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Explaining away Singular Non-existence Statements1

  • Karel Lambert (a1)


Nowhere in philosophy is there a more persistent kind of nuisance statement than the singular negative existential. Examples of this sort of statement are the descriptional statement

(1) The teacher at Sleepy Hollow doesn't exist,

and the referential statement

(2) Ichabod Crane doesn't exist.

Statements denying existence to a specific object have bothered philosophers from Parmenides to Ryle and Quine. Their high nuisance value rests in a simple paradox they generate. The paradox may be phrased as follows.



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2 The language is due to W. V. Quine; cf. Methods of Logic, 1961, p. 202.

3 In his review of Strawson's Introduction to Logical Theory, Quine is at some pains to show that solutions to philosophical problems do not, and need not, always proceed by direct attack. It is sometimes sufficient to present an analysis which outflanks or avoids difficulties arising in the usual or ordinary idiom. Russell's analysis of descriptional contexts is such an analysis. The point is vividly illustrated in the treatment of the existence paradox mentioned above. By treating singular descriptional contexts as paraphrasable (not translatable!) into general statements, the paradox of singular negative existentials is thus avoided. The conclusions in this paper are consistent with the spirit of this enterprise, (cf. “Mr. Strawson on Logical Theory”, Mind, October, 1953, pp. 433–450).

4 See, for example, Combinatory Logic by Curry, H. and Feys, R., North-Holland Publishing Company, Amsterdam, 1958.

5 W. V. Quine, Word and Object, 1960, p. 181.

6 Strawson, P. F., “Singular Terms, Ontology and Identity”, Mind, October, 1956, p. 447.

7 The theorem in question may be expressed as follows: (∃z) (y) (x = y ⊃ y = z).

8 Quine, Word and Object, p. 182.

9 Another way of putting the matter is this: a name ‘w’ can be translated in the manner of Quine if and only if ‘(∃z) (y) (Wy ⊃ y = z)’ is analytic, where ‘W’ is the predicate-correlate of the singular term ‘w’. I owe this phrasing to H. S. Leonard.

10 The Logic of Existence”, Philosophical Studies, June 1956, pp. 4964.

11 Nondesignating Singular Terms”, Philosophical Review, April, 1959, pp. 239244.

12 Existential Presuppositions and Existential Commitments”, Journal of Philosophy, Jan., 1959, pp. 125137.

13 Notes on E! III : A Theory of Descriptions”, Philosophical Studies, 1962, pp. 5159.

14 “The Definition of E(xistence)! in Free Logic”, Abstracts: International Congress for Logic, Methodology and Philosophy of Science, Stanford, 1960.

15 The claims in this paragraph are formally verifiable as follows: Russell's definition of The so and so exists may be phased in symbols as follows: (i) E! (ιx) ϕx = Df (∃x) (y) (ϕy = y = x). Letting ‘ϕ’ be ‘ = I’ (is identical with Ichabod Crane), (1) yields: (2) E! (ιx) (x = I) · = · (∃x) (y) (y = Iy = x). By virtue of Principia * 14.122, and the laws in Principia *10, (2) is equivalent to (3) E! (ιx) (x = I) · ≡ - : (∃x) (x = I). (∃x) (y) (y = Iy = x). A theorem in description theory is (4) y = (ιx) (x = y). (3) and (4) yield, (5) E! I · = : (∃x) (x = I). (∃x) (y) (y = Iy = x). (5) verifies the first sentence of the paragraph. But ‘(∃x) (y) (y = Iy = x)’ is a theorem in identity theory. Hence (5) reduces to: (6) E! I · ≡ · (∃x) (x = i). That is, Ichabod Crane exists if and only if something is identical with Ichabod Crane. And this is the desired thesis.

1 This paper is a slightly revised and amplified version of an address to the Canadian Philosophical Association, 1961.

Explaining away Singular Non-existence Statements1

  • Karel Lambert (a1)


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