existence, time, and properties

Existence, Time, and Properties by IEREMY WALKER

M C GILL UNIVERSITY

"Wx-mg~ x stands for a proper name, it seems to me that the form 'x exists' must be logically equivalent to, and definable as, 'There are facts about x,' ~64,x. If there are facts about x, I cannot see what further fact about x would consist in its existing. And when x no longer exists or does not yet exist, but there are nevertheless facts about x now, I do not know what the present- tense facts about x would be." (Prior, Time and Modality, p. 31.)

I want to begin by questioning that part of Professor Prior's view which claims that from 'There are facts about x' we can validly infer 'x exists.' My obiection is as simple as possible. I claim that an obiect can have properties ('There are facts about . . .') without existing. My two counter-examples are (i) a mythical entity and (ii) a 'historical' entity.

'Pegasus is a winged horse of Greek mythology.' Claiming the truth of this proposition is not all I am committed to, since it is possible to allow its truth while denying that it is the proposition it looks like. For instance, some would analyze it as really expressing the (true) proposition "Pegasus' is a name that occurs in Greek mythological writings, and is there used to designate a winged horse.' They would deny that 'Pegasus' occurs in the original sentence as the name of anything. But, first, it is hard to see any motive for so reconstruing this statement except the belief that we cannot infer from it 'There is some property which Pegasus has.' And, second, it is certainly possible to accept this reconstrual while also interpreting the original statement as a statement about Pegasus. Normally such statements can be taken either way. 'Wilson is Prime Minister' can be construed either as a statement about the person called Wilson, or as a (disguised) statement about 'Wilson,' i.e., the statement that 'Wilson' designates the P.M. (This is not to confuse 'use' and 'mention.' The statement in which Wilson is 'mentioned' is logically equivalent to the statement in which 'Wilson' is used.) If this maneuver is sometimes possible, why should it not be possible for Pegasus too?

Again, some people will deny that the original statement about Pegasus is true, and so deny that it entails the statement that there is some property Pegasus has. This denial might take the form of a Russellian claim that the statement is false, or a Fregean claim that it has no truth-value. Russell's motive for claiming the falsity of 'Pegasus is a winged horse etc.' is, I sup-

54

EXISTENCE, TIME, AND PROPERTIES 55

pose, that if true this would entail 'Pegasus exists,' which is, however, false. I agree this is false. But why should we not just deny that every true statement about Pegasus entails that Pegasus exists? Why (generally) should we not deny that every true statement of the form 'Fa' entails 'a exists'? (This would go well with my denial that 'X$4,a' entails 'a exists'). Against Frege, I think I should argue thus. There is a difference between the statements ('Pegasus is a winged horse ete.,' and 'Pegasus is not a winged horse etc.,' such that if either is true the other is false. The fact that the law of the ex- cluded middle does not hold for these statements, even if it is a fact, would not entail that the law of noneontradietion also fails to hold for them. This difference between these statements is enough like the ordinary difference between 'p' and 'not p,' both of which are truth-valued, for us to go on using the terms 'true' and 'false' here.

The ease of Julius Caesar is a stronger counter-example. I claim that the statement 'Caesar was the first Roman emperor' is a true statement about ]ulius Caesar. In Prior's words, it tells us a fact about Caesar. Here is something about which there are some facts, even though it does not exist. In terms of 'properties,' I elaim that the most straightforward reading of this statement is this: it ascribes the property of having been the first Roman emperor to Caesar. Again, in Prior's terms, we appear to have an object which does not exist but now possesses a certain property--about which there is a 'present-tensed fact.' (I complicate this later.)

There are alternative interpretations of this kind of statement, along lines similar to the Russellian and Fregean interpretations of statements about mythical entities. Before I get into these, with all the difficulties about tensed statements and their logical representation, there is a general point about past-tensed statements which casts doubt on any attempt to deny truth-value wholesale to such statements. There can be past-tensed statements about presently existing entities. 'Wilson taught at Oxford' is a past-tensed statement about a presently existing person. It ascribes to this person the property of having taught at Oxford. The expression 'taught at Oxford' can perfectly well be read as signifying a respectable (logical) predicate, distinct from the predicate 'teaches at Oxford.' There can be past-tensed predicates.

My argument for this (natural) interpretation of this sort of past-tensed statement is as follows. The statements 'W'ilson taught at Oxford' and 'Wilson is P.M.' are both about the same person, namely Harold Wilson. The name 'Wilson,' from the second statement, is clearly a term which can be used in the 'x' and 'y' places in the predicate calculus. So it looks natural to assume that the same is true of the same name ('Wilson') as it occurs in the first statement. And if the 'x' does duty for Wilson, it is natural to suppose that the '¢' does duty for the rest of the statement. If Harold Wilson

56 PHILOSOPHICAL STUDIES

is the (logical) subject of this statement, then 'taught at Oxford' must (it seems) be its (logical) predicate. The only way to avoid concluding that there can be past-tensed predicates, i.e., 'past-tensed facts,' is to deny that entities about whom past-tensed statements are made are the logical subjects of such statements.

There is a strong and a weak denial here. The strong denial consists in denying that entities like Harold Wilson or Julius Caesar can ever be logical subjects--they are not that sort of entity. This, classically, ends in the claim that the only logical-subject terms in our language are the words 'something,' 'everything,' 'nothing,' etc. There is nothing, as far as I can see, actually false in this view, but it is very odd, and odd even for a formal logician. For one motive behind the symbolism of the predicate calculus (e.g., Frege and Russell-Whitehead) was precisely to provide logical models for statements of the form 'Wilson is P.M.' If we can avoid the strong denial, we should be well advised to. The weak denial consists in allowing that in present- tensed statements about (say) Wilson, Wilson is actually the logical subject; but claiming that in past-tensed statements he occurs only as the 'apparent' subject. Past-tensed statements do not have the simple logical form they appear to share with present-tensed statements. They are 'systematically mis- leading.' This is, I think, Professor Prior's view.

Prior, with many logicians, rests his logical interpretation of tensed statements upon a particular reading of the 'existential' quantifier. Very roughly, such logicians want us to read ':~x~x' as asserting 'There now exists something which is ~.' The quantifier is read as asserting both the existence of something, and the presentness of this existence. So '~x~x' is, in fact, a present-tensed assertion of existence about something or other. Analogously, we are supposed to read ' ~ a ' as asserting 'There is some (true) fact about a,'i.e., as another present-tensed assertion, though not, I think, an assertion of the existence of some fact or other. Because the existential quantifier is read in this way, and because the inferences from 'Fa' to both '~x~X' and ' ~ a ' are accepted as valid, Prior has to deny that statements about 'historical' entities are, as they appear to be, of the '~x' form.

But, surely, it is unnatural to read the existential quantifier as asserting present existence, and those logicians (including Frege, Russell, Quine, and Smart) who read it as both tenseless and not asserting existence have taken the more natural (and economical) line. On this line, a correct reading of the formula ':~x~x' would be something like: 'It is not the case that the predicate ~ is applied falsely to all objects,' or 'It is not the case that the function is not a fact whatever its argument is taken to be.' In such readings no occurrence of the verb 'is' has the force of asserting existence or the force of an assertion about the present time. Now if we accept the tenseless and


nonexistential reading of the quantifier--perhaps we had better call it the particular quantifier or the numericaI quantifier instead--Prior's difficulties vanish. For instance, we shall now be able to infer '~xX was the first Roman emperor' from 'Caesar was the first Roman emperor'--as surely we desire-- without being committed to Caesar's present existence or the present existence of anything with the property of having been the first Roman emperor.

tt is not enough, obviously, just to assert as against Prior's view that exis- tentially quantified statements are tenseless, and that statements in the past tense are really about the objects they would be about if they were in the present tense. For any account of the logic of tensed statements must show that, and how, the truth-values of any two statements of the forms 'x was 6' and 'x is '6' are related. For 'x was '6' is true if and only if 'x is ,~' was true some time in the Fast. Prior points this out as something any logician must explain, and he is certainly right. The only doubt is whether his own account is the right one, or whether (say) the alternative account he ascribes to Professors Quine and Smart is not better. Or perhaps a third account.

The two accounts , briefly, are as follows. Prior believes that the tense of a statement's main verb qualifies not just the predicate of that statement but the whole statement, just as (say) negation qualifies not just predicates but whole statements. So he analyzes past-tensed statements of the form 'x was +' as 'It was true at a time t that x is ~.' The Fastness of tense is provided by an operator upon statements; and there are two such operators, one for the past and one for the future. The Quine-Smart account rests (as both Prior and Smart emphasize) on the notion of 'objects' as four-dimensional. For they think that logic, as a branch of science, should not be concerned with such particular matters of fact as the actual times of Julius Caesar's birth and death. On this view, so far as I understand it, statements of the forms 'x is '6' and 'x was 4; are not logically complete expressions as they stand. For to make it clear just what proposition they express, we must add an explicit reference to the time of their utterance and the time to which they allude. The statement 'x was '6,' if so completed, will be seen to express some such proposition as this: 'It is true at time t that x was/is 4 at time u.' (Both occurrences of the verb 'is' are timeless. We should read 'is' rather than 'was,' I think, except for a contingent oddity in our grammar.)

One difference between this account and Prior's is that 'It is true at time t that' does not here stand for an operator upon statements. It stands for an operator which turns certain incomplete sentential expressions into expressions of propositions ('statements,' perhaps?). Now Prior believes that Quine and Smart use it as an operator which forms propositions out of predicates. As he sees it, we start with a predicate of the form 'x's being 4~,' and complete this 'predicative expression' by a subject of the form 'Time t.'


The whole thing will then be read as expressing the proposition 'x's being is true of time t': or, in Fregean terminology, 'Time t falls under the concept x's being 4,.' On the other hand, we could take 'is true at time t' as denoting an operator which forms propositions out of logical subjects, i.e., a predicate. On this view, we start with a subject-term of the form 'x's being O'--if we like, we can think of this as the 'name' of some (timeless) fact-- and, by adding the predicative expression 'is the case at time t,' get a complete propositional expression. The whole thing will now be read as expressing the proposition "being the case at time t is true of x's being ~,' or something of the kind.

I do not think it matters much which reading of the Quine-Smart view we adopt, for on either we get the feature to which Prior takes exception, namely the implication that objects (and facts) are somehow timeless as far as logic is concerned. Now he admits that there are some features of some logical systems which make this ontology desirable, if not plausible. For example, there is Professor Ruth Barean Marcus's formula in 'quantified modal logic': CMXxoxXxM$x. This reads, roughly, 'If it is possible that there is something which is ~, then there is something of which it is possible that it is $.' There is an analogous formula in tense-logical terms, which can be read as 'If there is some time at which it is true that there is something which is ~, then there is something of which it is true that there is some time at which it is $.' On Prior's reading of the existential quantifier, this formula compels us to infer the present ex/stence of this 'something.' I have already argued that we need not so read the existential quantifier; the fact that these formulas crop up 'naturally' is, perhaps, further evidence for this.

My own view of tensed statements is much closer to the Quine-Smart view. I said earlier that I can see no conclusive reason for denying that past- tensed expressions of the form 'was ~' may signify genuine logical predicates. Now I agree that statements of the form 'x was ~' are logically incomplete. And I should read off the complete proposition (presumably) expressed by the completed statement as 'Being ~ at time t is true of x,' where the 'is' is timeless. Now 'Being emperor of Rome in 45 B.C.' is true of Julius Caesar; this expression denotes a property of Caesar, or 'names' a fact about him. This interpretation does not (as perhaps Prior thinks) commit me (or Quine or Smart) to the view that Caesar still, presently, exists. When Prior describes Quine-Smart views as involving the notion of timeless entities and truths, he appears to believe this means eternal entities and truths. And when Smart describes logic as, in his view, a logic of 'four-dimensional' entities he does seem to be saying this. But even if he is (which I doubt), he need not. Time- less entities are simply not eternal entities, if only because, for instance, to say that numbers and propositions are 'timeless' is not to say they exist eternally.


It is not even to say that they exist at all. It is much more like the denial that the notion of 'existence' can be sensibly applied to numbers and propositions. Generally, the point in describing formal logic as a logic of 'timeless' entities is just to stop people raising (senseless) questions about the dates and stretches of existence of anything the logician mentions. It is a way--a good one too--of shutting off all questions about 'existence,' including questions about 'eternal existence,' from logic. And this may include modal logic and tense-logic as well.

So far I have, in effect, been countering Prior's claim that (say) even possessing the property of having been emperor of Rome in 45 s.c. entails the present existence of Julius Caesar. So I must (as he points out) give some account of the difference between those properties (facts) which entail the thing's present ex/stence and those, like the one just mentioned, which do not. I think there is an answer available, though what follows is the merest sketch of that answer. Having the property 'Being emperor of Rome in 45 s.c.' entails existing in 45 s.c. It does not entail existing at any other period of time, including this time, i.e., the present (1967 A.D.). In general, if something possesses a property of the form 'Being such-and-such at time t,' then it must exist at time t; and (I think) if it possesses no property of this form, then it cannot exist at that time, namely t. One might reply: Julius Caesar possesses not just the property 'Being emperor of Rome in 45 B.C.,' but the (same or different?) property 'Having been emperor of Rome in 45 s.c., in 1967 A.D.'NOr, indeed, every property of the form 'Being or having been, or about to be, emperor of Rome in 45 s.c., for any time t.' Then would it not follow that Caesar existed (for the former) now, i.e., in 1967, or (for the latter) eternally? This would be a way of working back to a position much more like the 'four-dimensional' one held by Smart. But I think this reading of properties is both unnecessary and, unless designed to make all objects eternal, incoherent. It seems to be just an attempt to make explicit the fact that the property 'Being emperor of Rome in 45 s.c.' is what might be called a timeless property of Julius Caesar's: it is timelessly true of him: his falling under this concept is not itself datable, nor is this sup- position sensible.

So much for the claim that from ':~s~x' we can infer 'x exists.' Even if what I have said against this is granted, still it may well be thought obvious that 'x exists' entails 'Z~s~S~x.' If something exists, must it not possess some property or properties? Must there not be some fact or facts about it? I do not want to dispute this. But I want to claim that the necessity for an existing thing to possess some properties depends not on its existing but on its being a thing--a Gegenstand. (Again, I do not want to dispute the claims that: everything that actually has existed, does exist, or will exist does as a


matter of tact possess some property or properties.) It is the notions of object and property, not the notions of existence and property, which are logically related.

There are three ways of formulating the claim that something might exist although it possessed no properties (which is not my claim): (1) 'x exists, but possesses no properties'; (2) 'x exists, but no predicate is true of x'; and (3) 'x exists, but falls under no concept (truly).' The second is dull, since it may simply be taken as making a claim about the stock of predicative expressions in some actual language; and it is perfectly conceivable that no actual language should happen to contain any predicate which applies truly (or falsely) to x. It could be the case that no language contained any 'predicative expressions.' The interesting claims are (1) and (3).

It is not clear what the first claim could mean, unless it is just another way of putting the third. For it seems to raise the question of the existence of properties: and surely we cannot solve this problem until we have solved the problem of existence for objects. So Prior's (implicit) view that the first claim is self-contradictory is unhelpful. The claim (4) 'x exists, but there are no facts about it,' which he also thinks self-contradictory, raises a similar problem. Do we really have to decide what we mean by the existence of tacts before we can settle the problem for objects?

Nor can the formulation in terms of concepts help us, since this notion is at least as obscure as the notion of a property. What could it mean to say that a certain concept 4' exists? As far as I can see, it could mean only that this concept is not self-contradictory. Then on this view the concept not self-identical might be denied 'existence.' But this view is not secure. Frege, for one, thought that this particular concept 'existed' (he actually denies the propriety of this way of putting it) even though it was self-contradictory, supporting his claim by pointing out that at any rate it is an a priori truth that nothing does fall under this concept: its extension is perfectly definite. The only concepts Frege was inclined to reject were empirical concepts like the concept horse. And his grounds for rejecting them were precisely that their extensions were indefinite; he called such concepts, disparagingly, mere 'fluid conceptual constructions.' This is an extreme view, but not absurd. And it does help to show (some of) the great difficulties in the question: What is it for a concept to exist?

Let us turn back to the formulation in terms of properties. Prior's view implies that 'x exists, but possesses no properties' is necessarily always false. First, there is a (perhaps trivial) ad hominem point about the existence of properties, or facts. Are we committed, if we accept Prior's claim, to the further claim that no property (or fact) can exist which does not itself possess some property or properties (about which there are no facts)? (These

PARADOX REGAINED 61

would presumably be second-order properties or facts). Now one might claim that every property as such must possess at least one second-order property, namely the property of having some definite number N of in- stances. That is, if we allow talk of 'second-order' properties, and if we count instantiation as one. But this is not the same as saying that for any (first- order) property to exist is to have some second-order property or properties. For we can agree on this point about first-order properties without, I think, committing ourselves to any account of existence for properties. So the claim about the existence of properties, analogous to Prior's claim about the existence of objects, is not made out at all clearly. If (a huge ifl) Pilot's claim was intended as a general claim about existence, we might question it on some such grounds as these.

I said, implicitly, that the notions of (first-order) property and second- order property, but not the notions of (first-order) property and the existence of properties, are logically related. I think this is true, as I indicated, for 'objects' too. Suppose we read Prior as claiming (and surely he is) simply that for any object to exist is to possess some properties. This limited claim looks much more reasonable (because much safer) than the quite general claim I mentioned. But why? Surely it is only from the logical relation between the notions of 'object' and 'property.' Then what makes this look like a necessary, a priori, truth? Because it is entailed by the necessary truth: 'Any object possesses some properties.' And this brings me back to the question of reading the existential quantifier. For we certainly have to formulate this claim in the following way: II x :~q~qsx. It is only if you read the existential quantifier as asserting present existence (or 'existence') that this formula appears to have anything to do with the notion of existence.

Received January 19,1968

Paradox Regained by THEODORE DRANGE

WEST VIRGINIA UNIVERSITY

j. MICHAEL DUNS, in his "Drange's Paradox Lost," 1 tries to escape my non- communicator paradox, 2 but I do not think he is successful. His objection is that in my argument I go from "( 1 ) is meaningless" to " ' ( 1 ) is meaning-

existence, time, and properties

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