Abstract
In recent philosophical discussion regarding the nature of the concept of existence and the logical theory of cognate concepts, the tendency has been to view these problems in their Kantian setting, by focussing upon the question ‘Is “exists” a predicate?’ and the bearing which these considerations have upon the validity of the ontological argument.1 Now it is, to be sure, inevitable that the logical theory of existence must in the last analysis rest upon ontological and not purely logical considerations. As Russell has said, ‘Pure logic has no occasion for names, since its propositions contain only variables. However, the logician may wonder in his unprofessional moments, what constants could be substituted for his variables.’2 But it is clearly anomalous to hinge the entire theory of existence primarily or largely upon only one of its ontological implications. And this is especially inadmissable when it happens to be what is, after all, the most remote, abstruse, and metaphysical of the problems here involved. Furthermore, a denial that ‘exists’ is a predicate, if stemming solely from repugnance to the ontological argument and desire for its overthrow, would be highly captious, and would be as wholly indefensible as any other purely ad hoc determination made solely for the purpose of evading an unwanted consequence. It is necessary to find other reasons, wholly independent of the ontological argument, upon which a denial that ‘exists’ is a predicate can reasonably be based. However crucial the question whether ‘exists’ is or is not a predicate may be for the validity of the ontological proof, there is surely no justifiable course but to base this decision, in the final analysis, upon other grounds. Pivoting the logical theory of existence about the ontological argument is to put the cart before the horse; they go together, it is true, but not in that order.
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References
See, for example, the following: H. S. Leonard, The Logic of Existence’, Philosophical Studies 7 (1956) 49–64 (especially pp. 57–58); G. Nakhnikian and W. C. Salmon, “Exists” as a Predicate’, The Philosophical Review 66 (1957) 535–542.
Human Knowledge (New York, 1948), p. 74.
The dualism of sets and classes in the set-theory of von Neumann is analogous with this predicate versus attribute distinction: every set is a class, but only under special conditions are classes sets. J. von Neumann, Über eine Wiederspruchsfreiheitsfrage in der axiomatischen Mengenlehre’, Journal far reine und angewandte Mathematik 160 (1929) 227–241. Improved formulations of this system are due to P. Bernays and K. Gödel. P. Bernays, A System of Axiomatic Set Theory’, The Journal of Symbolic Logic 2 (1937) 65–77; K. Gödel, The Consistency of the Continuum Hypothesis (Princeton, 1940 ).
The pioneer studies are: R. Chisholm, The Contrary-to-Fact Conditional’, Mind 55 (1946) 289–307; and N. Goodman, `The Problem of Counterfactual Conditionals’, The Journal of Philosophy 44 (1947) 113–128. A particular helpful survey of the extended literature is: E. F. Schneider, `Recent Discussions of Subjunctive Conditionals’, The Review of Metaphysics 6 (1952) 623–647. See also N. Rescher, Hypothetical Reasoning (Amsterdam, 1964 ).
G. Nakhnikian and W. C. Salmon, “Exists” as a Predicate’, The Philosophical Review 66 (1957) 535–542 (see p. 539).
W. V. Quine, Designation and Existence’, The Journal of Philosophy 36 (1939) 701–709 (see especially pp. 707–708). This article is reprinted in H. Feigl and W. Sellars, eds., Readings in Philosophical Analysis (New York, 1949 ).
Definition of “Existence”’, Philosophical Studies 7 (1957) 65–69 (see pp. 67–69).
The Logic of Existence’, Philosophical Studies 7 (1957) 49–64 (see especially p. 58).
Indeed just this is the thesis upon which rests the objection to (E4) shortly to be developed.
This objection to (E4) was raised in my paper on Definitions of Existence’, Philosophical Studies 7 (1957) 65–68 (see p. 67). This motivated my proposed (and here rejected) definition (E3).
This is set forth in his paper On Denoting’, Mind, N.S. 14 (1905) 479–493.
Grundgesetze der Arithmetik (Jena, 1873 ), Vol. 1, p. 19.
Mathematical Logic (Cambridge, 1947), pp. 147–149. A convenient comparative discussion of alternative definitions of `i’ is §§ 7–8 of R. Carnap’s Meaning and Necessity (Chicago, 1947 ).
Review of Metaphysics 2 (1948) 21–38; see p. 22. Reprinted in Semantics and the Philosophy of Language, ed. by L. Linsky (Urbana, 1952), pp. 189–206.
Ibid., 23–24; L. Linsky, op. cit., pp. 189–206.
See H. Wang, ‘The Logic of Many-sorted Theories’, The Journal of Symbolic Logic 17 (1952) 105–116.
For details see N. Rescher, ‘Many-sorted Quantification’, Proceedings of the 12th International Congress of Philosophy (Padua, 1958 ).
Mind, N.S. 14 (1905) 74–81, 295–296, 390–397, 401–402, and 578–580.
B. Russell, The Existential Import of Propositions’, Mind, N.S. 14 (1905) 398–401; On Denoting’, ibid., 479–493 (see especially p. 491); A. T. Shearman, Note on Logical Existence’, ibid., p. 440.
On Denoting’, Mind, N.S. 14 (1905) 491.
Symbolic Reasoning, V’, Mind 12 (1903) 355–364 (see p. 356).
This chapter is a somewhat expanded version of a paper On the Logic of Existence and Denotation’ published in The Philosophical Review 68 (1959) 157–180.
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Rescher, N. (1968). The Logic of Existence. In: Topics in Philosophical Logic. Synthese Library, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3546-9_9
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