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| {{For|the linguistic term "grue", used for translation from natural languages|Distinction of blue and green in various languages}}
| | Hello, I'm Adolfo, a 25 year old from New York, United States.<br>My hobbies include (but are not limited to) Urban exploration, Insect collecting and watching How I Met Your Mother.<br><br>Feel free to surf to my weblog ... [http://www.eliteadomicile.com travail a domicile] |
| '''Grue''' and '''bleen''' are [[Predicate (mathematical logic)|predicates]] coined by [[Nelson Goodman]] in ''[[Fact, Fiction, and Forecast]]'' to illustrate "the new [[Problem of induction|riddle of induction]]". These predicates are unusual because their application to things are time dependent. For Goodman they illustrate the problem of projectable predicates and ultimately, which empirical generalizations are [[Scientific law|law-like]] and which are not.
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| <ref name="Goodman.1946">{{cite journal| author=Nelson Goodman| title=A Query on Confirmation| journal=The Journal of Philosophy| year=1946| month=Jul| volume=43| number=14| pages=383-385| url=http://wordsmatter.caltech.edu/~franz/Confirmation%20and%20Induction/PDFs/Nelson%20Goodman%20-%20A%20Query%20on%20Confirmation.pdf}}</ref>
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| <ref name="Goodman.1983">{{cite book|author=Nelson Goodman|title=Fact, fiction, and forecast|url=http://books.google.com/books?id=i97_LdPXwrAC|accessdate=8 March 2012|year=1983|publisher=Harvard University Press|isbn=978-0-674-29071-6|page=74}}</ref>
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| Goodman's construction and use of ''grue'' and ''bleen'' illustrates how philosophers use simple examples in [[analytic philosophy|conceptual analysis]].
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| ==Grue and bleen defined==
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| Goodman defined '''grue''' relative to an arbitrary but fixed time ''t'' as follows:<ref group="note">Historically, Goodman used ''"[[V-E day]]"'' and ''"a certain time t"'' in ''A Query on Confirmation'' (p.383) and ''Fact, fiction, and forecast'' (3rd ed. 1973, p.73), respectively.</ref>
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| An object is grue just in case it is observed before ''t'' and is green, or else is not so observed and is blue.
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| An object is bleen just in case it is observed before ''t'' and is blue, or else is not so observed and is green.<ref>http://plato.stanford.edu/entries/relativism</ref>
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| To understand the problem Goodman posed, it is helpful to imagine some arbitrary future time ''t'', say January 1, {{#expr:{{#time:Y}} + 10}}. <!-- The expression gives the current year plus two, for a date guaranteed to be in the future no matter when this page is retrieved. --> For all green things we observe up to time ''t'', such as [[emerald]]s and well-watered [[grass]], both the predicates ''green'' and ''grue'' apply. Likewise for all blue things we observe up to time ''t'', such as [[bluebird]]s or [[blue flower]]s, both the predicates ''blue'' and ''bleen'' apply. On January 2, {{#expr:{{#time:Y}} + 10}}, however, [[emerald]]s and well-watered [[grass]] are now ''bleen'' and [[bluebird]]s or [[blue flower]]s are now ''grue''. Clearly, the predicates ''grue'' and ''bleen'' are not the kinds of predicates we use in everyday life or in science, but the problem is that they apply in just the same way as the predicates ''green'' and ''blue'' up until some future time ''t''. From our current perspective (i.e., before time ''t''), how can we say which predicates are more projectable into the future: ''green'' and ''blue'' or ''grue'' and ''bleen''?
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| ==The New Riddle of Induction==
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| 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 [[Philosophy|philosophical importance]].<ref name="Goodman.1983"/><ref name="Godfrey-Smith">{{cite book|author=Peter Godfrey-Smith|title=Theory and Reality|url=http://www.press.uchicago.edu|accessdate=23 October 2012|year=2003|publisher=University of Chicago Press|isbn=978-0-226-30063-4|page=53}}</ref>
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| ===The Old Problem of Induction and Its Dissolution===
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| Goodman poses [[David Hume|Hume's problem of Induction]] as a problem of the validity of the [[prediction]]s 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, what is the justification for the predictions we make? We cannot use deductive logic 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 our observations of one kind of event following another kind of event result in our minds forming habits of regularity (i.e., associating one kind of event with another kind). The predictions we make are then based on these regularities or habits of mind we have formed.
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| 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 is on to something deeper. To illustrate this, Goodman turns to the problem of justifying a [[Deductive system|system of rules of deduction]]. For Goodman, the validity of a deductive system is justified by their 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.
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| 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.
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| ===Projectable Predicates===
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| [[File:US government example for Goodman's new riddle of induction.pdf|thumb|500px|US government example for time dependent predicates: [[List of Presidents of the United States#List of presidents|Before March 1797]], arbitrarily many observations would support both version of the prediction ''"The [[United States Armed Forces|US forces]] were always [[commander-in-chief#United States|commanded]] by { {{su|p=[[George Washington]]|b=[[President of the United States|the US President]]}} }, hence they will be commanded by him in the future"'', which today is known as { {{su|p=false|b=true}} }, similar to ''"Emeralds were always { {{su|p=grue|b=green}} }, hence they will be so in the future"''.]]
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| 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'' generalization 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.
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| What then makes some generalization ''lawlike'' and other accidental? This, for Goodman, becomes a problem of determining which predicates are projectable (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, known as ''Goodman's paradox'', is as follows. Consider the evidence that all [[emerald]]s examined thus far have been green. This leads us to conclude (by induction) 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 projectable predicates such as "green" and "blue" from non-projectable predicates such as "grue" and ''bleen''.
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| 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. ''Lawlike'' predictions (or projections) ultimately are distinguishable by the predicates we use. Goodman's solution is to argue that ''Lawlike'' predictions are based on projectable predicates such as "green" and "blue" and not on non-projectable predicates such as "grue" and ''bleen'' and what makes predicates projectable is their ''entrenchment'', which depend on their past use in successful projections. Thus, "grue" and "bleen" function in Goodman's arguments to both illustrate the new riddle of induction and to illustrate the distinction between projectable and non-projectable predicates via their relative entrenchment.
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| ==Responses==
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| The most obvious response is to point to the artificially [[Logical disjunction|disjunctive]] definition of grue. The notion of predicate ''entrenchment'' is not required. Goodman, however, noted that this move will not work. 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 [[Begging the question|beg the question]].
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| Another proposed resolution of the [[paradox]] (which Goodman addresses and rejects) 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. As we have just seen, this response also [[Begging the question|begs the question]] because definition ''blue'' can be defined in terms of ''grue'' and ''bleen'', which explicitly refer to time.<ref>Goodman 79</ref>
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| 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''. Although 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 ''x'''s 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.<ref>R. G. Swinburne, 'Grue', Analysis, Vol. 28, No. 4 (Mar., 1968), pp. 123-128</ref>
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| [[Willard Van Orman Quine]] investigates an approach to consider only "[[natural kind]]s" as projectable predicates.
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| <ref>{{cite book |editor=Nicholas Rescher et al. |booktitle=Essays in Honor of [[Carl G. Hempel]]| publisher=D. Reidel |location=Dordrecht |author=Willard Van Orman Quine |title=Natural Kinds |year=1970 |pages=41-56 |url=http://fitelson.org/confirmation/quine_nk.pdf}} Reprinted in: Quine (1969), ''Ontological Relativity and Other Essays'', Ch. 5.</ref>
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| [[Rudolf Carnap]] responded<ref>{{cite journal| author=Rudolf Carnap| title=On the Application of Inductive Logic| journal=Philosophy and Phenomenological Research| year=1947| volume=8| pages=133-148| url=http://www.hss.caltech.edu/~franz/Confirmation%20and%20Induction/PDFs/Rudolf%20Carnap%20-%20On%20the%20Application%20of%20Inductive%20Logic.pdf}} Here: p.139</ref> to Goodman's 1946 article.
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| <!---to do:------give brief summary of Carnap's response------>
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| ==Similar Predicates Used in Philosophical Analysis==
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| ===Quus===
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| In his book ''Wittgenstein on Rules and Private Language'', [[Saul Kripke]] proposed a related argument that leads to skepticism about meaning rather than skepticism about induction, as part of his personal interpretation (nicknamed "[[Kripkenstein]]" by some<ref>John P. Burgess, Gideon Rosen (1999). ''A subject with no object: strategies for nominalistic interpretation of mathematics'', p.53. ISBN 978-0-19-825012-8.</ref>) of the [[private language argument]]. He proposed a new form of addition, which he called ''quus'', which is identical with "+" in all cases except those in which either of the numbers added are equal to or greater than 57; in which case the answer would be 5, i.e.:
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| ::<math>\text{x quus y}= \begin{cases} \text{x + y} & \text{for }x,y <57 \\[12pt] 5 & \text{for } x,y \ge 57 \end{cases} </math>
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| He then asks how, given certain obvious circumstances, anyone could know that previously when I thought I had meant "+", I had not actually meant ''quus''. Kripke then argues for an interpretation of [[Wittgenstein]] as holding that the meanings of words are not individually contained mental entities.
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| ==See also==
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| * [[Blue-green]]
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| * [[N-universes]]
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| * [[Problem of induction]]
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| * [[Unsolved problems in philosophy#Qualia|Qualia]]
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| ==References==
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| <references/>
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| ==Notes==
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| {{reflist|group="note"}}
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| ==Further reading==
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| *[[Nelson Goodman|Goodman, Nelson]] (1955). ''Fact, Fiction, and Forecast''. Cambridge, Massachusetts: Harvard UP, 1955. 2nd edition, Indianapolis: Bobbs-Merrill, 1965. 3rd. edition Indianapolis: Bobbs-Merrill, 1973. 4th edition, Cambridge, Massachusetts: Harvard UP, 1983.
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| *{{Cite book
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| | last = Kripke
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| | first = Saul
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| | authorlink = Saul Kripke
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| | coauthors =
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| | title = Wittgenstein on Rules and Private Language
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| | publisher = Basil Blackwell Publishing
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| | year = 1982
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| | location =
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| | url =
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| | doi =
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| | ISBN = 0-631-13521-9 }}
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| *{{Cite journal
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| | last = Wolpert
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| | first = David
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| | coauthors =
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| | title = The Lack of A Priori Distinctions between Learning Algorithms
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| | journal = Neural Computation
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| | year = 1996
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| | pages = 1341–1390
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| | url =
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| | doi =
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| }}
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| *{{Cite book
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| | last = Stalker
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| | first = Douglas
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| | title = Grue! The New Riddle of Induction
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| | publisher = Open Court Publishing
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| | year = 1994
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| | ISBN = 0-8126-9218-7 }}
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| * Franceschi, Paul, ''Une solution pour le paradoxe de Goodman'', Dialogue, vol.40, 2001, pp. 99–123, [http://www.paulfranceschi.com/index.php?option=com_content&view=article&id=7:a-solution-to-goodmans-paradox&catid=1:analytic-philosophy&Itemid=2 English translation].
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| * Elgin, Catherine, ed. (1997). ''The Philosophy of Nelson Goodman: Selected Essays.'' Vol. 2, ''Nelson Goodman's New Riddle of Induction.'' New York: Garland. ISBN 0-8153-2610-6.
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| *[http://alum.mit.edu/www/tchow/grue.html Goodman's original definition of grue]
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| {{DEFAULTSORT:New riddle of induction}}
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| [[Category:Paradoxes]]
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| [[Category:Conceptual models]]
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| [[Category:Ludwig Wittgenstein]]
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| [[Category:Inductive reasoning]]
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