Nelson Goodman's Entrenchment Theory Howard Kahane Philosophy of Science, Vol. 32, No. 3/4. (Jul. - Oct., 1965), pp. 377-383. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196507%2F10%2932%3A3%2F4%3C377%3ANGET%3E2.0.CO%3B2-F Philosophy of Science is currently published by The University of Chicago Press.
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DISCUSSION: NELSON GOODMAN'S ENTRENCHmNT THEORY* HOWARD KAHANE University of Icansas
One of the fundamental problems in the fields of inductive logic and the philosophy of science is the one concerning inferences or projections containing so-called ct grue-like" or "pathological" predicates. This problem was first put into sharp focus by Nelson Goodman, who called it the "new riddle of i n d u ~ t i o n . " ~ Goodman has shown that the few attempts by others to solve this problem (which appear in the literature) are not a d e q ~ a t e .However, ~ very little has been written concerning Goodman's own attempt to solve the problem, namely his theory of entrenchment. The purpose of this article is to show that Goodman's entrenchment theory also is inadequate as a solution to the new riddle of induction. I shall try to do this by presenting two kinds of counterexamples to the entrenchment theory: one kind illustrating a general objection to the theory as a whole; the other kind, specific objections to particular (vital) parts of the theory.
1, The Grue Problem. As a reminder of the problem Goodman's entrenchment theory is designed to solve, consider the following example. Suppose one-hundred emeralds, all of them green, are observed for color. This would usually be considered good evidence for the hypothesis (H-I): "All emeralds are green." But now a new term, "grue," is introduced, referring to all things examined for color before a particular time t (say the present time) which are green, and to other things just in case they are blue. Then each of the one-hundred examined emeralds will be grue, as well as green, so that there will be just as much evidence for the hypothesis (H-2): cc All emeralds are grue," which predicts that all emeralds observed in the future will be grue, and thus blue, as for the hypothesis (H-I), which predicts that all emeralds observed in the future will be green. But no one would accept (H-2), no matter how much evidence has been found in its favor. The problem is to provide rules which eliminate all grue-like illegitimate inferences or projections such as (H-2), without at the same time eliminating any green-like legitimate ones such as (H-I). 2. Goodman's Solution. Briefly, Goodman's solution to the new riddle of induction depends upon the use of a kind of information not generally appealed to, namely the recovd of past projections of predicates in competing hypotheses. I n the case in question, the competing hypotheses are (H-I) and (H-2), and the pertinent predicates are "grue" and "green." Examination of the record of past projections will show that cc green" has been projected very many more times than has "grue." (That is, it has appeared in very many more different hypotheses, generalizations, etc., than has "grue.") I n Goodman's terminology, "green" is said to be much better entrenched
*
Received, May, 1963. For Goodman's exposition of the problem, see his article [4] and book [5]. Of interest also is Wesley Salmon's article [S]. For example, Rudolf Carnap's solution, appearing in [3], was shown to be inadequate by Goodman in [6], and the solution proposed by Barker and .4chinstein in [I] was shown to be inadequate by Goodman in [7].
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than "grue," and he eliminates (H-2) by means of an entrenchment rule (rule one) which rejects all hypotheses which conflict with the projection of other hypotheses having much better entrenched predicates. Goodman introduces a second entrenchment rule to eliminate unwanted projections such as (H-3): "All emeralds are grund" (where something is grund if it is examined before time t and green or not so examined and round). According to Goodman's second entrenchment rule A projected hypothesis with an ill-entrenched consequent is to be rejected if it conflicts with another hypothesis (I) that has the same antecedent and a much better entrenched consequent, and (2) that is either ( a ) both violated [disconfirmed] and supported [confirmed] or (b) neither ([5], pp. 101-102).
Rule two eliminates (H-3) because projection of that hypothesis conflicts, for instance, with the projection of the hypothesis "All emeralds are irregular in shape," which has been both supported and violated. Notice that, unlike rule one, rule two allows the elimination of hypotheses because of conflict with other hypotheses which then~selves could not have been projected. Finally, Goodman's third entrenchment rule is designed to eliminate unwanted hypotheses in which the grue-like terms appear in the antecedent rather than the consequent of the statement of the hypothesis. Consider the hypothesis (H-4): "All emerubies are green," where the term "emeruby" applies to emeralds examined for color before t and to rubies not so examined; and we suppose that all emeralds examined up to time t are green, but no rubies have been examined for color. Goodman's third rule is meant to eliminate (H-4) and similar hypotheses which have ill entrenched antecedents. T h e third entrenchment rule
... eliminates
a projected hypothesis when some other hypothesis with the same consequent could have been projected, and the antecedent A of the original hypothesis "disagrees" with the much better entrenched antecedent A' of the other hypothesis in the following way: although among things to which the common consequent has been determined to apply, A applies only to those that A' applies to, nevertheless A applies to some other things that A' does not apply to ([5], p. 104).
3. Critical Examination of the Three Entrenchment Rules. I think it is fairly easy to demonstrate that the specific entrenchment rules proposed by Goodman fail to do the job they were designed to do, thus demonstrating the inadequacy of the entrenchment theory as a whole.
( I ) Objection to the third ent~enchmefztrule. T h e seriousness of the grue problem arises in part from the fact that use of the usual inductive principles seems to enable us to prove concerning any given entity not yet examined for a particular property both that it has, and that it does not have, that property. (For example, they seem to allow us to conclude both that all not-yet-examined emeralds are green, and that they are not-green (blue), by means of hypotheses (H-1) and (H-2) respectively.) T h e purpose of the entrenchment theory is to eliminate such absurd consequences, but the following examples show that even if the entrenchment theory is adopted, the unwelcome results still can be obtained. Suppose (as before) that all emeralds so far examined for color are green, but that no rubies have been examined for color. Now let the term "A-emeruby" apply to all emerubies and also to a particular old shoe, A, examined for color and found to be green. Then the projection (H-5): "All A-emerubies are green," exactly the kind of
projection that entrenchment rule three was designed to eliminate, is not eliminated by that rule (or by any other entrenchment rule). It is not eliminated by rule three because there is no projectible hypothesis with which (H-5) 'disagrees' in the proper way. And, of course, we can infer from (H-5) that all rubies examined in the future will be found to be green. (And since rule three fails to eliminate (H-5), it also fails to eliminate the very hypothesis it was specifically designed to eliminate, namely the hypothesis (H-4), because (H-4) follows as a logical consequence of (H-5).) We can also infer that these rubies will be found to be not-preen bv the verv same " method. Suppose all roses so far examined for color are red, and a particular old shoe, B, is also observed to be red. Then the projection (H-6): "All B-rosebies are red," where "B-roseby" applies to all roses, all rubies, and old shoe B, is not eliminated by rule three (or any other rule of entrenchment). But of course we can conclude from (H-6) that all rubies examined in the future will be red, and thus not-green, contradicting the conclusion obtained from (H-5) that such rubies will be green. In general, we can prove in the same way that anything not already examined for a particular property both does, and does not have, that property. Thus the third entrenchment rule, which is supposed to remove this kind of trouble by eliminating the grue-like projections causing the difficulty, is seen to be practically useless.
(2) Background Izypotheses. I t may be suggested that perhaps the failure of entrenchment rule three to eliminate the projections which it was designed to eliminate is not fatal to the entrenchment theory, since these projections may be eliminated because of conflict with so-called "background" or "higher level" hypotheses. But this suggestion is not satisfactory. First, there are cases in which pertinent background information is not avaliable. (Perhaps this is the case with respect to (H-4).) And second, whenever legitimate background hypotheses are available,grue-like background hypotheses are also available to counteract their force, and it can be shown in the same way as for (H-4) that entrenchment rule three fails to eliminate pertinent grue-like background hypotheses. Goodman himself is well aware that the grue-like background hypotheses must be eliminated before background information can be utilized. But he erroneously assumes that they are eliminated by the three rules of entrenchment. One of his examples concerning the use of background information (in [5], pp. 109-111) is the following. Suppose that several marbles from a bag, B, of marbles in a stack, S , of bags of marbles, are examined and found to be red. This supports the hypothesis (H-7): "All the marbles in bag B are red." Then, if higher level information is obtained to the effect that other bags of marbles in stack S are uniform in color, supporting the background hypothesis "Every bagful of marbles in stack S is uniform in color," the credibility of (H-7) is increased. But suppose background information is obtained to the effect that all the naval fleets of the world are uniform in color, supporting the higher level projection (H-8): "All bagleets are uniform in color" (where something is a bagleet if it is either a naval fleet or bag B of marbles). In this case, obviously, the grue-like background hypothesis (H-8) does not increase the projectibility of (H-7). Goodman believes that the entrenchment theory works satisfactorily in this case, because he believes that the grue-like background hypothesis (H-8) is eliminated by entrenchment rule three. But he is mistaken on this point, for just as entrenchment rule three fails to eliminate grue-like projections on a lower level, so it also fails to do so on a higher level. (H-8) is not eliminated by entrenchment rule three because it follows as a logical consequence of the hypothesis "All 2-bagleets are uniform in
color" (where "2-bagleet" applies to all bagleets, and also to zig A, a particular helter-skelter selection of marbles, all observed to be red), which is not eliminated by the third entrenchment rule. Clearly, the failure of entrenchment rule three to eliminate hypotheses with grue-like antecedents on a given level cannot be overcome by appeal to hypotheses on some higher level if rule three is unable to eliminate the background hypotheses on that higher level which contain grue-like antecedents. And, as has just been shown, it is unable to do so.
(3) Objection to the first and second entrenchment rules. Entrenchment rules one and two both make use of the notion of conjict between hypotheses. They rule out the projection of an hypothesis only if it conflicts with the projection of an hypothesis with better entrenched predicates. T h e main objection to the first two entrenchment rules is simply that there seems to be no reasonable way to interpret the notion of conflict so that entrenchment rules one and two eliminate the projection of all and only those hypotheses they were designed to eliminate. Intuitively, it seems reasonable to suppose that two projections conflict if there is some entity which cannot satisfy both projections. For example, intuitively, it is assumed that (H-1): "All emeralds are green," and (N-2): "All emeralds are grue" conflict because it is believed that an emerald examined after time t cannot be both green and grue (in this case blue). T h e difficulty is with the exact nature of this belief, as is shown below. Coodnlan himself has not provided a satisfactory answer to this question. His only clue to his own thoughts on the matter is his remark that
... In saying these projections [(EX-I) and (H-2)] thus conflict we are indeed assurnitzg that there is some unexamined emerald to which on!y one of the two consequents' predicates applies ... ([5], pp. 94-95, italics mine.) But this only raises the question as towhen one can (and cannot) make such an assumption, a question which Goodman (in his writings) fails to answer, or even to raise. i. Three plausible answers to this question come to mind. First, conflict can be assumed for purely logical reasons. For example, we can assume that projection of the hypothesis "All emeralds are non-green" conflicts with the projection of (H-1), because logic precludes the possibility of an emerald being both green and non-green. Clearly, an assumption of this kind is acceptable, but if the entrenchment theory is to function properly, other reasons must be made available for the assumption of conflict, since (H-2), and most other unwanted hypotheses, cannot be eliminated in this way. Second, one might appeal to infornaation obtained via other inductive generalizations. For example, one might conclude that an emerald cannot be both green and blue because of an inductive inference such as "All green things are non-blue," for which there are innumerable confirming instances. But unfortunately, this won't do, because in every such case, a grue-like inference, equally well confirmed but with just the opposite implications, can be presented. For instance, the effect of "All green things are non-blue" can be counteracted by an equally well confirmed grue-like hypothesis such as "All green things are grue." Clearly, conflict cannot be determined by appeal to other inductive inferences. Finally, one might appeal to the meanings of terms used as consequent predicates. For example, onc might claim that (H-1) and (H-2) conflict because if something is grue after time t then it is blue, and it follows from the meanings of the terms "blue" and "green" that if something is blue it cannot be green. My own personal inclination
is to accept this line of reasoning, but for many philosophers it is forbidden. In particular, Goodman cannot accept it, since he denies the validity of the analyticsynthetic distinction, and it is only by means of that distinction that one can know without inductive evidence that if something is blue it cannot be green. ii. If the analytic-synthetic distinction is denied, and if other inductive inferences cannot be appealed to, then only logical information remains. But as already stated, there is no logical reason for assuming that the projection of (H-2) conflicts with that of (H-1), so if analytic truths are rejected, then (H-2) is not eliminated by the entrenchment theory. (The same is true for practically all of the unwanted hypotheses similar to (H-2).) If Goodman still claims that his entrenchment rules one and two do work satisfactorily without use of the analytic-synthetic distinction, it is up to him to show exactly how they do so. Specifically, he must provide a satisfactory definition of "conflict" not making use of analyticity, something I feel confident he cannot do. iii. But the difficulty confronting the entrenchment theory on this point is not due solely to the rejection of the analytic-synthetic distinction.-Even if analytic truths are accepted, no criterion of conflict seems likely which will enable entrenchment rules one and two to eliminate just the right class of hypotheses. Consider the hypothesis (H-9): "All emeralds are L-green" (where something is L-green if it is either examined before time t and green or not so examined and one ill-entrenched narrow shade of light green). Presumably, this unacceptable grue-like proiection is to be eliminated bv entrenchment rule one because of conflict with an " hypothesis such as (H-1), but even acceptance of the analytic-synthetic distinction fails to yield this result, for it does not follow from the meanings of the terms "green" and "L-green" that an emerald examined after time t cannot be both " green and L-green" (because the extensions of these two terms overlap). Consequently, there is no conflict between (H-1) and (H-9), and the latter is not eliminated by entrenchment rules one and two. (There are definitions of "conflict" which do eliminate (H-9) via entrenchment rules one and two, but they are all unsatisfactory. For example, "conflict" can be defined so that two hypotheses conflict if they have different consequents, P and (3, and the extension of P is a subclass of the extension of Q, or vice versa. The difficulty with this definition is that it is much too strong, so that its adoption would eliminate almost all projections, good or bad, utilizing new predicates in a field where other predicates are already well established. Consider projections utilizing color terms concerning, say, the color of emeralds, and assume for the moment that there is no well entrenched narrow color shade (such as emerald green) covering the color of all emeralds observed so far (so that hypotheses such as "All emeralds are emerald green" are not projectible). Then the hypothesis "All emeralds are E-green" (where "E-green" is a new, and thus ill-entrenched, color predicate covering the color span into which all emeralds so far observed fall), would be a perfectly acceptable hypothesis. But if the definition of conflict just given is employed, the projection "All emeralds are E-green" would be eliminated by entrenchment rule one because of conflict with (H-1): "All emeralds are green." My conclusion is that until a satisfactory definition of "conflict" is presented (an unlikely event), entrenchment rules one and two must be rejected. A
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4. General Objections to the Entrenchment Theory. Several objections of a more general nature can be raised against the entrenchment theory. Two are considered here.
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( I ) Introduction of terms in new jields. The obvious question to ask concerning the entrenchment theory as a whole is why or how just the right predicates happen to have become well entrenched. Goodman's reply is that just the right predicates have become well entrenched simply because the well entrenched predicates are the right ones. In other words, it is the fact that they are well entrenched which makes them right. It seems to me that this answer is unsatisfactory. There are many possible cases where the "wrong" predicates can become well entrenched, so that being well entrenched cannot be our criterion of rightness. In general, such cases arise whenever a completely new area is developed in which there are no well entrenched predicates. For example, consider the two projections (H-10): "All radium is radioactive," and (H-11): "All radium is radiotractive," where something is radiotractive if it is either examined for radioactivity before t and radioactive, or not so examined and not radioactive. Clearly, (H-11) is not acceptable (even though supported and unviolated), and the entrenchment theory does seem to rule out its present projection in favor of(H-10). But suppose weconsider the timewhen radioactivity hadjust been discovered. At that time the entrenchment theory was neutral with respect to (H-10) and (H-11), not eliminating either hypothesis, because at that time the terms "radioactive" and "radiotractive" had equal (namely zero) entrenchment ratings. But surely (H-11) was unacceptable then, just as it is now, despite the fact that the term "radioactive" had an entrenchment rating of Further, suppose that for some reason or other (H-11) had been projected at that time instead of (H-lo), so that "radiotractive" had become much better entrenched than "radioactive." Then the entrenchment theory would not have been neutral with respect to (H-10) and (PI-ll), rather it would have eliminated (H-10) in favor of (H-11). But surely this would have been an unreasonable result. I think that examples such as this one show that it is not entrenchment of predicates which is the criterion of projectibility. KO matter how well entrenched a predicate such as "radiotractive" (or "grue") may become, it still will not be projectible, whereas predicates such as "radioactive" (and "green") are projectible (under suitable conditions) from the very first.4 (2) The ~equired dzTerence in entrenchment. The three entrenchment rules are supposed to eliminate the projection of grue-like predicates when such projections conflict (or disagree) with the projection of better entrenched predicates. But how much better entrenched must one predicate be than another for the rules to be operative ? In [5], p. 96, Goodman states that the difference in entrenchment must be "great enough to be obvious," but it can easily be shown that this is not satisfactory. For The claim that (H-11) would have been eliminated by the entrenchment theory even then because parent predicates of "radioactive" mere better entrenched than parent predicates of "radiotractive" cannot be accepted unless and until proof is provided in terms of lists of parent predicates for both predicates, showing that the set of parent predicates of "radioactive" was better entrenched than the comparable set for "radiotractive." (Concerning parent predicates, see [ 5 ] , pp. 105-106.) This kind of counterexample to the entrenchment theory has been objected to because such examples concern possible, but not actual, cases. The claim is that the theory need only describe actual projective practice. This seems wrong to me, since the whole grue problem concerns possible, but not actual, cases; no on has actually projected hypotheses such as (H-2). Surely, a theory of inference must be able to handle possible as well as actual cases. (See [ 5 ] , pp. 79-80.)
example, although the difference in entrenchment between terms such as "green," "blue," etc., and perfectly good English color words such as "magenta," "turquoise," cc carmine lake," salmon," "dark claret brown," etc., is great enough to be obvious, we don't want to eliminate the projection of such color terms simply because of conflict with the projection of terms such as "green," "red," etc. For example, we don't want to reject the hypothesis (H-12): "All turquoise stones are turquoise in color" simply because of a difference in entrenchment ratings between "green" and "turquoise." But if the difference in entrenchment only has to be great enough to be obvious, then (H-12) will be eliminated by entrenchment rule two because of conflict with the hypothesis "All turquoise stones are green," since the latter is both supported and violated. Surely this is unacceptable.
5. Conclusion. My general conclusion is, first, that the three entrenchment rules proposed by Goodman are inadequate to solve the grue problem, and second, that Goodman's view that entrenchment is the important clue to a satisfactory solution is incorrect. The new riddle of induction remains unsolved.
REFERENCES
[I] ACHINSTEIN, Peter (with Stephen Barker), "On the New Riddle of Induction," Philosophical Review, Vol. 69 (1960,) pp. 511-522. [2] BARKER, Stephen (with Peter Achinstein), "On the New Riddle of Induction," Philosophical Review, Vol. 69, (1960), pp. 511-522. Rudolf, "On the Application of Inductive Logic," Philosophy and Phenomenological [3] CARNAP, Research, Vol. 8 (1947-48), pp. 133-147. [4] GOODMAN, Nelson, "A Query on Confirmation," Jouvnal of Philosophy, Vol. 43 (1946), pp. 383-385. [5] GOODMAN, Nelson, Fact, Fiction, and Forecast, Harvard University Press, 1955. [q GOODMAN, Nelson, "On Infirmities of Confirmation Theory," Philosophy and Phenomenological Research, Vol. 8 (1947-48), pp. 149-151. [7] GOODMAN, Nelson, "Positionality and Pictures," Philosophical Review, Vol. 69 (1960), pp. 523-525.
[S] SALMON, Wesley, "On VindicatingInduction," Philosophy of Science, Vol. 30 (1963), pp. 252261.
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[Footnotes] 1
A Query on Confirmation Nelson Goodman The Journal of Philosophy, Vol. 43, No. 14. (Jul. 4, 1946), pp. 383-385. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819460704%2943%3A14%3C383%3AAQOC%3E2.0.CO%3B2-U 1
On Vindicating Induction Wesley C. Salmon Philosophy of Science, Vol. 30, No. 3. (Jul., 1963), pp. 252-261. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196307%2930%3A3%3C252%3AOVI%3E2.0.CO%3B2-6 2
On the Application of Inductive Logic Rudolf Carnap Philosophy and Phenomenological Research, Vol. 8, No. 1. (Sep., 1947), pp. 133-148. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28194709%298%3A1%3C133%3AOTAOIL%3E2.0.CO%3B2-Q 2
On Infirmities of Confirmation-Theory Nelson Goodman Philosophy and Phenomenological Research, Vol. 8, No. 1. (Sep., 1947), pp. 149-151. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28194709%298%3A1%3C149%3AOIOC%3E2.0.CO%3B2-5
NOTE: The reference numbering from the original has been maintained in this citation list.
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2
Positionality and Pictures Nelson Goodman The Philosophical Review, Vol. 69, No. 4. (Oct., 1960), pp. 523-525. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28196010%2969%3A4%3C523%3APAP%3E2.0.CO%3B2-C
References 2
On the New Riddle of Induction S. F. Barker; Peter Achinstein The Philosophical Review, Vol. 69, No. 4. (Oct., 1960), pp. 511-522. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28196010%2969%3A4%3C511%3AOTNROI%3E2.0.CO%3B2-T 3
On the Application of Inductive Logic Rudolf Carnap Philosophy and Phenomenological Research, Vol. 8, No. 1. (Sep., 1947), pp. 133-148. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28194709%298%3A1%3C133%3AOTAOIL%3E2.0.CO%3B2-Q 4
A Query on Confirmation Nelson Goodman The Journal of Philosophy, Vol. 43, No. 14. (Jul. 4, 1946), pp. 383-385. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819460704%2943%3A14%3C383%3AAQOC%3E2.0.CO%3B2-U 6
On Infirmities of Confirmation-Theory Nelson Goodman Philosophy and Phenomenological Research, Vol. 8, No. 1. (Sep., 1947), pp. 149-151. Stable URL: http://links.jstor.org/sici?sici=0031-8205%28194709%298%3A1%3C149%3AOIOC%3E2.0.CO%3B2-5
NOTE: The reference numbering from the original has been maintained in this citation list.
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7
Positionality and Pictures Nelson Goodman The Philosophical Review, Vol. 69, No. 4. (Oct., 1960), pp. 523-525. Stable URL: http://links.jstor.org/sici?sici=0031-8108%28196010%2969%3A4%3C523%3APAP%3E2.0.CO%3B2-C 8
On Vindicating Induction Wesley C. Salmon Philosophy of Science, Vol. 30, No. 3. (Jul., 1963), pp. 252-261. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196307%2930%3A3%3C252%3AOVI%3E2.0.CO%3B2-6
NOTE: The reference numbering from the original has been maintained in this citation list.
