Whewell's Consilience of Inductions--An Evaluation Author(S): Menachem Fisch Source: Philosophy of Science, Vol

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Whewell's Consilience of Inductions--An Evaluation Author(s): Menachem Fisch Source: Philosophy of Science, Vol. 52, No. 2 (Jun., 1985), pp. 239-255 Published by: The University of Chicago Press on behalf of the Philosophy of Science Association Stable URL: http://www.jstor.org/stable/187509 Accessed: 25-07-2015 10:42 UTC

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This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions WHEWELL'S CONSILIENCE OF INDUCTIONS- AN EVALUATION*

MENACHEM FISCHt

Institute for the History and Philosophy of Science and Ideas Tel Aviv University

The paper attempts to elucidate and evaluate William Whewell's notion of a "consilience of inductions." In section I Whewellian consilience is defined and shown to differ considerably from what latter-day writers talk about when they use the term. In section II a primary analysis of consilience is shown to yield two types of consilient processes, one in which one of the lower-level laws undergoes a conceptual change (the case aptly discussed in Butts [1977]), and one in which the explanatory theory undergoes conceptual "stretching." In section III both consilient cases are compared to the non-consilient case in reference to L. J. Cohen's method of relevant variables. In section IV we examine the test procedures of the theory in all three cases, and it is shown that in the event of genuine consilience (consilience of the second type) a theory acquires ex- traordinarily high support. In the final section something is said of the short- comings of standard Bayesian confirmation theories that are highlighted by Whewellian consilience.

"Consilience of Inductions" was the name given by William Whewell in his celebrated Philosophy of the Inductive Sciences' to situations in which a causal explanatory theory is successfully conjectured to explain a known law (or laws) of phenomena, and is then found, without further

*Received January 1984; revised March 1984. tThis paper was written during a year of research at The Queen's College, Oxford. I wish to thank L. Jonathan Cohen, Prof. Mary B. Hesse, Prof. Joseph Agassi, and an anonymous referee for their helpful criticism of an earlier version of this paper. 'Whewell (1847, 2: pp. 65f., 77-78). The prediction of results, even of the same kind as those which have been observed, in new cases, is a proof of real success in our inductive processes. . . . But the evidence in favour of our induction is of a much higher and more forcible character when it enables us to explain and determine cases of a kind different from those which were contemplated in the formation of our hypothesis. The instances in which this has oc- cured, indeed, impress us with a conviction that the truth of our hypothesis is certain. No accident could give rise to such extraordinary coincidence. No false supposition could, after being adjusted to one class of phenomena exactly represent a different class, when the agreement was unforeseen and uncontemplated. That rules springing from remote and unconnected quarters should thus leap to the same point where truth resides. . . . And as I shall have occasion to refer to this peculiar feature in their evidence, I will take the liberty of describing it by a particular phrase; and will term it the Consilience of Inductions. (Whewell 1847, 2: p. 65)

Philosophy of Science, 52 (1985) pp. 239-255. Copyright (C 1985 by the Philosophy of Science Association.

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This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions 240 MENACHEM FISCH adjustment,to provide an equally successful causal explanation of another law of phenomena, one of a kind different from that contemplated in the formation of the theory. This "unforeseen and uncontemplated" agreement in which "rules springing from remote and unconnected quarters should thus leap to the same point,"2 was for Whewell the hallmark of certitude;his central "evaluative criterion"-as John Losee puts it (1983, p. 113)3 -for the truth of scientific theory. Yet Whewell never explained how or why consilience should lend a theory such a "stamp of truth" (1847, 2: p. 66). In fact he never put it forward as a derivative of his philosophy of science at all (and indeed it is not). Consilience was presented by him as a feature of (undisputedly) true theories, which is disclosed by the history of science:

2Whewell (1847, 2: p. 65). This interpretationof Whewellian consilience is considerably narrower than-though by no means contrary to-interpretations of some Whewell com- mentators. In Butts (1968, p. 18) consilience is described merely as the requirement that "a good hypothesis explains more than that which it was first introduced to explain." In his 1977, pp. 74-75, although more detailed, the description of consilience still glosses over the crucial point of the two laws finally explained, being of quite different kinds at the point when the theory is suggested. As if to illustrate my point the word "different" is omitted from his citing of Whewell's aphorism XIV on page 74 (the same mistake is made in Laudan [1971, p. 369]). In fact, according to Butts's analysis consilience can only be talked of when the difference is apparent, since the domains of evidence of the two laws have to be found eventually to overlap. (His account of consilience will be dealt with in more detail below.) Larry Laudan, in his 1971, p. 37 1f., suggests that what Whewell called consilience was either one of three cases; the first is: "When a hypothesis is capable of explaining two (or more) known classes of facts (or laws)"; the second roughly coincides with the account suggested here; the third is: "When an hypothesis can successfully predict or explain the occurrence of phenomena which, on the basis of our background knowledge, we would not have expected to occur." Mary B. Hesse, in her 1974, p. 206, follows Laudan ver- batim. Neither Laudan nor Hesse provide references to Whewell's work to support the claim that he had regarded their first and third cases as consilient. I would contest that the first case is anything other than (good-see n. 4 below) straightforward Whewellian induction characteristic of many of Whewell's own examples of false and non-consilient hypotheses (Ptolemy's epicycles, the horror vacui theory, etc.). As to their third case, interesting as it is, it is not mere surprise that lends a theory consilient support, it is the surprise upon finding different classes of phenomena accounted for by the same theory (i.e., their second case). Thus, only if the unforeseen phenomena predicted by the theory are of a different kind than those contemplated in its forming would we have consilience in Whewell's sense and that would be a variation on their second case. However, since it is not the aim of this paper to decide what Whewell took to be consilience, but ratherto decide whether or not what I take to be Whewell's idea of consilience holds any water; and since what I take to be Whewell's idea of consilience is not argued by Whewell's critics (what would be argued is that it is his only idea of consilience), I wish not to take this exegetical question any further here. 3Losee (1983, pt 113). Losee, however, goes on to talk of consilience rather loosely, describing it as "a conceptual integration in which less inclusive generalizations are incorporated into a more inclusive theory" (p. 114), which is again not more than what Whewell would call an ordinary induction.

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. . .we have a criterion of [the hypothesis'] reality, which has never yet been produced in favour of falsehood. (1858, p. 90; 1847, 2: pp. 67-68)4 The nearest he ever came to an explanation of why a consilient theory should be regarded as true was to offer seemingly self-evident meta- phorical examples (such as two decipherers working on different texts and arriving at the same alphabet5). Undoubtedly the historical record itself has since refuted his claim (that consilience is the mark of truth); his own paradigmatic examples-Newton's universal gravity and Huy- gen's and Fresnel's undulatory theory of light-have long been replaced. (And as for the metaphor of the two decipherers, rather than clarify the case, it seems itself in need of an explanation). Nonetheless, many would share the intuition that although consilience cannot be regarded as a mark of truth, one does (and should) feel more confident in a consilient theory (one that is found, surprisingly, to explain a second law of phenomena

4Whewell's philosophy of science, based on what he called "The Fundamental Antithesis of Philosophy" (1847, 1: p. 16f.) and (1847, 2: Appendix-Essay V), gives rise to a meth- odology of good science, which in Whewellian terms consists of well "explicated" con- ceptions successfully applied so as to "colligate" well "decomposed" phenomena. But for science to be good is not enough to ensure its being true. Truth is accommodated for by Whewell by means of two "tests" of hypotheses-consilience and the tendency towards simplicity-taken by him to be the marks of truth (1847, 2: 60f.). Many have conflated what Whewell held as good science with what he held to be true science mainly because Whewell insisted that in the process of "explicating" concepts necessary truths can be discovered and recognized; from which follows that good Whewellian science is not only true but necessarily true. This stems, I believe, from a fundamental misunderstanding of Whewell's notion of necessity. It is wrongly taken as meaning "empirical" necessity, that is, necessity of all possible (empirical) worlds. What Whewell really meant, I believe, was semantic or conceptual necessity, in the sense in which axioms of a "Euclideanized" system are necessarily true of the basic idea they articulate, and yet if they are found to apply to the world without, this truth would be contingent. (And indeed as regards the "necessarily" true laws of mechanics, Whewell admits that God could have created the world differently (1836, pp. 211-12). In any event, for those who hold that Whewell really talked of necessary truths in the strong in-all-possible-worlds sense, consilience would seem superfluous as a test of it for it is definitely an empirical affair. (Butts is thus forced to talk to Whewell's "two theories of induction" [1973], and Laudan actually accuses him of inconsistency [1971, p. 383].) By and large, I believe that Whewell's own philosophy of science has been unjustly underestimated both because of lack of emphasis on his "fundamental antithesis" and a misinterpretation of his notion of necessity. I have dealt with Whewell's complex theory of truth in my forthcoming article. This essay, however, attempts to evaluate "Whewellian" consilient situations against the backdrop of contempo- rary theories of support, and not against that of Whewell's own theory of science. 'Whewell (1860, pp. 274-75). For a discussion of the long pedigree of this analogy, see Laudan (1971, pp. 378-79, n.25). Laudan, however, fails to notice that Whewell's concept of an interpretation is very different from that of his seventeenth-century prede- cessors: whereas for them meaning was to be found within the text, Whewell followed Kant in maintaining that it was to be superimposed upon it; meaning was read into the text rather than out of it.

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions 242 MENACHEM FISCH not contemplated in its formation) than in a non-consilient theory (one that was initially designed to explain both laws). It is to the examination of this intuition that this essay addresses itself. We shall wish to examine two interrelated questions: (1) Does the fact that a theory undergoes a consilient process, as outlined above, in itself lend it support (i.e., would the theory have been less supported had it been applied to both laws in a non-consilient process), and if so why? That is, does our intuition mirror some (yet unarticulated) merit of our theory, or does it merely reflect the pleasant surprise upon having luckily guessed right? (2) Does the elucidation of consilient support require reference to pragmaticconsiderations such as time dependence, intended scopes, etc. ? Yet before turning to the elucidation and evaluation of consilience, it is importantto point out that the description of it differs considerably from what latter-day writers talk about when they use the same term. (This is a question quite different from the exegetical problem of deciding what Whewell meant by "the consilience of inductions" referred to briefly in note 2 above.) A short exposition of the problems taken up in the name of consilience in recent literature will serve two purposes: First, to emphasize that consilience, in what I take to be the original Whewellian sense, has not been adequately explored thus the reason for the present paper; and secondly, to highlight the fact that our proposed elucidation of it can be made to bear upon some of the other problems mistakenly discussed in its name. The problem dealt with by William Kneale (1952, p. 106f.) under the heading, "The Consilience of Primary Inductions," is that of explaining the apparentrise in the probabilities of "primaryinductions," L1, L2, L3, . by virtue of their explanation by the same "transcendent" (i.e., explanatory) theory. Roughly speaking, the setting is that in which Whewellian consilience can occur namely, lower-level generalizations "colligated" and explained by a higher level theory. However, Whewell was concerned with-to use Kneale's non-Whewellian terms-the rise in probability of the theory, not of the laws explained by it, and only in the special case in which the theory was (surprisingly) found to apply to another law, of a different kind, uncontemplated when the theory was devised. Whether or not these peculiar circumstances lend the theory extraordinarysupport, Kneale does not discuss. He treats the consilient and non-consilient on a par with each other. (Yet he claims, nevertheless, that his problem is suggested by Whewell's 1858.) Similarly, Mary B. Hesse's problem in her 1968 (taking up a point

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions WHEWELL'S CONSILIENCE OF INDUCTIONS 243 raised by H. Putnam in Schilpp [1963]) is to elucidate the fact that, "as- suming what Whewell called the 'consilience of inductions,' scientists do regard laws as better confirmed when they are consequences of theories than when there is only non-theoretical evidence available." This is ba- sically Kneale's problem, though (again) hardly Whewell's. 6 In his response (1968a) to Hesse's paper, L. J. Cohen talks of yet a different question he too associates it with Whewell's consilience that of explaining how the empirical evidence in support of one empirical generalization, L,, is rendered relevant, and even supporting, of another unrelated generalization, L2, in virtue of them both being explained by a higher-level theory. (This is also the point made in his 1968b, p. 70 and again, though with a different solution, in his 1970, p. 86f, and finally in his 1977, p. 157f. in connection with Lakatos's notion of progressive problem shifts). As in the Kneale-Hesse problem so in Cohen's, the focus is on the support bestowed upon the lower-level generalizations rather than upon the theory, and similarly the point central to Whewellian consilience regarding the question of the difference between applying a theory to designed and undesigned scopes is not taken up. In Hesse (1974, pp. 205-8) consilience is discussed once more; this time however as an attempt to recapitulate Whewell's original intention. His theory of induction and with it his notion of consilience are briefly sketched. (This may have been prompted by her exchange with Larry Laudan in The Monist [Hesse 1971; Laudan 1971] referred to in note 6.) Hesse's description of Whewellian consilience follows Laudan's. She correctly observes that Whewell's treatment of it is descriptive and in need of "backing up by cogent argument;" however the central point, that of the extraordinarysupport bestowed upon a theory found to apply to a surprisingly different law of phenomena, is brushed aside as obvious since the increase in a theory's confirmation is greater "the greater the initial improbability of the facts predicted" (p. 207). But surely this can be of no help in what I call consilience when what is unforeseen and improbable is not the second law itself, which is highly confirmed, but

6Curiously Laudan (1971, p. 391) claims that whereas Kneale does indeed discuss genuine Whewellian consilience, Mary B. Hesse does not. As far as I can tell, Kneale and Hesse discuss very similar if not identical problems neither of which falls under even Laudan's liberal interpretationof Whewellian consilience (see n. 2 above). Laudan's con- frontation with Hesse in the appendixes to Laudan (1971) fails to bring out any difference between Kneale's and Hesse's problems, nor to convince that Hesse's 1968 had any bear- ing on (my account of) Whewellian consilience. (This point is brought out even more forcefully in the light of Butts [1977], in which the Laudan-Hesse controversy is resolved against the backdrop of Butts's own interpretation of consilience. However, as I hope to show below, not only does Butts fail to point out genuine consilience [his treatment deals, as we shall see, with pseudo-consilient situations only], but also his confirmation theory falls short of being able to accommodate it adequately.)

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions 244 MENACHEM FISCH that the theory can explain it!7 And since Hesse agrees that such cases are (among others) genuinely consilient, she has not solved the problem. We conclude then that the questions taken up in the name of consilience by Kneale, Hesse, Cohen, Butts,8 and others, related as they are to Whewell's original notion, fail to tackle the intriguing issue lying at its core, namely, that of the difference in terms of a theory's support- between contemplating and not contemplating a well-supported generalization of a different kind found eventually to be adequately explained by the theory. This is the issue we take up here.

II To restate our first question more pointedly, we ask whether it is possible to find any nonsubjective difference between: (a) the nonconsilient case in which a theory is successfully conjectured to jointly explain two correlational generalizations each over a different class of phenomena; and (b) the consilient case in which the theory is successfully conjectured as an explanation of one such generalization, and it then surprisingly turns out to apply equally successfully to the other. Should our account of the merit of a theory turn on the increase gained in predictive and explanatory power alone, consilience in itself would clearly offer it no support since the increase in predictive and explanatory power is in both cases the same. The final state of knowledge in both (a) and (b) consists of the same theory applied to the same two generalizations. Therefore the difference between them, if at all, would have to lie in their case histories; that is, in the two different processes by which the theory arrived at its final state. Let us scrutinize this somewhat closer, and for the sake of clarity cast it in semi-formal garb. Let the two classes of phenomena be the Pl's and the P2's, and the correlational generalizations they are known to exhibit be respectively:

7This calls for some explanation. I do not contest the fact that if a theory T entails evidence E, then within Hesse's confirmation theory the increase in confirmation of T is correctly explicated in terms of the initial improbability of E. (It is easy to show within a Bayesian confirmation theory that P(T/E) o 1/PO(E)whenever T implies E.) I do oppose Bayesian confirmation theories in general, but that is not the point here. Consilience, as I hope to show in detail below, is a situation in which at a certain stage T is made to entail E, either by reformulating T or by reinterpreting one of the lower-level laws it is applied to. Bayesian confirmation theories accommodate for changes in the probability of T in the light of new evidence E only under the assumption that the relation between T and E remains unchanged throughout (in which case the smaller PO(E)the greater P(T/E)). Since this is not the case in consilient situations, and since in any case no improbable evidence is involved-for the lower-level laws are well confirmed prior to the suggestion of T-I do not believe that Hesse's move explains the rise in support of a theory undergoing consilience, or that her Bayesian confirmation theory is equipped to do so. (See also section V below.) 8Forreference to Butts (1977), see nn. 12 and 16 and section V below.

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L1: "All P1's possess propertyA" and L2: "All P2's possess property B' We lay no restrictions on the P's, on A or on B. The P's can be objects, processes, events, states of affairs, predicates, etc. Similarly, A and B can be observable features, dispositions, or structures expressed either qualitatively or quantitatively. The conjectured explanatory theory would always be presentable as a conditional of the form: T: "All C's possess properties H" where H designates the entire cluster (both conjecturedand already known) of features, dispositions, relations, mathematical correlations, etc., assumed of the C's. In the first and non-consilient case-in which T is conjectured as an explanation of both L1 and L2-it is assumedthat the P1's and the P2's are C's.9 What is conjectured and subsequently put to the test is that C's do indeed possess properties H which are the cause both of the A-ness of the P1's and of the B-ness of the P2's.10 (However, since T was construed from the very start as a causal explanation of L1 and L2, we will not be testing whether or not H causes A and B as much as whether or not C's do in fact possess properties H.) T acquires support by the fact

9In fact in many cases C will simply denote the joint class of P1's and P2's, and even if C denoted a wider kind to which the P's were assumed to belong, it would still be possible to state T as a conditional in which P1 P2 is the antecedent, and all additional features of C are accounted for in H. However, I prefer, even at the risk of seeming superfluous, to refer to the antecedent of T by means of separate notation because, as we shall see, it does not always retain the same referential meaning throughout the process. It is also interesting to note that P1 and P2 may even coincide referentially as in the following imaginary example. Let Pi and P2 both designate planets, and L1 and L2 Kepler's first two laws respectively. Let T be the theory that relates to each planet an inverse square force exerted on it by the sun which is proportional to its mass. Now, imagine it to be believed (as Kepler himself did) that the equal-areas-in-equal-times law derives from the stability, symmetry, and periodicity associated with their status as heavenly bodies, and that T is conjectured solely as an explanation of their elliptic path. Thus P2 would designate planets qua heavenly bodies, and P1 planets qua masses attracted by the sun. '?Although in what follows we shall talk loosely of A and B deriving from H, it will be assumed throughout that T is structured in a meaningful and nontrivial way. (Thus, where T is to be construed as

(x){(PIx V P2x) D [(PIx D Ax) (P2x D Bx)]} it would yield L1 and L2 trivially, although it would not count as either causal or explanatory.) We therefore take H to include as one of its conjuncts well-formed causes of A and B, or of the conditions that sustain them, or the impossibility of their negations, etc. Insofar as the matters discussed in this paper are concerned, the specific theory of causation employed is immaterial.

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions 246 MENACHEM FISCH that in varied circumstances, and for a variety of PI's and P2's, A and B are found to derive from H. (T of course could be supported by other favorable test results independent of L1 and L2-such as direct observa- tions of entities hypothesized in H. However, any support of T unrelated directly to L1 and L2 is of no significance to what follows.) An example of a non-consilient case would be the "Nebular Hypoth- esis" suggested by Laplace (Systeme du monde, Book 5, chap. 6). The hypothesis was offered as a causal explanation of the following well- confirmed laws: (a) all planets and satellites of the solar system revolve around the sun in the same direction; (b) all the orbits are almost in the same plane; and (c) all (observable) rotations are in the same direction. According to Laplace's hypothesis, the entire solar system originated in an "atmospheric" cloud rotating around the sun which in the course of contracting formed the planets by condensations in the plane of the solar equator. In a similar process the satellites were formed around the planets The P's, A and B, etc., would be the planets and satellites and the various features of their revolutions and rotations, the C's would be all the bodies of the solar system, and H would consist of all the features of such bodies represented as condensations of the conjectured spinning and contracting cloud. H is contrued so as to yield the various features of the solar system that the hypothesis was initially designed to explain. In the second and consilient case the process is somewhat different. T is initially conjectured and offered as an explanation of L1 only; that is, Pl's are assumed to be C's. T is then confirmed (as an explanation of L1) by testing H to yield A in varied circumstances and for a variety of PI's. When T is then forwarded as an explanation of L2 too, what will be tested (when in a variety of circumstances and for a variety of P2's, H is shown to yield B) is not so much T itself, but the claim that P2's are also C's. (A claim which as we remember is assumed in the non- consilient case.) However, one must differentiate furtherbetween two types of situation. T could be found to apply surprisingly to L2 either because T is reinterpreted so as to account for L2 (in L2's original meaning) or because L2 is reinterpreted and rendered explainable by T (according to T's original meaning). (In reality we would usually encounter a little of both but for the sake of clarity we shall proceed to analyze each case separately.) In the first case, P2 retains its original meaning (which is quite different from P1) and C is "stretched" and reinterpreted so as to include P2's (as for example when the theory of gravitation was conjectured to apply to all massy bodies not only to the sun and the planets, thus explaining, along- side Kepler's laws, also the law of free fall, the regularities of the tides, etc., without them changing their original meanings). L1 and L2 remain different laws of two distinct types of phenomena and are rendered similar

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions WHEWELL'S CONSILIENCE OF INDUCTIONS 247 only in the light of T."1In the second case, C retains its original meaning and P2 is reinterpretedso as to be included in C. (See, for example, the reinterpretationof Kepler's second law in the imaginary example in note 9 above. Such a move is also typical of explanations by reduction.) Here L2 is reconsidered, reinterpreted, and found similar to L1 irrespective of T (although probably inspired by T's success as an explanation of L1) thus paving the way for its explanation by T. In the second case, former categorical (or rather ontological) classification is reshuffled, in the first case it is not. 12 Let us now compare both of the consilient cases with the non-consilient case. At this stage no apparent difference can be pointed out between the non-consilient case and the first of the consilient cases. The difference seems to be entirely temporal. In the non-consilient case, C was construed from the start to accommodate both Pi's and P2's, whilst in the consilient case C was made to accommodate P2's only after it was tested over L1. However, there seems to be no difference between the two cases in neither the initial nor the final state of our knowledge: L1 and L2 retain their original meanings and in both cases are successfully explained by T. In the second consilient case, in which L2 (or at least P2) undergoes a change of meaning, although the final state of knowledge is the same as in the non-consilient case (i.e., T explaining both L1 and L2), knowledge of the nature of L2 is acquired during the process which in the non-consilient case was known all along. Thus one may conclude that whereas in both the consilient cases and in the non-consilient case the final states of knowledge are the same, in the second of the consilient cases more is learnt since we knew less about P2's to start with. This particular case of consilience inevitably involves an increase in knowledge due to a "reshuffle" of ontological classifications, forever absent in non-consilient inductions. This was pointed out with great clarity in Butts (1977).

"1WhenWhewell demands of consilient cases that "the hypothesis of itself and without adjustment for the purpose, gives us the rule and the reason of a class of facts not contemplated in its construction" (1847, 2: pp. 67-68) he is not referring to adjustments of scope, but to adjustments of what is conjectured of the scope-that is, of H. It is important that C is "stretched" (to include P2's) in a manner that does not change the nature of T's explanation of L,. 12Butts in his 1977 deals only with this second type of consilience. His treatment of it is extremely good, and both his conclusions, (a) that this type of consilience is marked "by indispensable semantic or conceptual changes" (p. 79), and (b) that this type of consilience adds "nothing new or important to the confirmation or corroboration of these hypotheses" (pp. 73-74), coincide with our own conclusions below. In this paper I shall not enlarge upon an analysis of the conceptual change undergone by L2 in the second type of consilient case. I am quite satisfied with the account of it in Butts (1977). The point here is not so much the nature of the conceptual change in the second case as that there are two distinct types of consilience. In what follows I shall wish to argue that it is in the first rather than in the second type of consilient process that a theory gains extraordinary support.

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III But our intuition, the soundness of which this paper set out to explore, was that in undergoing a consilient process a theory acquires greater support than it would have had had it undergone a similar non-consilient one. In order to assess such a claim in relatively undisputed fashion, we would have to compare both processes in reference to an agreed theory of inductive support. Needless to say no such undisputed theory exists. Thus there is no way one could proceed from here in a manner acceptable to all. Previous writers on consilience (with perhaps the exception of Butts) have always taken for granted that it represented a sound intuition, and proceeded to test the merits of confirmation theories against their ability to give a reasonable account of it. We wish to do exactly the opposite; that is, to test the merit of Whewell's intuition against an accepted theory of inductive support. Since in the past I have expressed my preferences towards one such theory-on grounds other than the elucidation of consilience13-I shall proceed to examine our claim in relation to it. It is L. Jonathan Cohen's method of relevant variables.14 Nonetheless, in order to avoid unnecessary dispute, reference will be made only to Coh- en's notion of scientific test, and to the consequent grading of support, for they offer, as I hope will be apparent from the short account that follows, a sound and intuitive elucidation of the type of controlled ex- periments utilized in testing lower-level scientific generalizations and the way in which their results are graded. I shall first briefly outline Cohen's theory of testing and support-grading of lower-level generalizations (such as L1 and L2). This will lead us to an assessment of the manner in which a theory (such as T) is assigned support by virtue of its successful explanation of lower-level generalizations. Finally, the non-consilient and two consilient processes outlined above will be compared and evaluated in the light of Cohen's theory. But first to experimental test. To test a correlationalgeneralization such as L1 is to investigate whether or not there is some P1 to be found that is not A. Testing is not carried out arbitrarilybut in deliberately contrived circumstances in which to the best of scientific knowledge, non A-ish P1's are most likely to be found. For every such hypothesis there exists a set of relevant circumstantial variables regarded by the scientific community as relevant to its test. (Thus, for example, hypotheses regarding drug administration would be

"3Seemy 1981 and 1984. Also discussed there are my reasons for rejecting the proba- bilistic confirmation theories; hence no attempt is made to cast consilience in Bayesian terms. As for Hesse's claim (1980) that Cohen's confirmation theory can be expressed in Bayesian terms, see n. 17 below. 14Cohen(1970) and (1977).

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions WHEWELL'S CONSILIENCE OF INDUCTIONS 249 tested in relation to age groups, sex, case histories, etc.; similarly, certain biological assumptions would be tested against variations of season, age, geographical location, etc.) The relevance of a variable, Vi, to L, is established by the fact that other hypotheses-regarded by the community as materially similar to Ll-were successfully falsified in the past whilst some variant of Vi prevailed. Given the set of an hypothesis' relevant circumstantial variables {V1, V2,. . ., V }, a "telescopic " series of n + 1 tests t1, t2, . . ., t,+1 are designed thus: In the first and most basic test, tl, all the effects of {V1,V2, . ., V, } are screened off and L, is instantiated. (This is to test whether being P1 in itself bars the possibility of having A.) In t2 {V2,. . ,VI} are screened off and Li is instantiated in all variants of V1. In t3 {V3,V4,. . .Vj} are screened off and L, is instantiated in all possible combinations of the several variants of V1 and V2. And so on until t,+1 in which LI is instantiated in all combinations of the entire set of V's. The set of tests t1, . . ., t,+1 are thus ordered according to their thoroughness, t,+1 being the most thorough test of LI science has to offer at a given time. Cohen measures the degree of support assigned to an hypothesis upon its passing test ti as i/n + 1, meaning: "Upon the evidence the hypothesis is supported to degree i out of a maximum of n + 1." (For an extremely illuminating example of this type of test procedure, see Cohen's account of Karl von Frisch's work on the behavioral abilities of bees in Cohen [1977, sec. 42] .) When an explanatory hypothesis, such as T, is offered as an explanation of lower-level correlationalgeneralizations such as L, and L2 (which for the sake of simplicity we presume already possesses maximum support) it too is tested by reference to a set of relevant circumstantial variables. These, however, fall under two different heads.1 In the first place, we have the lists of variables relevant to each of the L's. Secondly, T itself could belong to a class of materially similar theories in relation to which a second list of variables could be drawn up in a manner similar to the lists construed to test the L's. In what follows this second class of variables shall be ignored since it would be the same for both consilient and non-consilient processes in it not deriving from the generalizations that T is supposed to explain, but from the material similarity T bears to other theories.

"5Cohen'streatment of the support of explanatory theories is alltogether sketchy and vague, and in need of a far more detailed analysis (Hesse's remark to this effect (1980, p. 207) is in place although I disagree with her solution (see n. 17, below).) Thus he talks of relevant variables of the theory only in terms of the relevant variables of LI and L2 (Cohen [1970, p. 83f] and [1977, p. 151f.]). I shall not attempt a more comprehensive treatment here since, as regards consilience, we are concerned with whatever support Li and L2 lend T, and not with any supplementary support T acquires from different and unrelated tests.

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Cast in Cohen's terms, our claim that in a consilient process T gains a higher degree of support than it would have in a non-consilient process amounts to showing that T undergoes a more thorough test in a consilient process than in the non-consilient process; that is, a test in which a greater number of relevant variables are manipulated. In order to minimize obviously irrelevant pragmatic considerations, we shall assume that the consilient and non-consilient cases reflect a real difference in prior ontological commitment. Namely, that in the non- consilient case L1 and L2 are viewed from the start as laws of similar kind-reflected by the fact that an explanatory theory was indeed sought for them jointly-whereas in the consilient case they are viewed as laws of a completely different kind. We thus eliminate cases in which laws not really different were not contemplated because of mere oversight or carelessness. Now, to say, as in the non-consilient case, that L1 and L2 are regarded as similar enough to be considered explainable by one and the same theory, is to say that we suspect that whatever causes P1's to exhibit or sustain their A-ness (or bars the possibility of them exhibiting non-A-ness) is what causes P2's to exhibit or sustain their B-ness (or bars the possibility of them exhibiting non-B-ness). This, I think, is closely related to Cohen's basic notion of material similarity of hypotheses. The fact that it is in relation to the falsification of materially similar hypotheses that the experimenter selects the circumstances in which he thinks his own hypothesis is most likely to be falsified, reflects, I think, a belief in a similarity of cause. To test "All ravens are black" in circumstances in which otherwise white swans were found to lose their color, reflects a deeper (though usually unarticulated)scientific hunch that whatever causes or sustains the whiteness of swans also causes or sustains the raven's plummage hue. (Cohen himself does not discuss his classes of material similarity, what they reflect, and the ways in which they are apt to change. Some reflections on these topics may be found in my paper cited in note 11 above.) Thus it is reasonable to conclude that if LI and L2 had been elected as candidates for one and the same explanatory theory-as in the non-consilient case-one may assume that they belong to, if not the same set of materially similar hypotheses, then to sets closely akin. Similarly, if they are not contemplated for joint explanation-as in the two consilient cases-one may reasonably conclude that they initially belonged to quite different sets. Let us examine the test procedures of T in the non- consilient and the two consilient cases.

IV In the non-consilient case, in view of their mutual candidacy as ex- planandums of T, L1 and L2 can be assumed to belong to closely related

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions WHEWELL'S CONSILIENCE OF INDUCTIONS 251 sets of materially similar hypotheses. Consequently their two lists of relevant circumstantial variables would be very much alike. Let them be V = {V1,V2,. . .,V4 for L1, and V' = {V'1,V'2,. . .,V'jm for L2. We can assume that V n V' is substantial, and that more times than none actually equals V. The most severe test on T (not counting variables pertaining to a set of materially similar theories to which T itself may belong) is one in which both L1 and L2 are instantiated, and A and B are shown to follow from H1, in all variations of the joint set of circumstantial variables V U V'. However, since V and V' overlap, the set of variables actually varied would be: V u (V - v n v') (=(v u v') - (vn V)) which in the non-consilient case approaches V. (This, incidentally, explains why many times a law receives additional support when successfully incorporated [together with other laws] within a higher order theory,16 since the process of testing the theory could in- volve instantiatingthe law in circumstances other than those implied orig- inally by the set of materially similar hypotheses it belonged to. In fact, each time (V1- v n v') # ? Thus it is tested even more thoroughly than before and is therefore assigned a higher degree of support. Why these new circumstantial variables are to be regarded as relevant to the law derives simply from the fact that the suggested theory associates it with other laws that do not belong to its original set of materially similar hypotheses. The effect of conjecturing an explanatory theory is many times that of recasting the laws explained by it in terms of their material similarity. Cohen says this but not in so many words. He demands that laws should be instantiated in the new circumstances suggested by the theory, but does not discuss the issue in terms of the feedback effect an explanatory theory has on the original classification of the lower-level generalizations in sets of material similarity. This recaptures yet another Whewellian insight, namely, that each act of induction involves a new conception being superinduced upon old facts by which they are seen in a different light. The "different light" is here expressed in terms of a reconsideration of material similarity manifest in the supplementary relevant variables, and consequently-if the test is passed-further inductive support made inaccessible in the absence of the new conception, or rather, theory. In the two consilient cases, L2 and L2 are assumed to belong to sub-

6This is essentially Kneale's, Hesse's, and Butts's problem.

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions 252 MENACHEM FISCH stantially different sets of materially similar hypotheses. Hence, in both cases V n V' may be regarded as rather small, and V' - (V n V') as rather large. T is first conjectured as an explanation of L1. Consequently L1 is instantiated in all variants of the entire set of V, and in each case A is shown to follow from H. (Thus in the case in which an explanatory theory is designed to explain one correlational generalization only, only T gains support, whereas L1 does not since it is not tested in the process more severely than it was when established in the first place.) T is then applied to L2-a correlational generalization regarded as quite different from L1. The reasons for suddenly applying the theory to such a different type of law could be anything from sheer luck to a stroke of ingenious prophetic insight, and do not bear on the analysis. The only important point is that the case be genuinely consilient, i.e., that L1 and L2 are of kinds initially thought to be genuinely apart. In the first type of consilient case, that in which P2 retains its meaning throughout, T, after being applied to L2, is tested, as in the non-consilient case, by instantiating both L1 and L2 and assuring that A and B derive from H while varying the entire range of the combined set of variables: v u (Vt- v n v') However, in a genuine consilient situation V and V' would hardly overlap at all; thus the total number of variables manipulated in testing T would be much larger than in the non-consilient case. And consequently the test would be more severe and the support for it higher. It is important to emphasize, however, that the time element, or even the element of surprise-in fact all pragmatic considerations-are immaterial. What counts is to what extent L1 and L2 represent different kinds of phenomena. The greater the difference, the wider the spread of variables over which T is tested; if successfully, the greater the support. However, inasmuch as the difference of L1 and L2 reflect difference of orientation in terms of Co- hen's material similarity, and inasmuch as Cohen's material similarities reflect causal hunches, dissimilar generalizations will not usually be contemplated together when causes for them are sought; and the eventual application of T to L2 will usually indeed come as an unforeseen and surprising move. In the second type of consilient case (the only one recognized by Butts), P2 changes its original meaning to something far more akin to P1. This I take to represent a shift in L29s orientation in terms of material similarity, and thus also a replacement of V' by a different set of relevant variables, say, V", implied by the new orientation, which is as in the non- consilient case close if not identical to V. Consequently, in this case, as in the non-consilient case, the gain in support for T is modest. But unlike the non-consilient case this brand of consilience is always accompanied

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions WHEWELL'S CONSILIENCE OF INDUCTIONS 253 by that increase in knowledge the "reshuffle" of our prior ontological commitment-expressed by the replacement of V' by V".

To summarize, a consilience of inductions-a process in which a theory T, acting successfully as an explanation of a lower-level generalization, LI, is surprisingly found to explain equally well another quite different generalization, L2-can occur in two possible ways. In the first, the two generalizations retain their original (and different) meanings; the result is that support of T from empirical testing is considerably higher than it would have been had the two generalizations been more alike. The second type of consilient process is not really consilient at all, for in the process of applying and testing T one of the generalizations is reinterpreted and rendered less different from the other than was previously thought. Apart from this gain of knowledge-characteristic of all pseudo- consilient cases-it ranks with the non-consilient. The successful explanation of two quite different correlational generalizations by one and the same theory could result either in a conceptual (and ontological) shift in which L2 is rendered more like LI (as in the imaginary example in note 9, had the inverse square law been found to apply equally well as an explanation of Kepler's second law; as a result P2 would have changed its meaning from planets qua heavenly bodies to planets qua masses at- tractedby the sun). In this case the resulting support for the theory would not be much larger than it was before its application to L2 because of the great overlap between V' and V". On the other hand when it results in a reinterpretationof the theoretical terms in T with L1 and L2 retaining their original meanings (as when Newton's inverse square law was made to apply to both planets and sub- lunary massy bodies), upon application to L2, T (and with it LI and L2) acquires extraordinarysupport since V and V' hardly overlap at all, and both LI and L2 are tested more rigorously. In actual cases we should expect a bit of both effects; both some reinterpretationof L2 and some theoretical adjustmentof the scope of C. Hence one would expect as a result both some ontological "reshuffling" and some consilient support. The interesting thing is that in terms of support both effects are reciprocal; i.e., the larger the ontological shift (the larger the overlap of the V's) the smaller the consilient support, and vice versa. Thus arises the interesting difference between this account of consilience and the one in Butts (1977). According to Butts, for laws to gain support by virtue of their explanation by one and the same theory (and consequently, for the theory to gain support by explaining two apparently different laws), one must show that the domains of evidence (i.e., the

This content downloaded from 150.135.114.87 on Sat, 25 Jul 2015 10:42:42 UTC All use subject to JSTOR Terms and Conditions 254 MENACHEM FISCH classes of confirming evidence) of the two overlap. For according to Bayesian confirmation theory, to gain support of L by evidence E is for the probability of L to rise (in relation to its initial probability) by virtue of E. It follows that for evidence E1 that confirms L1 to support a different law L2, E1 itself must raise the probability of L2. It seems quite impossible on this account to explain how, for example, evidence of tide regularities can confirm laws of planetary motion (by virtue of gravitational theory) and vice versa. For two generalizations to lend each other support their evidence classes must to some extent overlap. The greater the overlap the greater the support. It follows that on Butts's account consilience is best achieved when it is apparent; that is, when the two laws thought quite different (with no overlap of evidence classes) at one time, are found not so different (with great overlap of evidence classes) at a later time. Hence consilience in the genuine sense-where the difference between the laws is sustained throughout-cannot occur. In Cohen's superior confirmation theory, rise in support is due to the outcome of severer tests, hence (one of) the effect(s) of explaining two laws by one theory is not that of rendering (some of the) evidence for each law relevant to the other, but of rendering each of the laws' test controls relevant to the other; from which follows that in the light of the theory, and as a test of it, the laws are retested in a more severe manner. The crucial point being that the smaller the overlap of relevant variables, that is, the more different the laws, the greater the severity of the test, therefore the greater the support. Although the primary concern of this paper was to articulate and evaluate consilience, and not to evaluate confirmation theories, the fact that genuine consilience eludes the type of Bayesian confirmation theory advocated by Butts and Hesse, does I believe highlight some of its shortcom- ings. 17

'7In her 1980, Professor Hesse makes the claim that Cohen's logic of inductive support is expressable in Bayesian terms. In an intriguing move she interprets the support assigned by Cohen to a generalization L having passed test ti as P(L/Lv,+ l) where Lvj+ is L restricted to a domain hewn out by normal values of Vi+, ., V,. Hesse disagrees with Cohen's contention that test ti requires variables V+, . . V, to be screened off on the grounds that it is "very artificial" (p. 207, n. 3), and requires that whilst V1, . . ., Vi are varied thoroughly, normal values of Vi+1, . . ., V, should be allowed to prevail. This might seem enough to render her account of Cohen's support function doubtful, because if the notion of the relevance of the V's to the test of L turns on a suspicion that variants of them could be causes for L's falsification, why can we assume that "normal" values of Vi+1, . . ., V, are exempt from such suspicion? When a variable Vi is such that it cannot be screened off (such as season of the year) test procedures must start with a test more thorough than ti+,! There is no requirement in Cohen's theory to go through the entire series of t's. Hesse's interpretationof Cohen's theory as one in which, as testing becomes more thorough, hypotheses of greater domain are tested, is, I think, mistaken too. Quite the contrary. As tests proceed the domain of the hypothesis is in a sense restricted from "random" or "any" P2's to only those found in carefully contrived and selected circumstances. It follows that L does not entail Lvj+ (or for that matter that Lvi+j does not entail Lvi), and Hesse's entire

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REFERENCES Butts, R. E. (ed.) (1968), William Whewell's Theory of Scientific Method. Pittsburgh: University of Pittsburgh Press. (1973), "Whewell's Logic of Induction", in Giere and Westfall, pp. 53-85. (1977), "Consilience of Inductions and the Problem of Conceptual Change in Science", in Colodny, pp. 71-88. Cohen, L. J. (1968a), "An Argument That Confirmation Functors for Consilience Are Emprical Hypotheses", in Lakatos, pp. 247-50. Reply to Hesse. . (1968b), "A Note on Consilience", British Journalfor Philosophy of Science 19: 70-71. (1970), The Implications of Induction. London: Methuen. (1977), The Probable and the Provable. Oxford: Clarendon. Cohen, L. J., and Hesse, M. B. (1980), Applications of Inductive Logic. Oxford: Clar- endon. Colodny, R. G. (ed.) (1977), Logic, Laws and Life-Some Philosophical Complications. Pittsburgh: University of Pittsburgh Press. Fisch, M. (1981), "The Paradoxes of Confirmation and Their Solutions", M. A. Thesis, Tel Aviv University. I (1984), "Hempel's Ravens, the NaturalClassification of Hypotheses and the Growth of Knowledge", Erkenntnis 21: 45-62. . (forthcoming), "Necessary and Contingent Truth in William Whewell's Antith- etical Theory of Truth", Studies in the History and Philosophy of Science 17. Giere, R. N., and Westfall, R. S. (eds.) (1973), Foundations of Scientific Method: The Nineteenth Century. Bloomington and London: Indiana University Press. Hesse, M. B. (1968), "Consilience of Inductions", in Lakatos, pp. 232-46. . (1971), "Whewell's Consilience of Inductions and Predictions", The Monist 55: 520-24. (1974), The Structure of Scientific Inference. London: Macmillan. (1980), "Inductive Appraisal of Scientific Theories", in Cohen and Hesse, pp. 202-17. Kneale, W. (1952), Probability and Induction. Oxford: Oxford University Press. Lakatos, I. (ed.) (1968), The Problem of Inductive Logic. Amsterdam: North-Holland. Laudan, L, (1971), "William Whewell on the Consilience of Inductions", The Monist 55: 367-91. Losee, J. (1983), "Whewell and Mill on the Relation between Philosophy of Science and History of Science", Studies in the History and Philosophy of Science 14: 113-26. Schilpp, P. A. (ed.) (1963), The Philosophy of Rudolph Carnap. The Library of Living Philosophers. vol. 11. La Salle: Open Court. Whewell, W. [1833] (1836), Astronomy and General Physics Considered with Reference to Natural Theology. A "Bridgewater Treatise." Cambridge. . (1847), The Philosophy of the Inductive Sciences Founded on Their History. 2 vols. 2nd edition. London. (1858), Novum Organon Renovatum. London. (1860), On the Philosophy of Discovery. London. argument seems to fall through. However it is not my intention at this point to attempt a thorough evaluation of Hesse's move which is rich and suggestive and could possibly sidestep my objections. For the sake of the position I wish to defend in this paper, it could very well be that Cohen's theory is expressible in Bayesian terms. What I wish to argue is that Bayesian confirmation theories of the type advocated by Butts (1977) and Hesse (1974) are not sufficient to elucidate Whewellian consilience, because the relevance of one law to another can only be measured by the amount of mutual confirming evidence they share. Upon Cohen's account laws can become relevant if they share test controls. Whether or not this can be explained in terms of Bayesian probabilities is an entirely different question, the answer to which cannot render Butts's or Hesse's theories any more plausible.

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