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Symposium: Is Existence a Predicate?

Author(s): W. Kneale and G. E. MooreReviewed work(s):Source: Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 15, What canPhilosophy Determine? (1936), pp. 154-188Published by: Blackwell Publishing on behalf of The Aristotelian SocietyStable URL: http://www.jstor.org/stable/4106413 .

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SYMPOSIUM: IS EXISTENCE A PREDICATE?By MR. W. KNEALE and PROF. G. E. MOORE.

I.-By W. KNEALE.I PROPOSE to begin by explaining how the controversyabout existential propositions has arisen. I shall then tryto expound the doctrine that existential propositions are asub-division of general propositions. In my third sectionI shall try to apply this doctrine in the elucidation of somerather curious existential propositions. Finally I hopeto show that while rejecting the view that existence is apredicate we ought also to reject certain accounts of thenature of propositions.

(1).No logician wishes to deny that in ordinary speechsentences such as " tame tigers exist " can be used withperfect propriety. Some of them may be false, but it isnot for the logician to determine which are and which arenot. If, however, we assume that grammatical form is asure guide to logical structure, we may be tempted to saythat in these sentences the word " existence " stands for a

predicate, where " predicate " has a logical sense distinctfrom its grammatical sense. That some philosophershave taken the word " existence " to stand for a predicatein the logical sense, i.e., for an attribute, may be seen fromtheir use of the ontological argument to prove the existenceof God.Descartes' exposition of the argument is clearer thanmost others. He starts from the position, supposed to bealready established, that we can know some propositions,e.g., simple theorems of mathematics, to be necessarilytrue. It does not matter for our purposes whether he

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IS EXISTENCE A PREDICATE ? 155thinks that his necessary propositions are analytic or syn-thetic, although we may remark in passing that the languagein which he refers to them suggests that they are analytic.He wishes to say that the proposition that God existscan be proved in the same way as that in which a necessaryproposition of mathematics is proved. He explicitlycompares it with the proposition that the triangle has interiorangles equal to two right angles. Thus he writes in theFifth Meditation: " I clearly see that existence can no morebe separated from the essence of God than can its havingthree angles equal to two right angles be separated fromthe essence of a rectilinear triangle."* And in his replyto Gassendi's objections : " You are plainly in error whenyou say that existence is not demonstrated of God as it isdemonstrated of the triangle that its three angles are equalto two right angles: for the two propositions are provedin the same way, except that the demonstration provingexistence in God is much simpler and clearer."t Andagain in the Principles of Philosophy: "Just as the mind,perceiving that it is necessarily involved in the idea of thetriangle that it should have three angles equal to tworight angles, is thereby absolutely persuaded that the trianglehas three angles equal to two right angles; so, from thefact that it perceives necessary and eternal existence to becomprised in the idea which it has of an absolutely perfectBeing, it must obviously conclude that this absolutely perfectBeing exists." IThis argument is based on the assumption that 'Godexists' is a proposition of the same sort as a theorem ofgeometry. Descartes writes as though both propositionspredicated something of a subject, the one being about' God,' the other about ' the triangle.' If he did not assumethis, he would not say that they can be proved in the samefashion. Gassendi was the first, I think, to criticize the

* The PhilosophicalWorksof Descartes,ed. Haldane and Ross, vol. i, p. 181.Later quotations are indicated by HR with volume number and page. Ihave slightly modified the translation in several places.t HR, ii, 229. + HR, i, 224.

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156 WILLIAM KNEALE.argument on the ground that existence is not a property ofGod or of anythingelse.* His criticismdrewfromDescartesthe interesting admission: "I do not see to what classof reality you wish to assign existence, nor do I see why itmay not be said to be a property as well as omnipotence,taking the word propertyas equivalent to any attributeor anything which may be predicated of a thing."t Nodoubt Descartes and those who agree with him would say,if questioned,that they wished to makea distinctionbetweenexistence and qualities such as redness. But refinementsof the theory of existence as a predicate only introducefresh difficulties. The theory is unacceptable.Unless all true existential propositions are analytic,which no one (except perhaps Leibniz) ever maintained,some subjects of which existence is to be predicated mustbe conceivable apart from existence. Even of God, whoseessence is said to involve existence, we establish that Hemay exist before we prove that He does exist.t That isto say, there must be some sense of " being " which islogically prior to existence and applicable to the possibleas well as to the actual. The subject consideredas havingbeing in this senseis apparentlya certaincomplex of univer-sals. It is the addition of existence which makes it intoan actual individual in the time series. For existence(with the exception of God's) is temporal, whereas thebeing which is logically prior to existence is timeless. Ifwe deny these principles, it is said that we abandon thegreat tradition of philosophy. Perhaps we do, but notwithout good cause. From the notion of a subject ofpredicates as a certain naturewe should find ourselves ledto the very strange conclusion that all propositions otherthan existential propositions must be analytic. For thenature of a thing is taken to include all its qualities. Weshould therefore be using a self-contradictory expressionif we said of something which was red " suppose this weregreen." We ought rather to say " suppose there weresomething like this in all other respects but green instead

* HR, ii, 185. t HR, ii, 228. . HR, i, 224 and ii,. 13

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IS EXISTENCE A PREDICATE ? 157of red." Worse consequences follow from the notion ofexistence as a temporal predicate. It is true, of course,that the verb " to exist" takes tenses, but in saying thiswe admit that if the verb symbolizesa predicate the subjectof the predicate must be capable of change. It has beenasserted,however, that the subjectof the predicateexistenceis a timelessly possible somewhat, and, however little wemay know about time, we know that the timeless cannothave different predicates at different times.We must try to find a satisfactoryplace for existentialpropositions in a revised logic. But here Gassendi andKant, who repeated Gassendi'scriticism of the ontologicalargument, offer us no help. Indeed Kant by lending hisauthority to a corrupt Aristotelianismprobably did some-thing to delay the necessary revision. For example, inhis definitions of analytic and synthetic propositions heassumed that every proposition must have a subject and apredicate. It was not until the end of last century thatany serious attempt was made to explain the nature ofexistential propositions. In order to understand whatmodern logic can add to Gassendi's criticism we mustconsiderthe notion of logical form, the clarificationof whichhas been the chiefdevelopmentof logic in the pastforty years.I shall not attempt to give a definition of logical form.I am not sure that a definition is possible. But I can indi-cate what is meant by saying that ' this is red ' has the samelogical form as 'that is green' and a different logicalform from either ' this is near that' or 'if Hannibal hadmarched on Rome, he would have taken it.'* Somedistinctions of logical form are so obvious that they couldnot be entirely ignored by the older logicians. Most manualsof logic contain disconnected references to hypotheticaland disjunctive propositions. What is peculiar to moderndiscussions s the attempt to work out a systematic accountof the various possible logical forms, that is to say, the

* In order to mark a distinction between a sentence and the propositionwhich it expresses, I use double quotation marks when I refer to the sentenceand single quotation marks when I refer to the proposition.

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158 WILLIAMKNEALE.

attempt to present them in a single scheme in which theyare arranged according to their similarities and in whichit is easy to detect the internal logical relations (i.e., entail-ment, etc.) which hold between them.

(2).We must begin with a distinction between simple andcomplex propositions. We may say somewhat looselythat complex propositions are about other propositions,and that simple propositions are those which are not'complex, but the phrase " about other propositions " istoo ambiguous to be suitable for a definition. It has beenmaintained that every complex proposition is a truth-function, i.e., a proposition which is about other proposi-tions, called its arguments, in the sense that for any arrayof truth-values (truth or falsity) of those other propositionsits own truth-value is determined. I cannot argue thatquestion here, but I wish to assert that no complex propo-sitions are of the subject-predicate form. Reflection willshow that, although we may use sentences of the gram-matical form "p is true," words which appear to standfor attributes of propositions do not in fact stand for anyattributes. It is not even correct to say that all simplepropositions are of the subject-predicate form, unless we

extend the meaning of the word " predicate " to coverrelations. For, if we refuse to admit relational propositions,we shall be driven to the monadism of Leibniz. In orderto avoid the various misleading associations of the word"predicate" we may speak of the elements of simplepropositions as constituents and components. We canindicate the meaning of the word " component " by sayingthat the component of' this is red ' is what it has in commonwith 'that is red' and the component of 'a is near b'what it has in common with 'c is near d.'Let us now consider a range of propositions which differamong themselves only in respect of one element in each,-e.g., ' this is red,' ' that is red,' etc. We cannot enumerateall the propositions of the range one by one, but we can

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* It shouldscarcelybe necessary o point out that " general" is not usedhere as a synonymfor " universal,"but some critics persist n assuming hatlt iS.

159S EXISTENCE A PREDICATE:indicatewhat range we are consideringby the use of anexpression uch as " x is red " which standsfor what iscommonto themall. This symbol s not the expression fa proposition,.e., of somethingwhich can be trueor false.The letter " x " is not the nameof anything n particular,and it does not stand indifferently or all things whichcan occur in propositions f the range ' x is red,' as a realvariablewould. It is merelya signto marka placewhichis filled by differentelementsin the variouspropositionsof the range. Fromconsideration f such a rangewe canderive two general propositions, he one existentialandthe other universal.* The existential proposition, ' forsome x, x is red,' is an adjunctionof the propositionsofthe range, that is to say, its form can be exhibited in asentence uchas " a is red orb is redor c is red,etc.,"where" or " has its non-adversativeense. The universalpropo-sition, ' for all x, x is red,' is a conjunctionof the samepropositions.In the examplewhich I have selectedthe propositionsof the range are attributivesimple propositionsand theelementsin which they differ are constituents. But thetheory of generalpropositionss not restrictedto rangesof this kind. We must recognizethat such propositionsas the followingare also general in the sensc defined:' for some x, x is not red.' ' for all x, x is not red or x isextended,' ' for somex, x is near this,' ' for some +, thisis + and that is +.' The ordinary expressionof thelast of these would be " this and that have some qualityin common." It is based on a range of propositionseach of whichis itself a conjunctionof two simplepropo-sitionswith the same componentand which differamongthemselves only in respect of that component. Thepropositionsn the rangefor generalizationmay even bethemselveseneralpropositions. Thus r3m hepropositions4for all x, x lovesJones,' ' for all x, x lovesSmith,'etc., we

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160 WILLIAM KNEALE.can pass to the range 'for all x, x loves y,' and from thatto the doubly-general proposition 'for some y, for all x,x lovesy,' of which the ordinary expression would be " thereis somebody whom everybody loves." In the technicalexpression of multiply-general propositions the order of theprefixes is of the utmost importance if the prefixes are ofdifferent kinds, i.e., not all existential or all universal.We must be prepared, for example, to distinguish the propo-sition to which we have just referred from the quite differentproposition 'for all x, for some y, x loves y,' of which theordinary expression would be " everybody has somebodywhom he loves." The one is an adjunction of conjunctions,the other a conjunction of adjunctions.In respect of their logical relations to other propositionsgeneral propositions resemble other adjunctive and conjunc-tive truth-functions. Just as ' p ' entails ' p or q,' so '$b (a) 'entails ' for some x, O(x).' And just as 'p and q' entails' p,' so 'for all x, O(x) ' entails ' k(a).'* Adjunction andconjunction can each be defined in terms of the other andnegation. So too 'for some x, 0(x) ' is strictly equivalentto ' it is not the case that for all x, not-b(x)' and ' for all x,S(x) ' strictly equivalent to ' it is not the case that forsome x, not-b(x).'In order to safeguard ourselves from misunderstandingwe must make clear that this account of general propositionsis not intended to explain away the peculiarity in virtueof which they have been called general. It is true that" for all x, x is red " is equivalent to " a is red and b is red

* Professor Moore has asserted that ' b(a) ' is not entailed by 'for all x,0 (x),' but only by the conjunction of that and ' a exists' (Arist. Soc. Sup.Vol.vii, p. 204). Is " a " supposed to be a logically proper name ? Thenwhat does he mean by " a exists " ? Is " a " a description of the form " the0 thing " ? Then " 0(a) " is equivalent to " for some x, O(x), and b(x) " ;but no one wishes to maintain that ' for all x, 0 (x) ' by itself entails ' for somex, 0(x) and f(x).' Of course, I cannot deduce ' 0(a)' from any otherproposition unless I can entertain ' 0(a).' Perhaps this is the point whichProfessor Moore wishes to make. But is it necessarily absurd to say that aproposition which I entertain may entail a proposition which I cannot enter-tain ?

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IS EXISTENCE A PREDICATE ? 161and c is red, etc.," but no expression in the conjunctiveform without " etcetera " would be an exhaustive analysisof the meaning of the original expression, because, aseveryone agrees, there is some sense of the word " about "in which a general proposition may be about things of whichwe have never heard and for which we have no names.Since " etcetera " means the same as " and so on for all thepropositions of the range," its use here is an admission thatwe are not able to resolve a general proposition into onewhich is complex but not general. If, then, we say thatgeneral propositions are adjunctive and conjunctive truth-functions and occasionally use an expression ending with" etcetera " in order to make the point clearer, we are onlyexplaining in what sense general propositions may rightly besaid to be complex. For a proposition to be a truth-functionof a certain kind it is not essential that it should be expressiblein a sentence consisting of a finite number of sentenceslinked by " and " or " or," but rather that its truth-conditions should be of a certain kind. An existentialproposition is about the propositions of its range in thesense that it is entailed by each of them and cannot betrue unless one of them is true, and a universal propositionis about the propositions of its range in the sense that itentails each of them and cannot be false unless one of themis false. The words " each " and " one " which occur inthese definitions are marks of generality, and their presenceshows that we have not explained away the peculiarityof general propositions. But it is important to realizethat general propositions are complex in the sense defined,since it is only by considering them as truth-functionsthat we can understand their place in the logical schemeof forms, the nature of the distinctions between multiply-general propositions which are expressed by the orderingof prefixes, and the logical relations of general propositionsto the propositions of their ranges.What distinguishes general propositions from othertruth-functions of the same types is the fact that by meansof them, or rather, by means of the sentences which expressthem, we are able to talk about propositions which we are

L

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162 WILLIAM KNEALE.unable to entertain, although only in the sense of " about "which I have tried to define. General propositions arecomplex but not completely exponible.* I admit that thisis a difficult notion, but I do not think that we can giveup the claim to be able to talk about all the propositionsof a range. Such attempts as I have seen to explainaway the need for the claim seem to me obviously unsatis-factory. It has been suggested, for example, that thestructure of the proposition ' for some x, x is red ' is shownmost clearly in the expression " redness has application."But we ought surely to deny that the proposition is of thesubject-predicate form, especially when we find that weare required to talk of a predicate called " having-applica-tion," supposed to be itself applicable to universals. Inorder to make sense of the phrase " has application " wemust add " to something," but then we have only a wordyparaphrase of " something is red." And in any case thesuggestion takes no account of such general propositionsas 'this and that have some quality in common.' Itmay perhaps be argued with some plausibility that it isimpossible to entertain a proposition without knowingwhat would make it true or false, and that therefore a generalproposition cannot be a truth-function of unentertainedpropositions. But the argument assumes too much.Anyone who entertains a general proposition has at leasta criterion by which to determine whether any propositionwhich he may come to entertain does or does not belongto the range of his generalization and, possessing thiscriterion, he is in a position to verify or falsify the generalproposition when suitable evidence offers itself. I cannotsee that more than this is required for the entertainmentof a proposition. I may add that it is obviously possiblefor a man to verify or falsify a general proposition in somesituation which he could not envisage at the time of firstentertaining the proposition, and that any acceptable-theory of general propositions must allow for this possibility.Of all the variety of general propositions which can be

* I owe the suggestion of this convenient mediaeval word to Mr. Ryle.

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IS EXISTENCE A PREDICATE ? 163and have been entertained traditional logic recognizesonly four forms, distinguished as A, E, I and 0. The Aform (with existential import) is 'for all x, if q(x) then0(x), and for some x, j(x).' The I form is 'for somex, 0(x) and 4i(x).' No doubt these forms have beenrecognized because they are of special interest in science.The A and E forms are the forms of easily stated laws, andthe 0 and I forms are the contradictories of the A and Eforms. Propositions of the form 'for some x, O(x),'where 0 is an unanalysable characteristic,may have beenignored because we rarelytrouble to assert them in ordinarydiscourse. We know that all such propositions are true.But it is interesting to notice that the reason why theymust be true belongs to epistemology rather than to logic.We could not entertain any proposition about 0 if wehad not been able at some time to assert a propositionof theform ' 0(a),' but any such proposition would entail 'forsome x, 0h(x).' Unfortunately, the traditional logicianswhile recognizing certain general propositions have triedto assimilate them in form to simple propositions such as'this is red,' calling them all categorical. It is theirobsession with the subject-predicate form which makesthem reject out of hand all attempts to reduce mathematicsto logic. I do not wish to asserthere that any of the attemptsis successful, but I do wish to maintain that no one whothinks that Aristotle exhausted formal logic can possiblyhope to understand any of the attempts which have beenmade. As a preliminary to understanding we must firstbe preparedto recognize general propositionsof such formsas 'for all x,y and z, if x is p toy, andy is p to z, then x isp to z,' which cannot be fitted into the traditional schemeof propositions. It is the same obsession which producesthe fallaciousontological argument.

If the logical theories which I have summarized arecorrect, we can now answer the question implicit inDescartes' remark : " I do not see to what class of realityyou wish to assign existence." Our answer must be that,if when Descartes talks of a class of reality he means sub-stances or attributes or relations, existence belongs to noL2

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164 WILLIAM KNEALE.class of reality. The word " existence " is not a symbolfor anything which can be either a constituent or a com-ponent of a simple proposition. It is only a logical auxiliarysymbol. The sentence " tame tigers exist " is just one wayof expressing the proposition 'for some x, x is tame and xis a tiger.' Other ways of expressing the same propositionare " there are tame tigers," " some tigers are tame,"" something is a tame tiger." The sentence " tametigers exist " may mislead philosophers into thinking thatexistence is a predicate, because it is grammatically similarto such sentences as " tame tigers growl " and " Rajahgrowls." Descartes fell into this confusion when heassumed that the proposition 'God exists' has the sameform as a theorem of geometry. It is true that accordingto the usages of our language each of the propositionscan be expressed in a sentence of the same grammaticalform as those used to express attributive simple propositions,and that for most purposes such expression would beunobjectionable. But the logical forms of the two propo-sitions are exhibited more clearly in the sentences " somethingis divine " and " if anything is a triangle, it has interiorangles equal to two right angles." And no one whostarted with the new sentences would ever dream of anontological argument. In short, the argument is merely aplay on grammatical form.

(3).I wish now to consider certain rather curious existentialstatements which are rarely if ever uttered by plain men.(a) " This exists." After an account of existentialpropositions from which my own is in large part derived,Mr. Russell tells us that the words "a exists " can have

no meaning if "a " is not a description but a logicallyproper name.* He allows that "a exists" may havemeaning when "a " is a grammatically proper name. IfI say " Mr. Russell exists " I may mean 'there is one and* Introductiono Mathematical hilosophy,p. 178.

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IS EXISTENCE A PREDICATE ? 165

only one man who wrote An Introductiono MathematicalPhilosophy,tc., and is called Mr. Russell.' " Mr. Russell "is then, as used by me, a unique description, i.e., a phraseconnoting a complex of characterswhich belong all togetherto nothing but Mr. Russell. It would only be a logicallyproper name if I could use it without connotation to referdirectly to something with which I was acquainted. Thefundamental distinction here is between direct and indirectreference. When we think that we are making an indirectreference we may in fact be referring to nothing at all.That, I suppose, was the situation of Greekswho, believingtheir own mythology, said " the goddess of wisdom be-friendedUlysses." But what of the sentence " this exists " ?Common sense insists that the words have a meaning, andyet " this " does not look like a description.It is true that if "a" were a logically proper namethe words "a exists" could have no meaning such as wediscover in the sentence " the Presidentof the United Statesexists." If there were any meaning it could only be 'forsome x, x is identical with a.' But in ordinary languagethere are no logically proper names. Symbols have sensebecause they are used according to habitual rules, and itis impossiblethat any symbol should be habituallyassociatedwith a particular which is a fleeting event. That we areable nevertheless to indicate to each other the particularsto which we wish to refer is due to the peculiarity of ourhabitual rules for the use of certain words such as " this,"" here," " now" and "I." Each token of a demon-strative type may denote a different thing, but each tokendenotes whatever it does denote by locating that thingas in a certain relation to itself which anything denotedby token of that type must have to the token denotingit. If anyone else understandsmy use of a demonstrativeword, he does so by apprehending the particular soundwhich I utter and consideringwhat thing can be in a certainrelation to that particular sound. The rules for the useof tenses in verbs must be explained in a similar fashion.From these considerations it follows that even accordingto Mr. Russell's account of existential propositions the

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166 WILLIAMKNEALE.sentence " this exists" may have a perfectlygood meaning,namely, 'there is something to which my token " this "has the deictic relation.'

(b) " Thereare universals." In view of the criticismswhich are sometimes brought against recent developmentsof logic, it is important to show that we can find a sensein which this statement is undoubtedly true.A universal is either a quality or a relation. Let usbegin by consideringthe statement " rednessis a quality"We may be tempted to think that it ascribesa predicate,namely, being-a-quality, to a thing. If, however, we tryto take it in that sense, we shall certainly end in confusion,puzzling ourselvesabout unreal questions, such as how thethings called qualities are related to the things calledparticulars. We must recognize that 'redness is a quality'is not a simple proposition. It seems rather to be aboutthe r61leof redness as a component in simple propositions.I suggest that the least misleading expression of it is " forsome x, x is red." If this analysis is correct, ' redness is aquality' is a general proposition. The proposition 'thereare qualities' must in consequence be doubly-general.It can be expressedin the form "for some 0, for some x,0(x)." By a similar argument we can show that 'thereare relations' can be expressed in the form " for some p,for some x, for somey, p(x,y)." " There are universals"is therefore equivalent to " for some 0, for some x, O(x),or for some p, for some x, for some y, p(x, y)."If we try to clarify the meaning of the statement " thereare particulars,"we find ourselves ed to adopt an expressionwhich differsfrom that just given in nothing but the orderof the prefixes. But the order of the prefixes makes nodifference to the sense of the whole expression when theprefixes are of the same kind. It follows that the twosentences, " there are universals" and " there are parti-culars," have the same meaning. At first sight this is avery startling conclusion, for it seems to suggest that thewords " universal " and " particular " have the samemeaning, which we cannot admit. But the false suggestionis the product of our own confusion. We have forgotten

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IS EXISTENCE A PREDICATE ? 167for the moment that the proposition which the two sentencesexpress is multiply-general. The moral (and surely avery respectable moral) is that we cannot talk of universalswithout also talking of particulars and viceversa. Universalsare components for constituents, and particulars areconstituents for components. To say either " there areuniversals " or " there are particulars " is only to assertthat something is somewhat or somehow to something,i.e., that there are simple facts. Universals and particularsare distinguished by their different r6les in simple facts.A universal or component is that element in a fact whichdetermines its internal multiplicity. This we show by theway in which we use the symbols for components. Wedo not say " this is red that " or " this is greater than."(c) " There may be three-termed elations." It has beensuggested that jealousy, owing and betweenness are three-termed relations. I agree that the words occur in sentencescontaining three nouns, but I do not think that thosesentences ever express simple propositions. That I owetwenty pounds to my bookseller is certainly not a simpleproposition. Betweenness is the most plausible of thesuggested examples, but examination shows that sentencescontaining the word " between" are about the logicalproperties of two-termed relations. If I say that b isbetween a and c, I mean that there is some aliorelativetransitive relation by which a is related to b and b to c.For my own part I cannot discover any genuine three-termed relation. This is the situation in which somelogicians say " there may be three-termed relations."They wish to vindicate for pure logic the right to considerthree-termed relationship as a possible form for simplepropositions. Any logician who is not prepared to confinehimself to consideration of propositional forms of whichhe can give examples must sooner or later defend himselfin this fashion. For who can instance a simple fact ofwhich the component is a thirty-seven-termed relation ?Now the sentence " there may be three-termed relations"seems to mean that it is not self-contradictory to say thatthere are three-termed relations. I am therefore required

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168 WILLIAM NEALE.to understand the meaning of the statement " there arethree-termed relations " while admitting that I cannotgive an example and do not know whether the statementis true. It is easy, of course, to write out a set of marksanalogous to that used in consideringtwo-termed relations.It will be " for some p, x,y and z, p(x,y, z)." But whenI wrote " for some p, x andy, p(x,y) " I knew the logicalform which I symbolized by writing " p(x, y)." If mynew set of marks is really the expressionof a quadruply-general proposition, it is about a four-fold array of propo-sitions all sharingthe same form. In orderto refer to thosepropositions I must at least know their form. And thewhole difficulty in the present case is that I do not knowany example of a form for which " p(x, y, z) " would byanalogy be an appropriate symbol. I suggest that whenlogicians say "there may be three-termed relations"they are thinking only of the possibility of an extensionof the rules according to which they manipulate markslike p and x. The only relational symbols o which theextended rules can be applied are incomplete symbols inMr. Russell's sense, i.e., such words as " owing," which donot stand for elements of simple propositions.(d) " There s a naturalnumber hich. . ." It may bedifficult to explain the meaning of such statements as" 7 4- 5

-12." I have nothing to say about that problem

except that numeralsare neither propernames nor symbolsfor qualities. If, however, we can explain such statements,we should find no special difficultyin existential statementsof the form "there is a natural number which . .. "The fact that mathematicians sometimes make repeatedtrials in order to establish an existential propositionof thiskind shows that the propositionis of the form ' one satisfiesthe conditions or two satisfies the conditions or threesatisfies the conditions, etc.' But it has been suggestedrecentlythat such existentialpropositionsarevery mysteriousand even that the principle of excluded middle does notapply to them. I think that the difficulty may perhapshave arisenfrom a failure to distinguish propositionswhichare contraries from propositionswhich are contradictories.

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IS EXISTENCE A PREDICATE ? 169Let us consider a universal proposition to the effect thatno number satisfies certain conditions. We may symbolizeit by the letter N. The contradictory of this is the existentialproposition that some number satisfies the conditions,which we may symbolize by the letter S. Now S mightperhaps be established by repeated trial, i.e., we mightfind a number satisfying the conditions after a finite numberof trials. But N can never be established in that way,since we cannot make trial of all numbers. When mathe-

maticians establish a universal proposition they do so bydemonstrating for what they call the general case or bymathematical induction (which is quite different fromcomplete enumeration). They establish not simply Nbut the proposition that N is necessarily true, which we maysymbolize by ! N. N and ! N must be distinguished, for thecontradictory of ! N is not S, but the proposition that S ispossible, which we may symbolize by *S. The logicalrelations between the four propositions can be seen mostclearly if they are arranged in a square of opposition asfollows: !N S

N *SEach higher proposition entails that below it. Those atthe opposite ends of a diagonal cannot both be true andcannot both be false. Those in the upper row cannotboth be true but may both be false. Those in the lowerrow cannot both be false but may both be true. Since Sis sufficient to refute ! N, mathematicians, who are inte-rested especially in ! N, may sometimes assume that S is thecontradictory of ! N. If they do so, they will later findthemselves led to the strange conclusion that the principleof excluded middle does not hold in mathematics. For!N and S, being contraries, admit a tertium, namely, theconjunction of N and *S. The conjunction of N and *Sseems to be a very queer proposition, but I would ratherrecognize it as a genuine tertium between contraries thandeny the principles of logic. What consequences would

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170 WILLIAM KNEALE.follow in the philosophy of mathematics from its recognitionI do not know.

(4).The fundamental thesis of those who believe existenceto be a predicate is that there is a sense of" being " logicallyprior to existence and applicable to the possible as well asto the actual. When we have rejected the theory thatexistence is a predicate we must be prepared to meet thedoctrine of prior possibility in another form. Somelogicians who accept the analysis of existential propositionswhich I have outlined argue as follows : " Logic is concernedwith the forms of propositions. Propositions must bedistinguished both from sentences and from facts. Fordifferent sentences may express the same proposition, asany one admits who says, for example, that the speakers

at an international conference are all discussing the sameproposition although they speak in different languages.And not all our thinking is the knowing of facts: weoften suppose that a were 0 when we know that a is not 0.Now we must find a place somewhere for propositions,and it seems most reasonable to say that they are possibilities.For all facts are possibilities, but not all possibilities arefacts." This theory can be stated without the use of theword " existence," but it is in effect a modern version ofthe doctrine which underlay the treatment of existenceas a predicate by older philosophers. Here instead of exist-ence as a predicate of possible things we have factualityas a predicate of possible states of affairs. Sometimes,indeed, the word " existence " is used in the statement ofthe theory. Mr. Wittgenstein, for example, seems tohave held some such view when he wrote : " The existenceof atomic facts [Sachverhalten, .e., states of affairs] we alsocall a positive fact [Tatsache], their non-existence a negativefact."We must admit that in its application to simple propo-sitions this theory is free from the defects which we discoveredin the doctrine of subsistent possible things. It need

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IS EXISTENCE A PREDICATE ? 171not involve us in any strange heresies about particularsand universals or about time. For it allows us to supposethat some particular were otherwise than in fact it is, andit does not require us to say that factuality or existencebelongs to timeless possibles at certain times. We cango further and admit that whatever we think must insome sense be a possibility. But I think that we oughtnevertheless to reject this form of the doctrine of priorpossibility if it is offered as a finally satisfactory accountof the nature of propositions.What can we mean by the phrase " contemplating apossibility? " Some philosophers prefer to speak ofknowing an analytic fact of the form 'p is possible.'* Ifthis language is intended to provide an explanation of thenature of propositions, it assumes what it should explain,for the p of' p is possible ' is presumably a proposition whichwe must entertain in order to know that it is possible. Otherphilosophers who use the word " possibility " in their accountof propositions apparently treat it as a synonym for " whatis possible." According to them we are acquainted with ahost of possibilia as objectives in their own right. But theword " possible " cannot stand alone as a description ofanything. In order to give it a sense we must say that it isshort for " possible fact." I suspect, however, that wesometimes talk of possible facts as though they were factsof some peculiar kind, which is obviously absurd. Let usthen substitute for " possible fact " the less dangerous phrase" what might be the case." There is no doubt that attimes we can use this phrase intelligibly, but I refuse toadmit that the words ever describe an objective with whichI am acquainted. To admit that they do would be tosay that I know something which has the remarkable statusof being ready to be a fact. Insistence that the objectiveis logically prior to what is the case and conceivable apartfrom all actuality only adds to the absurdity.These considerations need not lead us to give up speakingof propositions, or even of possibilities, but they do suggest

* Lewis and Langford, SymbolicLogic,ch. xiii.

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172 WILLIAM KNEALE.that we must treat propositions as logical constructions,i.e., that we must be prepared to translate sentences aboutpropositions into sentences in which the word " proposition "and its synonyms do not occur. There is a commonview (once defended by Mr. Russell in his polyadic relationtheory of supposal) according to which thinking is doingsomething with elements abstracted from facts. But itseems clear that the elements of facts cannot be separatedin such a way that a man may be acquainted with a con-stituent or a component when he is not knowing a factin which it is constituent or component. That the elementsof facts cannot be separated is the truth of the theory ofuniversalein re. Nor is it enough to say that entertaininga proposition is imagining a as 0. For in its looser usage" imagining " is merely a synonym for " supposing," andin its stricter usage it means apparently having an imagewhich is numerically distinct from a and only characterizedby 0 in some Pickwickian sense. Images may play somer6le in the situation which we call entertaining a proposition,but I think that the puzzle is to be solved only by considera-tion of the way in which we use symbols. The doctrineof subsistent propositions, or prior possibilities, arises fromthe assumption that when sentences are not used to statefacts they have meaning in precisely the same sense aswhen they are. In each case, it is supposed, symbolsare used only to express something of which we think withoutthe help of symbols. I doubt whether there is any thinking,as distinct from knowing, without the use of symbols.I wish to suggest, on the contrary, that thinking in therestricted sense is a certain use of symbols, and that pro-positions are logical constructions out of sentences. Thedetailed development of this theory would take too muchtime. I can only draw attention to some points of thedevelopment which are especially important.We must begin by considering the habitual use ofsymbols in sentences which state facts. For it is only byreference in the last resort to this situation that any symbo-lism can be explained. We must then give definitions ofentailment and equivalence for primary sentences, i.e., for

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IS EXISTENCE A PREDICATE ? 173sentences which are used to state facts. In this connexionwe shall find that primary sentences do not all state factsin the same sense of " state." We have next to define theequivalence of secondary sentences, i.e., of sentences whichhave been constructed out of old symbols according to therules of combination which those symbols obeyed whenpreviously used to state facts. Here we shall require thenotion of analogous substitution. With these definitionswe must go on to explain how various statements aboutpropositions can be transformed into statements aboutsentences which are equivalent in either the primary orthe secondary sense. In particular we must explainwhat we mean when we say that a sentence expresses aproposition, that a proposition has elements, that oneproposition entails another. We shall find that for aproposition to be complex it is not necessary that thesentences which are said to express it should contain othersentences as parts of themselves. Finally we must explainin what sense it is true to say that a man always understandsa secondary sentence with which he thinks although he isnot aware of anything which it represents. I think it willappear that the understanding of a secondary sentence isfor the most part not knowing anything, but rather freedomfrom bewilderment, ability to detect its relations of entail-ment to other sentences, and readiness to determine insuitable circumstances whether the sentence does or doesnot state a fact according to the old rules of usage.It will be realized that if this account of propositions iscorrect the fundamental problem in all logical analysisis the determination of the way in which symbols are usedin sentences which state facts. I have remarked that notall true sentences state facts in the same sense of " state."This can be illustrated by consideration of existentialsentences, with which we are especially concerned. Wemay say, if we like, that the sentence " something is red "states an existential fact, but it is obvious that what wecall an existential fact is not a fact of the same level as otherfacts. For I cannot know that something is red withoutknowing that a nameable particular is red. And, since

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174 WILLIAM KNEALE.the knowledge which justifies my assertion that somethingis red would also justify my assertion that the nameableparticular is red, it seems better to say that the existentialsentence states incompletely the same fact which the othersentence would state completely.* Obviously, the existen-tial sentence states the fact incompletely because it is adaptedto state any one of many different facts for the completestatement of which many different definite sentenceswould be required. And yet it is impossible to give alist of all the definite sentences for which the existentialsentence might incompletely deputize. We can see whyit is impossible, if we remember that the meaning of anysymbol is determined by its rules of usage. The adjective" red " means what it does because it is habitually usedin the statement of facts which have redness for theircomponent. The word " some " does not stand for anyelement of facts, but its employment is governed by anhabitual rule, namely, that a sentence containing the word" some " may be used to state a fact incompletely whenevera sentence of a certain sort (determined by the other wordsof the " some " sentence) can be used to state a fact morecompletely. Since we are not omniscient, we cannot hopeto foresee all the cases which may be brought under such arule. This is the explanation and justification of thedoctrine that an existential proposition is an inexponibleadjunctive truth-function of the propositions of a range.

* Cf. J. Wisdom in Mind, vol. xlii, p. 192.

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II.-By G. E. MOORE.I AM not at all clear as to the meaning of this question.Mr. Kneale says that existence is not a predicate. But whatdoes he mean by the words " Existence is not a predicate " ?In his second paragraph, he says that the word"predicate " has two different senses, a logical sense anda grammatical one. If so, it would follow that the words" Existence is not a predicate " may have two differentmeanings, according as the person who uses them is using" predicate " in the logical or the grammatical sense. AndI think it is clear that he means us to understand that whenhe says " Existence is not a predicate," he is using " predi-cate " in the logical sense, and not in the grammatical one.I think his view is that if anyone were to say " Existence isa predicate," using " predicate" in the grammatical sense,such a person would be perfectly right : I think he holds thatexistence really is a predicate in the grammatical sense.But, whether he holds this or not, I think it is clear thathe does not wish to discuss the question whether it is or isnot a predicate in the grammatical sense, but solely thequestion whether it is so in the logical one.Now I think it is worth noticing that if we assert"Existence is a predicate," using "predicate " in thegrammatical sense, our proposition is a proposition aboutcertain words, to the effect that they are often used in acertain way; but not, curiously enough, about the word" existence " itself. It is a proposition to the effect that theword " exists " and other finite parts of the verb " to exist,"such as " existed," " will exist " or " exist " (in the plural)are often the predicates (in some grammatical sense) ofsentences in which they occur; but nobody means to saythat the word " existence " itself is often the predicate ofsentences in which it occurs. And I think Mr. Knealeimplies that, similarly, the proposition which anyone wouldexpress, if he asserted " Existence is a predicate," using

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176 G. E. MOORE." predicate " in the logical sense, is again equivalent to aproposition, not about the word "existence" itself, but aboutthe word " exists," and other finite parts of the verb" to exist." He implies that " Existence is a predicate,"with this use of " predicate," is equivalent to the propositionthat the word " exists," and other finite parts of the verb,often do " standfor a predicate in the logical sense." Itwould appear, therefore, that one difference between thetwo different meanings of " Existence is a predicate " is asfollows : namely that, if a person who says these words isusing " predicate " in the grammatical sense, he is notsaying that the words, " exists," etc., ever " stand for apredicate in the logical sense "; whereas, if he is using" predicate " in the logical sense, he is saying that they do(often, at least) " stand or a predicate in the logical sense."What Mr. Kneale himself means by " Existence is not apredicate " is apparently some proposition which he wouldexpress by saying : " The words, ' exists,' etc., never standfor a predicate in the logical sense."What I am not clear about is as to what is meant bysaying of a particular word (or particular phrase) in aparticular sentence that it " stands for a predicate in thelogical sense "; nor, therefore, as to what is meant bysaying of another particular word in another particularsentence that it does not " stand for a predicate in the logicalsense." Mr. Kneale does, indeed, tell us that a " predicatein the logical sense " is the same as " an attribute " ; but,though I think that the meaning of the word " attribute "is perhaps a little clearer than that of the phrase " predicatein the logical sense," it still seems to me far from clear:I do not clearly understand what he would mean by sayingthat " exists," etc., do not " stand for attributes." But,from examples which he gives, it is, I think, clear that hewould say that in the sentence " This is red " the word" red," or the phrase " is red " (I am not clear which), does" stand for an attribute "; and also that in the sentence" Tame tigers growl," "growl" so stands, and in thesentence " Rajah growls," " growls " does. It is, therefore,presumably some difference between the way in which

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IS EXISTENCE A PREDICATE ? 177" exists," etc., are used in sentences in which they occur,and the way in which " is red " (or " red ") and " growl "and " growls " are used in these sentences, that he wishesto express by saying that, whereas " exists," etc., do not" stand for attributes," these words in these sentences do.And if we can find what differences there are between theuse of finite parts of the verb " to exist," and the use of" is red," " growl " and " growls," we may perhaps findwhat the difference is which he expresses in this way.I.-It will, I think, be best to begin with one particularuse of " exist "-the one, namely, which Mr. Knealeillustrates by the example " Tame tigers exist." He clearlythinks that there is some very important difference betweenthe way in which " exist " is used here, and the way inwhich " growl " is used in " Tame tigers growl " ; andthat it is a difference which does not hold, e.g., between theuse of " scratch " in " Tame tigers scratch " and the useof " growl " in " Tame tigers growl." He would say that" scratch " and " growl " both " stand for attributes,"whereas " exist" does not; and he would also say that" Tame tigers exist " is a proposition of a different formfrom " Tame tigers growl," whereas I think he would saythat " Tame tigers growl " and " Tame tigers scratch " areof the sameform. What difference between " Tame tigersexist " and " Tame tigers growl " can be the one he hasin mind ?(1) That there is a difference between the way in whichwe use '"exist " in the former sentence and " growl " in thelatter, of a different kind from the difference between ourusages of " scratch " and " growl " in the two sentences" Tame tigers scratch " and " Tame tigers growl," can,I think, be brought out in the following way.The sentence " Tame tigers growl " seems to me to beambiguous. So far as I can see, it might mean " All tametigers growl," or it might mean merely " Most tame tigersgrowl," or it might mean merely " Some tame tigers growl."Each of these three sentences has a clear meaning, and themeaning of each is clearly different from that of either ofthe two others. Of each of them, however, it is true that

M

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178 G. E. MOORE.the proposition which it expresses is one which cannotpossibly be true, unless some tame tigers do growl. Andhence I think we can say of " Tame tigers growl " that,whichever sense it is used in, it means something whichcannot possibly be true unless some tame tigers do growl.Similarly I think it is clear that " Tame tigers exist " meanssomething which cannot possibly be true unless some tametigers do exist. But I do not think that there is anyambiguity in " Tame tigers exist " corresponding to thatwhich I have pointed out in " Tame tigers growl." So faras I can see " Tame tigers exist " and " Some tame tigersexist " are merely two different ways of expressing exactlythe same proposition. That is to say, it is not true that" Tame tigers exist " might mean " All tame tigers exist,"or " Most tame tigers exist," instead of merely " Some tametigers exist." It always means just " Some tame tigersexist," and nothing else whatever. I have said it is neverused to mean " All tame tigers exist," or " Most tame tigersexist "; but I hope it will strike everyone that there issomething queer about this proposition. It seems to implythat " All tame tigers exist " and " Most tame tigers exist "have a clear meaning, just as have "All tame tigers growl"and " Most tame tigers growl"; and that it is just anaccident that we do not happen ever to use " Tame tigersexist " to express either of those two meanings instead ofthe meaning " Some tame tigers exist," whereas we dosometimes use " Tame tigers growl " to mean " All tametigers growl" or " Most tame tigers growl," instead ofmerely " Some tame tigers growl." But is this in fact thecase ? Have " All tame tigers exist" and " Most tametigers exist " any meaning at all ? Certainly they have nota clear meaning, as have " All tame tigers growl " and" Most tame tigers growl." They are puzzling expressions,which certainly do not carry their meaning, if they haveany, on the face of them. That this is so indicates, I think,that there is some important difference between the usageof " exist " with which we are concerned, and the usage ofsuch words as " growl " or " scratch " ; but it does notmake clear just what the difference is.

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IS EXISTENCE A PREDICATE ? 179I think this can be made clear by comparing theexpressions " Some tame tigers don't growl " and " Sometame tigers don't exist." The former, whether true orfalse, has a perfectly clear meaning-a meaning just as clearas that of " Some tame tigers do growl " ; and it is perfectlyclear that both propositions might be true together. Butwith " Some tame tigers don't exist " the case is different." Some tame tigers exist " has a perfectly clear meaning:it just means " There are some tame tigers." But themeaning of " Some tame tigers don't exist," if any, iscertainly not equally clear. It is another queer andpuzzling expression. Has it any meaning at all ? and, ifso, what meaning ? If it has any, it would appear that itmust mean the same as: " There are some tame tigers,which don't exist." But has this any meaning ? And if so,what ? Is it possible that there should be any tame tigerswhich don't exist ? I think the answer is that, if in thesentence " Some tame tigers don't exist" you are using" exist " with the same meaning as in " Some tame tigersexist," then the former sentence as a whole has no meaningat all-it is pure nonsense. A meaning can, of course, begiven to " Some tame tigers don't exist" ; but this canonly be done if "exist" is used in a different way from thatin which it is used in " Some tame tigers exist." And, ifthis is so, it will follow that " All tame tigers exist " and" Most tame tigers exist," also have no meaning at all,if you are using " exist " in the sense with which we areconcerned. For " All tame tigers growl " is equivalent tothe conjunction " Some tame tigers growl, and there is notame tiger which does not growl " ; and this has a meaning,because " There is at least one tame tiger which does notgrowl " has one. If, therefore, " There is at least one tametiger which does not exist " has no meaning, it will follow

that " All tame tigers exist " also has none ; because " Thereis no tame tiger which does not exist " will have none, if" There is a tame tiger which does not exist " has none.Similarly " Most tame tigers growl " is equivalent to theconjunction " Some tame tigers growl, and the number ofthose (if any) which do not growl is smaller than that ofM2

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180 G. E. MOORE.those which do "-a statement which has a meaning onlybecause " There are tame tigers which do not growl " hasone. If, therefore, " There are tame tigers which don'texist " has no meaning, it will follow that " Most tametigers exist " will also have none. I think, therefore, wecan say that one important difference between the useof " growl " in " Some tame tigers growl " and the use of" exist" in " Some tame tigers exist," is that if in theformer case we insert " do not " before " growl," withoutchanging the meaning of " growl," we get a sentence whichis significant, whereas if, in the latter, we insert " do not "before " exist " without changing the meaning of " exist,"we get a sentence which has no meaning whatever; andI think we can also say that this fact explains why, with thegiven meaning of " growl," " All tame tigers growl " and" Most tame tigers growl " are both significant, whereas,with the given meaning of " exist," " All tame tigers exist "and " Most tame tigers exist " are utterly meaningless.And if by the statement that " growl," in this usage," stands for an attribute," whereas " exist," in this usage,does not, part of what is meant is that there is this differencebetween them, then I should agree that " exist," in thisusage, does not " stand for an attribute."But is it really true that if, in the sentence " Some tametigers exist," we insert " do not " before " exist," withoutchanging the meaning of " exist," we get a sentence whichhas no meaning whatever ? I have admitted that a meaningcan be given to " Some tame tigers do not exist " ; and itmay, perhaps, be contended by some people that themeaning which " exist " has in this sentence, where it issignificant, is precisely the same as that which it has in" Some tame tigers exist." I cannot show the contrary asclearly as I should like to be able to do; but I will domy best.The meaning which such an expression as " Some tametigers do not exist " sometimes does have, is that which ithas when it is used to mean the same as " Some tame tigersare imaginary " or " Some tame tigers are not real tigers."That " Some tame tigers are imaginary " may really express.

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IS EXISTENCE A PREDICATE ? 181a proposition, whether true or false, cannot I think bedenied. If, for instance, two different stories have beenwritten, each of which is about a different imaginary tametiger, it will follow that there are at least two imaginarytame tigers ; and it cannot be denied that the sentence" Two different tame tigers occur in fiction " is significant,though I have not the least idea whether it is true or false.I know that at least one unicorn occurs in fiction, becauseone occurs in " Alice Through the Looking Glass "; andit follows that there is at least one imaginary unicorn, andtherefore (in a sense) at least one unicorn which does notexist. Again, if it should happen that at the presentmoment two different people are each having an hallucina-tion of a different tame tiger, it will follow that there are atthe present moment two different imaginary tame tigers;and the statement that two such hallucinations are occurringnow is certainly significant, though it may very likely befalse. The sentence " There are some tame tigers which donot exist " is, therefore, certainly significant, if it means onlythat there are some imaginary tigers, in either of the twosenses which I have tried to point out. But what it meansis that either some real people have written stories aboutimaginary tigers, or are having or have recently hadhallucinations of tame tigers, or, perhaps, are dreaming orhave dreamed of particular tame tigers. If nothing of thissort has happened or is happening to anybody, then thereare no imaginary tame tigers. But if " Some tame tigersdo not exist " means all this, is it not clear that " exist "has not, in this sentence, the same comparatively simplemeaning as it has in " Some tame tigers exist" or in" No tame tigers exist " ? Is it not clear that " Some tametigers do not exist," if it means all this, is not related to" Some tame tigers exist," in the same simple way in which" Some tame tigers do not growl " is related to " Sometame tigers growl "?

(2) There is, I think, also another important differencebetween this use of " exist " and the use of " growl," whichmay be brought out as follows.

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182 G. E. MOORE.Mr. Russell has said* " When we say 'some men areGreeks,' that means that the propositional function ' x is aman and a Greek' is sometimes true " ; and has explainedjust previously that by " sometimes true " he means " truein at least one instance." With this explanation of whathe means by "sometimes true," I do not think that hisstatement as to the meaning of " Some men are Greeks "is strictly correct ; since I think that the use of the pluralimplies that " x is a man and a Greek " is true in morethanone instance, that is to say, in at least two instances. Letus suppose that he would accept this correction and saythat what " Some men are Greeks " means is not, strictly,that "x is a man and a Greek" is true in at least one

instance, but that it is true in at least two. He has furtherimplied (p. 158) that to say of a propositional function thatit is true in at least two instances is the same thing as to saythat at least two " values " of it are true ; and he has toldus (p. 156) that the " values " of propositional functions arepropositions. With these explanations, his view wouldappear to be that what " Some men are Greeks " means isthat at least two propositions, related to the propositionalfunction " x is a man and a Greek " in some way which heexpresses by saying that they are " values " of that function,are true. Now I cannot imagine what sort of propositionswould be " values " of " x is a man and a Greek," exceptpropositions of the following sort. There are propositionswhich we express by pointing at (or indicating in some otherway), an object which we are seeing (or perceiving in someother way) and uttering the words " This is a so and so "(or equivalent words in some other language). Let ussuppose that the kind of propositions which would be" values " of " x is a man and a Greek" would bepropositions of this sort, where the words used were " Thisis a man and a Greek." Mr. Russell's doctrine would thenbe that " Some men are Greeks " means that at least twodifferent true propositions of this sort could be made : thatthere must have been at least two different objects at which

* Introductiono Mathematical hilosophy, . 159.

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IS EXISTENCE A PREDICATE ? 183a man might have pointed and said truly " This is a manand a Greek." And, if this is his doctrine, it seems to meto be true. Surely " Some men are Greeks" cannotpossibly be true, unless there are at least two differentobjects, in the case of each of which a man might haveseen it, pointed at it, and said with truth " This is a manand a Greek " ?On this view " Some tame tigers growl " means that atleast two values of "x is a tame tiger and growls " aretrue ; and this means that there are at least two objects,in the case of each of which a man might have seen it,pointed at it, and said with truth " This is a tame tiger andgrowls." Now in this sentence " This is a tame tiger andgrowls " it is clear that, except for the difference consistingin the fact that " growls " is in the singular and " growl "in the plural, the word " growls " has the same meaning ashas the word "growl" in " Some tame tigers growl."We can say, then, that one feature about our use of " growl "is that, if we consider a " value " of the propositionalfunction which is such that " Some tame tigers growl"means that at least two values of it are true, then the singularof " growl " can be used, with the same meaning, in theexpression of such a value. And perhaps this may be partof what is meant by saying that " growl " " stands for anattribute." It may perhaps be meant that to point at anobject which you are seeing, and utter the words " Thisobject growls," is significant-that the words and gesturetogether do really express a proposition, true or false.But now consider " Some tame tigers exist" : is thesame true of " exist " in this sentence ? Mr. Russell says*:" We say that 'men exist' or 'a man exists' if thepropositional function 'x is human' is sometimes true."And he goes on to protest that though the proposition" Socrates is a man" is " equivalent" to " Socrates ishuman," it " is not the very same proposition." For mypart I doubt whether we ever do use " is human " in sucha way that " Socrates is human " is equivalent to " Socrates

* Introductiono Mathematical hilosophy,pp. 171--2.

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184 G. E. MOORE.is a man." I think Mr. Russell is using "is human " in avery special sense, in which nobody but he has ever used it,and that the only way of explaining how he is using it isto say that he is using it to mean precisely that which weordinarily express by " is a human being." If this is so,and if we are allowed to distinguish, as I think we ought,between " men exist " and " a man exists," and to say that" men exist " means, not "'x is a human being' is true inat least one instance," but "' x is a human being' is truein at least two instances,"then I think his doctrine is true ;provided, again, that we are allowed to regardthe sort ofpropositions which we express, e.g., by pointing at anobject which we are seeing and saying the words " This isa human being," as being those which are values of " xis a human being." Surely " Human beings exist " can betrue if, and only if, there are at least two objects,such that,if a man were to see and point to one of them and utter thewords " This is a human being," he would be expressingatrue proposition by what he did ?Now, if this is right, we see at once that the use of" growl " in " Some tame tigers growl" differs from thatof " exist " in " Some tame tigers exist," in the respectthat, while the first asserts that more than one value of" x is a tame tiger andgrowls" is true, the second asserts,not that more than one value of "x is a tame tiger andexists" is true, but merely that more than one value of" x is a tame tiger " is true. Owing to this view of his that" Some tame tigersexist " means the same as " Some valuesof the propositionalfunction ' x is a tame tiger ' are true,"Mr. Russell has been led to say* " Existence is essentiallya property of a propositional function" and (p. 196)" It is of propositional functions that you can assert ordeny existence" and (p. 197) that it is a fallacy to transfer" to the individual that satisfies a propositional functiona predicatewhich only appliesto a propositional unction" ;so that, according to him, existence is, after all, in thisusage, a " property" or " predicate,"though not a propertyof individuals, but only of propositionalfunctions! I think

* Monist,April, 1919, p. 193.

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IS EXISTENCE A PREDICATE ? 185this is a mistake on his part. Even if it is true that" Some tame tigers exist " means the same as " Some valuesof' x is a tame tiger' are true " it does not follow, I think,that we can say that "exist " means the same as "is sometimestrue," and " some tame tigers " the same as "x is a tametiger " : indeed, I think it is clear that we can not say this ;for certainly " ' x is a tame tiger' exists " would not meanthe same as " Some tame tigers exist." But what I thinkdoes follow from this interpretation of " Some tame tigersexist " is another thing which Mr. Russell himself holds,namely, that if a proposition which you express by pointingat something which you see and saying " This is a tametiger," is a " value " of " x is a tame tiger," then if, pointingat the same thing, you were to say the words " This exists,"and, if you were using " exists " merely as the singular of" exist " in the sense in which it is used in " Some tametigers exist," what you did would not express a propositionat all, but would be absolutely meaningless. That is to say,there is between " Some tame tigers growl " and " Sometame tigers exist," not only the difference that, whereas thefirst asserts that some values of "x is a tame tiger andgrowls " are true, the second asserts only that some valuesof " x is a tame tiger " are true ; there is also the furtherand more important difference that, why the second assertsonly that some values of" x is a tame tiger " are true, is notbecause we happen to use " This is a tame tiger " to meanthe same as " This is a tame tiger and exists," but becauseby pointing and saying " This exists " we should expressnopropositionat all, so long as we were using " exists " as thesingular of the use of " exist " with which we are concerned,whereas by pointing and saying " This growls " we certainlyshould be expressing a proposition, even though we wereusing " growls " merely as the singular of " growl" withthe meaning it has in " Some tame tigers growl." " Thisis a tame tiger, and exists " would be not tautologous, butmeaningless.This, I think, gives us a second true thing, which mayperhaps be sometimes part of what is meant by saying that" exist," in this usage, " does not stand for an attribute."

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186 G. E. MOORE.II.-So far I have been solely concerned with the useof " exist " in such sentences as " Some tame tigers exist,"and have tried to point out two differences between its usehere and the use of" growl " in " Some tame tigers growl,"which may perhaps be part of what is meant by saying that" exist," in this usage, does not " stand for an attribute,"whereas " growl " does. But I cannot help thinking thatthere are other significant uses of " exists " ; and I want,in particular, to try to point out two such, and to considerwhat, if anything, true can be meant by saying that inthese usages also " exists" does not " stand for anattribute."(1) I have just said that to point at a thing which yousee and say " This exists " seems to me to be meaningless,if " exists " is the singular of " exist " in the sense in whichit is used in " Tame tigers exist " ; but I cannot helpthinking that in the case of anything to point at which and

say " This is a tame tiger " is significant, it is also significantto point at it and say " This exists," in some sense or other.My reason for thinking this is that it seems to me that youcan clearly say with truthof any such object " This might nothave existed," "It is logically possible that this shouldnot have existed"; and I do not see how it is possiblethat " This might not have existed " should be true, unless" This does in fact exist" is true, and therefore alsosignificant. The statement " It is logically possible thatthis should not have existed " seems to mean" The sentence' This does not exist' is significant " ; and if " This doesnot exist" is significant, " This does exist" must besignificant too. Now I cannot help thinking that in everycase in which I point at an object which I am perceivingand say significantly " This is a tame tiger," " This is abook," my proposition is in fact a proposition about somesense-datum, or some set of sense-data, which I am per-ceiving; and that part of what I am saying is that thissense-datum (or these sense-data) is " of" a physical object.That is to say, I am saying of some sense-datum that it is" of" a physical object in the sense in which it is true tosay of an after-image which I see with my eyes shut that

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IS EXISTENCE A PREDICATE ? 187it is not " of" a physical object. And I think that part,at least, of what we mean by " This exists," where we areusing " this " in the same way as when we point and say" This is a book," is " This sense-datum is of a physicalobject," which seems to me to be certainly significant.If " of" here stood for a relation, we might say that " Thisis a book " was short for " The thing which this sense-datumis 'of' is a book," and therefore " This exists " short for" The thing which this sense-datum is 'of' exists " ; inwhich case the use of " exists " in question would be thatwhich in Principia Mathematica is symbolized by E! , andthere would be the same sort of reason for saying that itdoes not " stand for an attribute " as in the case of the" exist " which occurs in " Some tame tigers exist." I donot believe, however, that " of" here does stand for arelation, nor therefore that " This " in " This is a book "can be said to be short for the sort of phrase which Russellhas called " a definite description "; and, this being so,I am not at all clear as to what that is true could be meantby saying that "exists," in this usage, " does not stand foran attribute." The only suggestion I can make is this.It seems to me that " This exists " (in this usage) alwaysforms part of what is asserted by " This is a book," " Thisis red," etc., etc., where " this " is used in the manner withwhich we are now concerned; and possibly part of whatis meant by saying that " is a book," " is red," etc., " standfor attributes," is that part but not the whole of what isasserted by any " value " of " x is a book," " x is red," etc.,is " This exists." In that case " exists " in " This exists "would not " stand for an attribute," solely because thewhole of what it asserts, and not merely a part, is " Thisexists."

(2) Another reason why " This exists," where " this "is used as it is in "This is a book" seems to me to besignificant, is because it seems to me not only significant tosay of a given sense-datum " This is of a physical object "or " This is not of a physical object," but also to say of thesense-datum itself " This exists." If this is so, we have todo with a new sense of " exists," since certainly no part of

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188 G. E. MOORE.the meaning of such an assertion with regard to a sense-datum is that it, or any other sense-datum, is " of" aphysical object. But my reason for holding that it issignificant for me to say, for instance, of an after-imagewhich I am seeing with my eyes shut, " This exists," issimilar to that which I gave in the last case : namely thatit seems to me that in the case of every sense-datumwhichany one ever perceives, the person in question couldalways say with truth of the sense-datum in question " Thismight not have existed " ; and I cannot see how this couldbe true, unless " This does in fact exist" is also true, andthereforesignificant. That " this exists " has any meaningin such cases, where, as Mr. Russell would say, we areusing " this " as a " proper name " for something withwhich we are " acquainted," is, I know, disputed ; my viewthat it has, involves, I am bound to admit, the curiousconsequence that " this exists," when used in this way, isalways true, and " this does not exist " always false ; andI have little to say in its favour except that it seems to meso plainly true that, in the case of every sense-datumI have,it is logically possible that the sense-datum in questionshould not have existed-that there shouldsimply have beenno such thing. If, for instance, I am seeing a bright after-image with my eyes shut, it seems to me quite plainlyconceivable that I should have had instead, at that moment,a uniform black field, such as I often have with my eyesshut; and, if I had had such a field, then that particularbright after-imagesimply would not have existed.But, supposing " This exists," in this usage, has ameaning, why should we not say that "exists" here" stands for an attribute " ? I can suggest no reason whywe should not, except the same which I suggested in thelast case.