In Defence of the Predicate `Exists'

Mind Association

In Defence of the Predicate `Exists'Author(s): Barry MillerSource: Mind, New Series, Vol. 84, No. 335 (Jul., 1975), pp. 338-354Published by: Oxford University Press on behalf of the Mind AssociationStable URL: http://www.jstor.org/stable/2253554 .

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In Defence of the Predicate 'Exists'

BARRY MILLER

Problems about existence are almost as old as philosophy itself. But for a brief period in this century they seemed to some to have been finally dissolved. It was then confidently asserted that if 'exists' were a predicate or existence a property, 'it would follow that all existential propositions were tautologies, and all negative existential propositions are self-contradictory'.' No need to distinguish between singular and general existential propositions, nor to make any distinction within general propositions. No matter where it occurred, 'exists' was not a predicate.

Few would take that view today. Many would hold that 'exists' is a predicate, though they would hasten to add some qualification. Pears2 would say that it is a 'peculiar' predicate, Salmon and Nakhnikian3 that it has 'special characteristics', Hintikka4 that it is 'redundant', Quine5 that it is a second-level predicate, and Kearns6 and Redmon7 that it is a metalinguistic predicate. Diverse though these positions be, they are at one in denying the view I defend in this paper-that 'exists' is ambiguous, being sometimes a first level predicate and only sometimes (not always) a second level one.

I A. J. Ayer, Language, Truth and Logic (2nd ed., London, I947), p. 43. 2 D. Pears, 'Is Existence a Predicate?', in P. F. Strawson (ed.), Studies in

the Philosophy of Thought and Action (Oxford, I968). 3 W. Salmon and G. Nakhnikian, ' "Exists" as a Predicate,' Philosophical

Review, lv (I957), 535-542. 4 J. Hintikka, Models for Modalities (Dordrecht-Holland, I969). 5 W. V. Quine, Word and Object (Cambridge (Mass.), I960). 6 J. T. Kearns, 'The Logical Concept of Existence', Notre Dame Journal of

Formal Logic, vol. 9 (I968): 'To say that ah individual exists, then, is to endorse it (or its name) as a candidate for certain kinds of statement' (p. 320). 'It ["exists"] is the basic concept of an interpreted system (for thinking about individuals), and it cannot be reduced to more fundamental concepts' (p. 322).

7 R. B. Redmon, ' "Exists",' Mind, vol. lxxii (I973): ' .. . "exists" as used when we have a sentence of a form "a exists" or "a does not exist" when "a" is a proper name, tells us something about the name "a" ' (p. 59).

" .. . a exists" is a metalinguistic means of pointing out that "a" has a use' (p. 64).

338



IN DEFENCE OF THE PREDICATE 'EXISTS) 339

I

Their unanimity is grounded largely in the view that to admit 'exists' as a first level predicate would lead on the one hand to the absurdity of regarding existence as a property, and on the other to the paradox generated by negative existential propositions.

As to the first, presumably it is thought that if existence were a property, then non-existence would be one also. And that would give rise to the ludicrous situation described by David Londey, when he invites us to 'reflect on the absurdity of a sheep-farmer who daily inspected his flock with the aim of sorting the existing sheep from the non-existent ones-searching for the stigmata of existence'.1 In thus concluding that existence is not a property he enters distinguished company, for Kant had declared that ' "Being" ... is not the concept of something which could be added to the concept of anything',2 and Hume that the idea of existence, 'when conjoined with the idea of any object, makes no addition to it'.3

As to the paradox generated by negative existential propositions, it arises in this way. If 'exists' is a predicate, then its negation should be a predicate also. But if 'does (do) not exist' is a predicate, then in 'Dragons do not exist' it is predicated of dragons. But, it can be predicated of dragons only if dragons exist. And similarly for all negative existential propositions-paradoxically, if it is to be predicated at all, 'does (do) not exist' can be predicated only of what does exist.

Nor do singular propositions like 'Socrates does not exist' seem to fare any better than general ones like 'Dragons do not exist'. Despite his demise there are of course many true predications that can still be made of Socrates, e.g. that he was a philosopher, that he was Greek, and the like. But all of these were true of Socrates while he was yet alive. If, however, 'does not exist' were true of him, it could be so only after there was any Socrates for it to be true of. So precisely the same paradox arises with Socrates as arose with dragons.

We can escape it by treating 'exists' as something other than a first level predicate. In doing so we also remove perhaps the strongest ground for regarding existence as a property. And thus in one move we avoid putative paradox and absurdity alike.

I D. G. Londey, Philosophia Arhusiensis, no. i, I970, p. 6. 2 Critique of Pure Reason, B626. 3 A Treatise of Human Nature, bk. i, part II, section VI.



340 BARRY MILLER:

II

Russell succeeded in doing exactly that with his widely accepted view of existence as a property not of things but of propositional functions, a proposal made in connection with his treatment of definite descriptions. As such, its immediate application is only to general existential propositions, but not to propositions like 'Socrates exists'. Since Russell regarded 'Socrates' as merely a disguised description, he himself would have rejected this re- striction. But for those who do not share Russell's view on 'Socrates' and the like, there is the proposal of Quine and Hintikka that 'Socrates exists' can be reparsed as '(Ex) (x = Socrates)'.

If this is correct, then we have a means of handling existential propositions that treats them as neither tautologies nor contra- dictions, yet without the difficulties that would arise if 'exists' were a predicate. Further advantages are claimed for it. Basically, singular existential propositions may be treated in the same way as general ones. There is no need for multiple senses of 'exist'. Indeed, 'exists' itself is made redundant, being replaceable by the more general apparatus of quantifiers and identity. And, finally, there is no need to recognise, as the early Russell did, entities that subsist in addition to those which exist. Thus the theory seems not only to solve the problem, but to do so with an economy that enhances its appeal.

Why then not accept it? Simply because it is flawed by failure to distinguish between two kinds of uniqueness.' One is the uniqueness of a precise individual, which, while characteristic of non-fictional proper names, is unattainable by descriptions or predicates of any kind. The other is the uniqueness of precisely one individual, which is the most that predicates and descriptions can achieve.

Let me enlarge on this briefly with the help of the following two propositions: i. 'The one and only individual that F's is thinking dark thoughts.' 2. 'Socrates is thinking dark thoughts.' Now, in regard to (2) it would make perfectly good sense to point to an individual and ask, 'Is that the individual that (2) is about?'; for the proposition can be made true only by a particular individual, viz. Socrates. On the contrary, there is no particular individual

I have developed this point at some length in 'Proper Names and Their Distinctive Sense', Australasian Yournal of Philosophy, li (I973), 2oi-2IO.



IN DEFENCE OF THE PREDICATE 'EXISTS' 341

required to make (i) true. It would be true if there were any (though admittedly only one) individual that F's. For that reason, although it would make sense to point to an individual that F'd and ask 'Is (i) satisfied by that individual?', it would make no sense whatever to ask 'Is that the individual that (i) is about?'. The individual pointed to may make (i) true, but it cannot be the one that (i) is about, since any individual that F'd would make (i) true. Precisely one individual is required to make (i) true, but no precise one.

It is only by ignoring the distinction between a particular individual and exactly one individual that Russell is able to assimilate all existential propositions to the model of general ones like 'Dragons exist' or 'The King of France exists'. By reparsing the former as 'Some things are dragons', and the latter as 'One and only one thing is a King of France', each proposition is shown to conform to the one logical pattern.

Apparently one way of imposing that pattern on singular existential propositions -as well would be simply to convert their logical subject into a predicate. In this way 'Socrates exists' would become 'One and only one man is a philosopher, a Greek, a teacher of Plato, . . .', the blank being filled by additional general terms. I do not concede that any number of such terms would make the proposition true in principle. But even if they could, the resulting proposition would still not be an adequate reparsing of 'Socrates exists'. Whereas 'Socrates exists' can be made true only by a precise individual, its putative reparsing could be made true by any (though only one) individual that is a philosopher, a Greek, etc. That difference is an irreducible one. It would remain, even if the Identity of Indiscernibles were true; it effectively bars any elimination of non-fictional proper names in favour of descriptions or predicates.

Not a few, however, continue to urge that at least one kind of predicate is not covered by my conclusion. Surely predicates like '= Socrates' or 'has Socrates-identity' would be true not merely of precisely one man, but of a precise one, viz. Socrates. In which case 'Socrates exists' would be adequately rendered by '(Ex) (x- Socrates)', thus conforming to the same pattern as general existential propositions.

It can be shown that Socrates-identity is in fact identical with Socrates. So, since a property cannot be identical with what it is a property of, Socrates-identity cannot be a property. But that need



342 BARRY MILLER:

not be argued for here since, although an individual can have no property for which a corresponding first level predicate is not possible, it is by no means evident that for every first level predicate there must be a corresponding property. Hence one could deny that Socrates-identity is a property, but still affirm that '= Socrates' is not merely a unique predicate but a singular one to boot. But there is no need to try to refute that claim either. For it suffices to show that, even if '- Socrates' were a singular predicate, 'Something is identical with Socrates' or '(Ex) (x = Socrates)' would be an inadequate reparsing of 'Socrates exists'.

At least part of its inadequacy concerns tensing. Whether tenses are eliminable is a topic too big to be pursued here, so on that point I merely nail my colours to the mast. Mine is the not very popular thesis that the truth of a proposition need not be indifferent to temporal perspective. I agree with Lucas that 'the principle of date-indifference is a principle [that is] not of logic'.' And if that is so, it is correct to say that, once true, 'Socrates exists' can sub- sequently be false. Its suggested reparsing, however, cannot. It would make no more sense to say 'Someone was identical with Socrates' than to say 'Socrates was identical with Socrates'. On the contrary, however, it would make perfectly good sense to say 'Socrates existed (in the fifth century B.C.)'. Hence the reparsing fails.

That, then, rather puts paid to the attempt to treat singular existential propositions in the same way as some general ones. To be able to do so would require that proper names be eliminable in favour of existential quantifier and predicates. This could take two forms, depending on whether the predicates used were general or (allegedly) singular. But, as it now appears, neither way can do the job. So 'exists' is not always a second level predicate, nor existence always a property of propositional functions.

III

So much for criticism of that thesis. A positive alternative is provided by the following argument to show that 'exists' has not one, but two senses.

Whatever can be predicated of a kind differs absolutely from what can be predicated of an individual. But 'exists' is predicated of both individuals and kinds.

I J. R. Lucas, A Treatise on Time and Space (London, I973), p. 299.



IN DEFENCE OF THE PREDICATE 'EXISTS) 343 Therefore, 'exists' has two senses-one as predicated of individuals, the other as predicated of kinds.

Against the major someone might admit that some predicates of individuals are clearly inapplicable to kinds, but say that it is not clear that all are. Could not 'exists' be unique in this respect? Such an objection may rest on the view that if an object falls under a first level concept and that first level concept itself falls under a second level concept, then surely it is not impossible that the object should also fall under the second level concept. This of course would prove too much, since it would prove that an object falling under a first level concept should fall under any second level concept that the first level concept falls under. But there are clear cases where that is not true. For example, although Eric may be an elephant, and elephants may be numerous, it would make no sense to say that Eric is numerous.

The flaw in the original suggestion lay in regarding the relation of object to first level concept as no different from that of first level concept to second level concept. But, as Frege pointed out, 'the relation of an object to a first-level concept that it falls under is different from the (admittedly similar) relation of a first-level to a second-level concept. (To do justice at once to the distinction and to the similarity, we might perhaps say: An object falls under a first-level concept; a concept falls within a second-level concept.)'1

Although there are two ways in which a predicate might be conceived as being applicable to both kinds and individuals, it is not difficult to show that neither is tenable. One way would be for a second level predicate to be said of both individuals and kinds, the other for a first level predicate to be said of them. As regards the first case we must be clear as to precisely what kind of expression can be said of what a first level predicate refers to (e.g. a kind, or Fregean concept). If we consider the proposition '(Ex) (x is F)', the first level predicate is '__ is F'. The second level predicate attached to it is however not simply '(Ex)', but '(Ex) (x

)'. If we now ask whether the second level predicate could equally well be attached not only to a first level predicate but to a proper name as well, it is clear that it could not. The bound variable, which filled the gap in '__ is F', has nowhere to go when '__ is F' is replaced by a proper name. The expression that results from such a combination is therefore meaningless. I 'On Concept and Object', in Peter Geach and Max Black, Philosophical

Writings of Gottlob Frege (znd ed., Oxford, I960), pp. 50-5I.



344 BARRY MILLER:

Nor does anything better come of the second alternative mentioned above. If ' is F' and ' - is G' are two first level predicates, then the result of combining them would be '( is G) is F' or '(-- is F) is G'. Either combination would still be an open sentence, as the gap would be filled by neither a bound variable nor by a proper name. Hence this kind of expression, too, is nonsensical.

Since no predicate can be attached to both proper names and first level predicates alike, it is clear that no predicate, whether first level or second level, can be said of both individuals and kinds. And that establishes the major premise.

The minor premise can be proved in two ways-either by con- trasting singular existential propositions with one kind, of general existential proposition or by drawing attention to the fact that there are two kinds of general existential proposition. In regard to the first way, we have 'Socrates exists', which is about an individual (Socrates), and 'Men exist', which may not be about individual men at all but simply about being a man. This would be the case if 'Men exist' were translated as '(Ex) (x is a man)', for this says merely that being a man is instantiated at least once. The only way of eliminating the difference between 'Socrates exists' and the foregoing rendering of 'Men exist' is to reparse 'Socrates' as a predicate, and that move has already been discredited.

But even with no recourse at all to singular existential propositions 'exists' can still be shown to be predicable of both individuals and kinds. It is done by showing that not all general existential propositions are about kinds, but that some are about individuals. In support of this claim I offer the example of 'elephants exist' in the following:

(a) 'Elephants exist, but mermaids do not'. (b) 'Elephants exist, but dinosaurs do not'.

In (a) 'exist' is being said of being an elephant, not about individual elephants, whereas in (b) it is being said of individual elephants, not about being an elephant.

This can readily be substantiated. Since, in (a), 'elephants exist' is being contrasted with 'mermaids do not', the sense in which 'elephants' is being used will be the same as that in which 'mermaids' is being used. Now 'mermaids do not exist' makes sense only if it means that all predications of the form 'x is a mermaid' are false. And it cannot mean that any proper name which turns



IN DEFENCE OF THE PREDICATE 'EXISTS' 345 'x is a mermaid' into a true statement will turn 'x does not exist' into a true one, the simple reason being that there are no non- fictional proper names available for substitution in 'x is a mermaid'. Hence 'mermaids' is being used to refer to being a mermaid, not to individual mermaids. And so 'elephants' in the accompanying clause must refer to being an elephant.

I think that the only way to escape this conclusion would be to say that proper names can be substituted in 'x is a mermaid', something that Quine would no doubt be prepared to do, since he allows that fictional entities can have proper names. But this is inadmissible. There is the same absolute distinction between fictional proper names and non-fictional ones (i.e. names of individuals that do or have existed) as was noted earlier between predicates and non-fictional proper names. A non-fictional proper name refers to a particular individual. On the contrary, a fictional proper name is only a disguised definite description, and as such is applicable to exactly one individual but to no one in particular. So there are no grounds for saying that genuine proper names can be substituted in 'x is a mermaid', and so no grounds for saying that 'mermaids do not exist' can be indifferently about kinds or individuals.

In (b), on the contrary, neither do 'elephants' refer to being an elephant nor 'dinosaurs' to being a dinosaur. If they did, the proposition would not only be false, but the 'but' would be quite misleading since there would be no point of contrast between the first and second clauses. The only way in which the contrast can be retained is if 'elephants' and 'dinosaurs' refer to individuals. So, in (b), 'Elephants exist' is a general existential proposition that is about individuals, as contrasted with the same clause in (a) which is not about individual elephants but merely about being an elephant.

Thus the minor premise-that 'exists' is predicated both of kinds and of individuals-has been vindicated. From it and the major it follows that 'exists' has two senses, one as predicated of individuals, the other as predicated of kinds. These are called by Geach the actuality and there-is senses respectively.'

From what has been said, it is obvious that these senses are not univocal. This is evident too from the fact that 'Elephants exist (there-is sense)' no more implies the true proposition 'Elephants

I P. T. Geach, 'What Actually Exists', Proceedings of the Aristotelian Society, Supp. vol. xlii (I968), 7-I6, especially 7-8.



346 BARRY MILLER:

exist (actuality sense)' than does 'Dinosaurs exist (there-is sense)' imply the false proposition 'Dinosaurs exist (actuality sense)'. But nor are they equivocal, as Dummett suggests they should be.' If they were, then 'Elephants exist (actuality sense)' would not imply (as it does imply) 'Elephants exist (there-is sense)', i.e. 'There are such things as elephants'. Thus the senses of 'exists' are not casually ambiguous, but merely systematically so.

IV Doctrines about 'exists' are often inseparable from doctrines about existence. Thus the view of 'exists' as a univocal expression and as exclusively a second level predicate is inseparable from the view of existence as a property not of things but of propositional functions. The conclusion just reached is of 'exists' as a systematically ambiguous expression, a predicate not exclusively of second level but sometimes of first level. Does this too have implic^ations for existence? Does it mean that existence is a property of things? If being wise is a property corresponding to the predicate 'is wise', existence would seem to be a property corresponding to the predicate 'exists'. As will appear, however, this question does not admit of so simple an answer.

It seems to assume that there are properties of things, that being wise is one of them, and is in fact the referent of 'is wise'. It assumes too that existence would be the referent of 'exists'. We may or may not agree with such assumptions, but let us go along with them, since it is only on that basis that it is worth discussing whether existence is a property. My intention then is to consider a necessary condition for being wise to be a property, to pursue the implications of that condition, and then to see whether the same or different conclusions would be applicable to existence.

Let me first make a concession to literary convenience. Although strictly the property corresponding to 'is wise' would be being wise, I think misunderstanding can easily be avoided even if I use 'wisdom' in its stead; so that is what I propose to do. Now the first point I want to make is that, contrary to what Platonists may hold, wisdom is not individuated in se. The wisdom of Socrates, or of Plato, or of Einstein may have featured in the universe, but never wisdom tout court.

I am saying not merely that wisdom occurs only as individuated; M. Dummett, Frege, Philosophy of Language (London, 1973), p. 386.



IN DEFENCE OF THE PREDICATE 'EXISTS) 347

I am saying also that it is not individuated in se, but simply by what it is a property of. To deny that position-to say that individuals are individuated by their properties-it would not suffice to prove the Identity of Indiscernibles true. The Identity of Indiscernibles could guarantee no more than that a certain set of properties was limited to one and only one individual. It could provide no clue whatever as to just which individual that is. If properties alone were to provide that kind of knowledge, they themselves would have to be individuated in se.

That kind of individuation, however, would require sense to be made of the possibility that a property of one individual should become the numerically identical property of another individual. If individuals in their own right, properties ought to be able to migrate from one bundle to another with in principle no more difficulty than people migrating from country to country. Sense would have to be made, therefore, of a sheet of paper A acquiring not merely the same degree of hardness as sheet B, but B's hardness. And to make sense of that situation the hardness in question would require a criterion of identity that was independent of both A and B. Precisely because there is no such criterion, one may conclude what in any case seems intuitively evident, viz. that properties are individuated by what they are properties of. That of course is not to say that individuals could be devoid of properties -the bare particular theory finds no support in the thesis that properties are individuated by individuals.

If the latter is correct, however, the role of Socrates vis-'a-vis wisdom is that of individuater. One might then ask what demands such a role places on Socrates, what requirements he must satisfy if he is to be an individuater of properties. For example, could he be one if he were not a philosopher, or not a Greek? Clearly, yes. If he were not a man? Yes, again. Naturally, he would have to be some kind of thing; but it is not required that he be any one kind of thing rather than another. Could be he an individuater, if he were himself not individuated? Obviously not. As an individuater he himself must be individuated; and that means that he must be identical with himself.

That conclusion may seem a truism, and indeed it is. But to appreciate its significance we have only to reflect that not all terms are appropriate for use on either side of the identity sign. 'Socrates' can be so used, but 'wisdom' can not. Since only referring expressions can occupy that position, 'wisdom wisdom' for



348 BARRY MILLER:

example would make no sense whatever, 'wisdom' not being a referring expression. In other words, identity-the minimal reflexive relation between objects, as Dummettl puts it-is not a relation that could be had by wisdom. Hence it is not without point to note that Socrates (unlike wisdom) is identical with himself, and that this is a prerequisite for his being an individuater of properties.

There is, however, a further prerequisite. For, though it is true even today that Socrates is identical with himself, it is not true that Socrates can today individuate anything. No doubt he did so in the past (e.g. wisdom was individuated by him), but that is not the point. Whereas it would make no sense whatever to say 'Socrates was identical with Socrates', it would make quite good sense to say 'Socrates was wise'. The former makes no sense because, once true, 'Socrates Socrates' can never be false. The latter does make sense because 'Socrates is wise' can be true only when 'Socrates exists' is true, and that is not always.

Hence, for Socrates to function as an individuater of properties, it is not sufficient that he be identical with himself: 'Socrates exists' must be true as well. And, since for the purposes of the present discussion existence is being taken as the referent of 'exists', it now appears that a necessary condition for Socrates to be an individuater of wisdom is that there be some relation between him and existence. So, wisdom has turned out to be related to Socrates as to its individuater, and Socrates to be related to existence as to a necessary condition for functioning as an individuater. These relations might be depicted thus:

(individuated by) R A. wisdom > Socrates > existence

Much the same needs to be done for existence if it is to be compared with wisdom; but this can be quite brief. The discussion on wisdom began by showing it to be individuated by what it is the wisdom of, e.g. Socrates. But existence, too, is found only as individuated by what it is the existence of. Consequently, the same conclusions can be drawn for existence as were drawn for wisdom. Existence must be individuated by Socrates, and must also be related to Socrates as a necessary condition for his having the role of individuater. Paralleling (A), therefore, we have,

(individuated by) R B. existence > Socrates- > existence

M. Dummett, Frege, Philosophy of Language, p. 544.



IN DEFENCE OF THE PREDICATE 'EXISTS 349

What then are we to say? Is existence a property or not? The answer must be a conditional one. But if there are properties and if wisdom (or being red, or being hot) is a property, then an answer can be given, though not a straight yes or no-. For it has emerged that existence is like wisdom and every other property in being individuated not in se, but by individuals. On that score it might well be regarded as a property. But it is also unlike wisdom and every other property in that its possession by an individual is a necessary condition of that individual's being individuated. So, existence could rightly be called a property, but only if it were also said to be a unique one.

V

It is interesting that two recent objections to 'exists' being a first level predicate seem to assume it would mean that existence was a property. C. J. F. Williams bases his objection on the thesis that 'to predicate something of an object is to presuppose the existence of the object at the time which the predicate is said to hold of the object'.' If correct, then to predicate non-existence of Socrates would paradoxically presuppose the existence of Socrates at the time of the predication. For, 'while there is no difficulty about my now, in I967, predicating of the G.W.R. that its labour relations were bad in the nineteen-thirties, it would be very odd, given that the G.W.R. ceased to exist in I947, for me to predicate of it that its labour relations were good in the nineteen-fifties. Again if my Scottish terrier died in I96I I could hardly say of him that he had distemper in i963'.2 Although Williams states his case in terms of predicates and predication, his distemper example indicates that he would be equally happy to do so in terms of properties.

It seems that basically his objection is to the possibility of something changing after it no longer exists. If that is his point, it is quite unexceptionable. No one, I take it, would seriously suggest that Socrates could become wise in the twentieth century, nor that Williams' dog (d. I96I) should contract distemper in the I97os. Changes simply cannot occur in the non-existent.

But Williams apparently thinks that this is precisely what would have to be denied, if 'exists' were a first level predicate. His argument, as I understand it, is:

I C. J. F. Williams, 'On Dying', Philosophical Quarterly, xliv (i969), 222-223.

2 Ibid. p. 223.



350 BARRY MILLER:

If 'exists' is a first level predicate, then to say 'Socrates does not exist' is to say that some change has occurred in a non- existent Socrates. But no change can occur in the non-existent. Therefore, 'exists' can not be a first level predicate.

The error in the major becomes evident by reflecting that Socrates' beginning or ceasing to exist could be a change in Socrates only if the former were regarded as the acquisition of something (existence) and the latter as a corresponding loss. Now it is fairly clear that Socrates could acquire existence only if there were already a Socrates to be its recipient. For that reason, although Socrates might acquire wisdom, or height, or a bad cold, he could never acquire existence. So, neither (A) 'Socrates began to exist' nor (B) 'Socrates ceased to exist' can entail that any change occurred in Socrates. It would therefore be logically more per- spicuous to render them,

A'. 'It began to be the case that Socrates exists.' B'. 'It ceased to be the case that Socrates exists.'

Now, (C) 'Socrates does not exist' can be treated in similar fashion, by exporting the negation operator thus:

C'. 'It is not the case that Socrates exists.' What is predicated (though not asserted) of Socrates is 'exists' (not 'does not exist'), and what is asserted is that it is not the case that Socrates exists. Since 'exists' could perfectly well be predicated of Socrates during his lifetime, there is now no ground for Williams' objection.

Dummett, however, has raised a different point, claiming that the error in treating 'exists' as a first level predicate 'may be recognized by asking whether "Cleopatra no longer exists" says that Cleopatra no longer has a certain property. There is as much absurdity in saying that there is such a person as Cleopatra, who no longer has the property of existing, as in saying that there is such a substance as phlogiston, which lacks the (timeless) property of existing. Beauty is a property which Cleopatra had when a woman, and may have lacked as a baby; but existence, even when atemporal, is not a property that may be first acquired and later lost.'1

Despite recognizing that 'Cleopatra' is a referring term and 'phlogiston' is not, Dummett still seems to find some parallel I M. Dummett, Frege, Philosophy of Language, p. 387.



IN DEFENCE OF THE PREDICATE 'EXISTS' 35I

between 'Cleopatra no longer exists' and 'Phlogiston does not exist', such that if the latter is absurd so too is the former. The absurdity of 'Phlogiston does not exist' is supposed to become obvious by rendering it as 'There is such a substance as phlogiston, which lacks the (timeless) property of existing.'

That of course assumes that the latter is an adequate reparsing of 'Phlogiston does not exist'-a false assumption as it happens. If 'Phlogiston does not exist' is true, then 'phlogiston' can be only a predicate, but never a name. But in the proposed reparsing, which is only a long way of saying 'Phlogiston is a substance, which lacks the (timeless) property of existing', 'phlogiston' is used as a name. Yet that is possible only if phlogiston had existed, a possibility ruled out by the rest of the proposition. Hence the absurdity in the reparsing (though not in the original). But there is no parallel absurdity in 'There is such a person as Cleopatra, who no longer has the property of existing'. Whatever may be thought of its adequacy as a reparsing, it does not attempt to use 'Cleopatra' as a name whilst at the same time precluding the very situation that would make that use possible. It says merely that Cleopatra no longer exists, not that she has never existed.

Dummett, however, could quite well concede this, without detriment to his position. For it is precisely 'Cleopatra no longer exists' that he sees as posing the main problem, which I take to be this:

It is wrong to think of beauty as a property: 'only things like being beautiful at a certain stage in one's life are properties.' 'Properties, thus understood, are atemporal, that is things of which it makes no sense to say that one acquires them or loses them.'" But if 'exists' is a first level predicate, then to say 'Cleopatra no longer exists' is to say 'Cleopatra no longer has a certain property', i.e. that Cleopatra has lost a property. But that makes no sense, for properties are atemporal. Therefore, 'exists' is not a first level predicate.

The argument is not strengthened by its reliance on a philosophical doctrine (embracing a four-dimensional ontology) that is controversial in a way that its counterpart in physics is not. But even waiving all reservations on that score, the argument would still fail. The point is that 'Cleopatra no longer exists' does not imply that Cleopatra has lost a property (even if we agreed to I Ibid.



352 BARRY MILLER:

regard existence as a property). As has been seen, 'Cleopatra no longer exists' should be rendered, 'It is no longer the case that Cleopatra exists'. As this carries no suggestion that Cleopatra has lost anything at all, Dummett's objection lapses.

Moreover, as a result of discussing his and Williams' observa- tions there is now no difficulty in avoiding both the paradox and absurdity alleged to arise from 'exists' being a first level predicate. The paradox occurs only if 'Socrates does not exist (any longer)' is construed as containing the predicate 'does not exist (any longer)'. We have just seen, however, that the proposition is to be rendered, 'It is not the case (any longer) that Socrates exists'. And since this does not contain the offending predicate, the paradox does not arise.

Similarly for the absurdity of regarding non-existence as a property. A necessary, though insufficient, condition of non- existence being a property is that 'does not exist' be a logical and not merely a grammatical predicate of individuals. But the condition is not satisfied even in the case of 'Socrates does not exist'. So, although it would indeed be absurd to treat non-existence as a property and so to risk joining Londey's sheep-farmer in 'sorting the existing sheep from the non-existent ones', it is not an absurdity that follows from 'exists' being a first level predicate.

VI The view that 'exists' is a first level predicate has been seen to rest on a fourfold distinction, viz.

i. between external and internal negation; 2. between the uniqueness of a particular individual and that

of exactly (though no particular) one; 3. between predicates appropriate to individuals and those

appropriate to kinds or attributes; 4. between Socrates being identical with himself and Socrates

existing, i.e. between 'Socrates = Socrates' and 'Socrates exists'.

We are now able to take a synthetic view of their respective roles. The first distinction has just provided simple answers to a

number of objections, and in particular to the perennial one based on the fear of paradox and absurdity. In dispelling such fears it has eliminated one powerful reason for seeking any alternative doctrine on 'exists'.



IN DEFENCE OF THE PREDICATE - EXISTS' 353

But another reason for espousing some alternative doctrine has been the view that even non-fictional proper names are eliminable by descriptions-preferably by ordinary ones, but where necessary by ones like 'the thing that is identical with Socrates' or 'the thing that socratizes'. Ordinary descriptions, however, have proved inadequate because they violate distinction (2), and Quinean descriptions because they violate (i).

Distinction (z) not only undermines the attempt to restrict 'exists' to one sense, it also undergirds (3), which is the heart of the argument for 'exists' having two senses-as a first and as a second level predicate respectively.

This conclusion is, I think, inescapable. All the same, it does give rise to the familiar puzzle as what difference existence can possibly make to a thing. Maybe the well-known paradox of singular existential propositions is not insoluble, and maybe the one-sense thesis of 'exists' is based on a mistake, but maybe too there is some flaw in the two-sense thesis. For, if 'exists' is a first level predicate, existence should make some difference. But- shades of Kant and Hume-what possible difference can it make?

No answer is possible until we pinpoint what exactly the puzzle is; and it could be any of three. First, it may arise from trying to imagine some difference between Socrates as existing and as not existing. If so, that need give no more trouble now than does the case of Londey's sheep-farmer: to accept 'exists' as a first level predicate is not to accept that non-existence is a property.

Second, it may stem from difficulty in finding any difference between Socrates as (putatively) imagined before conception and Socrates after birth. But that can arise only by overlooking distinction (2). For, before his conception no one could have imagined Socrates, though it would have been perfectly possible to have conceived that exactly one individual would have all the attributes that Socrates later had.

Third, it may be grounded in inability to see that 'Socrates exists' adds anything to 'Socrates - Socrates'. It is here that (4) is relevant. That there is a difference between Socrates being Socrates and Socrates existing is evident from the fact that, once true, 'Socrates Socrates' can never be false whereas 'Socrates exists' can.

Acceptance of the four distinctions and the conclusion they support does not, however, mean rejecting all points made by opponents of the two-sense thesis. Thus, one can agree that in

I2



354 BARRY MILLER: THE PREDICATE 'EXISTS'

many general existential propositions 'exists' is used as a second level predicate; and to that extent I have no quarrel with Russell, Quine and Hintikka. One can accept from Pears that 'exists' is a 'peculiar' predicate, a conclusion which is inescapable if we reflect that the difference noted between existence and wisdom will be paralleled by a difference between the predicates 'exists' and 'is wise'.

One can agree with Kearns that 'the difference between existing and not existing is not a difference between individuals that we encounter',1 but still not accept his contention that it is a merely 'linguistic difference'. He is correct in thinking that 'exists' is 'the basic concept of an interpreted system (for talking about individuals)',2 but wrong in thinking with Redmon that its role is a metalinguistic one. Admittedly, 'Socrates exists' can ground metalinguistic conclusions, e.g. that 'Socrates' is a non-fictional proper name. But that is possible only because the existential proposition tells us something about Socrates, i.e. because in it 'exists' is a first level predicate. And that is the thesis I have tried to defend.

UNIVERSITY OF NEW ENGLAND

I J. T. Kearns, 'The Logical Concept of Existence', Notre Dame J7ournal of Formal Logic, ix (i 968), 3 20.

2 Ibid. p. 322.



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In Defence of the Predicate `Exists'

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