Abstract
Shouldn’t we expect a proper account of existence sentences to do justice to claims involving empty names, especially those denying the existence of objects such as Pegasus and Vulcan? Pegasus is a product of ancient mythology and Vulcan an unnecessary and discarded posit of nineteenth century astronomy. A test of such accounts is how they deal with the problem Quine named ‘Plato’s Beard’. I begin by posing the Plato’s Beard problem as it appears in Quine and then as involving identity.’ David Wiggins extended the scope of this problem. Quine’s version concerned objects that do not exist. Wiggins extended it to objects that exist but might not have done so. I discuss Wiggins’ solution and one of two conceptions of “free logic”. I then suggest a solution along the lines of a second conception of free logic that has its roots in an older Aristotelian tradition.
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Notes
There are several ways of dealing with these problems. In Orenstein [2000] I examine the problem without appealing to identity. In Orenstein [1990] I take up Quine’s statement of the problem in Mathematical Logic (see Quine [1940]).
Cf. Wiggins [1994]. There are many varieties of the slogan that exists is not a real predicate. It is a mistake to cite Kant as in the Frege-Russell-Quine tradition of construing existence in terms of quantification. Kant in his general/formal logic is in the Aristotelian Terminist-Lesniewskian tradition of construing existentials in terms of the copula. See the last section of this paper and Orenstein [ 1978 ].
Wiggins on p.94 cites two strings which are translations into English of German sentences judged meaningless by Frege ‘There is Julius Caesar’ and ‘Julius Caesar exists’. I believe most who disagree with Frege would say that the second makes sense and is meaningful, but the first does not appear to be well formed and to constitute a sentence by itself. The first appears more well formed when we insert an article, i.e.,‘There is a Julius Caesar’.
Wiggins suggestion differs from Quine’s in that for Quine ‘= a’ is a fused predicate and has no logical structure so that one cannot existentially generalize with respect to ‘a’ (Quine [1960], pp.176–81). Wiggins allows such generalizations.
Not to be confused with views such as van Fraassen’s supervalutations and many-valued approaches where there is a truth vehicle but it may not have a truth value or may have more values than truth and falsity.
I think it fails to do so for him because he believes that it does not meet certain conditions for identifying the referent of a name (see Sainsbury [1990] and Wiggins [1994]).
It has also been used for issues concerning the empty domain though this aspect will not concern us here. (see Orenstein [1995]).
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Orenstein, A. (2002). Existence, Identity and an Aristotelian Tradition. In: Bottani, A., Carrara, M., Giaretta, P. (eds) Individuals, Essence and Identity. Topoi Library, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1866-0_5
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DOI: https://doi.org/10.1007/978-94-017-1866-0_5
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