absurd in the idea that nonexistence is a property, a. Nonetheless, I am convinced that nonexistence is a property. It is up to me to show, then, that this idea is not ...
ARNOLD CUSMARIU
NONEXISTENCE
WITHOUT NONEXISTENTS
(Received 13 May, 1977) The view that existence is a property, although as old as Plato 1 , has been a natural one to take since Frege's discovery of quantification. Once we paraphrase 'x exists' as ~ (y = x ) ' , it becomes easy to see that existence is a property, since it is expressed by an open sentence in one free variable. While this view of existence is a natural one, it has a consequence which has seemed less natural. For, given that every property has a complement a view also to be found in Plato 2 _ the view that existence is a property implies that nonexistence is also a property. But there seems to be something absurd in the idea that nonexistence is a property, a Nonetheless, I am convinced that nonexistence is a property. It is up to me to show, then, that this idea is not absurd.
I
One might be inclined to think that nonexistence is not a property because of an argument of the following sort: (1)
Necessarily, for any x, x exemplifies F-hess i f f x is F. 4
Realism
(2)
Necessarily, for any x and for any property F, if x exemplifies F then x exists. Necessarily, for anyx, ifx exemplifies nonexistence then x exists. Necessarily, for any x, ifx exemplifies nonexistence then x does not exist. Necessarily, f o r a n y x , if x exemplifies nonexistence then x exists and does not exist. .'. Nonexistence is not a property.
Premise
(3) (4) (5) (6)
Philosophical Studies 33 (1978) 409-412. All Rights Reserved Copyright 9 1978 by D. Reidel Publishing Company, DordrechL Holland
From 2 From 1 From 3, 4 From 5
410
ARNOLD
CUSMARIU
But this argument is invalid. (6) does not follow from (5). What follows from (5) is that (7)
Nonexistence cannot be a property of anything.
That is true: (7) merely says that it is necessary that everything exists. To get to (6) we would need either (8)
There are only those properties which are exemplified,
a view Aristotle may have held, s or the weaker (9)
There are only those properties which can be exemplified,
a view Chisholm has called 'Cautious' Realism. 6 But (8) and (9) would be denied by Realists who accept the standard reading of (1), that is, by Radical Realists, who accept (1) for any monadic 'Fx' and who are therefore entitled to distinguish sharply between the existence of a property and its exemplification. To support (8) and (9), Aristotelians and Cautious Realists would have to impose appropriate syntactical restrictions on 'Fx' in (1) - though it is far from obvious what these restrictions might be. From the Radical standpoint, there is no reason to bridle (1) any more than is absolutely necessary once one accepts a Realist framework, v
II What now follows from the fact that nonexistence cannot be a property of anything? One consequence is that negative existentials 8, such as (10)
Santa Claus does not exist
and (11)
There are no roundsquares
cannot be analyzed via (12)
Santa Claus exemplifies nonexistence
and (13)
Roundsquares exemplify nonexistence
because if (10) and (11) are true, then, given (2), (12) and (13) must be
NONEXISTENCE
WITHOUT NONEXISTENTS
411
false. So, it would be misleading to represent the logical form of (10) and (11) by means of (14)
Santa Claus is nonexistent
and (15)
Roundsquares are nonexistent.
But the fact that nonexistence is of no use here does not leave the Realist without a view of negative existentials. Propositions of this kind can be dealt with (partly) by putting to use the Fregean view that existence involves identity. Thus we can render (10) and (11) as (16)
Nothing is identical with Santa Claus
and (17)
Nothing is both round and square,
which may then be translated Realistically on the model of (1) as (18)
Nothing exemplifies being identical with Santa Claus
and (19)
Nothing exemplifies being round and square.
III
The resulting view is Deflationist, a s Cartwright would say, 9 for it shows how negative existentials can be true without implying, self-contradictorily, that there are those things whose existence is being denied in them. Since Radical Realists accept unexemplified properties, they are not committed to the existence of Santa Claus or roundsquares given that they accept the properties being identical with Santa Claus and being round and square - nor need they engage in obscure talk of nonexistent being. (Note that our view is not open to proponents of (8) and (9), who must deal with negative existentials some other way.) Further, my view makes it possible for the proposition that Santa Claus does not exist to be about Santa Claus in a sense o f ' a b o u t ' that is shared by the proposition that Caesar crossed the Rubicon) ~ The proposition that
412
ARNOLD CUSMARIU
Santa Claus does n o t exist is about Santa Claus in that it has as one o f its constituents a p r o p e r t y involving the c o n c e p t 'Santa Claus'; likewise, the p r o p o s i t i o n that Caesar crossed the R u b i c o n has as one o f its constituents a p r o p e r t y involving the c o n c e p t 'Caesar'. This m a y n o t be the sense o f ' a b o u t ' a child has in m i n d w h e n he wonders w h e t h e r the p r o p o s i t i o n that Santa Claus has a beard is a b o u t Santa Claus; b u t t h e n the p r o b l e m s generated b y such w o n d e r are strictly for adults, w h o find it harder t o be naive.
Salve Regina College
NOTES i See esp. Parmenides 142B, Theaetetus 186A and Sophist 259A. 2 See in particular Protagoras 332C-D. Good background discussions here are R. M. Gale, Negation and Non.Being, American Philosophical Quarterly, Monograph No. 10 (1976) and A. Plantinga, The Nature of Necessity, (Oxford Univ. Press, 1974), Chs. 7 and 8. 4 For Plato's own statement of this view, see Phaedo 100C-D and Parmenides 130E-13 lB. 5 An interesting recent interpretation of Aristotle's view is M. J. Cresswell, 'What is Aristotle's Theory of Universals?', Australasian Journal of Philosophy 53 (1975), 238247. 6 See R.M. Chisholm, 'Ein zuriickhaltender Realismus', Freiburger Zeitschrift fi~r Philosophie und Theologie (1976), 190-7. 7 There is more on this last and on problems with the view that (1) holds for any monadic 'Fx" in my dissertation A Platonist Theory of Properties (Brown University, 1977), Ch. VIII. 8 See the paper of the same title by R.L. Cartwright in Journal of Philosophy LVII (1960), 629-39. 9 See p. 631. lo See Cartwright, p. 633, where this requirement is suggested.
