proceedings of the aristotelian society, new series, vol. 1 (1900 - 1901), pp. 103-127

8/12/2019 Proceedings of the Aristotelian Society, New Series, Vol. 1 (1900 - 1901), pp. 103-127

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IdentityAuthor(s): G. E. MooreReviewed work(s):Source: Proceedings of the Aristotelian Society, New Series, Vol. 1 (1900 - 1901), pp. 103-127Published by: Blackwell Publishing on behalf of The Aristotelian SocietyStable URL: http://www.jstor.org/stable/4543659 .Accessed: 02/08/2012 07:43

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103

VII.-IDENTITY

By G. E. MOORE.

I AM very anxious it should not be thoug,ht that the subject ofthis paper is of merely departmental interest. What I have

to say is nlot addressed to those who are interested in anyparticular science, such as logic, definition, or psychology, butto all who are interested in the question what the world is. Itappears to me that if what I shall say be true, most of thosetheories about the nature of the world, which are of the mostgeneral interest and which attract the most disciples for thevarious schools of philosophy, must be either false or purelychimerical. It is Inot, indeed, iny object to show that theseimportant consequences follow ; it is possible that they do not,and I have not space to argue that they do. But I wish itshould not be assumed that they do not. My own view isthat, whether what I say be true or false, it is certainly veryimportant, and that is my main reason for raising the question

of its truth. What I miiost fear, then, is not that it should beproved to be false, but that it should be admitted true withoutenquiry, on the ground that, though true, it is unimportant. Ifear that inany of the doctrines I shall put forward will appearto be mere platitudes. They, or others very like them, are, Ithink, constantly so regarded; and yet those, who thus admittheir truth, are not thereby prevented from holding otherdoctrines, on questions of far greater intrinsical importance,which flatly contradict these truths they admiiit and despise.That such a state of things is possible will scarcely be denied.For my own part I am convinced that the characteristicdoctrines of most philosophers, no less where they agree thanwhere they differ, are chiefly due to their failure to trace

the consequences of admitted principles. To remember the


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104 G. E. MOORE.

possibility that this may be so with the principles of identity,may, I hope, lend solue interest to my discussion of the subject.

I will give an instance of the kind of purpose which Ihope the discussion miiay serve. Considerable use is madenow-a-days by a certain sclhool of philosoplhical writers of tbe

phrases " idenitity in difference " anid " unity in difference." Ido not kniow whether as a rule the two phrases are used in thesame or in different senses; but certainly they are ofte?n used

as if they were equivalent. The same is true, I think, ofanotlher pair of phrases, wlicll are also iimuch used by the samewriters-namely, " individual ' and " organic uinity." Further,this second pair is, I believe, supposed to be connected xvith thefirst, in suclh a way, that if you know a tlhing to be ain "indi-vidual " or " organic unity," vou can always infer that it exhibitsboth " identity in difference " and " uniity in difference"; and Ishouldl be very miiuch sutrprised if, onl examination, it did notalso prove that the converse inference was very frequientlymcade. Now I do not know that imianiy eople wouild regardthe knowledge that they were " individuals " or that the worldwas an " organic unity" as having mnuch mportance in itself:although I tlhink the phrases are vaguely impressive and(l onvey

the notion that anythling to whichl they are applied Imiust be ofworth. Buit a very great derivative imiiportance hey certainilyhave; since the writers wlho use them ldraw conclusions by theirmieans, which no one can regard wvitl indifference.

Yet, what is miieanit y these phrases ? In a sense it wouldseem plain that any complex thinlg whatever exhibits identityin difference, sinice it has at least two different predicates and(l

yet is one and the same thing. IBut t is plain that no inferencesof importance can be drawni fromii his fact, since the possessionof comnplexity is comiipatible with almost every difference ofquality we can think of. " Identity in (lifference " inust, there-fore, if it is to yield us valuable information, miean somethingother thani mere complexity; and, as 1 shiall show, there seemllto be a great mrlany ther things it miiighlt meani. The phrase is


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IDENTITY. 10d

therefore ambiguous; anld, thouoh it is certain that manycorrect inferelnces cani be drawni by miieans f ainbiguous words,even where their special sense is lnot defined, it is no less certainithat tlle giravest errors nmay be incurred by arguing that whatis true of a tlini,g to wlhich suclh a word applies in one sense, isalso truie of that to which it applies in another. A philosoplhercertainly, althoulgh nothing can replace for Ihim the power ofrecoa,nisint, hat the truttlhs he lhaindles re different, wlhere they

are so, and(l houglh tlis is perlhaps hiisimost valuable gift, cannotsafely trust to tlhat power alonie if lhe wishes to go far, but mustemploy the additionial safeguar-d of attempting to discover andfix in Ihis mind the points wherelinie hey differ. To a certainiextent he inay b)e lhelpecl in. this task by the work of others,and to supply as mulich of this help as I am aile, by dis-criminatingy he poinlts of difference betweeni trutlhs whiclh weexpress ain(i must colntinuie o express by tbe use of the wordidentity, is the oblject of this paper.

The fir'st poinlt to wlicih I wouldi call atten-tionl with reg ardto truths in. wlicih we assert idlenitity is a very obvious one,It is that we iimay ssert of two things that they have the samiiepredlicate, alnld yet are different from one another. Tlhuis t is

true that mylV oat is. black, and also true that Imy waistcoat isblack; anid yet it is Inot true that imy coat is the same as mywaistcoatt. This state of timings does niot at 1-irst ihlit appear to

present any dlifficulty. It seems obvious enoughli that the twog(arments, hough tlhey htave one predicate in coimoni, yet lhaveeaclh of them at le


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106 G. E. MOORE.

would not be two, buit only one. But is it absolutely certainthat there cannot be two thiings exactly alike? Put in thisabstract form, it does not seem certain. If so-if there may bethings exactly alike, which yet are two, why should not thisbe the case with the blackness also ? Why should the blacknessof both be one and the same, and niot that of each a singleblackness exactly like the otlher ? There is, in fact, a realdifficulty of deciding whether, in the case wlhere two things

have the same predicate, the predicates are two or only one.There is this real difficulty uniderlying the question whicharises in Plato with reg,ard to his "ideas," whenever he saysthat they are in things or that things are copies of them. Canone and the same tlhincg be in two places at once, or must therebe two ? The copy certainly is different both from the thingcopied and fromii ainy otlher copy of the samiie. With regard tothe third form in wl-ichl lie raises a difficulty-where, namely,lie says that things partake of the idea-the difficulty is thesame, if by "partake" be miieant "have it as well as otherqualities." But it is entirely different if by " partake " bemeanit " have part of the idea."

What the above discussioni is designed to briina out is that,

even when we assert truly that two tlhing,s have the same ora commioin predicate, there is a serious difficulty in decidingexactly wlhat it is that is true. Our first suggestion was thatthe predicate of each was in iio sense differenit from that of theotlher, and that the two thliing,s iffered from one another only inthe sense that they had differen-t predicates. We may label thisview as that which holds that 11o difference except conceptualdifference is involved in two things having, the saiime predicate.On this view wheni you say there are two things, you nmean hatthey differ conceptually only, i.e., it is imiipossible that theklifference implied in duality should be otlher thani conceptuallifference. It follows that to talk of two things exactly alike,

or with no conceptual difference, is to talk sheer nonsense-mere words. But so

extreme a judg,ment seems open to


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IDENTITY. 107

suspicion. Even if there are no two things exactly alike, itseems far from self-evident that there could not be. It wasthen suggested that there may be; and this view I propose tolabel as that which holds that beside conceptual differencethere is also involved in two tlhings having the same predicate,another kind which may be called numerical difference. But ifwe tbus admit a separate kind of difference, compatible withthe absence of conceptual difference, it is plain that this kind

of difference may separate fromi one another not only the things,which we have said possess a common predicate, but also thepredicates of each which we have hitherto said to be one andthe samiie predicate. And hence our first view may be wrongnot only in asserting that the two things differ from one anotherin one sense only, but also in asserting that the predicate of theone is in no sense different from that of the other. What reallyis the truth about this mnatter

And, first: Is there such a thing as numerical difference,different kind of difference from conceptual difference ? Philo-sophers have commonly enough spoken as if there were. Evenif it be asserted that two thinigs which differ in the one wayalways also differ in the other, this is to assert that there are

both kinds of difference. Thus, in so far as Leibniz deduceshis principle of the Identity of Indiscernibles from the Law ofSufficient Reason, he is admitting that numerical and coni-ceptual difference are different things. That any two thingsshould differ numerically without also differing conceptuallycannot be a self-contradictory proposition, if it requires the Lawof Sufficient Reason to prove it; and hence Leibniz is guilty of

inconsistency, when he remarks that to suppose two thingsindiscernible is to suppose the same thing under difterentnames.* Our question is, which of these two views is the right

* This point does Inot appear to have been noticed by Mr. Russell inhis iintricate discussion of Leibniz's principle (PhIlos. of L., pp. 54-56).If Leibniz is to be held to this remark, his doctrinie is indistinguiishablefrom that which Mr. Russell attributes to Mr. Bradley. In any case,

the


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108 G. E. MOORE.

one? Let us suppose that there is no such thilng as numericaldifference. In that case, when two things have the samepredicate, the only difference between them coIlsists in thedifference between two different predicates, one of which belongsto one and the other to the other. But wlhat are the things towhichl these diffeneiit predicates belolng ? We predicate of thetlhinigs both a comniol predicate, and a different predicate ofeach. Either then we must say that the things are the

different predicates, and that it is to those that the comimonprecdicate beloings; or else we nmust say that the tlhings areanothier pair of differenit predicates, to each of which one of thefirst pair and to both of which the comn-mon redicate belongs.But in either case the common predicate belongs to or ispredlicated of that whiclh is different in each of the thing,s.And( when we sa.y t has this relation of beloniging or predicatiointo each of two differenit things, we certainly may mnean thatit has the same relationi to each of them. Accordingly our twomust each be analysed into: (1) poinit of difference; (2) relationof predication; (3) common point; of wlhich (2) and (3) areabsoluitely idenltical in eaclh. But, if this is so, the thing,s turnout to bc merely their points of differenice. Of the group (1)

(2) (3), whiclh is what we originally supposed to constitute athing, nothinCg cali be true except that they are three. Wecaninot say of (a) (2) (3), whicel is what we oriainally called theone thing, that it is differenit from the otlher (b) (2) (3). It isonly (a) andl (b) wlichl diffetr frolm one another anld are two.In fact our oricriinal uppositioii was that (3) could only bepredicate(d of (a) aii(d (b), inot of anything else. AInd if this

fact that he imade t proves that lhewas Inot always clear as to the meaningof his priniciple. And the same conclusioni ollows fiom the fact that, ifhe allows nuimerical differenice o differ from coniceptual difference, he isalso bounid, n consistenicy with anxother pplication of the Law of SufficientReasoni, o hold that tlle world does inot exist (ib., p. 57), since there mustfor each thing in it be somnething onceivable differing from that thingnumerically only.


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IDENTITY. 109

supposition holds it is plaini that anything else which we nighttry to predicate of the group, as suchl, would turn ouit to bepredicated only of (a) and (b). We can lnever by any possi-bility get a iiunuber of predicates to comblbine ll forming a newthing, of which, as a whole, anything can be predicated. Wemust start, on this theory, with two points of difference-twosimple predicates having conceptual difference fromi one anotherthis is essential to there being two things at all. And then we

may try to form new things, also differing from one another, byfinding predicates of these points of difference. But whateverwe find and however many we add, we still leave the points ofdifference as they were-the only things of wllich duality canreally be predicateed. For anythinig we predicate of themll, ndthe relation of predication itself, may always both belong tosome other point of diflerence, so that every property by whichwe may try to distinguish our new thiing froimi he old, willmerely identify part of the new thillgC with sonmethingl else,without producing any whole, which, as a whole, differs fromieverything else in the world, in the way in wlich our orig nalpoints of difference differ froim onie another. 'We cani neversay, "This red differs fromn hat red, in virLue of having a

different position"; or "in virtue of lhaving a-c iffereilt spatialrelation to this other thing"; or " as being, the one I think ofnow, whereas that was the onle I thouglht of theni." The posi-tions differ, the spatial relations differ, my thinking now differsfrom my thinking then; but it is always the sanme ed wlhich isat both positions, and is thought of at both times. Anid whenieverwe attempt to say anything of the red at this positioln, as, for

instance, that it was surrounded by yellow, or that it led mne othink of a soldier's coat, exactly the samle must be true of thered at that position, which was surrounded by blue or led meto think of a house on fire. We are unable to distinguish thetwo except by their relation to other thingrs, and by whlateverrelations we attempt so to distinTuish them we always fincld ehave not succeeded. We can never say, "1The red I mean is


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110 G. E. MOORE.

the one surrounded by yellow, and not the one surrounded byblue." For the one surrounded by yellow is also surroundedby blue: they are not two but one, and whatever is true ofthat which is surrounded by yellow is also true of that which issurrounded by blue.

All this I regard as a reductio ad absurdunm f the theorythat there is no difference but conceptual difference. If anyone can avoid assuming that something may be true of a quality

at one position, which is not true' of the same quality atanother positioni, then he will be entitled to assert that alldifference is conceptual difference. But this will at all eventsnot be possible for those who hold that things conlceptuallythe same may be distinguished by their relations to otherthings. If any one asserts or implies that a difference betweenithis and that can be established by the fact that this is relatedto one thing whereas that is related to something different, hecannot without contradiction deny numerical differenice. Forthis and that cannot have different relations, unless the relationpossessed by the one is not possessed by the other. Unless,therefore, the one has a difference from thie other over andabove the difference of relations, it will be true of one alnd

the same thing that it both has and has nlot a given relationto something else. And for the same reason it is equallyimpossible to assert that it is only the whole, this thing, in thatrelation, which differs from the whole, the samiie hing in thisother relation. For unless this which we call the samie thingis in some sense two things, it has both relations, and everythingwhich is true of the thing, with the one relation will also be trueof the thina with the other. It cannot be true that the wholeformed of the thing in one relation is different from the wholeformed of it in the other, unless the thing itself is different;although that it should have the one relation mighlit be adifferent truth from its having the other.

I conclude then that there is such a thing as numericaldifference, different from conceptual difference. And since


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this result has been obtained by pointilng out truths in whicha thing conceptually the same is said both to have and not tohave a given relationi to sometliing, else, we have also aniswereda second question, and have shown that there not only may bebut are things exactly similar; and further, since the things,which turned out to be so, were instances of what we originiallytook to be a commoil predicate of two different things, it is alsoplain that a common predicate, in its application to one thing,

may differ numerically from the same predicate in its applicationto another. We have therefore refuted the principle of theIdentity of Indiscernibles in both the forms which Leibnizfailed to distinguish. We have found both (1) that Identityis not conceptually identical with Indiscernibility; there is adifference not only in name but in fact; and (2) that thingswhich are indiscernible are not always identical. On the otherhand, we have accepted the principle fre(uently implied inPlato that the idea in a thing, iimay be different fromn he ideain itself; and we have still to see whether there is any insur-mountable objection to this view.

The view we have accepted is that in some cases where twothings are truly said to have a common predicate, there exists

in each a predicate exactly similar to that which exists in theother, but not numerically identical with it. And I confessI see no objections to this view, except what seem to rest ona bare denial of the difference between conceptual and numericaldifference. These two exactly similar thingfs are, I may be told,identical in content: exact similarity mieans dentity in content.I admit that they are so. In that case, my adlversary may

retort, they are the same thing; there is no difference betweemithem; they are not two but one. But this is merely to becthe point at issue. What I have urged is that many of ourjudgments plainly imply that there may be twvo hings, thingshaving a kind of differenice which I call numierical, whichl yethave not aniother kind of differeiice whiclh I call conceptual.And I explain the phrase, identity of content, as applying only


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112 G. E. AIOORE.

to two such thlinlgs, which have no coniceptuial difference. Thetwo things, are, I a(linit, in one sense the santie; buit that theyare not thlerefore also on, and the samie is just wlhat I havetried to show.

Or, again, it may be urced:-Does not this idenitity ofcontent between the thlingbs onsist in their botlh having thesame predicate-a commoni eleml-ent IlBt, if so, then, on yourview, this commoni predicate wotuld 'uself be two; and these two

predicates would agrain need a commnion lement to explain theiridentity of content, which would ag,ain be two, anid so onad infinitum. So that, if youi onlce admllit a singrle pair ofexactly similar thliings, or each pair tlhtus admritted you haveto admit an infinite numiber of otlher pairs. Anid (it ilay beadded) if this is nlot absurd enough,ll, aclh pair will be eintirelyindistinguislhable frormi all the others, so tlhat you will not even

be able to distinlguislh your first pair as 3your first, fromii those

whiclh it inmplies. To suich ani objection I slhouild answer:(1) That the pairs wvill not on miiy view be indistingauislhable.Each member will differ numierically froimi all the rest, anidwlhere this is the case any two, of an inifinite number, maybe distinlgulislhed s this anid that, since it is the very meaningr

of numerical differenice that things wlhichl have it are thusdifferent and needl not be mistaken for one aniother. And(2) if this is the case, I see no absurdity in the infinite regress.There mnay, or all I kniow, be an intfinite nulmiber of exactlysimnilar dhings; but if we canl distinguish whlat is true ofany one, fromii wlhat is true of any of thie rest, I see nothing(,to refute mie in the suaggstion. It is at all eveints true,that, if there is not an infiniite number of exactly similarthings, there is an infinite number of conceptually differentones. So that, even, if the admissioni of an infiniite implies,as some hold, a contradiction, this fact caninot be urged infavour of conceptual as agailnst numerical difference. But(3) even if the last two objections were uinanswerable, theydo not touch my theory. For I (lo miot hold that in cvcry


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IDENTITY. 113

case, where a common predicate is truly asserted, the predicatesare two. I found miyself force(d to niacijtain that in somecases they wer e so. But it seeims to me tlhat, as a matterof fact, whlerever two predicates are exactly similar, theirrelation to that wlichl is the samiie in each of them, is quitedifferent froimi he relation of eachl to that of which it is thepredicate. That there may be said to be in each an identicalelernent I admnit. But this idcentical elemiient appears to me

to be not onily tlhe same, but also one andl tl/c sacoe. Nor,in default of further objectionis, do I see any reason for thinkingthat it cannot be so.

But, lastly, it miiay be said: If in the case of two exactlysimilar things there is always also a third thing, as you havejust adimitted, which is one and thc same anid different fromeither, mriust here not also be a fourtlh related to the first andthird, as the third is related to the first and second; and a fiftlirelated to the second and third in the saine way, and so ona(d infinitum ? In other words, if, as I'lato wouldl say, thesimilarity between two particulars is to be explained by thesimilarity of both to one aind the samne dea, muist not thesamie explanation be given of the similarity of eaclh to this

idea? To this objection acgain I should reply, in the firstplace, that a mere infinity of nuimnerically demitical thincgs(loes inot appear to imie to be imnpossible. But if, as seemsto be imiplied in the second form of words, the objection isnot to this infinity but to a definiitioni of exact similaritywhichl consists in sayin.lg that two thing"s are exactly similarto one another when each is exactly similar to a third thing,

then I admit that such a definiition is invalid. Certainly ifthe relation of the idea to eachl of its particulars were exactlythe same as their relation to one aanotlher, we could not definetheir relation to one another by means of their relation toit. We slhould lhave to admlnit hat exact similarity was anunanalysable relation, and that ideas, even though there mightbe infinite numbers of them, were suiperfluous hypotheses so

H


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114 G. E. MOORE.

far as it was concerned, and could not be iilferred from itsreality. And this objection does not, as did the last, failaltogether to touch my theory; for I did intend to definethe relationi of exact similarity between two thing,s as involvingrelation to a third tling, anid not nmerely to make thearatuitous and irrelevant assertioni tlhat, wlhenever two thingsare exactly similar, there is also suelh a tlird thling. To meetthis objection, then, I miust assert, wlat has inot been made

plain hitherto, that the relation between the idea anid itspartictular is not the saitme as that -of one particular tothe other: that the idea is not exactly sinmilar to itsparticuilar. And this assertioti does, 1 admit, seeml straingeat first sight. If they are niot exactly similar, wlhat, itmay be asked, is the difference betweeln tlhem ? We grant youthey have numerical difference, buit you yourself admit thatthey have no conceptual differenice, anid what nmore han this canbe meanit by exact similarity ? My aniswer is that somietlhing,more than this is meant by exact similarity, namely, the factthat each of the tlhings said so to be has a peculiar relation toa third tlhing, numnierically ut niot conceptually different fromthem, which they have not to one aniother. This third thing is

the Platonic i(lea, or, as we mnay nloW call it, the universal.And this thir(d thing is nlot exactly similar to either of theparticulars, just because there is nio fourth thing to wlhich ithas the relation which they have to it. To this view of thecase I can discover no further objection. It is true it would bedesirable to have some sinale terni to express the fact thatthe universal differs niumerically from the particular, without

differing conceptually from it, although it has not that furtherrelation to which I have just confined the term exactsimnilarity. The term exact simiiilarity niaht, indeed, be usedfor this purpose. But then it would be necessary to lhaveanother term to express the additional fact that each particularis also related to the otlher through the universal; and since therelation of particular to particular is probably far miiore often


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IDENTITY. 115

spoken of under thi3 lname, and is also far more often an objectof discussion, it seems desirable to employ the familiar terni

with this complex miieaining. How any term is to be used isnot, however, the question in whiclh I anm nmainly nterested atpresent. The point upon which T am concerned to insist isthat the relation of a particular to its universal is, in fact,different from that of a particular to a particular, which woul(dcommonly be said to be exactly siinilar to it, although of b)othpairs it is true that they differ

numiiericallywithout

differing,conceptually. This point appears to me necessary if we onceadmliit, s I have tried to show we mIust, that things do differinumerically without differing conceptually. For this theorythreatened to obliterate the distinction between particularsand universals, since it deenied that any distilnction could befound in the fact that the particular was the uniiversal in

relation to some other or others coniceptually different fromtiit. Whereas it seems impossible to deny that universals dodiffer from particulars, since different things are true of them:as, for instance, that particulars certainly exist, while it is atleast doubtful whether any universals do; and that universalsmay be predicated of particulars, while particulars cannot bepredicated of universals nor yet of one another. Thus itseems certain that this red and that red do exist, but verydoubtful whether redness itself does. And equally certainthat this red is red; wlhereas undoubtedly red itself is niotthis red, nor this red that red. I can thus claim for mytheory, that it partially unites the views of those who insistoon he recality of self-identical universals, but feel themselves

tlherefore bound to deny any difference but difference of content,with the views of those wlho maintain exact similarity of par-ticulars, but feel inclined to deny that any identity, save thatof each particular with itself, is involved in this.

The admission of numerical difference seernms, henl, to beniecessary; and we have failed to find any fatal objections-to it. It has, however, becomiie plain that several inmportant

H 2


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116 G. E. MOORE.

consequiences, not generally recognised, follow fromii ts admnis-sion; and it will now be well to suimi these up.

First, then, any two thing,s of whicih one has a relation whichthe other has not, or of onie of wlhich somethingr s true whichis not true of the other, are numerically different frnom oneanother. But all such pairs of things are divided into twoclasses, according as the pair in quiestion also have another differ-ence called conceptual difference or have not. It is imiipossible

to escape the conclusion that one ancd he same pair miiay haveboth kinds of dlifference. For if it be said that by their con-ceptual difference is imerely meanit that a conceptually differentuniversal is related to eaclh then each iiiay ilndeed differniumerically onily frorn the other, buit must differ conceptuallyfrolmi he universal to which it is related. But this universallhas to it a relation which it lias not to the other. Accordinglyby definition the universal is numllerically different fromll t; andsince it is also conceptually different, we lhave one anid thesame pair possessingy botlh kinids of difference. To proceed:Any two universals have botlh niuinerical ancd conceptualdifference from one another. Btut every particular has somneone universal from which it cliffers numiierically nly. To this

uiniversal it also has a pectuliar nameless relation, wlhich theuniversal has not to it, and wlichl it lhas not to any otlher par-ticular. All particulars which have this relationl to the sam-euniversal differ from one ano'tler numerically only; but theydiffer conceptually also from any particular whiclh has thisrelation to a different universal. This namiieloss elation wlhicheach particular has to onle, and onily onie, uiniversal, is not thlesame as the relation of a member of a class to its class-concept;since the member of a class may differ conceptually from itsclass-concept, and since also two universals imiayboth belolng tothe samiie class. But, it may be said, what is the differencebetween a particular and a universal, since they do not neces-sarily differ conceptually ? The difference is that they belongto different classes: the

class-concept" universal " differs from


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IDENTITY. 117

the class-conicept " particular." And the classes muay e definedas follows: Anything is a particular whichl has to some otherthings, differing from it numerically only, the peculiar namiielessrelation above mentionled. Anything, is a universal which hasthis relation to nlothinig else at all. Thus there nmay beuniversals having onily one particular, or having no particularswhatsoever: buit every particular lmlust have a universal. Tlleniame " universal" must niot therefore be understood to inmply

particulars, but onily to note the fact, that if there be more thantwo thing,s differing from one alnotlher numerically onlly, thereis one amilonig hemii having, a relationi to a1l the rest, wlhich noneof the rest have to it or to one aniotlher. A class-concept, onithe other lhand, does imiply at least one mcmber coniceptuallydifferenit from it; and if tlhere are more, it has to Cal a relationwhich none of theni lhave to it or to one another. It is, miiore-over, always also a universal, but may have lno particulars.Great care is therefore needed in distilnguishing the differentrelationis it imay have to different tlhings in either character.

We are now in a positioni to say something with regard tothe imieaning, f identity. Witlh regard to assertions of identityin genieral, it seems plain that they imiay take two different

forms. We may eitlher assert that this is identical with that,or that this is identical with itself. The latter formii s thatuised in the logical " Law of Identity," A is A; everything isidentical witlh itself. Of this law Hegel complains in one

place* that those who assert it also assert its "opposite," andimmediately afterwards, that utterances in accordanice with it' deserve " to be " reputed silly." I canniiot ake upon miiyselfto decide wlhether or niot he regards these cbarges as the same,and whetlher or niot he mleans by opposite " contradictory."The instaiicees he gives (" A planet is-a planet; Magnetismis-nmagmietisrmi; Mind is mindi") seem to be justly accused ofsilliness. But are they untrtue ? I do not know that eitlher he

* Smaller Logic,?

115, Wallace'sTrans., p. 214.


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118 G. E. MOORE.

or any of h-is disciples have maintained that Mind is lnot mind,althouah they may lhave maintained that Matter is iiot matter.It would seem, then, that some even of these silly instanceslhave cointradictories, which are false; anid that when Hegeltells us that in asserting the Law of Identity we also assertits opposite, he olnly means that we mtust assert something elseof Mind as well as the fact that it is Mind; not that wemay assert it is not Mind. Accordingly, his first complainit

would seem to amount to no more than a comment on theambiguity of the copula, pointing out that many differentthings may in different senses be predicated of one and thesame thing; a comment which is very true, and would be veryuseful if those who made it, or those who heard it, could beinduced thereby to remember it in practice.

But theere still seems room to ask why these remarks aresilly if they are true. I think, in the first place, it is becausethe same worid happens to be used in subject and predicate.It is true, as Hegel himself remarks, that the propositionalform always " promises a distinction betweeni subject andpredicate," and if a distinction is meant, it usually seems sillyto use the same symbol for what is miieant o be distin(guished.

Cases are rare in which the double meaning of a symbol is sowell understood that we can calculate upon a distiilction beinlgperceived in spite of our usingT the same symbol. We cannotenunciate all truths in the fornm f puns; and, even if we could,we could not expect the joke to be appreciated in all companies."A bull is a bull" mig,ht conceivably be the best way ofexpressing a judgment of the relation between such verydifferent thinigs as an animal and an Irish form of wit; butthe differenice miust be very obvious, or wve hall have to explainour joke. Hegel is, tlherefore, uinfair to the Law of Idenitity inhis choice of symbols to express its instances. Supposing wesay, "Mind is somiething of whicht propositions are true wbichare not true of anythin(g else wlhatever," it is by no meansobvious that the utterance is silly, altlhough our meaning migllt


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IDENTITY. 119

be exactly the saine as we shotuld express uinder other circum-stances by sayinig, " Mitidl is mind." But what is our meaningwhen we use such expressions? I lhave assumed that theremust be some distinction which we are trying to express; butit is obvious, from the fact that we are ever tempted to expressit by " Mind is mind," that it is a distinction which is soinewhat(lifficult to catch. When we say, " This is identical with itself,"the truth of which we are thlinkingt eeins to belong to the class

of trutlhs of which the general form is, " This is identical withlthat," and it seemus as if in all such cases "this" and " that"mutst have some difference fromii nie another, and tlherefore that,in this case, the thing imust be different from itself in order tobe identical. This, I believe, is the conclusion to which Hegelwislhes to drive us; an(l yet it is undoubtedly this which theLaw of Identity wishes to dceny. We must, therefore, find apoint of difference between what we mean by " This is identicalwith itself," and what we mean by " This is identical witlh that,"if we are to hold that any instanice of our Law does not imiiplyits own comitradictory; and yet we inust miiaintain hat any suchinstance asserts a relationi between two different things, ifwe are to hold that it is not )urei nonsense and can have a

contradictory.Such a point of differenee miiay be found, in the first place,in the fact that wheni we say, " Mind is self-identical,"' weare assertingt somiiethlingir f it wlhich is also true of everything,else; whereas wheni we say, " Matter is identical with lmlind,"we are asserting, somethlincg f a pair of tliings, wlich is not trueof every other pair. In ishort our Law is: "Everytlhing is self-

identical"; it is not " Everything, is identical vithi somethingelse." It would thus seem, at first siglht, that " Mind(l s mnind"is as far as possible fromi being an instanice of our Law, or ani" utterance in accordance with it," since it appears to be, aniattenipt to assert of imind soumething whlicih s true of notlhingelse, whereas, by the very termas of the law, any instanice of itmust assert of something, a predicate wlliclh is also truie of


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everything else. The Law of Idenitity asserts of everythin,gthat it belongs to a certain class : let us say, the class ofsubjects. An instance of the law wotuld then be: "Mind isa subject." But, thein, so Care "matter" and hosts of otherthings. Yet we do not inean to assert that it is just likethese: we feel that our assertion was meant to be uniquie.We want to say not only that it is a suibject like otherthings, but which subject it is; anid we are faimiiliar witlh

only onie mnetlhod of specification-that whlichl asserts ofa giveni particular the uiniversal to which it is related.When we say, vaguiiely enoug-h, buit witlh a very definitemeaning, " Tlis exists," an(d we are asked " Wlichl this (1oyou mean ? " the answer " The this wlichli is red " generallyproves satisfactol-y: we lhave suiecee(led in specifying a pointwlherein it diffen; fromii iiost otlher tlhings. Bit wlhen the"this " of wlichl we are speahking is " This red " or is theuniversal itself, this mtietlhod s no longoc openl to uls. Wecannlot specify any point in wlichli it differs frolmi otlher thlinlgs,because it is itself a imiere poinit of differenice. We cani say ofit, it is a subject, a point of (lifierece : andi we are sure thatthis is unamiibiguouis. 13utt f any one asks, " Whiech ubject is it ?

we can only reply, " The subject whlichl it is," although we havetllereby added nothing to our imeaning. Tlhis, I take it, is howwe comle to say " Mintd s miniid." We fancy that the unique-ness of a thlingi ought in every case to be capable of beingexpressed in somne predicate, because this miietlhod provessuccessfuil in imiost rdiniary cases. Butt the fact is that everypredicate we can assicrgn oes also beloDng to somle other thling,though Inot in greneral to all or miiost; and that the onily thingwlich gives absolute unliqueness o any proposition is the subject.Any proposition- will differ fromil ome other in respect both ofits subject and(I ts predicate; but it canl differ froin all othersonly in respect of its suibject.

Tf then we take our ineaning, xvhlen e say " Mind is inind,"

to be that " Minid is a suibject," s it still silly -f Certainly tlhis


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IDENTITY. 121

particular case of the Law of Identity malay e thought so; andso, uinder certain circumstances, may any other: for the factsthey enuniiciate are oftenl obvioits to every one. But the Lawitself (loes niot tlherefore lose its implortance. For it assertsthat this is truie of everytlhing; wlhereas every plhilosopher whoholds that Appearance differs from R1eality mnust assert thatsome tlhing,s are miiere redicates.

The first miieaniing, hen, wlvicli we can give to an assertion

of Ideentity, is that the assertion that a thing, is identical witlhitself is equiivalenit o the assertion that it is a sulbject. Identityis n(^)t here a relationi between two thingbs, nor does it imiiply nyliffereince. The assertion that such and suclh a thing is a

subject has beeti commrnon nough in philosoplhy, and thereforemight seeim to llee(l no explanation. Moreover, the notion

subject " is itself a subject, aild therefore undefinablie. I may,however, atteimipt to convey a notionl of its meaning byspecifyiing its relations, and by recalling the terms xvlhichhave been used for it. To begin witlh the latter: It is, inthe first place, imuticlh lhat Spinoza mnetint by Substance; anidliis " Attributte," too, is mulch wliat I inean by predicate. It isnuchl what is commiionily meant by "Indlividual," and it is

wlhat Mr. Bradley aind others have called a " This." Nowwhat is intenided to be coniveyed by predicatinga any of thesetermns of a thin g-by sayincg that so and so is a Stubstainceor a SLlljject, or an Individual, or a " This "-appears to bemiiainly that the thing so said to be is a thinlg of whiclhsomething is true whiclh is niot truie of anytliing else wlhatever.But it this be takeni to miieani thingr wlichl- lhas a predicatewhicelh nothig, else hias, he sealch for suclh a thing obviouslybecomnes very dlitheult. Hence arises a tendenicy to supposethat a suibstance must l)e a tlhingiswitlh a very great varietyof predicates; sinice, if youassig,n it enlough, there is soImie hopethat there will be nio otlher thingr of whichl it is true that it hiasall those pre(licates. In this way we obtain suclh definitions ofStubstance as that it is that vlhichli nites all positive predicates;


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122 G. E. MOORE.

or of an Individual, as that it combinies the greatest possibledifferentiation with the greatest possible unity. But all sucllattempts leave unexplained the fact, whiclh they cannotbut recognise, that the predicates themselves, if they are(lifferent, iiulst each have that very property, which theirconmbiniation s supposed to bestow on Substance-namely,that somethingr is true of each, which is not true of any-tlhingb lse. Either tlley Care not eaclh uniiquie; n which case

the Substance also lhas lost its uiniqtueness: or else they are;and theni the collection of aniy nuilmber s no whit more so thaneach one singly. It is nlot theni by its predicates that aSubstaice cani be distinguishe(l. SoIi1ething s true of it whiclhis not truie of anythinig else, butt this caniiot mean that it haseither one or anly number of predicates whicll notlhing else has.There is in fact an anmbiguity n the expression, " that which istruie of a thing," to point out wlhich is all that I cani do in theway of defining,r subject. It is the case with any subject, notonly that something is true of it, wlich is true of nothing else,but that everything, which is true of it is true of nothing else.Butt this does not meain that it may not lhave the sanme elationlto other things which something else has; it may and must

have some relation to some other thiing, whlich everything elsehas. Wlhat is imieanit s that the fact of its lhaving, that relationiis not the same fact as that anything else lhas it. That it isa subject, for instance, is a (liflereint truthl frorn the truth thatanything else is so, altlhoughl-i hat eachl asserts to be true of thesubject in questioin is exactly the saimie.

(1) Our first kind of "Identity," then-self-sameness or

individuiality-neither affirms nor deinies difference. It is truethat if two things are numerically different, eacli is an irLdi-vidual. But to assert that a thing is not an individual is notequivalent to asserting that it is not nunierically different from-some other. Nunmerical (lifference can onily be asserted ordenied of two individuals ; indivi(duiality can be asserted or:denied of one. The mlotive of botlh deniials is indeed the same,


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IDENTITY. 123

niamiely, he desire to prove that a single individual possessesboth of two predicates, of which it is obvious that it possessesone. But wlhereas the denial of nulnerical difference wouldleave it doubtful which of the two was to ba benefited, thedeniial of individualitv makes it plain that the advantages ofthe transaction are not to accrue to that of which it is denied.Thus, for instance, in order to prove a Spiritualism by trans-ferrinig to mind some of the predicates which appear to attach

to inatter, it is necessary both to deny their numerical difference(wllich by itself inight lead to Materialisnm), nd also to denythe individuality of imiatter (wllich by itself miglht lead toAgnosticism).

(2) The above com-bination of these two denials gives us asecond sense of ideiitity. A thingc, may be said to be numericallyidentical witlh another, when it is denied both to have indi-viduality ancd to be numerically diffei'ent fronm hat other. Anassertion of idenitity in this sense is obviously never true; justbecause aim assertion of it in the first sense always is so.Neitlher the deniial of individuality nor thie denial of numericaldifference is ever trute. Yet both are frequently deenied. Thereasoni seems to be that we frequelntly wish to assert that twvo

relationis botlh attacll to one individual. In suclh cases thetrutlh that the onie relation attaclhes to the individual is adiffereint trtutlh from tlle trutlh that the otther attaches to it;ancd ince the trutlhs are different it is assunmed hat they lhavedifterent suibjects. Tlhus the difference betweein truths whiclhconisists in their asserting, (lifferent relations of the same subjectis confused witlh that whlichl onsists in tleilr asserting the same

relation of differeilt subjects. Tlhuis, f we say, " The red I amtlinkiing, of niow is the same as that of wlich I was tlhinkingtlheni," t is easy to suppose that the identity predicated is ofthe same kind as whlenwe say, " The red at this place is thesamiie as the red at that place." In the seconid case, however,we are asserting th(at two tlhings numerically differenit have thesamle relation to onie universal (a particular tint of red), whlereas


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124 G. E. MOORE.

in the first we mnay be m-lerely redicatinga wo different relationsof a singrle ndividual. Wheni oince, in this way, we have comseto suppose that we cani deny of a thing that it differs nlumnericallyfrom itself, it is colmlparatively asy to persuade ourselves thatthe dellial may extenid to other things.

But (3) we may deny coniceptual differeilce, of two thingsntumerically different. We may then be said to assert thatthey are colnceptually identical. In a11 uch cases the assertion

of identity is the assertionl of a relation between two differentthings: identity does really imply difference. The relationasserted miay, according to what was said above, be eitlher therelation of two particulars to the samiie univerlsal, or the relationlof the universal to a particular, or that of a particular to auiniversal. All three relationis are differelnt, but all are alike inimiiplying, he denial of conceptual differenlce. It is plaini that

in suicIl cases it is very easy to suppose that, since we assertidentity in spite of ilnumierical differen'ce, we are also denyingniumerical differenice. Aind if niumerical difference could bedenied in the case of colnceptual identicals, tlhere would be noobjection to its denlial in the case of things con-ceptuallydifferent, since they are niot a bit miiore numiilerically iffereiltthan the others. Moreover

(4) Thin1gs wlich are botlh conceptuially and numliiericallydifferent fromii one Canother reueiltly hiave to one another arelationi wllich is very liable to be confused witlh the relationi ofparticular to particular: I mzeani he relation of nmemlbers f aclass to onle another. If a number of redls of the same tiilt aresaid to have in commliloni he fact that they are all just that red,we are liable to

suipposethat a inubler of reds of different tinlts

lso have in coimmRloni n the saImie way the Jact that they are allred. If the first set mnay be said to exliibit identity of conitent,why nlot the second ? And if the seconid, why not the series ofniiiiibers, &c. ? It imust, I thinik, be adlmitted that 2 and 3are somwetiines aid to exlhibit identityiin difference for n1obetterreasoln than that they. are both niulm-bers. It is tlhouight hat


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I DENTIT Y. 125

their beiun numubers enters into tleilr iature as individuals, in

the same way as its redness conistitutes the nature of "tlhisred." Yet it inmust e insisted that 2 and ' are qot conceptuallyidentical. Their relation to number is quite different fromn hatof two particulars to their uniiver.sal. Tlhougbh his, therefore, isa case in whichl identity i's predicated, I think the usalge is onewhich mihlit well be giveln up. The coinfusioni caused by it islargely responisible for that coniceptioni f " concrete " or " self-

differentiatin('T uiniiiversal," which is so powerutil ani instrumentfor persuading to the dleinial of numerical diflerenice betweenindividuials. If thle coniceptioni numnher be regarded as havillnto the lifferenit uniubers he relationi of a iuniiversal to its par-ticulars, tlhen, in virtue of their difference, it is calledl a "self-liffereintiatilio uiniversal." Mforeover, the niumiber " to, in

virtue of its relationi to it, miiay be calle(d a (partially) concreteuiniversal. And ftirther, since it is ver) easy to conifouindl heclass-concept with the class, why shoul(d niot the wliole series ofnumbers (if onily it were niot infinite ) he rerar(led as a self-differentiating or colicrete iuniversal ? (I do Iiot kniow whliclhexpression, or wlhethier ithier, would be considered appropriatein this instanice.) And, lastly, sinlce lhere we have a grrouip f

different thing(,s, ach withi ani intimilate elationt to one cowmmonconlcept, with regar(d o which the identity in difference clharac-teristic of a concrete uiniver al is so remarkalde, whyshould we not, wherever we liave a grouip of diffterenit hings,each of whiichi s related to one coiiinion concept, even if thatcomnmon concept be only their miembershlip f the grouip, callthat grouip, too, a concrete uniiversal ? hlenice a state is aconcrete uiniversal, a nman s a conicrete universal; Ilot bec>ausestates ind men have some properties in comImioni, nor evenbecauise all the parts of each is a member of a single class, hutbecause of each of the parts of each it may be said that it is amemnber f the state, a part of man. Such extravag,anices arequite soberly conmmitted by philosophers of reputation. But

the inain pity of it is thiat, wheni they liave thlius nvested a-


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126 G. E. MOORE.

group with the title of concrete universal or individuial (perhapsthese are the same ?), they then hark- back and begin to investthe group with the properties whiclh belong to a real uniiversal:as that, without their relation to the universal, the particularswould not be what they are; that the group, as a whole,possesses all the attribuites wlichl its particulars lhave singly;that they, conversely, possess all its attributes-are microcosmsto its miacrocosm. By such methods it is easy to prove that

the world is an individual; that all differeiices are transcendedin it; that its capability of remiiaining one, in spite of them, isadmirable.

But to return : (5) If two things iillnerically different maybe conceptuially the same, may not two thingas conceptuallydifferent be nuinerically the sam


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IDENTITY. 127

conceptually identical. Conmplexes are theni capable of being

subjects, bothl as wholes, and also in that certain predicatesattach to all their parts wlhich do niot attaclh to eachl singly.But it is very important to distinguish these cases from thosein which a inere relation between the parts is asserted. Thus,when I say that myly oat is black, I may be understood to assertthat, if niot all, yet a great number of, its parts are so. Buit theassertion that each one of tlhelm s black is not to be uinderstood

as an assertion of the relation of particulars to a uniiversal, butof black particulars to other particulars. Accordingly, when itis asserted of one of themi that it is black and woollen, this isnot to be understood as an assertion that one individual lhas twopredicates, but that two inidividluals have a certaini relation.The parts of my coat, then, understood in this sense, lhaveneither conceptual nor iiiinuerical identity. In each case itis possible to distingtuish some one individuial related to aconceptually different individual; and it is these relationswhich are asserted when all are said to be black. The asser-tion of identity through change, and of personal identity, alwaysinvolves relationis of this kind. When the samne dentical thingis said to persist, it is always meant that two or miiore articulars,

conceptually identical, are continuous in timie; anid the cliancgeresolves itself inlto the fact that each of two conceptuallydifferent particulars has the same relationi to each at a differenttimne. Thus the "material identity " of a thintg may be saidto consist in the conitinuious existence of conceptually idenlticalparticulars, wlhich have at different timnes he saine relation todifferent particulars.

proceedings of the aristotelian society, new series, vol. 1 (1900 - 1901), pp. 103-127

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