Bad Company: A Reply to Mr. Zabludowski and Others Joseph Ullian; Nelson Goodman The Journal of Philosophy, Vol. 72, No. 5. (Mar. 13, 1975), pp. 142-145. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819750313%2972%3A5%3C142%3ABCARTM%3E2.0.CO%3B2-T The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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142
THE JOURNAL OF PHILOSOPHY
BAD COMPANY: A REPLY T O MR. ZABLUDOWSKI AND OTHERS *
Mr. Zabludowski attempts to show that "projectibility is no good" by producing complicated examples challenging the rule of projectibility proposed in the last chapter of Fact, Fiction, and Forecast.' These examples can be dismissed on either of two grounds: (i) the implicit conditions for the rule's application; (ii) a principle concerning the relative simplicity of hypotheses. We consider these in turn; obviously, neither is in any way affected by the changes in Zabludowski's proposals suggested by Kennedy and Chihara.2 As has been observed elsewherelathe theory so far attempts only coarse, qualitative distinctions. I t is not quantitative, is not sensitive to distinctions between numbers of positive instances, and is only a first step toward an inductive theory. I t imposes limits both on what it accepts as input and what it aims a t as output. The rule of projectibility is for use in choosing in certain cases between two competing hypotheses. Its application requires that only certain information be taken into account and that only certain assumptions be made. Just as paradoxes arise when quantitative data are fed into a qualitative theory, so paradoxes may arise whenever the limitations on admissible information are transg r e ~ s e d As . ~ an obvious example, if the truth value of one of the competing hypotheses is already known or assumed on grounds other than examination of its instances, then the rule is surely not intended to apply; for there is no choice to be made. The principle of admissible information for using the rule may be put positively. What is admissible- and needed-as information or assumption is just the following: (1) Some cases of each hypothesis have been examined and all found to be positive (i.e., the hypotheses are supported and unviolated) ; (2) One and only one
* See his "Concerning
a Fiction about How Facts Are Forecast," this JOURNAL., 4 (Feb. 28, 1974) : 97-112. 1 Indianapolis and New York: Bobbs-Merrill, 3rd ed. 1973, p. 101. The rule given there first appeared in Goodman, R. Schwartz, and I. Scheffler, "An Improvement in the Theory of Projectibility," this JOURNAL, LXVII, 18 (Sept. 17, 1970) : 605-608. It differs from the rules set down in the earlier editions of Fact, Fiction, and Forecast. a R. Kennedy and C. Chihara, ''An Improvement on Zabludowski's Critique of Goodman's Theory of Projection," in this issue of this JOURNAL. I t becomes evident below that Kennedy and Chihara have misidentified what it is that undermines Zabludowski's arguments. Their proposed repairs leave entirely untouched the fatal flaws, discussed below, in Zabludowski's argument and theirs. a In Ullian, "On Projectibility," t o appear in Nods. 4 For an interesting analogous case of making use of inadmissible information, in a quite different context, see Goodman's Problems and Projects (Indianapolis, Bobbs-Merrill, 1972), pp. 273/4.
LXXI,
COMMENTS AND CRITICISM
I43
of the two consequent-predicates applies to something to which both antecedent-predicates apply (i.e., the hypotheses conflict). In view of ( I ) , the instance in question must be unexamined ; and one must not know or assume which of the consequent-predicates applies, since that would be to know or assume that a given one of the hypotheses is false. (3) Irrespective of their truth values, either the two hypotheses are about equally well-entrenched or else a particular one of them is the much better entrenched. The only further admissible information or assumption beyond (1)-(3) has to do with competition between either hypothesis and some further hypothesis ; and even that is restricted to the same three sorts. Now Mr. Zabludowski contends that for any hypothesis such as (H)
( x )( ~ 1 1>~ Nx) -
we can construct another such as
(K)
( x )( A x > ( B x v N H x ) ) ~
that will compete with H and destroy its proje~tibility.~ But his argument depends crucially on the assumption that some As are known not to be Bs. Since B is not the antecedent or consequent of either hypothesis, the assumption does not fall under any of the three allowable headings. That is, use of such an assumption is in violation of our principle-is not admissible in applying the rule of projectibility. But without the assumption, the hypotheses do not conflict under purview of the rule. We may decide to make the weaker but admissible posit of conflict between H and K :
( 3 x ) ( M x . A x :( N x .
-
Bx.Hx) v (-Nx.Bxv ~ H x ) )
But K will still not compete effectively with H under the rules; for now, since K will be well-entrenched only if H is true and K therefore false, condition (2) cannot be met. Zabludowski goes on to a succession of other examples designed to correct various deficiencies in this first one; but all the cases he constructs invoke an exactly parallel inadmissible assumption. So the rule of projectibility is not applicable to any of them as they are stated. Although nothing further is needed, Zabludowski's cases may also be ruled out by a second, more specialized principle which is perhaps of some independent interest. Recall that the theory of The example appears on p. 102 of Zabludowski's paper; 'Hx' applies to x just in case H is true. Zabludowski retreats to more complex examples (pp. 104 ff.) in order to covrr all cases, but that further complexity does not affect our point.
I44
THE JOURNAL OF PHILOSOPHY
Fact, Fiction, and Forecast was to apply only to simple universal hypotheses. On one construal, any hypothesis can be expressed as a simple universal one; so lest the restriction be empty, as was not intended, that construal must be abandoned. But fortunately, there is no need here for a theory of simplicity of hypotheses. All we need do is rule out competitions between certain hypotheses that are of conspicuously unequal simplicity. More specifically, we may plausibly outlaw as a competitor for a hypothesis H any hypothesis that wantonly embeds H itself within it. This will give us a principle of wanton embedding that will by itself block all of Zabludowski's examples. Loosely stated, the core idea is this: J is not to count as a competitor of H if determination of the positivity or negativity of some of J's instances threatens to depend on and require information about instances of H that are still unexamined. If it does so threaten, J embeds information about H, since then equally, sentences about positivity or negativity of J ' s instances threaten to allow us to recover information about H that goes beyond its examined instances. Now let us formulate this idea more carefully. Let us recall what we need from an old ana1ysis.l A sentence Q is about k if Q implies some sentence T differentially with respect to k, that is, if T follows from Q, T contains an expression designating k, and no universal generalization of T with respect to any part of that expression follows from Q. Q is about k relative to R if Q. R implies a sentence T differentially with respect to k where T follows from neither Q nor R alone and passes a test of being no "loose composite" of separate consequences of Q and R. Now we will say that Q adds to the k-information in R if Q is about k relative to R or Q implies some sentence differentially with respect to k which R alone does not imply and which is, as before, no loose composite. Whenever Q so adds it yields, given R, a new consequence about k. As before, let H be '(x) (Mx > Nx)'. Let U be the class of undetermined cases for N ;if H is unexhausted, U is nonempty. For convenience, write 'U*' for ' U - {XI'. Let p embody the information and assumptions deemed pertinent. We treat p as a single sentence, but extension to the case where p is allowed to be infinite poses no problem. Let the schematic letters '0'and '$' represent the antecedent and consequent predicates, respectively, of J. Then J Goodman, "About," Mind,LXX, 277 (January 1961) : 1-24. The concept there developed for statements is here applied also to some open sentences.
I45
NOTES AND NEWS
wantonly embeds, and so is not in competition with H, if either $x or N+X adds to the U*-information in p . dx. This second principle rules out all of Zabludowski's cases and many more that might be created in their image. Consider the cases offered on pages 102-107 of Zabludowski's paper. In each case the statement that x is a negative instance of the contrived hypothesis J yields information about U* that was not available when x was assumed only to be an instance of J. T h a t is, --$xadds, in each case, to the U*-information in p . 4 ~ .Using Zabludowski's notation, we record the newly derivable information by cases: h* (p. 102) ( Y ) (Y E U*> NY) h * ~ (p. 104) Sx 3 ( y )(Y E U* 3 NY) h*2 (p. 104) NSX 3 ( y )(Y E U*> NY) h** (p. 106) --Bx. Cx. > ( y )( y E U* 3 N y ) h*** (p. 107) NBX.CX.> (y)( y E U*. A Y . > .N y
Cy)
Mr. Zabludowski's contrivances are not, as he claims, "good companions to grue-like generalizations," but very bad company. And the failure of his intricate and ardent objections argues in favor of the rule of projectibility as it stands. JOSEPH ULLIAN
Washington University NELSON GOODMAN
Harvard University NOTES AND NEWS On the occasion of the fifth anniversary of the death of Roman Ingarden there will be an international conference on the theme: The Phenomenology of Roman Ingarden and Dialectical Materialism, organized jointly by the editorial board of Dialectics and Humanism: T h e Polish Philosophical Quarterly, the Institute of Philosophy and Sociology of the Polish Academy of Science, and the Institute of Philosophy of the Jagrillonian University in Cracow. I t will be held at Jadwisin near Warsaw, June 19-22, 1975. The program will include papers and discussion oriented around the topics of (I)Praxis, (2) Language, (3) Values. For information write directly to: Redakcja Dialectics and Humanism, Nowy Swiat 49, Warsaw, Poland. The co-organizer of the conference in the Western countries is The International Husserl and Phenomenological Research Society, which plans a commemorative session on Ingarden's thought and a celebration of his death anniversary in his home in Poronin, near Cracow, on June 24/25.
The Philosophy of Language sessions of the Southeastern Conference on Linguistics, to be held March 20 and 21 at Vanderbilt University, will focus
