On Infirmities of Confirmation-Theory

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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 Philosophy and Phenomenological Research is currently published by International Phenomenological Society.

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('arnap's paper '*On the Application of Inductive Logic"' sets forth certain assumptions on the basis of which he seeks to ansxer the question raised in my "Query on C~nfirmation."~S o t much comment on these assumptions is necessary; the reader may decide for himself whether he finds them acceptable, as Carnap does, or quite unacceptable, as I do. The root assumption is that there are absolutely simple properties into which others may, and indeed for some purposes must, be analyzed. The nature of this simplicity is ob~cureto me, since the question whether or not a given property is analyzable seems to me quite as ambiguons as the question whether a given body is in motion. I regard "unanalyzability" as meaningful only with respect to a sphere of reference and a method of analysis, while Carnap seems to regard it as having an absolute meaning. L:.way of partial justification for the restrictions Carnap places upon the interpretation of the predicates admissible in his system, he argues that these restrictions are also necessary for deductive logic. The analogy does not seem to me I\-ell-drawn. He says that in deductive logic, knowledge of such matters as the independence of predicates, etc., is necessary if we are to be able to determine whether or not a statement is analytic. But certainly we do not need such knowledge in order to carry out perfectly valid deductions; I can infer S1 from S1.S2 quite safely nithout knouing anything about the independence of the predicates in~olvedin these sentences. On the contrary, in the case of C'arnap's system of inducti~~e logi-c, I cannot safely make an inductire inference without such knou ledge; I must have this knonledge before I can tell whether the computation of a degree of confirmation \\-ill be at all correct. The analogy Carnap seeks to draw wot:ld seem to me convincing only if he could show that theassumptions necessary to guarantee the correctness of inductive inference (by his methods) are like\\ise necessary to guarantee the ~ a l i d i t yof deductive inference. Furthermore, even supposing all predicates to have been classified into purely qualitative, positional, and mixed, we are offered no evidence 01argument in support of Carnap's conjecture that either the class of purely qualitative predicates is identical uith the class of intuitively projectible predicates, or that such predicates as are intuitively projectible though not purely qualitative will also prove to be projectible by his definition. The Philosophy and Phenonlenological Research, Vol. VIII, no. 1.

Journal of Philosophy, Vol. XLIII (1946), pp. 383-385.

149

first alternative seems prima facie dubious since predicates like "solar," "arctic," and "Sung" appear to be intuitively projectible but not purely qual~tative;the grounds for the second alternative are not evident. I n the last page or two of his article, Carnap seems almost to be claiming that no such question of intu~tiveadequacy any longer exists. E e maintains that ~vithhis present restrictions on the interpretation of primiti~c predicates, his formal system of indcctive logic provides a definition of projectibility ; and he suggests therefore that anyone \\ ho has queries about projectibility can find out the ansners by studying his system, just as one can learn about right triangles by stcdying Ecclid. The catch is, though, that the question whether the formal system is intuitively adequate is quite pertinent both to Euclid's system and to Carnap's. I n fact, the only difference in the tn o cases is that I am better satisficd that the triangles to ~vhich the Pythagorean theorem applies are just those I know as right triangles than I am that those properties to which Carnap's formula in terms of c* applies are just those which are intuitively projectible. Concerning the principle of total evidence, a rather comples discussiorl has gron n ont of a subsidiary point that I apparently did not explain very well. The point I\-as just this: it might 1:ave been possible to claim that a criterion of projectibility is unnecessary b ~ c a c ~the e evidence need never contain any non-projectible predicates. I3xamples show, however, that such predicates as those of order must be admitted into our evidence if we are to avoid counterintuitive results. If it is therefore required that order and all other properties be covered in our evidence-statement, then we shall have to have a criterion of projectibihty in order to determine which are to be expected t o attach to future cases; if no scch distinction is made in our formal system, or in the rules for applying it, we shall reach the absurd conclusion that future cases \\ill probably have all the properties common to past cases. (Incidentally, Carnap's example of an investigator who omits all cases unfavorable to the hypothesis being tested is not parallel to mine and does not bear on tl;e same point; for in my example, no cases were omitted but only, quite co~~ciously, some information about these cases.) One further point concerning my examples having to do with order. I 11as in effect asking how the obviously relevant fact of order was to be taken into account by the theories in qcestion, and pointing out that in trying to devise a method for doing this, 11 e must face the fact that regular orders influence our expectations in a n a y that irregular ones do not. Thus if a method should give a high degree of codrmation for repetition of the pattern rcd, rcd, not-red, on the evidence that this pattern had repeatedly occurred, it ~i-ouldseem Lkely that this method would be in danger of giving a high degree of confirmation for tlle repetition of a wholly irregular pattern of, say, 96 tosses. I n effect, if not technically, we ~vouldseem to be regard-

ing each occurrence of a pattern as a confirming instance; hence in the irregular case we have the equivalent of one positive and no negative instances. I am not clear as to ho~vCarnap's proposal mould render regular order effective without rendering irregular order equally effective and thus leading to counterintuitive results. Carnap cannot say antecedently that regular order is relevant and irregular order isn't. This ~ ~ o u mean l d just that the latter but not the former affects the c* computation, and ~ ~ o u l d indeed, were it t'rue, provide us n-it,h an interesting definition,of degree of regularity. But. I am afraid that if order is so to affect the computation as to give intuitive results when t'he order is regular, it \\-ill be difficult to avoid getting counterintuitive results when.the order is irregular. It is worth noting, however, tha,t this difficulty might be overcome by a definition of degree of confirmation for which the numbw of confirming cases is always important, since an irregular order is perhaps one that does not consist. of repetitions of a smaller pattern. But the consideration of the examples involving order are in any case quit,e secondary t,o my main point which is adequately illustrat,ed by t,he other esamples I gave. I regret that Carnap's method of dealing xith it involves assumptions I cannot accept and that no other ansn-er has been forthcoming. For until this problem is solved, we are seriously hampered in our efforts to solve certain ot,her important problems.8

9 For example, see my "Problem of Counterfactual Conditionals," Journal of Philosophy, Vol. XLIV (1947), especially pp. 127-128.