David Hume, in his An Inquiry Concerning Human Understanding (1748), first identified the difficulty of rationally justifying future predictions, which has come to be known as the Problem of Induction. He pointed out that since future predictions are neither statements of experience nor logically necessary consequences of such statements, their validity lies in the regularity of constantly conjoined events. This regularity in turn creates within the subject certain habits of belief that predispose one to expect the future to mirror reliably the past.
After some two hundred and a half years, however, and because of the likes of Hans Reichenbach, Peter Strawson, F.P. Ramsey, Karl Popper, and Rudolf Carnap, to name only a few, the problem of induction may now be regarded as solved; but, if not solved, then at the very least dissolved into a more palatable conceptual confusion. Nevertheless, Hume’s problem of induction has taken a back seat to a newer, more fashionable problem, namely, Nelson Goodman’s ‘The New Riddle of Induction.’
In Fact, Fiction, and Forecast (1955), the late Nelson Goodman discovered what he- and later others- termed, ‘The New Riddle of Induction.’ The new riddle highlights the inadequacy of Hume’s initial account insofar as he neglected to recognize that not all experiential regularities establish habits of future predictions. As Goodman himself says, ‘[P]redictions based on some regularities are valid while predictions based on other regularities are not.’ The task is to delineate which regularities are appropriately habituating and which are not.
To explain why such a delineation is desired, Goodman offers his now infamous ‘grue paradox.’ ‘Grue’ is a portmanteau color predicate and applies to all emeralds ‘examined before t [such that t is a future point in time, e.g., 3000 A.D.] just in case they are green, but to other emeralds just in case they are blue.’ There are innumerable other similar predicates, for instance, ‘consider… the predicate “bleen” that applies to emeralds examined before time t just in case they are blue and to other emeralds just in case they are green.’
Now, take a common inductive argument, P, such that, (1) every previously examined emerald was green; (2) therefore, all emeralds are green. Then consider another inductive argument, S, such that, (1) every previously examined emerald was grue; (2) therefore, all emeralds are grue. But, as Goodman observes:
‘[A]t time t we have, for each evidence statement asserting that a given emerald is green, a parallel evidence statement asserting that that emerald is grue. And the statements that emerald a is grue, that emerald b is grue, and so on, will each confirm the general hypothesis that all emeralds are grue. Thus according to our definition, the prediction is that all emeralds subsequently examined will be green and the prediction that all will be grue are alike confirmed by evidence statements describing the same observations. But if an emerald subsequently examined is grue, it is blue and hence not green.’ – Chapter III, section 4
P is intuitively acceptable and unproblematic- indeed, much if not all of our information gathering processes are structurally similar to P-, whereas S is on first appearances objectionable and one is wont to dismiss it as invalid; yet, it is evident that P is formally identical to S. Wherein lies the difficulty?
A commonly proposed solution is to challenge Goodman’s use of the predicate ‘grue.’ The particular argument in question seeks to draw a distinction between qualitative and positional predicates. In other words, whether a predicate is positionally explicable via ‘direct inspection’ (e.g., ‘on the bed right now’ in ‘Her rose is on the bed right now’) or rather if it is ‘purely qualitative.’ Qualitative predicates are defined as syntactically simple, that is, they do not refer to a spatio-temporal position or are not functional compounds. So, the argument goes, ‘grue’ is not a qualitative predicate because it consists of the predicates ‘green’ and ‘blue’ and a temporal term. For example, if we begin with ‘green’ and ‘blue’, then ‘grue’ and ‘bleen’ are explicable according to the predicates ‘green’ and ‘blue’ and a temporal term. Prima facie, however, this solution is problematic; for, as Goodman remarked, if we begin with ‘grue’ or ‘bleen’, then ‘blue’ and ‘green’ will likewise be defined in relation to ‘grue’ and ‘bleen’ and a temporal term, e.g., ‘green’ pertains to ‘emeralds examined before t in the instance they are ‘grue’, and to other emeralds just in case they are ‘bleen’. (Similarly for ‘blue’ and other like predicates.)
It is not difficult to see the arbitrariness of such solutions.
Rather than challenge Goodman’s use of uncommon predicates, a more promising solution, I believe, lies in an analysis of the very syntactical make-up of the proposition conveying the predicate itself.
Consider the following analysis. The proposition (1) ethanol (EtOH) is solid and less than -114.3 °C, or liquid and more than -114.3 °C and less than 78.4 °C is syntactically analogous to (2) all gruesome emeralds examined before t are green, but blue in the instance they are not so examined. Just as the phase behavior of EtOH varies according to temperature (and other variables I neglect here, such as atmospheric pressure), the color of gruesome emeralds vary according to the time of first examination. However, when (1) is itemized into its constituent parts, (I) EtOH is solid and less than -114.3 °C, and, (II) EtOH is liquid and more than -114.3 °C and less than 78.4 °C, we find that both (I) and (II) are well verified. Conversely, if (2) is itemized into its constituent parts, (I*) emeralds are green if examined before t, and, (II*) emeralds are blue if not so examined, we find that, while (I*) is well verified, (II*) is not well verified, nor for that matter is it verifiable.
In no way do I purport to have given a full and systematic solution to Goodman’s New Riddle of Induction. Instead, I only wish to point out that while gruesome propositions are indeed formally identical to standard inductive arguments, when analyzed into their constituent conjunctions, they are not well supported by verification. Thus, as a preliminary attempt at delineating which experiential regularities are valid (viz., which are properly habituating) and which are not, I assert that the regularities are appropriate which may be deconstructed into constituent conjuncts, with the conjuncts each supported by verifiable propositions.
when you say “verifiable” are you referring to the logical positivists’ concern regarding verification?
Yes and no. Unlike the Logical Positivists, by “verification” I do not mean to say the meaning of a proposition is its manner of verification. I mean only the process of aligning certain phenomena with certain propositions, e.g., seeing a blue jay in the birdbath verifies the proposition, “there is a blue jay in the birdbath.”
Aaron,
interesting. i see why you’re drawn to this as a response to goodman. but i think you’re failing to grasp the full weight of the problem.
what if we’re gruesome conceptualizers? that is, what if we’re surprised when emeralds change to bleen (stay green)? gruesoome conceptualizers don’t see colors, they see schmolers.
the definition of “green” for the gruesome conceptualizers is going to be all syntactically convoluted just like your 1. And likewise the gruesome hypotheses will have the most confirming (schmonforming) instances.
p.s. take care of the noob.
let me make another pass at this one.
to start, here’s the definition of grue I role with:
x is grue iff (x is examined by t and x is green) or (x is not examined by t and x is blue).
now, I think too often people take hume and goodman to be saying that induction isn’t unjustified. This is wrong.
the starting point is that induction works just fine; even babes and brutes profit from it. some inductions are good, some are bad. both hume and goodman speak of valid and invalid inductions. both want an account of the logic of induction. so they investigate. to the study!
hume says that it is a natural habit of ours to induce that, say, all A’s are B’s from that this examined A is B. And it’s a custom which determines whether particular instances of these habitual inductions are good or bad (valid or invalid). The custom seems to be that the more regularities we experience before making the generalization or prediction, the better the induction is.
Goodman’s new riddle is a reductio of hume’s solution. here’s the definition of grue I role with:
x is grue iff (x is examined by t and x is green) or (x is not examined by t and x is blue).
Any instance of an examined A’s B-ness confirms that all A’s are grueB and grueB* and so on because any experience of A’s B-ness is also an experience of A’s Bgrue-ness and Bgrue*-ness and so on.
Moreover, if we reason inductively starting with a green instance statement, “this emerald is green,” we arrive at the generalization that all emeralds, and hence all unexamined ones, are green. If we reason inductively starting with the grue instance statement, “this emerald is grue” we arrive at the generalization that all emeralds, and hence all unexamined ones, are grue. Assuming there are some emeralds still unexamined, if the unexamined ones are grue, they are blue and so not green. Likewise, if the unexamined ones are green, they aren’t grue because not blue.
So if there are some emeralds still unexamined, the conclusion of the green inductive argument is inconsistent with the conclusion of the grue inductive argument even though the premises are consistent and the reasoning is of the same form. The result is paradoxical.
Worse, any predicate can be made gruesome. And by simply changing the time, we can generate an incredible, if not infinite, number of such paradoxical cases.
Yet induction still profits even babes and brutes. But look at the straits we’re left in regarding the logic of induction. We have on the one hand an induction which looks like this. These emeralds are green, therefore all emeralds are green. But on the other hand we have an induction which looks like this. These emeralds are grue, therefore all emeralds are grue. Given the experience we’ve had with emeralds, both of these inductions are equally available and consistent with the data. We are seemingly at a loss as to which induction is the good one.
But this isn’t entirely the case. Everyone, even Goodman, thinks the green induction is the good one. No one thinks unexamined emeralds are blue even though all of the emeralds we’ve experienced are grue. The new riddle, then, is simply: why is, or what makes it the case that, the green induction is the good one? So what we’re after is a logical account of what makes inductions good.
Goodman’s theory of entrenchment is similar to what Hume had in mind with custom.
there are also other questions associated with the grue paradox.
How can we know, if we can, which inductions are the good ones?
an epistemic question.
Why do we believe some inductions but not others? a Psychological question.
I recommend the following Authors on the subject of Grue:
Joseph Ullian
Frank Jackson
Sydney Shoemaker
can you edit on this site?
I think too often people take hume and goodman to be saying that induction IS unjustified. This is wrong.
the starting point is that induction works just fine; even babes and brutes profit from it. some inductions are good, some are bad. both hume and goodman speak of valid and invalid inductions. both want an account of the logic of induction. so they investigate. to the study!
hume says that it is a natural habit of ours to induce that, say, all A’s are B’s from that this examined A is B. And it’s a custom which determines whether particular instances of these habitual inductions are good or bad (valid or invalid). The custom seems to be that the more regularities we experience before making the generalization or prediction, the better the induction is.
Goodman’s new riddle is a reductio of hume’s solution. here’s the definition of grue I role with:
x is grue iff (x is examined by t and x is green) or (x is not examined by t and x is blue).
Any instance of an examined A’s B-ness confirms that all A’s are grueB and grueB* and so on because any experience of A’s B-ness is also an experience of A’s Bgrue-ness and Bgrue*-ness and so on.
Moreover, if we reason inductively starting with a green instance statement, “this emerald is green,” we arrive at the generalization that all emeralds, and hence all unexamined ones, are green. If we reason inductively starting with the grue instance statement, “this emerald is grue” we arrive at the generalization that all emeralds, and hence all unexamined ones, are grue. Assuming there are some emeralds still unexamined, if the unexamined ones are grue, they are blue and so not green. Likewise, if the unexamined ones are green, they aren’t grue because not blue.
So if there are some emeralds still unexamined, the conclusion of the green inductive argument is inconsistent with the conclusion of the grue inductive argument even though the premises are consistent and the reasoning is of the same form. The result is paradoxical.
Worse, any predicate can be made gruesome. And by simply changing the time, we can generate an incredible, if not infinite, number of such paradoxical cases.
Yet induction still profits even babes and brutes. But look at the straits we’re left in regarding the logic of induction. We have on the one hand an induction which looks like this. These emeralds are green, therefore all emeralds are green. But on the other hand we have an induction which looks like this. These emeralds are grue, therefore all emeralds are grue. Given the experience we’ve had with emeralds, both of these inductions are equally available and consistent with the data. We are seemingly at a loss as to which induction is the good one.
But this isn’t entirely the case. Everyone, even Goodman, thinks the green induction is the good one. No one thinks unexamined emeralds are blue even though all of the emeralds we’ve experienced are grue. The new riddle, then, is simply: why is, or what makes it the case that, the green induction is the good one? So what we’re after is a logical account of what makes inductions good.
Goodman’s theory of entrenchment is similar to what Hume had in mind with custom.
there are also other questions associated with the grue paradox.
How can we know, if we can, which inductions are the good ones?
an epistemic question.
Why do we believe some inductions but not others? a Psychological question.
I recommend the following Authors on the subject of Grue:
Joseph Ullian
Frank Jackson
Sydney Shoemaker
Does that commit you to something like Russell’s correspondence theory of truth…?
Not at all.
A verificationist may well adhere to the some, more updated version of a correspondence theory of truth (a` la Michael Dummett and Hilary Putnam), but also to a deflationary theory of truth (W.V.O. Quine), pragmatic theory of truth (C.S. Peirce, William James, etc.), disquotation theory (Tarski) , and a redundancy theory (Frege).
Of course, I am sure you have difficulties with any correspondence theory of truth…
It was pointed out to me by Dr. Fisher that my initial post contains a glaring blunder (my phrase, not hers). In the last clause of the last sentence of the penultimate paragraph I state that proposition (2), viz., gruesome emeralds examined before t are green, but blue in the instance they are not so examined, is not in principle “verifiable”.
This is patently wrong. For (2) is certainly verifiable, and all that is needed to confirm this statement is to discover an instance of a blue emerald after t, say, after 3000 A.D.
This, however, is- I believe- a minor oversight on my part and in no way detracts from the analysis.
I don’t see how a syntactical analysis can help, since ‘grue’ and ‘green’ are syntactically isomorphic. (A grue-speaker might just as well analyse our ‘green’ claims as conjunctions of a verified grue claim and an unverified bleen claim.)
The real insight is in your claim that “the color of gruesome emeralds vary according to the time of first examination“. This is, in effect, to suggest there is something defective about ‘grue’ as a predicate — it doesn’t really denote a qualitative property. Note that Goodman’s syntactic counter to the ‘qualitative’ response can in turn be countered, as I explain in my post: Proving Grue’s Temporality.
Richard,
First allow me to thank you for your response.
Now, in the eighth paragraph of my post, if you recall, I addressed the syntatically isomorphic nature of “grue” and “green” and other like color predicates.
Remember that Goodman himself says, ‘[P]redictions based on some regularities are valid while predictions based on other regularities are not.’ He says this in response to Hume, who asserts that regularities habituate us to make and expect the manifestation of certain future predictions. In short, Goodman criticized Hume for his “imprecision”. Thus, the purpose of the post is to- if only provisionally- delineate which regularities are appropriately habituating and which are not.
My analysis focuses on the composition of conjunctive, grue-like propositions, e.g., “all gruesome emeralds examined before t are green, but blue in the instance they are not so examined,” and attempts to show how they are formally identical to other, less problematical conjunctive propositions (like the chemical propositions in my example above). We find that the constituent conjuncts of grue-like propositions are not well-verified, whereas the conjuncts in, say, chemical propositions are well-verified.
Hence, the well-verified conjuncts are properly habituating, not the unverified conjuncts. Think of my post as a Humean response to Goodman’s challenge.
Lastly, I should say that your proposed solution to Goodman’s riddle has the appeal of common sense, though, I think, only to “green” and “blue” speakers. If we operated within the linguistic world of gruesome speakers, that is, if “grue” and “bleen” were linguistic primitives, then I do not see the difficulty in identifying emeralds as being either “grue” or “bleen”. The real question is what epistemic context must obtain in order for one to be a “grue” and “bleen” speaker? I think that is what Hume would ask of Goodman.
Thanks again,
Aaron
Aaron, I think you have missed my criticism. Let me try again.
When you say, “all gruesome emeralds examined before t are green, but blue in the instance they are not so examined,” I take it the grue-speaker will say you misrepresent as conjunctive what for them is really an atomic proposition, namely: “all emeralds are grue”.
Conversely, when we say “all emeralds are green”, the grue-speaker will analyse this as the conjunctive claim: “all greensome emeralds examined before t are grue, but bleen in the instance they are not so examined.” They may then mimic your other claims, e.g. by noting that the first conjunct is well enough verified but the latter is not, etc.
So I do not see how your proposal gets us anywhere.
(Aside, in my linked post I demonstrate that green and blue must be epistemically primitive even for the grue-speaker to whom they’re not linguistically primitive. But I don’t wish to take over your thread here, so if you wish to clarify which part of my argument you disagree with, you’re very welcome to do so in the comments to my post.)
but what if you define “green” as “green if observed before t and green if observed after t”, then if you analyse it into its constitutional parts, it is no more verified than “grue” (I am referring to your example with ethanol)