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.