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Predicates and Projectibility
Published online by Cambridge University Press: 01 January 2020
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Nelson Goodman's new riddle of induction wears many faces. In one of its guises the new riddle of induction appears as the problem of providing a general account of the distinction between projectible and non-projectible predicates. This is the form of the riddle which is supposed to point up a lacuna in the foundations of confirmation theories such as Carnap's which, Goodman charges, work only to the extent that one builds into them just the right (projectible) predicates. As a new riddle of induction, the problem of distinguishing projectible from non-projectible predicates has the virtue that it is in fact new—a virtue not shared by some other forms of the riddle.
Philosophers had recognized previously that some predicates are more projectible than others in the sense that, for instance, the prediction that a certain toss of a die will turn up an even face is safer and more likely to be true than the prediction that the same toss will turn up six.
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- Copyright © The Authors 1971
References
1 Other guises,
(a) What distinguishes lawlike from accidental statements. Facts, Fiction, and Forecast, 2nd ed. (hereafter FFF), (Indianapolis: Bobbs-Merrill, 1965) 73.
(b) “What hypotheses are confirmed by their positive instances?” FFF, 81.
(c) What constitutes valid projecting from any set of cases to others? FFF, 83.
(d) What distinguishes projectible hypotheses from nonprojectible hypotheses? FFF, 83.
(e) What distinguishes confirmable from noncomfirmable hypotheses? FFF, 81.
(f) Which prediction based on regularities are valid? FFF, 82.
2 Perhaps this form of the problem is most clearly stated in Nelson Goodman, “Comments”, The Journal of Philosophy. Vol. LXII, No. 11. (May 26, 1966) 329.
3 Someone might have observed in regard to the degrees of projectibility mentioned in the text that contradictory predicates are nonprojectible, i.e. that the prediction that some individual will have a selfcontradictory property is audacious in the extreme. No doubt this hardly seemed worth observing.
4 One might object that self-contradictory predicates are obviously nonprojectible, but
(a) there is no new problem in distinguishing self-contradictory predicates from others,
(b) self-contradictory predicates are not what Goodman has in mind as nonprojectible predicates,
and
(c) self-contradictory predicates vacuously satisfy most definitions of “projectible”, i.e. there are no cases from which to project.
5 Strictly speaking, (1) and (2) are true for certain only of predicates definable in terms of the primitive predicates in one's language. In particular they are not, in Carnap's, language systems, true of ‘positional predicates': Rudolf Carnap, “On the Application of Inductive Logic”, Philosophy and Phenomenological Research, Vol. 8 (1947-48) 146.CrossRefGoogle Scholar This limited applicability of (1) and (2) may well be an infirmity in Carnap's system, for, as I argue below, positional predicates are projectible. When, in a particular case, they should not be projected, the reason is not that (1) and (2) are false of positional predicates, but rather that there is additional evidence bearing on the particular projection. Accordingly, for the present I place no restriction on the sorts of predicates substitutable in (1) and (2).
6 Hereafter I shall omit special reference to the projectibility of P relative to Q. The necessary qualifications can be supplied by the reader with little difficulty.
7 Goodman, FFF, 73.
8 True, we also apparently have no reason to believe that it isn't. But we might. For instance, if it were found that third sons have a marked tendency to pursue a certain career, say education, then assuming that people in the same profession are often found together in public places, the fact that someone in the room is a third son would increase the credibility of statements asserting that other men in the room are third sons. It is an interesting and little noted consequence of Carnap's approach to inductive logic that events of the same kind (i.e. described by the same predicates) are never independent.
9 Jeffrey, Richard C. “Goodman's Query” in The Journal of Philosophy, Vol. LXIII, No. 11. (May 26, 1966) 288.Google Scholar Readers will recognize this as the troublesome half of Goodman's predicate in “A Query on Confirmation”.
10 Thomson, Judith Jarvis takes this sort of question to be the central problem of the grue paradox and argues that what she calls “R-grue” (the fact that all heretofore examined emeralds have been grue) is less a reason to think all beryls grue than R-green is to think them green: “Grue” in The Journal of Philosophy, Vol. LXIII, No. 11. (May 26, 1968)Google Scholar. I agree with this, but should like to go farther and say that R-grue is no reason to think all beryls grue.
11 Jeffrey, 288. Jeffrey's function s(P,Q,n) is defined by our (2) p. above minus the \documentclass[12pt]{minimal} ''\underset{11\to x}{\mathop{\lim }}\,'' \end{document} .
12 For instance, Mrs. Thomson writes,
Goodman's own definition is ambiguous, and has been differently interpreted by different writers. It does not matter, however; an acceptable solution to this puzzle would have to be reproducible for each of the possible variant readings of Goodman's definition.
Thomson, 290. n. 4. In another paper which attributes the other “grue” 's not to an ambiguity in Goodman's definition but to misunderstandings of that definition the following appears.
Since an adequate solution to the general problem of projection would have to handle a “gruelike” predicate on any construal, we shall feel free to make use of all of these definitions in our discussion.
Hullet, James and Schwartz, Robert “Grue: Some Remarks”, The Journal of Philosophy, Vol. LXIV, No.9. (May 11, 1967) 260 n. 3.Google Scholar
13 Barker, Stephen Induction and Hypothesis. (Ithaca: Cornell University Press, 1957) 188.Google Scholar
14 One can easily think up troublesome cases where it is just not clear whether, given the above definition, we should apply the term “grue”. E.g. Suppose a house receives a new coat of paint every few years and is variously red, green, and magenta before 2000 and yellow, blue, and chartreuse after 2000. Is the house gruel Is a green and blue beachball, manufactured before 2000 and lasting until after 2000, grue?
15 Robertson, Stuart and Cassidy, Frederic G. The Development of Modern English. 2nd ed. Englewood Cliffs: Prentic Hall, 1954) 274.Google Scholar
16 Here it may be helpful to understand things as including temporal slices of objects.
17 FFF, 74. Tedious as it is, it should be noted that “grue”, is somewhat unclear. For instance, Haskell Fain and I once had a heated and inconclusive debate over the grueness of a certain marble x with the following history.
(a) x was examined before t and was green then.
(b) x was examined after I and was red then.
Query: Is x grue? Fain maintained that it is because of (a). I claimed that it isn't because it was examined before t and it is not green. for Fain's half of the argument see “The Very Thought of Grue”, The Philosophical Review, Vol. LXXVI, No.1. (January, 1967) 63.
18 E.g. Carnap, 146.
19 FFF, 80. In my view this reply is entirely off the mark. I should argue (as in section I) that positional predicates are projectible.
20 FFF, 79. I take it that “emerald” in the definition (explanation!) of ‘bleen’ is a slip of the pen and that “things” is intended instead.
21 FFF. 95.
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