A Nonessential Property Gilbert H. Harman The Journal of Philosophy, Vol. 67, No. 6. (Mar. 26, 1970), pp. 183-185. Stable URL: http://links.jstor.org/sici?sici=0022-362X%2819700326%2967%3A6%3C183%3AANP%3E2.0.CO%3B2-O The Journal of Philosophy is currently published by Journal of Philosophy, Inc..
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A NONESSENTIAL PROPERTY
183
This, not the indeterminacy of translation, is the substance of ontological relativity. There are two ways of pressing the doctrine of indeterminacy of translation to maximize its scope. I can press from above and press from below, playing both ends against the middle. At the upper end there is the argument, early in the present paper, which is meant to persuade anyone to recognize the indeterminacy of translation of such portions of natural science as he is willing to regard as underdetermined by all possible observations. If I can get people to see this empirical slack as affecting not just highly theoretical physics but fairly common-sense talk of bodies, then I can get them to concede indeterminacy of translation of fairly common-sense talk of bodies. This I call pressing from above. By pressing from below I mean pressing whatever arguments for indeterminacy of translation can be based on the inscrutability of terms. I suppose Harman's example regarding natural numbers comes under this head, theoretical though it is. I t is that the sentence '3 e 5' goes into a true sentence of set theory under von Neumann's way of construing natural numbers, but goes into a false one under Zermelo's way. But a limitation of this example, as Harman recognizes, is that '3 E 5' rates as nonsense apart from set-theoretic explications of natural number. In these pages I prefer not to speculate on how much better one might do from below, or from above either. My purpose here is to separate the issues and identify the arguments; and this may be managed most effectively by leaving the reader to consider what more might be proved. Harvard University
W. V. QUINE
A NONESSENTIAL PROPERTY
I
S the number of planets necessarily a composite (nonprime) number? We are sometimes told that the answer depends on whether de dicto or de re necessity is in question.* If de dicto necessity is at issue, the answer is supposed to be "no" since it is not a necessary truth that the number of planets is a composite number. 4 Gilbert Harman, "An Introduction to Translation and Meaning," in Words and Objections, p. 14. Also in Synthtse, ibid., p. 14. * Supported in part by the National Science Foundation.
1 E.g., Alvin Plantinga, "De R e et De Dicto," Nozis, III, 3 (September 1969):
235-258.
I 84
THE JOURNAL OF PHILOSOPHY
However, if de re necessity is at issue, the answer is supposed to be "yes" on the grounds that being a composite number is an essential or necessary property of the entity (namely, the number 9) which happens to be the number of planets. I t is not often noted that the claim that numbers have such essential properties is incompatible with the familiar idea that number theory can be reduced to set theory in various ways. According to the latter idea, the natural numbers can be identified with any of various sequences of sets. Zero might be identified with the null set, and each succeeding natural number might be identified with the set whose only member is the set identified with the preceding number. Or a natural number might be identified with the set of all natural numbers less than it. And there are an infinity of other possible identifications, all of which allow the full development of the theory of numbers. A particular set will be a composite number given certain reductions but not others. Apart from one or another of these reductions, we cannot say that a particular set is or is not a composite number. If de re necessity is in question, no set is necessarily a composite number. Being a composite number is not an essential property of any set. Therefore, if numbers can be identified with sets and de re necessity is in question, no number is necessarily a composite number. Being a composite number is not an essential property of any number. This does not count against the reduction of number theory to set theory unless there are independent reasons for believing that being a composite number is an essential property of certain numbers. One putative reason to believe this relies on the theory of "standard names." Such names are supposed necessarily to denote the entities they denote. Therefore it is supposed that the presence of standard names in necessary propositions can yield necessities de re as well as de dicto. In particular it is said that '9' is a standard name of 9. I t is necessarily true that 9 is a composite number. Therefore it is inferred that being a composite number is an essential property of 9. But this argument simply begs the question and provides no independent reason for its conclusion. Why assume that '9' necessarily denotes whatever it denotes? This is incompatible with the idea that number theory can be reduced to set theory, since on that idea what '9' denotes depends on which reduction is chosen. T h e incompatibility counts against the reduction only if there is inde2 Cf. David Kaplan, "Quantifying In," Synthtse, 178-214.
XIX,
112 (December 1968):
NOTES AND NEWS
185
pendent reason to suppose that '9' necessarily denotes whatever it denotes. No such independent reason has been provided. Defenders of de re necessity say little about how one is to determine what essential properties various entities have. Plantinga does suggest something like this: Baptise that entity which, as it happens, is the number 9. For example, call it "Charlie." Now ask whether it is necessarily true that Charlie is a composite number. If so, being a composite number is an essential property of 9. This test works only if we are given some idea how to decide whether it is necessarily true that Charlie is a composite number. But we are told nothing useful about that. The theory of de re necessity seems to be put forward less as an empirical hypothesis than as a metaphysical or religious doctrine. This impression is strengthened by the fact that its proponents rarely agree on cases. That many of them do agree about numbers is not obviously a point in their favor. Why should we take them seriously? GILBERT H. HARMAN
Princeton University
NOTES AND NEWS The Eastern Division of the American Society for Aesthetics will have its next meeting on Friday, April 17, 1970, 8:30 P.M. in the Faculty .Lounge (7th floor) of the New School for Social Research, 66 West 12 Street, New York City. Matthew Lipman, Professor of Philosophy, Columbia University, will speak on "The Arts of Prometheus". Professor Michael D. Bayles, Department of Philosophy, Brooklyn College, will preside. The Department of Philosophy at the University of Georgia announces a symposium on "Ontological Commitment" to be held April 2-4, 1970. Papers on various aspects of this topic will be read by Professors Charles Chihara, University of California at Berkeley; Romane Clark, Duke University; James W. Oliver, University of South Carolina; L. B. Cebik, University of Georgia; Bowman L. Clarke, University of Georgia; and Richard H. Severens, University of Georgia. Each paper will have a commentator; and the results of the symposium will be published by the University of Georgia Press. T h e University of Massachusetts at Arnherst is pleased to announce the appointment of Vere C. Chappell as Professor and Head of the Department of Philosophy. T h e present Head, Bruce Aune, will remain with the Department as Professor of Philosophy.
