What is Goodman's New Riddle of Induction? How, if at all, can it be solved?


Nelson Goodman first presented his "new riddle of induction" in a 1946 paper(1) and then elaborated on his idea in 1955 in his Fact, Fiction and Forecast(2).  Before describing Goodman's riddle, I must first say a few words about what he would refer to as the "old riddle of induction".  This will set the stage for the solution I offer to Goodman's "new riddle".  The solution I offer to the riddle is based on the notion of pattern recognition, where projectible predicates are those that describe patterns in the data and non-projectible predicates are those that describe patterns that extend beyond our experiences.

The "old riddle of induction" is the problem of how we justify the assumption that the future will be like the past.  Goodman is of the opinion that Hume offered what is the only possible solution to this riddle.  Hume argues that the experience of constant conjunction fosters a "habit of the mind" that leads us to anticipate that the future will be consistent with past experienced regularities.

"First we may observe, that the supposition, that the future resembles the past, is not founded on arguments of any kind, but is derived entirely from habit, by which we are determined to expect for the future the same train of objects, to which we have been accustomed. This habit or determination to transfer the past to the future is full and perfect; and consequently the first impulse of the imagination in this species of reasoning is endowed with the same qualities."
                                                                                    Dave Hume(3)

In modern evolutionary terms, we have evolved and ability to notice regularities (patterns) in our environment and our experiences, and to base our choices and decisions on the assumption that those regularities / patterns will persist into the future.  There would be no evolutionary advantage in the ability to recognize patterns in our experiences, and hence no evolutionary pressure to evolve the ability, if we could not successfully make use of such information by anticipating the future on the basis of past patterns.  In other words, we are evolutionarily predisposed to assume that the future will be like the past.  But note that this evolutionary take on inductive reasoning understands induction in terms of pattern recognition -- a skill we are particularly good at, a skill for which our neural-net brains are particularly well constructed.  The difference between an acceptable and an unacceptable inductive inference, on this understanding, becomes the difference between a pattern within our experiences for which we have good evidence versus a pattern for which we do not have good evidence.  In particular, when discussing Goodman's new riddle of induction, it will become the difference between patterns for which we have evidence versus patterns for which we have no evidence. 

Goodman argues that both our rules of deduction and our rules of induction are justified in the same virtuously circular fashion -

"A rule [of reasoning] is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend."(4)

He concludes that this is all that is possible to offer in the way of justifying either our premise of "futurity" (that the future will be like the past), or our premise that nature is deductively consistent.  The defined rules of deductive logic may dictate that the conclusion of a deductively valid argument is necessarily true if the premises are true, but you still have to check reality from time to time to see if the conclusion is indeed true, no matter how firmly you believe the premises to be true.  The assumption underlying the defined rules of deductive logic is just the same "futurity" assumption that underlies inductive reasoning -- in the future, reality will continue to exhibit deductive consistency, because it has done so in the past.

That Goodman considers the "old riddle of induction" to be adequately resolved by Hume's "habit", means that the context in which his "new riddle of induction" must be addressed needs to presuppose this resolution.

Goodman presents his new riddle in the context of Hempel's theory of confirmation(5) and a discussion of how we can tell which hypotheses are confirmed by any given evidence.  Goodman's new riddle of induction thus involves not the question of how we can justify the futurity assumption, but the question of how we can justify our choices of the regularities / patterns onto which we apply that futurity assumption.  How, in Goodman's words, do we distinguish between law-like, confirmable, projectible predicates from non-law-like, un-confirmable, non-projectible predicates?

From the collection of particular observations that all emeralds so far observed have been green, Goodman proposes that two incompatible hypotheses (patterns) can be supported:

(a)     All emeralds are green, and

(b)    All emeralds are grue.

The predicate "grue" Goodman defines as applying "to all things examined before t just in case they are green, but to other things just in case they are blue."(6)  (Note that contrary to many interpretations(7), "grue" does not entail that things already observed will change colour after time t, and need not be understood as a colour predicate)  It is Goodman's point that we readily recognize that "grue" is a perverse predicate.  His "new riddle of induction" is the problem of explaining in a principled way just why it is that "grue" but not "green" is perverse.

Goodman's choice to discuss emeralds in the context of his "grue" predicate was unfortunate.  Emeralds are green by definition(8).  A non-green emerald-like thing would not be an emerald.  Emeralds are a variety of the mineral beryl (Be3Al2(SiO3)6) coloured green by trace amounts of chromium or vanadium.(9)  We now understand enough about the physics of photons to understand just how it comes to be that that beryl with trace amounts of chromium or vanadium appear to be coloured green.  So, if after some time t, we discover some gem that is blue (as would be anticipated on the basis of a persisting "grue" pattern), then that gem would either not be beryl, or not be doped with trace amounts of chromium or vanadium.  In other words, either such a blue gem would not be an "emerald", or the physics of photons would have changed dramatically.  Hence, given the background information we have about the nature of emeralds, the predicate "grue" can be dismissed as not really identifying a possible pattern in the stock of past experiences we have about green emeralds.  But I'll ignore this quibble for the remainder of this essay, and pretend that "emeralds" might possibly be blue.

There is, however, an even more global reason for dismissing perverse predicates like "grue".  All grue-like predicates contain within them a reference to some boundary -- either temporal (as in grue), spatial, or relational -- across which is proposed some kind of change in the observed pattern, a change for which we have no evidentiary support.  And it is the existence of that anticipated, but inexplicable, change that makes the predicate perverse.  The fact that all the emeralds we have so far examined have been green, offers no support whatever to the hypothesis that after some time t, the next emerald we examine will be blue.  This difficulty exists for all grue-like predicates.

This difficulty persists, even though Goodman argues that the boundary in the case of "grue" is not a necessary feature of the predicate.  He argues that "green" and "blue" can be defined in terms of "grue" and "bleen" -- and within those definitions, it is "green" and "blue" that would contain the temporal boundary, while "grue" and "bleen" would be the unbounded predicates.  Goodman suggests that by defining "green" and "blue" in terms of "grue" and "bleen" we would be making "green" and "blue" the perverse predicates, to the salvation of "grue" and "bleen". 

But by doing so, Goodman seems to gloss over the significance of what it would mean to recognize a pattern in our experiences, and how that would translate into the meaning of an unbounded predicate.  You can't meaningfully recognize a new pattern in our mass of experiential data if the collection of data we are limited to is an isolated subset of that greater mass.  Any pattern recognized within the subset, would be applicable only to the subset, not to the whole mass.  Hence, any proper analysis of induction must necessarily take place within an "all things considered" environment.  To recognize a globally meaningful pattern in our experiential evidence, we need to consider the global mass of that evidence.

Consider Ms. Grue, who speaks Gruelish -- a language in which "grue" and "bleen" are basic pattern description predicates.  It is then true that Ms. Grue would converse with Mr. Green (who speaks Greenlish -- also known as English) by translating the Greenlish words "green" and "blue" into concepts that refer to the Gruelish predicates "grue" and "bleen" and a temporal boundary.  So that, as Goodman suggests, Ms. Grue can argue that it is Mr. Green who is operating with the perverse predicates.  But based on her recognized pattern of "grue" emeralds, what does Ms. Grue anticipate will be the appropriate pattern predicate of the next emerald she examines after that boundary time t?  Ms. Grue, speaking Gruelish, and thinking in terms of the pattern "grue", will naturally anticipate that after time t emeralds will continue to be grue.  But the question is just what that anticipation entails in an "all things considered" framework.

Suppose, first, that Ms. Grue can distinguish (somehow, either anatomically or technically) between photons of roughly 520--570 nanometres and photons of roughly 440--490 nm.  Then this will mean that if Ms. Grue's identified "grue" pattern is to persist, after time t chromium doped beryl will transmit photons in the 440--490 nm range instead of the so far observed 520--570 nm range.  In other words, by recognizing that "green" and "blue" can be defined in terms of "grue" and "bleen" and some boundary time t, Ms. Grue is acknowledging that her "grue" pattern predicate is anticipating a change in the physics of photons.  A change for which she must admit she has no experiential support.  Hence, Ms. Grue, in Gruelish, must acknowledge that her "grue" predicate is perverse.

Suppose, on the other hand, that for some reason, Ms. Grue is not able to distinguish between photons of roughly 520--570 nm and photons of roughly 440--490 nm.  Then Ms. Grue will not be able to discern any change taking place in the emeralds she observes as the time progresses past the boundary time t.  Emeralds will continue to be observed to be "grue" -- her "grue" pattern nicely persists.  In this case, to Ms. Grue, her "grue" predicate is not perverse at all.  So one can argue that non-perverse predicates (in Goodman's term, "projectible" predicates) are the ones that do not involve any discernable change (a change not part of the observed pattern within existing experience, that is).

In her discussions with Mr. Green, Ms. Grue will maintain that the Greenlish terms "green" and "blue" are but two different words for the same pattern within the evidence.  And she will be completely at a loss to explain why Mr. Green should choose to switch words for the same pattern at some time t.  Now, of course, there are two alternative reasons why Ms. Grue might not be able to distinguish between photons of 520--570 nm and photons of 440--490 nm.  On the simple side, Ms. Grue may not be equipped, either anatomically or technically, to detect any unexplained change in the evidentiary data underlying her "grue" pattern.  In which case, Ms. Grue may not be able to detect that her "grue" predicate is perverse, but Mr. Green certainly can.  On the complicated side, the Universe may, in actual fact, change at time t, such that there is no difference discernable by either Ms. Grue or Mr. Green.  In which case Ms. Grue has the non-perverse predicate while Mr. Green will discover that his "green" predicate is perverse.  But for neither of them, is there any experiential basis for claiming a pattern in the evidence that anticipates a Universal change in the physics of photons.

But the obvious perverseness of Goodman's Grue, does nothing to resolve the deeper point that Goodman was attempting to demonstrate.  The only support we have for the predicates that we project into the future, are the patterns that we recognize in the evidence we have experienced.  And the only basis for preferring one pattern hypothesis versus another pattern hypothesis within the same body of evidence, is that one pattern covers a greater body of experience (without lapping over the limits of the data) than another.  If, as Goodman supposes in the case of "grue" versus "green", there is no discernable difference in the suitability of two identified yet incompatible patterns, then there simply is no basis on which to prefer one pattern hypothesis over another.  But induction never takes place in isolation.  It is always a process of "all things considered" pattern recognition.  The patterns we detect within our body of experience will change as that body of experience grows.  In many cases, old patterns will be seen to be smaller parts of larger patterns.  In some cases, larger patterns may invalidate our earlier identification of smaller patterns.  As in the case of "grue", our larger experience with photon transmission in beryl invalidates the smaller hypothesized pattern of "grue".  But until we discover our own Mr. Green, or until we actually pass the boundaries, we will never discover if one, some, or all of our pattern predicates have been perverse.


Notes & References

(1)  Goodman, Nelson;  "A Query on Confirmation" in The Journal of Philosophy, Vol 43, No 14 (Jul 1946), pp383-385.

(2)  Goodman, Nelson;  Fact, Fiction, and Forecast, (1st edition), Modern Thought: Philosophy, Harvard University Press, Cambridge, Mass. 1955.

(3)  Hume, David;  A Treatise of Human Nature, Book I, Part III, Section XII, Of the Probability of Causes, URL=<http://nothingistic.org/library/hume/treatise/treatise050.html>.

(4)  Goodman, Nelson;  Fact, Fiction, and Forecast, Third Edition, Hackett Publishing Company, Cambridge, Mass. 1979. ISBN 0-672-61347-6. Pg 74

(5)  Hempel. Carl G.;  "Studies in the Logic of Confirmation" in Aspects of Scientific Explanation and other Essays in the Philosophy of Science, The Free Press, Macmillan Publishing Co., New York, New York, 1965.

(6)  Goodman, 1979, Op.Cit. Pg 74.

(7)  See, for example --

Barker, S.F. & Achinstein, P.;  "On the New Riddle of Induction" in Philosophical Review, Vol 69 (1960), pp 511-522.

Swinburne, R.G.;  "Grue" in Analysis, Vol  28 (1968), pp 123-128.

Hesse, M.;  "Ramifications of Grue" in British Journal for the Philosophy of Science, Vol 20 (1969), pp 13-25.

Blackburn, S.;  "Goodman's Paradox" in Studies in the Philosophy of Science, American Philosophical Quarterly Monograph Series, No. 3 (1969), pp 128-142.

Kripke, S.A.;  Wittgenstein on Rules and Private Language, Blackwell Publishing, Oxford, England, 1982.

(8)  Klein, Cornelis;  Manual of Mineralogy (after James D. Dana) 21st Edition, John Wiley & Sons Canada, Ltd., 1998. ISBN 978-0-471-31266-6.

(9)  Wikipedia contributors. "Emerald" in Wikipedia, The Free Encyclopedia. URL=<//en.wikipedia.org/w/index.php?title=Emerald&oldid=454474611>.


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