificial predicates, coined as two portmanteaux of "green
" and "blue
" by philosopher Nelson Goodman
in his book Fact, Fiction, and Forecast
. The words are used to illustrate what Goodman calls "the new riddle of induction
".
"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, .
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
(which Goodman addresses and rejects) 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.
Swinburne gets past the objection that green be redefined in terms of grue and bleen by making a distinction based on how we test for the applicability of a predicate in a particular case. He distinguishes between qualitative and locational predicates. Qualitative predicates, like green, can be assessed without knowing the spatial or temporal relation of x to a particular time, place or event. Locational predicates, like grue, cannot be assessed without knowing the spatial or temporal relation of x to a particular time, place or event, in this case whether x is being observed before or after time t. Whilst green can be given a definition in terms of the locational predicates grue and bleen, this is irrelevant to the fact that green meets the criterion for being a qualitative predicate whereas grue is merely locational. He concludes that if some xs under examination - like emeralds - satisfy both a qualitative and a locational predicate, but projecting these two predicates yields conflicting predictions - namely, whether emeralds examined after time t shall appear blue or green, we should project the qualitative predicate, in this case green.
proposes a related argument that leads to skepticism about meaning rather than skepticism about induction, as part of his personal interpretation (nicknamed "Kripkenstein
" by some) 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.
Green
Green is a color, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 520–570 nanometres. In the subtractive color system, it is not a primary color, but is created out of a mixture of yellow and blue, or yellow and cyan; it is considered...
" and "blue
Blue
Blue is a colour, the perception of which is evoked by light having a spectrum dominated by energy with a wavelength of roughly 440–490 nm. It is considered one of the additive primary colours. On the HSV Colour Wheel, the complement of blue is yellow; that is, a colour corresponding to an equal...
" by philosopher Nelson Goodman
Nelson Goodman
Henry Nelson Goodman was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism and aesthetics.-Career:...
in his book Fact, Fiction, and Forecast
Fact, Fiction, and Forecast
Fact, Fiction, and Forecast is a book by Nelson Goodman in which he explores some problems regarding scientific law and counterfactual conditionals and presents his New Riddle of Induction...
. The words are used to illustrate what Goodman calls "the new riddle of induction
Problem of induction
The problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:...
".
Grue and bleen defined
The word grue is defined relative to an arbitrary but fixed time t as follows: An object X satisfies the propositionProposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
"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, .
The new riddle
The problem, known as Goodman's paradox, 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 induction can be used to confirm that things are "green" but not to confirm that things are "grue".Responses
The most obvious response is to point to the artificially disjunctiveDisjunctive
Disjunctive can refer to:* Disjunctive population, in population ecology, a group of plants or animals disconnected from the rest of its range* Disjunctive pronoun* Logical disjunction...
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
Begging the question
Begging the question is a type of logical fallacy in which the proposition to be proven is assumed implicitly or explicitly in the premise....
.
Another proposed resolution of the paradox
Paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...
(which Goodman addresses and rejects) 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
Begging the question
Begging the question is a type of logical fallacy in which the proposition to be proven is assumed implicitly or explicitly in the premise....
given that the above definition of blue in terms of grue and bleen also refers to time.
Swinburne gets past the objection that green be redefined in terms of grue and bleen by making a distinction based on how we test for the applicability of a predicate in a particular case. He distinguishes between qualitative and locational predicates. Qualitative predicates, like green, can be assessed without knowing the spatial or temporal relation of x to a particular time, place or event. Locational predicates, like grue, cannot be assessed without knowing the spatial or temporal relation of x to a particular time, place or event, in this case whether x is being observed before or after time t. Whilst green can be given a definition in terms of the locational predicates grue and bleen, this is irrelevant to the fact that green meets the criterion for being a qualitative predicate whereas grue is merely locational. He concludes that if some xs under examination - like emeralds - satisfy both a qualitative and a locational predicate, but projecting these two predicates yields conflicting predictions - namely, whether emeralds examined after time t shall appear blue or green, we should project the qualitative predicate, in this case green.
Kripke's Wittgenstein
In his book Wittgenstein on Rules and Private Language, Saul KripkeSaul Kripke
Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
proposes a related argument that leads to skepticism about meaning rather than skepticism about induction, as part of his personal interpretation (nicknamed "Kripkenstein
Kripkenstein
Wittgenstein on Rules and Private Language by philosopher of language Saul Kripke was first published in 1982. The book contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a devastating rule-following paradox that undermines the possibility of us ever...
" by some) of the private language argument
Private language argument
The private language argument is a philosophical argument introduced by Ludwig Wittgenstein in his later work, especially in the Philosophical Investigations. The argument was central to philosophical discussion in the second half of the 20th century, and continues to arouse interest...
. 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 also
- section Qualia in Unsolved problems in philosophyUnsolved problems in philosophyThis is a list of some of the major unsolved problems in philosophy. Clearly, unsolved philosophical problems exist in the lay sense . However, philosophers generally accord serious philosophical problems specific names or questions, which indicate a particular method of attack or line of reasoning...
- Problem of inductionProblem of inductionThe problem of induction is the philosophical question of whether inductive reasoning leads to knowledge. That is, what is the justification for either:...
Further reading
- Franceschi, Paul, Une solution pour le paradoxe de Goodman, Dialogue, vol.40, 2001, pp. 99–123, English translation.
- Elgin, Catherine, ed. (1997). The Philosophy of Nelson Goodman: Selected Essays. Vol. 2, Nelson Goodman's New Riddle of Induction. New York: Garland. ISBN: 0815326106.
- Goodman's original definition of grue