Abstract
Meinong’s object theory suggests the possibility of making progress in a third alternative with respect to the long-standing apparently intractable collision in the metaphysics of Platonic realism versus nominalism. Meinong’s own views on the existence of such abstract mathematical entities as numbers and geometrical figures are considered, and the possibility of treating relations in particular as nonexistent Meinongian intended objects is developed at length. Russell’s argument that relations must exist as universals, even if qualities at first are not assumed to be existent, in order to do justice to the truth conditions of our predications of ordinarily properties to multiple ordinary objects, is also considered in this context as potentially undermining the Meinongian interpretation of relations as nonexistent. The effect of making relations nonexistent despite Russell’s argument is to achieve a considerable ontic reduction in a logic’s referential semantic domain, in accord with the methodological principle of Ockham’s razor not to multiply entities beyond explanatory necessity.
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Notes
- 1.
See Ross 1961, for an excellent discussion of Plato’s theory and Aristotle’s criticisms. Plato’s formulation of the ‘secret doctrine’ of Protagoras in Theaetetus 152c–153d, reverses the usual reduction of relations to qualities by holding that qualities do not obtain absolutely, but only in relation to a perceiver. Aristotle, Categories 7.
- 2.
An informative account of the medieval dispute over the ontology of properties and relations is presented by Carré 1946 and Henninger 1989. See Berkeley 1949–1958b, a, Three Dialogues, Works, II, 192-4; A Treatise on the Principles of Human Knowledge, Works, II, 29-45. Hume 1975, 154-5; 1978, 17. See also Armstrong 1978, Vol, 2. Loux, ed. 1970. Wolterstorff 1970.
- 3.
Russell’s pronouncements about the British empiricists having ignored the theory of relations in favor of concepts of qualities are misleading in the extreme. To consider just Hume’s Treatise, there is such an extensive treatment of the concept that the analytical index for ‘Relation’ in the Nidditch edition runs to two full pages in small print. It is worth remarking that Hume’s rejection of universals is not directed exclusively toward unary qualities or properties, but toward ‘abstract or general ideas’, without further qualification (Hume 1978, 17). It is at least conceivable that Hume regarded the distinction between qualities and relations as superficial, and therefore subsumable and subject to the same criticisms under the same category. Meinong wrote his Habilitationsschrift at the University of Vienna, the Hume-Studien I, II, respectively on Hume’s nominalism and theory of relations. See supra Chap. 8, note 7; Barber 1970, 1971.
- 4.
- 5.
If we begin with the abstract, Z = λx[¬xx], and the abstraction equivalence principle ∀y[λx[…x…]y ↔ (…y…)] holds, then from ZZ ∨ ¬ZZ, it follows that ZZ ∧ ¬ZZ. To avoid diagonalizations of this kind, and forestall logical paradox without invoking type theory, restrictions of various kinds are sometimes placed on abstraction equivalence. I present several ways of constructing diagonalizations within the constraints of simple type theory in Jacquette 2004c, 2010a, 234–47, 2013a.
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Jacquette, D. (2015). Virtual Relations and Meinongian Abstractions. In: Alexius Meinong, The Shepherd of Non-Being. Synthese Library, vol 360. Springer, Cham. https://doi.org/10.1007/978-3-319-18075-5_12
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