McGinn, Colin Professor of Philosophy, RutgersUniversity

Logical PropertiesIdentity, Existence, Predication,

Necessity, TruthPublication date 2000 (this edition)Print ISBN-10: 0-19-924181-3Print ISBN-13: 978-0-19-924181-1

doi:10.1093/0199241813.001.0001

Abstract: This book discusses the nature of identity,existence, predication, necessity, and truth. Its mainclaims are that identity, existence, and truth are logicalproperties, that predicates are singular terms that referto properties, and that necessity (and other modalities)are modes of instantiation of properties by objects. Thebook develops a realist anti-naturalist stance on logicalproperties, which takes logical notions at face value, andrefuses to reduce them to other notions. Two furthercontentions central to this work are, first, that thequantifier has been overrated as an instrument of logico-linguistic analysis; and secondly, that past attempts todefine logical notions such as identity or existence havebeen largely unsuccessful.

Keywords: existence, Frege, identity, logic, logicalproperties, metaphysics, Colin McGinn, necessity,predication, Quine, realism, Russell, truth

Logical Properties

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Logical Properties

Identity, Existence, Predication, Necessity,

Truth

CLARENDON PRESS · OXFORD

2000

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McGinn, Colin, 1950-Logical properties : identity,

existence, predication, necessity,truth / Colin McGinn.

p. cm.Includes bibliographical references

and index.1. Logic. I. Title.

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Preface

The first philosophy course I ever taught wason truth, back in 1974. At that time I wasprimarily a philosopher of language andlogic. In later years I became drawn to topicsin the philosophy of mind, as well asmetaphysics and epistemology. My interestin philosophical logic went into abeyance fora decade or so. The work in this book wasbegun about five years ago, though some ofthe ideas date back to the 1970s and 1980s.For some reason I started thinking seriouslyabout these topics again, and I found that mythoughts on each of them shared somecommon themes. Thus, after many years ofnot working on philosophical logic, I decidedto put together a short book on the subject.

It has been a pleasure to work on suchabstruse, pure, and rigorous topics afterspending so much time thinking about messysubjects like consciousness (not to mentionevil, beauty of soul, etc.). In philosophicallogic it is possible to achieve real results,develop sharp arguments, come to definite

conclusions. It has also been a pleasure towrite an avowedly specialist book, withouthaving to worry about accessibility to a wideraudience.

I have written this book as clearly andeconomically as I can. I have not burdenedthe text with detailed discussions of recentliterature, preferring to maintain a smoothflow of argument; the footnotes address someof the relevant literature, as well as respondto possible objections.

Philosophical logic is perhaps a less thrivingsubject than it was in my student days. I thinkthat this is in part because it became tooformalistic and divorced from philosophicalconcerns. The reader will observe that thereare very few formulas or symbols in thisbook, and I have strived constantly to keepthe philosophical issues

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in mind; my aim has been to bringphilosophy back into philosophical logic.What makes topics like existence andnecessity so fascinating is the way theycombine perplexing metaphysical concernswith issues of logical analysis and linguistics.I hope it is apparent in this book that I havesteered clear of the kind of formalisticfetishism and scholasticism that hascharacterized too much philosophical logic inrecent years.

The general theme of the book is a kind ofrealist anti- naturalism about logicalproperties. My tendency is to take logicalnotions at face value, instead of trying toreduce them to something else. As elsewherein philosophy, I believe in respecting theappearances. One of my contentions is thatthe quantifier has been overrated as a tool oflogical and linguistic analysis; another is thatthe urge to define the various logical notions

dealt with here has not in general been asuccessful project. Logical properties arewhat they are and not some other thing.

The book is intended for readers with somesophistication in philosophical logic, but Ithink it could be used in an advancedundergraduate course if suitablysupplemented with background reading.

I am grateful to E. J. Lowe and Andre Galois,who as referees for Oxford University Pressgave me detailed comments on thepenultimate draft; many of the footnotes areresponses to points they raised. I am alsograteful to Stephen Neale, with whom I taughtthis material in a graduate seminar atRutgers, as well as to the students whoattended.

C.McG.

New York

March 2000

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Contents

1. Identity 12. Existence 153. Predication 524. Necessity 695. Truth 87

Bibliography 109 Index 111

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1 Identity

Abstract: Four central claims about thenature of identity are formulated. Identity isunitary, indefinable, fundamental, and it is agenuine relation. This general conception ofidentity is appealed to in later chapters whendiscussing other topics.

Keywords: criteria of identity, Frege,identity, Leibniz's law, numerical identity,qualitative identity, relative identity

Colin McGinnMy purpose in this chapter is to formulate acluster of claims about the nature of identity.I shall not enter into an elaborate defence ofthese claims, since they are generallyuncontroversial and have been defendedadequately by others. My aim is to articulatea position that will be useful for laterdiscussions of other topics. In many waysidentity is a paradigm for other logicalnotions, and it serves to focus thought inother areas to be as clear as possible aboutthe concept of identity. My general theme willbe the simplicity and primitiveness of thenotion of identity, and its absolutelyfundamental role in our thought.

My first thesis is that identity is unitary.Frege writes: 'Identity is a relation given to usin such a specific form that it isinconceivable that various forms of it shouldoccur.'1 I want to explain the import of thisdictum and to spell out what we arecommitted to denying if we take the dictumseriously. So let us ask: What kind ofproperty or relation is not unitary in thesense Frege intends? Take the propertyexpressed by 'x is blue' or the relationexpressed by 'x is more intelligent than y':these do admit of various forms—shades ofblue, types of intelligence. Frege's thought isthat identity does not in this way divide upinto sub-varieties (one could not write a good

book entitled The Varieties of Identity2 ).There is no equivocation or vagueness in thenotion of identity, and it operates as adeterminate property not a determinable one.It is, as Frege also said, that unique

1 Basic Laws of Arithmetic, ii. 254; quotedin Peter Geach, Logic Matters, 238. Geachcites Frege in order to disagree with him,holding that identity is relative to a sortalcount noun.2 In the way that Gareth Evans's Varietiesof Reference emphasized the very differentways in which different types of terms refer(despite some common themes).

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relation a thing has to itself and to no otherthing—period.3 Its logical properties arereflexivity, symmetry, and transitivity. It issimply the relation x has to y when x isnothing other than y, when there is nodistinction between x and y, when xisy. Andwhen we grasp the notion of identity weimplicitly understand that it admits of noqualification or variation. That is the Fregeanthesis.

In order to appreciate better what theFregean thesis comes to, let us considerthree ways in which it might be challenged,noting the errors of these challenges. First, itmight be said that identity divides into twobasic sub-types: numerical identity andqualitative identity. Numerical identity relatesan object only to itself, while qualitativeidentity can relate numerically distinct objectsthat share some number of properties—objects that are merely exactly similar.Thus I am qualitatively identical to my twin,but not numerically identical to him. Thisdistinction is allied to, indeed equivalent to,the distinction between type identity andtoken identity: two occurrences of the letter'a' are type identical without being token

identical—that is, they are similar enough tobe declared qualitatively the same. Are there,then, two types of identity relation at workhere? Well, there is obviously a distinctionbetween similarity relations and the(numerical) identity relation, but it isconfused to interpret this as implying thatidentity comes in two varieties. In fact, astatement of so-called qualitative identity isreally a statement of numerical identity (thatis, identity tout court) about the properties ofthe objects in question: it says in effect thatthe properties of x and y are (numerically)identical.4 My properties (or many of them)are the same as those of my twin; theproperty the token 'a' has of being aninstance of a certain letter

3 See 'On Sense and Reference'.4 Of course, I am assuming here thatdifferent objects can share the sameproperties, i.e. that there are genuineuniversals. A trope theorist will need adifferent account of similarity betweenobjects, since he will not be able to explainthis in terms of the numerical identity ofdifferently instantiated properties. But evenfor a trope theorist it should be clear thatso-called qualitative identity is really justsimilarity and not another species ofidentity. It would be better to drop talk of'numerical' and 'qualitative' identityaltogether, speaking instead simply ofidentity and resemblance.

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type is shared (that property) by this second'a'. In the limit, if x and y share all theirproperties, then this amounts to the fact thatevery property x has is a property y alsohas: for any property F that x has there is aproperty G that y has such that F is identicalto G. So-called qualitative identity is justnumerical identity of qualities on the part of

possibly distinct objects. Put another way, ifyou find that for any property F that x hasthere is an identical property G that y has,and vice versa, then x is qualitatively identicalto y. Thus qualitative identity is analysable interms of numerical identity. And similarly fortype and token identity: to say that x and yare type identical is to say that there is asingle type T that x and y both are, i.e. thetype that x exemplifies is identical(numerically) to the type that y exemplifies.There are not two identity relations at playhere but merely a unitary notion of identityrelating distinct kinds of entity. It is not that'identical' is an incomplete predicate until weare told whether it is to be preceded by themodifiers 'numerically' or 'qualitatively'. Whenwe use 'identical' to relate distinct objects weare simply saying that the objects have thesame properties or are of the same kind,where this latter is plainly an example ofstraightforward (numerical) identity. When Isay that this dog is the same breed as thatdog I am simply affirming the identity of theirrespective breeds, not introducing a new kindof identity relation over and above the oldone—as it were, a special non-strict kind ofidentity that fails to obey Leibniz's law. It isnot that we have to countenance a 'looser'brand of identity to be set beside the originalarticle. All identity is strict identity—or rather,the qualifier 'strict' is pleonastic here.5

5 I take it to be obvious enough that it wouldbe a mistake to think that there are twomodal kinds of identity, the necessary andthe contingent. All identity is necessary,though there can be contingently trueidentity statements—those that containnon-rigid designators: see Saul Kripke,'Identity and Necessity'. But even those whobelieve in contingent identity should not betempted to construe this as a new type ofidentity relation, any more than theadjacency relation should be taken to have

two forms or be 'incomplete' becausenumbers stand in necessary adjacencyrelations while chairs do not. It is the samerelation that admits of the two modalqualifications. Compare the question ofwhether there are two kinds of truthproperty, corresponding to necessary truthsand contingent truths.

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A second reason for questioning Frege'sdictum might be the alleged sortal relativity ofstatements of identity. The idea here is that tosay that x is the same as y is not yet toexpress a complete proposition—we need tosay what sort of sameness is in question.Until we answer the question 'same what?' wehave said nothing truth-evaluable.6 On thisview, 'same' is radically syncategorematic,like 'er' in 'longer than'. A properly completeidentity statement must have the form 'x is thesame F as y', for some sortal F. This viewcertainly entails the denial of Frege's dictum,in either the view's strong form or its weakform. The strong form says that identity isrelative, so that we can have instances inwhich x is the same F as y but not the sameG. The weak form denies such relativity butinsists that identity statements stand in needof sortal supplementation, where the varioussortals generate distinct types of identityrelation.7 Thus 'same man' is not composedof a complete relation word 'same' that maystand alone between singular terms,combined with the common noun 'man';rather, the noun is required to complete thesense of the incomplete symbol 'same'.

I would reject both the strong and weakversions of the sortal-dependence claim forfamiliar reasons. The strong relativity thesisconflicts with the indiscernibility of identicals,since if x is the same F as y but not thesame G then x has a property y does not

have, viz. being the same G as x. For if yhas this property then it is the same G as xafter all. Identity of x and y under the sortal Ftells us, by Leibniz's law, that y must havewhat x has; but then if x has the property ofbeing the same G as x, which it surely does,then y should have this property too—but thiscontradicts the claim that x

6 As Geach puts it in 'Identity Theory':'When one says "x is identical with y", this,I hold, is an incomplete expression; it isshort for "x is the same A as y", where "A"represents some count noun understoodfrom the context of utterance—or else, it isjust a vague expression or a half-formedthought' (Logic Matters, 238).7 The strong position is defended byGeach, and the weak position sometimesseems intended by David Wiggins inSameness and Substance, ch. 2.

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is not the same G as y.8 And once the thesisof relativity is abandoned the motivation forthe incompleteness claim vanishes: any forcethere is in the claim that 'this is the same asthat' is incomplete is better explained by theobservation that the singular terms needsupplementation in order to achievedeterminate reference; once we know whichobject is at issue it is completely determinatewhether this object is or is not identical tosome other determinately specified object.9Unsupplemented identity statements are nomore incomplete than 'x is blue', where alsowe can raise doubts about which thing isblue—as when I point in the direction of amostly red car with a blue hood and say 'thatis blue'. And really it is bizarre to think thatidentity could need supplementation in thisway, since it is quite clear what relation isexpressed by the simple sign of identity: ifyou put ' ' between any pair of determinate

singular terms the proposition expressed isas clear as a proposition could be.10

A third reason for denying that identity isunitary might issue from the recognition thatobjects come in many kinds and that theconditions of their persistence varydepending upon what kind of object is inquestion. Here we encounter the idea thatobjects have different 'criteria of identity',different conditions under which x may besaid to be the same as y. Sets are the sameiff they have all the same members; materialobjects are the same iff they are 'spatio-temporally continuous'; times are the same iffthe same

8 See Wiggins, Sameness and Substance,ch. 1, for this type of argument. Of course,the argument assumes the validity of theclassical Leibnizian law, which a defenderof relative identity might opt to reject. But Ithink that this law is so fundamental to thenotion of identity that rejecting it amounts tochanging the subject. I also believe, thoughI will not argue it here, that the thesis ofrelative identity enjoys no indispensableexplanatory advantage over classicalabsolute identity; again, see Wiggins, ibid.23 ff.9 See John Perry, 'The Same F', for aconvincing defence of this line.10 It seems natural when someone says'this is the same as that' to press thequestion 'same what?'; but it is equallynatural to respond 'what is the same?' Thebare demonstratives leave the propositionunderspecified, but the fault lies with themand not with the identity concept. Comparebaldly asserting 'this exists', where theindeterminacy clearly lies with thedemonstrative and not with the concept ofexistence.

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events happen at them; events are the sameiff they have the same causes and effects;selves are the same iff they exhibitappropriate 'mental connectedness' or havethe same bodies. But, however plausible thisidea of varying 'criteria of identity' might be,it is confused to believe that it shows that theidentity relation itself admits of such variation.Many different kinds of objects can be blue,too—solids, liquids, gases, rays of light,persons—but this does not show thatblueness itself reflects the differences inthese objects. Similarly, though many kindsof objects stand in the identity relation, itdoes not follow that this relation itself reflectsor incorporates the kinds in question. Wemight indeed allow that identity can besupervenient on a variety of bases in objects,depending upon the kind of object inquestion, but this does not imply that whatthus supervenes is not a unitary property.11It is the same with existence, which we shalldiscuss in the next chapter: many differentkinds of object exist, and their existence'consists in' different kinds of conditions, butit does not follow that 'exists' is equivocal orincomplete. Identity is always reflexive,symmetrical, and transitive, and alwaysobeys the indiscernibility of identicals,despite the fact that it applies to many kindsof object. Identity is not a different relationwhen applied to concrete and abstractobjects, say, despite the deep differencesbetween these types of object. We just havethe same old identity concept applied to avariety of objects, that is all.

I take it, then, that Frege's unitary thesis isnot threatened by these kinds ofconsideration. Identity is such a specificrelation, as specific (say) as the successorrelation in arithmetic, that it is indeedinconceivable that it might fall into a variety offorms loosely classified together under'same'. The concept of identity is quite unlike

the family resemblance concept expressedby 'game',

11 Compare the property of goodness: itsupervenes on a variety of descriptivebases, but this does not compromise itsconceptual integrity. Similarly, identity mightbe constituted by different things fordifferent types of object, but it does notfollow that identity itself shifts its identityfrom case to case (identity does not sufferfrom identity problems).

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which is given to us in a highly unspecificform and admits of many subvarieties.Objects that fall under 'game' are not linkedby a single common feature, but 'identical'expresses a quite definite concept thatremains rigidly the same (!) from case tocase.

The next question I want to ask is whetheridentity is definable: is its specificity theresult of a sharp definition or is itconceptually primitive? In particular, canidentity be defined by Leibniz's law, namely'x y iff for all P, Px iff Py'? There are threemain problems with this proposal, whichagain I will simply summarize rather thandefend. First, the sufficiency of theright-hand side notoriously depends uponwhether we include identity-invokingproperties in the range of the second-ordervariable: that is, do we include the propertyof being identical with x as one of theproperties y has? If we don't, then thecondition looks insufficient; if we do, then itinvolves a circle. It is certainly sufficient for xto be identical to y that x have the property ofbeing identical to y! We don't want thedefinition to succeed only by embroiling it insuch a gross circularity.

Second, and less familiar, the definition

presupposes the notion of property identity.This is because we are saying precisely thatx and y have the same properties: if x has allthe same properties as y, then x y. So weare using one application of identity toexplain another application. We could, ofcourse, go up a stage and try to defineproperty identity by means of Leibniz's law:properties are identical iff they have all thesame (second-order) properties. But thisbrings in the idea of identity again; andobviously the regress is vicious here. Thepoint is even clearer if we formulate thedefinition in terms of parts or classes: x y iffx and y have all the same parts or belong toall the same classes. Here it is obvious thatwe are presupposing the idea of identity forparts and classes, so we cannot claim to begiving a general definition of identity. It mightseem that the biconditional does not employthe notion of identity for properties or partsor classes, since it does not explicitly use theword 'same'; but the concept of identity isimplicit in the use of

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variables, since we must assume that thesame properties are assigned to thevariables. In the same way, if we say 'forsome x, x is F and x is G' we are makingtacit appeal to the idea of identity in using 'x'twice here: it has to be the same object thatis both F and G for this formula to come outtrue. In fact, this point about Leibniz's law justrestates what we have already noticed aboutso-called qualitative identity, namely that itinvolves the numerical identity of properties.The case is really no different, in respect ofcircularity, from defining sameness ofproperty by way of the condition thatproperties are the same iff they apply to thesame objects: clearly this presupposesidentity for the case of objects.

Third, any definition must presuppose the

notion of identity precisely because adefinition affirms the identity of two concepts.What Leibniz's law says, construed as adefinition, is that the concept of identity is thesame concept as the concept ofindiscernibility. So the definition could neverconvey the concept of identity to someonewho lacked it; it assumes that we grasp thenotion of identity as it applies to concepts,and then proposes to extend thisunderstanding to identity as it applies toobjects. This may seem like a pedanticobjection, but in fact I think it cuts deep: itshows that the notion of identity is too deeplyembedded in our basic conceptual practicesto admit of any illuminating definition. Thevery idea of definition itself presupposes it. Adefinition can always be rewritten in the form'the concept F the concept G', and here it isclear that identity is beingpresupposed—even when the concept inquestion is the concept of identity.12

Oddly enough, Frege himself affirms thatLeibniz's law defines identity, saying: 'NowLeibniz's definition is as follows: "Things arethe same as each other, of which one can besubstituted for the

12 I am being strict about definability here,and there are looser notions of definitionthat would not be subject to the circularity Iam alleging. But my essential point is thatthe concept of definition as sameness ofsense between definiendum and definiensitself contains the notion of identity—whichis not the case for the vast majority ofconcepts we might hope to define. Truth,meaning, and identity are implicated in thenotion of definition; but the same could notbe said for the concepts of redness orjustice or pain.

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other without loss of truth". This I propose to

adopt as my own definition of identity.'13Perhaps he fails to notice the circularity inthis because of the substitutional formulationhe borrows from Leibniz, but this becomesapparent once we observe that the principlehas to mean substitutivity in the samecontexts (compare sharing the sameproperties)—not to mention the other twopoints I have made. It is, of course, true thatidentity obeys Leibniz's principle of theindiscernibility of identicals; but this is a farcry from the claim that the principle providesa non-circular definition of identity.

Let me also note the oddity of supposing thata singular statement should be analysable bymeans of a universally quantified statement.If I say that Hesperus is identical toPhosphorus, I seem to be making a singularrelational statement about a given object,logically on a par with (say) 'Hesperus isbrighter than Phosphorus'. But according tothe Leibnizian definition I am doing no suchthing: I am quantifying second-order-wiseover properties and making a statement ofgenerality. The two-place relation word turnsinto a quantifier and a biconditional—hardlywhat the surface grammar would suggest. Onthis view, identity statements are not reallyrelational statements after all; in logicalgrammar they express a higher-ordercondition on properties, and are replaceableby quantified statements that do not have arelational form at all.

The upshot is that identity is not only unitary,it is also indefinable (assuming that Leibniz'slaw is the only plausible attempt to defineidentity). Identity is a primitive concept, anda concept that exists in only one form.

When a concept is primitive it is apt to bebasic relative to other concepts. What I wantto suggest now is that identity has auniversality and basicness that is hard to

overstate; concepts don't get more basic thanthis—or more indispensable. Every object (orany

13 Foundations of Arithmetic, 76.end p.9

other entity—property, function, you name it)is self-identical; identity is not a relation anentity can fail to stand in to something. Theconcrete, the mental, the abstract—allinstantiate the univocal concept of identity. Inthis respect, as in others, identity resemblesexistence; but it is even more universal thanexistence, since it holds even of non-existentobjects. Sherlock Holmes does not exist, buthe is self-identical; he is certainly notidentical to Dr Watson, who enjoys his ownidentity relation to himself.14 Even if thesefictional entities are impossible objects theyare still self-identical. Identity is a veryundemanding relation; it holds even ofobjects that are purely intentional, not evendenizens of some possible world. This ispresumably one of the reasons it is typicallycounted a logical notion—its extremegenerality. 'No entity without identity', Quinesays; we might add, 'Identity with or without(existent) entity'. Whenever we have asubject of predication—existent, merelypossible, non-existent—we have anapplication of the concept of identity to thatsubject. Identity is ontologically generous.

Second, the notions of identity anddistinctness are given in the very idea ofpredication. When we predicate a property Fof an object x two types of multiplicity areinvolved: that it is x and not some other objecty that we are saying is F, and that F is butone of many properties that might bepredicated of x. We are singling x out from amultiplicity of possible subjects ofpredication, and we are selecting F fromamong a range of properties that might be

ascribed to x. So we have the thought of aplurality of at least possible objects that mightor might not be F, and we have the thoughtthat x may instantiate a range of otherproperties while not instantiating all otherproperties. But both these thoughts involvethe idea of identity, since they bring in theidea of objects and properties that are notidentical to x and F. The embedded notion ofplurality is defined in terms of the notion ofidentity. The very idea of

14 I am here assuming that non-existentobjects can have properties, such as beinga detective and being self-identical. Thisassumption will loom large in the nextchapter.

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the extension of a predicate incorporates theidentity concept. So even to venture thethought that some object is some way is tointroduce the twin ideas of identity anddistinctness. And if predication is the mostbasic structure of thought, then identity isright there at the foundations.

Third, the logical law of identity has someclaim to be basic among the traditional logicallaws. The law of identity is banality itself:'everything is identical to itself ', or 'for all x, xx'. Now consider the law ofnon-contradiction: 'nothing can be both Fand not F'. What this says is that no singleobject can have a property and itscontradictory. Of course distinct objectscould be both F and not-F, since one couldbe F and the other be not-F. What is logicallyimpossible is that one object should havecontradictory properties. But to formulate thisthought we need the concept of identity: thesame object cannot be both F and not-F. Inother words, if ever we have a case in whichx is F and y is not-F then we can deduce that

x is not identical to y; negating a propertythat x has always takes us to another object,not identical to the first. Understanding theway negation works here involves graspingthe role of the concept of identity in fixing thislaw. The law of excluded middle workssimilarly. This law says that everything iseither F or it is not-F. Take any object, youwill find that it either has some property or itlacks that property; there is nothing inbetween. But this involves a cross-referencethat signals a use of the notion of identity: xis either F or x (the same thing) is not-F. Thethought is not that either x is F or some otherobject is not-F; it is that either x is F orit—that very object—is not-F. But this cross-reference involves the thought that we aredealing with an identical object at the twooccurrences of the variable or pronoun. Inother words, the apparatus of variable-binding, or pronominal anaphora, invokes thenotion of identity.15 This is equally true, ofcourse, of the law of identity itself, so that theconcept of identity is needed

15 I cannot recall now where I firstencountered this point about variables andidentity, but I think it is generallyappreciated.

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to understand it also. My point is that weneed this law to understand the other twolaws; and if anyone failed to see that identityobeys the classical law then that would be areason to doubt that they knew what theywere talking about. Maybe it could also beargued that we need the other two laws inorder to understand the law of identity, inwhich case we should rest with the weakerconclusion that identity is presupposed in theother laws—and not the stronger claim that itis more basic than those laws. In any case,the law of identity will be presupposed in the

other two laws: without a grasp of the law ofidentity the other two laws are not even somuch as intelligible.

The very ubiquity and indispensability ofidentity has sometimes worked as anincitement to declare it a pseudo-relation.Thus Wittgenstein wrote in the Tractatus: 'Itis self-evident that identity is not a relationbetween objects' (5.5301); and 'Roughlyspeaking, to say of two things that they areidentical is nonsense, and to say of one thingthat it is identical with itself is to say nothingat all' (5.5303). He goes on to refer tostandard identity sentences as 'pseudo-propositions' (5.534), stipulating a notation inwhich they cannot even be formulated; heprefers to express identity by sameness ofsign, not by a special sign for the identityrelation (5.53). The feeling that identity is apseudo-relation is doubtless connected to theapparent triviality of the relation: it comes toocheaply, being found in every objectwhatsoever. It is therefore felt to be aredundant concept, a mere flourish. Butconsider the concept of distinctness, whichis defined simply as the negation of identity.We might characterize distinctness,parodying Frege, as 'that relation which anyobject has to every object except itself '.Does this relation have the look of a pseudo-relation? Well, certainly not because it onlyrelates an object to itself! On the contrary, itrelates an object to a vast range of otherobjects. Surely it is clear that distinctness isa genuine relation between things; but thenidentity must also be, since it is simply thenegation of distinctness. Negation cannottake us from a genuine relation to a pseudo-relation.

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Both relations are important simply becausewe don't always know the truth about

distinctness and identity; and it can be amatter of great moment whether or not it isthe same or distinct things that are both Fand G (e.g. whether two crimes werecommitted by a single person). If we wereomniscient about identity, then indeedidentity truths would not inform us ofanything; but the same could be said of anykind of truth. Identity propositions are notalways analytic or a priori, as Frege long agotaught us, so there is nothing trivial aboutsuch propositions. The claim of redundancyignores the epistemic role that the concept ofidentity plays. (We shall encounter moresuch redundancy claims in later chapters.)

But what kind of relation is identity,metaphysically speaking? This is one ofthose loaded philosophical questions ofwhich the ontologically anxious are so fond.Is it physical or mental? Is it causal orfunctional? Is it spatial or non-spatial? Wheredoes it fit into our preferred set of allowablecategories? Clearly, the answer is that it isnone of the above. It is, for want of a betterword, a logical relation. It is not a perceptiblerelation, since there is no sense-impressionof self-identity. Nor is it a relation thatgenerates causal powers—unlike, say, 'beingof greater electrical charge than'. We mightsay that it is an abstract relation, if we insiston trying to categorize it; but then we mustremember that it holds of concrete objectsand that 'abstract' is little more than a labelreserved for what is agreed to be neithermental nor physical. We shall beencountering several more such logicalproperties as we proceed, and I shall havemore to say about their metaphysical statuspari passu. For now, we can simply conformwith tradition in classifying identity as alogical relation. And let us note that it is theonly relation that is counted as a logicalconstant. All the other standard logicalconstants—the connectives and

quantifiers—are operators on closed andopen sentences. This makes ' ' semanticallyquite unlike the other logical constants. Thereason for so counting it is, presumably, thatidentity is the only relation that has a claim totopic-neutrality, which is to say universality:

end p.13

identity holds of every entity in every possibleworld, and is part of our very framework ofthought.16

I have endorsed four main theses aboutidentity: (i) it is unitary, (ii) it is indefinable,(iii) it is fundamental, (iv) it is a genuinerelation. I do not suppose that any of this isvery controversial, putting aside some detailsof the ways I have chosen to state thesetheses. My aim has been to set out a generalconception that will be useful later when weapproach more difficult and controversialtopics. This is the first instalment in a seriesof studies of what we might call logicalontology—the ontological character andstanding of certain (broadly) logical notions. Ishall be defending views of our other topicsthat mirror what I have said here aboutidentity.

16 Identity is also bound up with theapparatus of quantification, since variablesare interpreted by means of it, as I notedearlier.

end p.14

2 ExistenceAbstract: The 'naïve view' of existence,according to which 'exists' is a genuinepredicate, expressing a genuine property, isdefended against the orthodox Russellianview, which maintains that to predicateexistence of an object is really to say of

some property that it is instantiated. It isargued that the orthodox view facesintractable problems, which the naïve viewdoes not face, and that the latter fares betterthan the former in three specific contexts inwhich the notion of existence plays a centralrole: the cogito, essentialism, and theontological argument.

Keywords: cogito, essentialism,existence, existential quantifier,ontological argument, predication,quantification, Russell

Colin McGinnConsider these sentences: 'Bill Clintonexists', 'Superman does not exist', 'Vulcanexists', 'Hillary Clinton does not exist'—thefirst two true, the second two false. It isextremely natural, going by surface syntax, tointerpret these sentences as simplepredications, having the same logical form as'Bill Clinton runs', 'Superman does not drink','Vulcan spins', 'Hillary Clinton does notbreathe'. Putting it in the material mode, it isnatural to regard existence as a property thatthings may have or fail to have. Of course,this formulation is only as clear as the notionof a property, which is not altogether clear.About the best that can be said to define therelevant notion of property is that a propertyis something that objects have or instantiate.But if we ask what an object is we are soondriven back to the idea that an object is whathas or instantiates properties.1 The twonotions are woven inextricably together. Weshould certainly not adopt some tendentiouscriterion, such as the idea that a property iswhat, when instantiated, makes a causaldifference to how the world works, or beperceptible, or not be instantiated byeverything that exists. Nor is it any help to fallback on the grammatical form of sentences,as when we say that a property is what a

predicate expresses. Aside from beingdubious in itself, this presupposes the notionof a predicate, which threatens to be definedas a term that expresses a property. Perhapsall we need to say, for present purposes, isthat a property, in the intended sense, iswhat is instantiated by an object in a wayanalogous to the

1 Additionally, we cannot informativelycharacterize the notion of property by usingthe notion of instantiation, since that notionis itself parasitic on the notion of property.

end p.15

way in which (say) redness is instantiated byan object: that is, choose a paradigmproperty and declare a property to beanything that resembles this paradigm.2 Inany case, the traditional opposition to theidea that existence is a property has notrelied upon the charge that the whole notionof a property is too unclear to make the claimwell-formulated, or that the notion is beingstretched too far when made to includeexistence. Indeed, it has typically beenassumed that the claim is clear enough to beknown to be demonstrably false: we knowwhat it means to call existence a property; itis just that it is no such thing. Existence isnothing like redness or maleness orevenness, according to one tradition. Butthis, as I say, is not how statements ofexistence naively appear.

Assuming, then, that we have an adequategrip on the notion of property, and alliednotions, we find it natural to talk in thefollowing way. Not everything that we refer toexists: Venus does, Vulcan doesn't; horsesdo, unicorns don't. There are merely fictionalentities as well as things that really exist. Toexist is to have a property that only some ofthe things we refer to have—those that existas opposed to those that are merely fictional.

Thus existence is a property that is universalto entities that exist, unlike (say) the propertyof being blue (which is, however, universal toentities that are blue3 ). This universality isshared by certain other properties—such asself-identity and logical properties like notbeing blue and not blue at the same time. Butdespite the universality of the property ofexistence over existent things, the word'exists' still does important distinguishingwork, since not everything we talk aboutexists. Since there are objects of referencethat don't exist, it is useful to have a word thatascribes the property of existence to asubset of what we refer to. This word has thelogical role of a

2 This is surely how the debate aboutwhether existence is a property has beentraditionally conceived: the question hasalways been whether 'exists' belongs withparadigm property terms like 'red' or 'fast' or'prime'.3 In fact, there is no very clear sense inwhich existence is more universal thanblueness: every blue thing is blue, as everyexisting thing exists; some existing thingsare not blue, as some blue things do notexist. More things exist than are blue,perhaps—but that is all.

end p.16

predicate in statements of existence, so that'Venus exists' and 'Venus spins' have thesame logical form: they are both singularsentences involving a proper name and aproperty-ascribing predicate. Just as we sayof Venus that it spins, so we say of it that itexists. The ontological status of existence asa property of objects has its semanticcounterpart in the grammar of statements ofexistence: 'exists' is a predicate. It is apredicate that singles out the existent entitieswe talk about from those that are merely'intentional'—fictitious, wrongly reified,

hallucinatory, dreamed up, mistakenlyposited. This sounds like a mere articulationof the common-sense view of existence, butof course it has been widely rejected, and itsvery coherence has been doubted. In thischapter I shall defend the naive view againstthe main rival position. The rival position, Ishall argue, has severe and unfixableproblems, while the naive view remainsunthreatened. Let me first lay out the rivalview as clearly as possible, before arguingagainst it.

It is extremely important to state as clearly aspossible what it is that the orthodox rival viewmaintains, so that we fix in our minds exactlywhat the doctrine is. It is only too easy tomiss the import of the doctrine in aformalistic haze. The thesis is that when yousay that Bill Clinton exists you do not attributeto a certain object the property of existence,since there is no such property; what you dois say that some property is instantiated—where this property is not the property ofexistence itself but some other property towhich you are alluding. Instead of attributinga property to an object you attribute aproperty to a property—the second-orderproperty of having an instance. When youthink of an object as existing what you arereally thinking is that some property has aninstance. You may try your hardest to focuson Clinton himself and ascribe to him theproperty of existence, but you cannotsucceed in that endeavour, since the thoughtin question must always be to the effect thata certain property has an instance—as itmight be, the property of being a USpresident who was once governor ofArkansas. It cannot be that two conceptualingredients make up

end p.17

your singular existential thought—the concept

of Clinton and the concept of existence;rather, there must be a third ingredient,corresponding to the property to whichinstances are ascribed. When you think thatClinton is male you can make do with just thetwo ingredients, but when you attributeexistence to him you are driven to introducesome further property that Clinton has. Yourthought is thus really about that property, notabout Clinton, though it may seem otherwiseto you.4 The same goes for generalexistential thoughts: when you think thattigers exist you do not think of certain felineobjects that each has the property ofexistence; rather, you think, of the propertyof tigerhood, that it has instances—no mentalact of predicating existence of any objecttakes place. The orthodox doctrine gives thevery analysis of the content of yourthought—what the concept of existenceintrinsically involves. The concept of anobject existing simply is the concept of aproperty having instances. To think thatClinton exists is to think that the property ofbeing a US president who was once governorof Arkansas has an instance.

Russell is the main architect of the orthodoxview, or at least its most unflinchingproponent. He fully grasped exactly what thedoctrine says about what he would call thestructure of an existential fact; he wasn'tsimply offering a notational reformulation ofordinary existential sentences. His cleareststatement of the view runs as follows:

When you take any propositionalfunction and assert of it that it ispossible, that it is sometimes true,that gives you the fundamentalmeaning of 'existence'. . . .Existence is essentially a propertyof a propositional function.

4 Imagine checking off a list of assertions

about Bill Clinton, to the effect that he ispresident, that he smiles a lot, that he isintelligent, that he is imprudent, that heexists. For the first four items your thoughtis a subject-predicate thought about acertain concrete entity, but when it comesto the fifth item your thinking suddenly goessecond-order as you mentally invoke somesuitable propositional function to pin yourexistential thought upon. But doesn't it seemthat you engage in the same kind ofsingular predication for the fifth case as forthe first four? What, one wants to ask, is tostop you thinking singularly about Clintonwhen you essay an existential thought abouthim?

end p.18

It means that the propositionalfunction is true in at least oneinstance. . . . We have got to havesome idea that we do not define,and one takes the idea of 'alwaystrue', or of 'sometimes true', asone's undefined idea in thismatter. . . . It will be out of thisnotion of sometimes, which is thesame as the notion of possible, thatwe get the notion of existence. Tosay that unicorns exist is simply tosay that '(x is a unicorn) ispossible'.5

Russell goes on to compare 'exists' with'numerous', saying that neither can bemeaningfully predicated of individuals; wecan only attach 'numerous' to a termexpressing a propositional function, as in'dogs are numerous'. He says: 'Exactly thesame applies to existence, that is to say thatthe actual things that there are in the worlddo not exist, or, at least, that is putting it toostrongly, because this is to utter nonsense.'

The correct thing to say is that 'it is ofpropositional functions that you can assert ordeny existence.'6 It is a logical categorymistake to ascribe existence to objects.

We can divide Russell's position here intothree sub-theses: an ontological thesis, asemantic or logical thesis, and a definitionalthesis. The ontological thesis has a negativeand a positive part. Negatively, the claim isthat existence is not a property thatindividuals instantiate. Positively, the claim isthat for something to exist is for someproperty (propositional function) to haveinstances. In the metalinguistic terms Russellprefers, existence consists in a predicateyielding a truth under certain substitutionsinto its argument-place: there are truesentences containing that predicate and asubstituted name. For example, 'tigers exist'means 'there are true sentences of the form"a is a tiger' ", where 'a' is a name of sometiger. So to say that an individual existsalways involves a reference to some propertyor predicate of which it is said that it holds ofsomething. Thus we have the semantic thesis

5 'The Philosophy of Logical Atomism',232-3.6 Ibid. 233. Actually, this is a misformulationon Russell's part: it is not that you canpredicate existence of propositionalfunctions; rather, all statements of existenceare equivalent to statements saying ofpropositional functions that they haveinstances. Propositional functions have theproperty of having instances, not theproperty of existence (there is no suchproperty, for Russell).

end p.19

that statements of existence are reallyhigher-order statements involving referenceto a property or concept or predicate orpropositional function. The subject of the

statement is never a term for an individual butalways a term for a property, with the notionof existence being carried by a predicate thatattaches to that other predicate term.Statements of existence are always andnecessarily second-order statements,analogous to 'blue is delightful to the eye'.And now the definitional thesis is that 'exists'can be defined in these terms: when 'exists'occurs in a statement it can always beparaphrased in terms of the notions of apropositional function and being 'sometimestrue' or 'possible'. Presumably Russell intendsthis definition to be non-circular, so that weare not compelled to explain the definiens byrecourse to the definiendum; as he says, we'get the notion of existence' out of these othernotions. The notion of existence getsswallowed up into these other notions, nolonger to masquerade as a predicate ofindividuals. In a perfect language the wordneed never occur, its job always being doneby 'sometimes true' and its adjuncts.

Nowadays this Russellian position is routinelyput by saying that existence is what isexpressed by the existential quantifier andonly by it. All natural language sentences thatspeak of existence can be translated intosentences that employ only the existentialquantifier, with no use of 'exists' aspredicative. The existential quantifier isconceived, following Frege, as a functionfrom first-order concepts to truth-values, sothat nothing corresponding to a first-orderpredicate is involved in its semantics.7 So theassumption is that the Russellian conceptionof existence receives its canonicalformulation in the thesis that 'exists' alwaysmeans 'there is an x such that'. The thesis isthat we can always translate existentialstatements into this form of words. This ishow a perfect language expresses the ideathat existence consists in a property havinginstances.

7 For the Fregean view of quantification asa second-level function see MichaelDummett, Frege: Philosophy of Language,ch. 3.

end p.20

I take it all this is familiar enough, even to thepoint of tedium. But I think that almost noneof it is right: the Russellian thesis and itscustomary Fregean formulation are riddledwith problems.

I shall consider four kinds of objection to theorthodox view. First, let us enquire into theinnocent-seeming phrase 'has instances'.What does it mean? It can be taken in anobjectual or a substitutional sense. In theobjectual sense, the doctrine is that forsomething to exist is for there to be objectsthat are instances of some suitable predicate.Here are some objects, and they areinstances of F. But that can only mean thatthese objects exist, so that we are sayingthat there exist instances of F, for some F. Ifthey did not exist, then the existentialstatement would not be true after all. But howis that use of 'exists' to be analysed? Clearlyit will be no help to say that they areinstances of 'instances of F', since these willagain need to be existent instances. Thenotion of existence is presupposed in theanalysis, so the analysis does not settle whatkind of notion it is. It might even be apredicate as it occurs in that use: for there tobe instances of F is for there to be objectsthat exist, predicatively, and are instances ofF. The instances have to be existent objects,so we are presupposing the notion of anexistent object in our account of what aninstance of a predicate is. We can put theobjection this way: Consider 'planets exist'and ask whether Vulcan is an instance of'planet'. If it is, then we have not correctlyanalysed existence, since Vulcan doesn'texist, and hence its planetary instancehood

doesn't show that planets exist. But if it is not,then that can only be because it doesn'texist—thus demonstrating that the relevantnotion of instance must import the concept ofexistence. If we say that 'planets exist' is truebecause 'Mars is a planet' is true and 'Vulcanis a planet' is not, that can only be because'Mars' refers to an existent object while'Vulcan' does not. The reason we get a truthin the one case and not the other is preciselythat existence is ascribed to the reference ofone term and not to the other. Why elsewould the one be true and the other not be?Nor will it help to introduce a distinctionbetween fictional

end p.21

truth or fictional instance and literal truth orliteral instance in order to rule out this kind ofcase, since this also presupposes the notionof existence. The point is that paraphrasingexistence statements into statements aboutthe instantiation of a property does notestablish that existence is not a predicate,since the notion of instantiation must betaken to have existence built into it—it mustbe existent things that instantiate theproperty. It is this circularity that prevents theorthodox view from claiming to haveestablished that existence is not a predicate.

I think Russell was at least subliminally awareof this problem, which is why he tended toformulate the doctrine in more substitutionalterms. He preferred to say that there are truesingular propositions or sentences that areinstances of the propositional function inquestion, rather than say that there areinstancing objects that satisfy that function.And what he liked best of all was theformulation in terms of possibility—'(x is adog) is possible'—because that put him asfar as possible away (he thought) from theconcept of existence. It makes it look as if we

are analysing—non-circularly analysing—thenotion of existence in terms of modal notionsand propositional functions. But this does notreally help with the underlying problem. In thefirst place, it is necessary to assert theexistence of certain propositions orsentences on this analysis, and the questionmust arise as to what this is supposed toamount to. It had better not mean that certainpropositions or sentences have the propertyof existence.8 But, more obviously, there isthe problem of how to analyse the singularpropositions themselves: what are their truthconditions? Clearly we cannot allow 'Vulcanis a planet' to be a substitution instancecorresponding to 'planets exist', but that canonly be because the referent of 'Vulcan' doesnot exist. For a singular statement to be truein the sense needed is for there to be anobject referred to by the singular term andfor that object to satisfy the attachedpredicate. So, again, the

8 I return to this later when I discuss what itmeans to ascribe existence to properties orpropositional functions.

end p.22

notion of existence is smuggled inunanalysed. It is perfectly consistent with thehigher-order paraphrase that existence isactually a property of objects: we canparaphrase existential statements that way ifwe like, but we are tacitly assuming thatexistence is a property of objects, for all thatthe paraphrase tells us. What is really beingsaid, according to the paraphrase, is thatamong the objects that have the property ofexisting at least one of them is F—hence Fhas instances. Of course, this does not yetprove that 'exists' is a predicate—though itmight incline us to think that—but it doesshow that the orthodox view has not refutedthat doctrine, or made it redundant, simply byproviding a plausible-sounding paraphrase in

terms of properties and their instances. Forthe question precisely is what it is for aproperty to have instances—if not for objectsthat exist to instantiate the property.

We must here guard against adopting aformalistic approach to the issue. Russell didnot make this mistake, but those in thetradition he initiated (with others) have tendedto think that the issue could be settled simplyby seeing whether existence statementscould be translated into statements employingthe so-called existential quantifier. But thatcannot be right, because it is possible tointerpret the quantifier by using a predicateof existence, along the lines of 'for some x, xexists and x is F' (I will come back to this).The question is whether the fundamentalnotion of existence can be explained in sucha way as to avoid predicating it of objects,and merely giving a quantificationalparaphrase does not show this, since itdepends upon how the terms in theparaphrase are to be interpreted. Thequestion can only be settled by directphilosophical argument, not by offering somepurely formal translation of existencestatements. We need to know whether theconcept of existence contained in the symbolfor the existential quantifier is or is not thefirst-order concept of predicative existence.9

9 It is perfectly consistent to hold that ' x' isa second-level expression, so that it formssentences from first-level expressions, andthat ' x' abbreviates a condition containinga first-level concept of existence—as isevident from the conjunctive paraphrase of ' x' that I suggest in the text and to which I

will return.end p.23

The second problem has more of thecharacter of a proof that the orthodox viewcannot be a general analysis of the notion of

existence, and not just a challenge to theadequacy of the account. Consider theexistence of properties or propositionalfunctions or predicates themselves. Theseexist in the same sense that other thingsexist, despite their being (presumably)abstract and non-individual. Thus we cansay, 'the property of being a planetexists'—as we might if insisting (rightly orwrongly) upon the truth of realism asopposed to nominalism about universals. Buthow might this statement be analysed? Onthe orthodox view, we must make referenceto some property that the entity said to existis an instance of. It plainly cannot be theproperty of being a planet, since the propertyof being a planet isn't itself a planet. But whatelse could it be? We might try finding sometrue description of the property and insertingthat into the analysis—say, the property ofbeing currently under discussion; then forthe property of being a planet to exist is forthat property to have instances. But thedifficulties now are obvious. First, there is theproblem of securing uniqueness. But second,and worse, we are now launched on avicious infinite regress, since we must askwhat the existence of the higher-orderproperty consists in, thus requiring a furtherproperty to be a property of that property.10The problem, evidently, is that to analyse theexistence of a property we need anotherproperty that the first one instantiates, and soon ad infinitum. Not only is it doubtful thatthere always are these further properties, butalso we will not succeed in getting any ofthem to exist without the existence of furtherones that raise the same question. Intuitively,

10 We don't avoid this regress by invokingthe property of being identical to a certainproperty and then using this as the neededpropositional function. That is, suppose wewant to know what it is for property P toexist, and we suggest that it is for the

propositional function 'P' to have aninstance. This still refers to P, of course,but it jumps up a level by forming thehigher-level function 'P', so that when weask what it is for the referent of 'P' to existwe will need a function that expressesidentity with that higher-order property—towit, the property of being identical to theproperty of being identical with P. And soon up. Invoking identity in this way does notwork to confine the generated propertiesmerely to the property P we started out with.

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the existence of a property is intrinsic to it; itis not a matter of some relation that theproperty stands in to some other property ofwhich it is an instance. And if we construe itas such a relation, then we generate avicious regress, as each new property raisesthe question of its own existence.11

Matters look less troublesome when we areconsidering the existence of individuals,since they always have properties toinstantiate, and their existence doesn'trequire the existence of other individuals; butwith properties themselves we find that wehave to postulate extra properties for them tofall under, and we are then being faced withthe question of their existence. No propertywill be able to exist unless a whole infiniteseries exists. But there is no such series,and anyway it would never get off the groundbecause of the regress. In effect, theorthodox view makes it impossible to attributeexistence to properties; this would have to bedeclared ill-formed and meaningless (notmerely false). And it is noteworthy thatRussell never attempts to extend the analysisto this area of existence. One suspects thathe (and others) simply take the existence ofproperties for granted, as if it needs noanalysis. But this is no better than defendingthe thesis that existence is to be analysed as

occupancy of space simply by declining toconsider the existence of abstract entities likenumbers. Any good theory of existenceneeds to be able to handle the full range ofuses of 'exists'. In fact, this difficulty aboutproperty existence acts back on the analysisof individual existence, since the property theindividual instantiates must itself exist, andthis cannot be explained in terms of theorthodox view. Individuals cannot be said toexist if the properties (or predicates) theyinstantiate

11 The problem here is not that theexistence of any given property requires theexistence of infinitely many otherproperties. There is nothing inherentlyobjectionable about that—indeed,something like this appears to be manifestlytrue for the existence of numbers. The pointI am making is rather about the analysis orexplanation of what it is to exist: theviciousness comes in when we try toanalyse or explain what it is for X to existand find that we must presuppose that wealready know what it is for Y to exist (whereX and Y are both properties here). Ingeneral, regresses are only vicious in thecontext of some explanatory aim, not inthemselves.

end p.25

cannot be said to exist, since the formerrequires the latter: for x to exist is for there toexist some property (or predicate) F suchthat x instantiates F.

The third objection arises from a family ofsentences that resist the orthodoxparaphrase. Some of these have becomefamiliar, though their polemical power hasbeen underestimated. In view of theexistence of these sentences, there has beena tendency to declare that 'exists' has twosorts of interpretation, predicative and

higher-order. But this bifurcating view isunworkable and we are compelled to take alloccurrences of 'exists' as predicative. Thus ithas often been pointed out that singularattributions of existence are hard to slot intothe orthodox schema, on pain of distortingthe semantics of singular terms likedemonstratives and proper names: we getpushed towards a description theory ofreference for these terms that has internalproblems.12 The point I want to make is thataccepting this problem about singularstatements cannot but affect the way we view'exists' in general statements. Consider'Venus exists and is a planet' and 'at leastone planet exists': the former entails thelatter. But how can that be if 'exists' in thesingular sentence is predicative while in thegeneral sentence it is not? We simply haveno term common to premises and conclusionif we bifurcate 'exists' in the suggested way;we must either take the singular sentence tobe analysable in the orthodox style or wemust revise our views of the generalsentence. As I will explain below, I favourtreating 'Fs exist' along the lines of 'for somex, x exists and x is F', which allows me tofind the common term with the predicative'exists' in 'a exists'. But my point now is thatthe orthodox view has to do something tosave the entailment—it can't just declare that'exists' is sometimes predicative andsometimes not. And of course it is deeplyunattractive to suppose that 'exists' has thekind of ambiguity the bifurcating accountproposes.

12 See Kripke, Naming and Necessity.Kripke discussed the topic of existence andnames extensively in his 1973 John LockeLectures in Oxford, which I attended, butwhich have not yet been published.

end p.26

The problems of analysis for the orthodox

view are made vivid by the sentence'something exists'. This is a perfectlymeaningful and true sentence, which followsfrom such sentences as 'Venus exists', but itshould itself not exist according to theorthodox view. For it is not paraphrasablewithin the terms of that view, there being nopredicate around to pin the instances on:what property are we saying is instantiatedhere? The problem is worse than with propernames and demonstratives because at leastin their case we could try to appeal to adescription theory of singular reference; butthere isn't even any reference going on withthe word 'something'. If we try to translate thesentence in the standard way we get thegibberish, ' x(x)', with no predicate to writedown. You might think we could do betterwith ' x(Thing x), but this is pleonastic, giventhe usual meaning of ' x'. Also, it is unclearwhat the predicate 'thing' is supposed tomean here if not 'exists'.13 The naturaltranslation is I think the right one: ' x(Existsx)'—'for some

13 A tempting alternative suggestion is that'something exists' means the same as'something is self-identical' or 'the propertyof self-identity has at least one instance'.Thus the formula that captures ourrecalcitrant sentence is '( x)(x x)', where ' 'plays the role of the missing predicate. Butis this really what 'something exists' says?Where is the sign of identity in the originalsentence? There is no name to extract itfrom, as with classic description theories,and it is hard to see how it could plausiblybe taken to be expressed by 'something'.Moreover, 'something exists' follows from'Venus exists', so presumably it will have tobe held that the latter sentence means '(x)(x Venus)', thus construing singularexistence statements as asserting theidentity of something with a named entity.The problem here, in addition to the

previous objection, is that such aparaphrase looks irremediably circular,since it presupposes that we alreadyunderstand what it is for Venus (say) toexist. The invoked predicate ' Venus'embeds the name 'Venus', and thecondition will only work to secure existenceif this term is taken to refer to an existententity. Consider ' Vulcan': satisfying thispredicate will not secure existence (Vulcanclearly satisfies it!), and the reason issimply that Vulcan does not exist. Satisfying' Venus' secures existence only because ofthe existence of Venus, which we weremeant to be analysing. I think Russell wasaware of this point, which is why he neverchose the likes of ' Venus' as thepropositional function on which to pinexistence. In the case of other predicates,such as 'planet next to Mars', the existenceof the property does not depend upon theexistence of Venus itself, and hence is notstraightforwardly circular in the way 'Venus' is. And there is also the point thatbringing in identity in this way undermines acentral motivation for the Russellian view,since self-identity has precisely the kind ofuniversality Russell found objectionable in apredicate of existence.

end p.27

x, x exists' (see below for more on this viewof ' x'). In any case, it is difficult to see how'something exists' could succeed in beingmeaningful on the orthodox view, because itlacks the kind of reference to a property thatis required for that view to get a foothold (thesame goes for 'nothing exists'). I wouldregard such unspecific existential sentencesas test cases for any theory of existence(they also block metalinguistic analyses alongthe lines of " 'Venus" denotes', since'something' is not a denoting term). Again,the orthodox view does not have thegenerality we should expect of a theory of

existence.

The fourth objection focuses on therequirement that any existent thing should fallunder some property or other. This impliesthat nothing could exist that failed to fallunder some property—other than existence,obviously. To exist is to be an instance of aproperty, so necessarily whatever exists hasat least one property. This rules out, as amatter of the meaning of 'exists', thepossibility of what we might call 'bareexistence'—a thing that exists without havingany (further) properties. What should wethink of this alleged possibility? The questionseems to be a substantive metaphysicalquestion, open to rational debate. Maybebare existence is actually a metaphysicalimpossibility, though how one might argue forthat is not clear.14 But, in any case, it doesnot appear to be analytic or tautological toassert that bare existence is impossible—which it would have to be according to theorthodox view. It would have to be equivalentto saying, 'there could not be an instance ofa property that was not an instance of aproperty'. That is, it would have to becontradictory to assert the possibility of bareexistence, as in 'an instance of a propertycould be an instance of no property'. This issimply because existence is being analysed

14 Again, we have the question of what tosay about self-identity: is it contradictory tosuppose that an object exists and lackseven the property of self-identity? This doesseem to me quite impossible, but I am notconvinced that it is actually formallycontradictory. In any case, it is of no realhelp to the defender of the Russellianthesis, since this seems precisely the wrongkind of property to invoke in order toanalyse what it means to say that somethingexists, for the reasons mentioned in theprevious footnote.

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as property instantiation, so we could notthen go on to say that the existent thing hasno properties. But it seems to me that there isno actual contradiction in the idea of bareexistence, even though it may well be somesort of metaphysical impossibility: 'x existsand x has no properties' certainly does notappear to be a straightforwardly self-refutingsentence. I think the idea of an object thathas only the property of existence is notintrinsically self-defeating, but it would haveto be if existence simply consisted inproperty instantiation.

Actually, the problem here spreads, becausethe orthodox view requires, not merely thatevery existent object have some property, butalso that it have some property unique to it.For the existence of an individual object issaid to consist in the instantiation of aproperty sufficient for that object to exist andnot some other object. Thus the theorycharacteristically claims that some definitedescription or individual concept isinstantiated, this serving to single out theindividual in question. But this implies that inevery possible world in which an individualexists that individual has some property thatno other individual has. Surely that is a verystrong claim, and not one that we ought to beobliged to accept just by the simple analysisof the concept of existence.15 The analysisof existence ought to be neutral on the point.On the face of it, there seems no logical barto a range of individuals existing in a worldwithout there being a property that singleseach of them out uniquely—as it might be, acollection of indiscernible red steel spheres.We surely don't want our theory of existenceto settle the vexed question of

15 Of course, identity with an object isalways a property unique to it, as with 'Venus'; but as we have seen, this is not the

right kind of property to use incharacterizing existence: the individuatingproperty must be one that does not itselfpresuppose the existence of the entity inquestion. There is also the point that if weinsist on using self-identity as the propertythat is uniquely instantiated in the case ofassertions of singular existence, then wedisconnect such assertions from assertionsof general existence, as with 'tigers exist'.We don't want to end up saying that theexistence of each individual tiger consists inits instantiating identity with itself but that theexistence of tigers in general consists ininstantiating the property of being a tiger.The restriction to the self-identity propertylooks ad hoc, designed simply to secureuniqueness.

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the necessary identity of indiscernibles. Andwhy should existence necessarily attach tothe property, if there is one, which the objecthappens uniquely to instantiate, instead of allthe other properties the object has? Itcertainly does not seem contradictory toinsist that an object could exist that differed inno respect from a numerically distinct object.Yet it would have to be contradictoryaccording to the orthodox view of singularexistence statements.

Taken together, these four objections implythat the orthodox view simply has not got holdof the concept of existence. It only seems tohave done so for certain limited casesbecause it presupposes the notion ofexistence, as when it employs the locution'has instances'. But the theory cannot dealwith property existence, it cannot handle thefull range of existential statements, and it linksthe possibility of existence too intimately tothe idea of (uniquely) instantiating aproperty. In short, the concept of existence isnot identical to the concept of property

instantiation (even though this concept itselfinvokes the concept of existence). Let menow work out the first-order property viewmore thoroughly, responding to somequestions that might be raised about it.

The property view says that everyoccurrence of the word 'exists' is logicallypredicative, just as 'man' and 'blue' are. Italso says all existential statements can beanalysed by means of this predicate. Andthis is just the semantic counterpart to theontological thesis that existence is alwaysand everywhere a property of objects. It is aproperty universal to all objects that exist,somewhat like self-identity; but it is lessuniversal than identity because (as I noted inthe previous chapter) that relation holds of allconceivable objects, not merely those thathappen to exist.

What problems might be raised by thissimple view? Why has it been so consistentlyrejected? It is surprisingly difficult to find anyworked-out objections to it, despite thesuspicions it arouses. The only point thatRussell makes, and it is a recurrent theme, isthat existence is, so to speak, too universal tobe a property: 'There is no

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sort of point in a predicate which could notconceivably be false. I mean, it is perfectlyclear that, if there were such a thing as thisexistence of individuals that we talk of, itwould be absolutely impossible for it not toapply, and that is the characteristic of amistake.'16 There are two problems with thisargument. First, it proves too much, sinceself-identity and logical properties (such asthe property of not being both red and notred at the same time) are counter-examplesto it: these apply to all conceivable objects,but we should hardly wish to analyse them ashigher-order properties. And why should

there not be such absolutely universalpredicates? Can't there be features that allobjects share (such as being an object)?17There may not be much point in speaking ofsuch properties, given that they have nocomplement class, but that is not to say thatthey are not true of everything: there aremany truths that are not worth mentioning inordinary contexts. Second, it is just wrong ofRussell to say that 'exists' applies to allconceivable objects and hence has no utility.It precisely does not apply to all conceivableobjects, since some of the objects weconceive do not exist. Of course, it applies toall objects that exist, but we have a good usefor the word simply because we makemistakes about existence. The word 'exists'indeed applies to all existent objects and tonothing else, but sometimes we take it toapply when it doesn't.18 It can be extremelyuseful to be told that something exists

16 'The Philosophy of Logical Atomism',241.17 Or 'having properties', or 'standing inrelation to something', or 'being nameable'.In fact, Russell himself has to invoke such auniversal property to make his theory work,namely 'being an instance of some propertyor other': since existence consists ininstantiating some property, he has topresuppose that every existent object hassome property or other to which itsexistence attaches. Indeed, it is hard to seehow such universality could be avoided ifwe are to find an analysis of existence thatapplies to every case.18 This is why it is a mistake to think thattrue singular statements of existence mustbe trivial and false ones contradictory, onthe grounds that reference itselfpresupposes existence. The reason this is amistake is simply that the audience forexistential assertions may not know that agiven singular term refers to something that

exists, so that it is informative to couplesuch a term with a predication of existence.If we are discussing planets and I say,'Venus exists but Vulcan does not', this canbe informative to you precisely becauseyou do not know which of 'Venus' and'Vulcan' is the empty term. Of course, Iknow, because I am aware of the existentialfacts, and so the statement is notinformative to me—but no statement isinformative to me in that sense, because Ialready know the fact I am stating. Myaudience may be clueless about matters ofexistence, so they are unapprised of thesemantic status of the singular terms I use;what they learn from my existentialassertions is that those terms either refer tosomething that exists or not, as the casemay be. See David Pears, 'Is Existence aPredicate?' for a formulation of the kind ofargument I am here rejecting.

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when you had supposed that it does not (andvice versa). So this objection from generalityfails to cut much ice.

There are two main areas in which thepredicate view needs careful handling andwhere it might be thought to run into trouble:the interpretation of the quantifiers and thenature of non-existence. I shall deal withthese in turn.

We have become accustomed to speaking ofthe 'existential quantifier' and to supposingthat it conveys existence in a nonpredicativefashion; thus we suppose that existence isnot always expressed as a predicate. As Ipointed out, this divided position is unstable,especially in view of the entailments that needto be captured. But, more fundamentally, theview is misconceived at root: for it may bethat ' x' is rightly defined by using theexistence predicate, so that it is not an

alternative to the predicate view. And I thinkit is easy to show that it can be defined inthis way; also that this is intuitively the rightway to think about it. Take the formula 'forsome x, x is F and x exists', and take this totranslate 'Fs exist'. The point here is that theprefix 'for some x' does not itself carryexistential import; it simply conveys howmany things are being said to be thus andso. Now I claim that this formula conveys thesense of the existential statement, and itexpresses existence predicatively. What theprefix does is indicate the quantity of Fs inquestion—it says that some are; it is left upto the predicate 'exists' to express existence.The word 'some' by itself is existentiallyneutral, on this view, much as 'all' is usuallytaken to be19 —and I

19 I mean here that it is customary to take'all men are mortal' as existentially neutralon account of the material conditionalembedded in it. It is true that in standardlogic '(x)(Fx)' implies '( x)(Fx)', but it isdeemed correct to regard typical universalstatements as lacking existential import invirtue of the possible vacuous truth of theembedded conditional. What I amsuggesting, then, is that a similar leniencyshould be applied to our use of 'some'. I willhappily accept that 'all' implies 'some', as instandard logic, but I deprive 'some' ofexistential import: if all the gods aretyrannical, then indeed some are—but ofcourse no gods exist.

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would say the same for 'most', 'many', 'a few',as they occur in statements of existence, asin 'most superheroes exist'. To defend thisview I need to suggest a plausible semanticsfor the conjunctive formula and to motivatethis way of thinking about quantifier words.

I can think of three possible sorts of

interpretation for the formula, which are notunfamiliar. First, we could introduce aMeinongian ontology, letting the variablesrange over subsistent as well as existententities. Then the conjunction says of theseentities that some both exist (as opposed tosubsist) and are F. On this interpretation, 'forsome x' has ontological import but notexistential import, since not everything in ourMeinongian ontology exists; 'exists' thennarrows down the ontological field among allthe Fs there are. Second, we could gosubstitutionalist and deprive 'for some x' ofany objectual function: the formula then saysonly that 'x' can be replaced with a term 't'such that 't exists and t is F' comes out true.That is, we interpret 'some' purelysubstitutionally in the standard way, then weintroduce existence by means of an explicitpredicate. On this interpretation, ' x' simplyabbreviates the substitutional quantifier plusits appended existence predicate; we thusbreak apart the existential and the quantitativeaspects of the complex symbol ' x'. Third, wecould introduce a special quantifierexpression that is equivalent to 'some of thethings we talk/think about' (what we might callthe 'intentional quantifier') and then appendexistence in the usual way. Thus 'Fs exist'means: 'some of the things we talk/thinkabout are both F and exist'; symbolically, 'I x,x is F and x exists', where 'I x' is theintentional quantifier.20 The function of'some', again, is purely to convey the

20 As I have defined it here the intentionalquantifier ranges only over objects ofreference. If we want to include objects thatexist and have not been referred to, then wecan simply make the quantifier disjunctiveand include in its domain both intentionalobjects and those ordinary objects that existwithout ever being referred to. In this waythe universal intentional quantifier canrange over real and fictional objects in 'all

men are mortal'—in which case thatstatement turns out false by dint of immortalfictional characters. We can then rely onconversational context to convey suitableimplicatures when we want to speak only ofreal people.

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quantity of things that we talk about that bothexist and are F. We could thus quitemeaningfully say, 'for some x that we talkabout, x does not exist': this would follow, forexample, from the truth that Vulcan does notexist. On this interpretation, to be (to exist) isemphatically not to be the value of a variable.The idea here is to interpret the variable sothat its values are both existent entities andmerely intentional ones, where a merelyintentional object does not even subsist (Ishall have much more to say aboutnonexistent intentional objects shortly). So itseems that we can assign a coherent andplausible interpretation to our formula andhence show that the 'existential quantifier' isanalysable in terms of the predicate ofexistence. I think this is intuitively right, and itsolves the problem of the univocity ofexistence statements. We also see that inadopting the predicate view we can preserveour usual logic of quantifiers, suitablyinterpreted; we don't need to go back toold-fashioned logic in which 'Fs exist' is asubject-predicate statement with 'Fs' figuringas the subject. In 'some men exist' it is notthat 'some men' is the subject and 'exists' thepredicate, which gives rise to notoriousabsurdities with 'no men exist'; we can hangon to the standard paraphrase that treats'some' as a second-order predicate, not as asingular term.21 Existence is alwayspredicated of individuals, not of mysteriouspluralities.

But is this a good way to think about 'some'?Does 'some', taken by itself, really lack

existential import in ordinary language? Thisis quite a big question, but I think there areclear considerations in its favour—it is notmerely that it is required by the correcttheory of existence. To begin with, quantifierwords are precisely that—they tell you howmany, what proportion. But that is not aninherently

21 Notice that 'some' is treated assecond-order while 'exists' is treated asfirst-order; so it is wrong to reason thatsince 'some' is a second-order concept'exists' must also be. The question of thesemantic level of quantifier words isorthogonal to the issue of whether existenceis predicative.

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existential concern. We do better to call'some' the partial quantifier, on analogy withthe universal quantifier—neither logicallyimplies existence. The same should be saidof the non-standard quantifiers, 'most','many', etc. In the orthodox notion expressedby ' x' we have conflated two distinctlinguistic functions into the ' x' symbol—thefunction of saying how many and thefunction of implying existence (and the name'existential quantifier' only captures this latteraspect). But, as we have separated thesefunctions for 'all', so we should for 'some'.22And this fits the linguistic data, because wedo use 'some' in contexts in which existenceis not implied, even conversationally. Thus wecan say, 'some of the things you're talkingabout don't exist', 'some superheroes areentirely fictional', 'some cities are purelyimaginary'. In these sentences 'some'expresses a proportion, but it does not implythat this proportion exists—quite the opposite,since the predicates negate existence. If youtry to translate these uses of 'some' into theexistential quantifier, so called, you getoutright contradictions. Better to take 'some'

neutrally and then leave it to 'exists' to dowhat it does best—assert existence.

On this view, 'some' only acquires existentialforce as a matter of conversationalimplicature. But this implicature can becancelled without contradiction, as when oneannoyingly says 'some of the things I've justbeen referring to don't exist' or (lessannoyingly) 'some of the gods aretempestuous, but of course no gods exist'. Asimilar point can be made about the word'object': it can seem that this word carries animplication of existence, so that speaking ofnon-existent objects sounds contradictory,especially when you lay stress on the word'object'. But I think it is clear that this is amere implicature, since we do use the wordquite correctly to speak of

22 So I am going further than free logic instripping quantificational logic of existentialassumptions. Where free logic gives upexistential generalization, I give up theexistential import of the sign for partialquantification itself, i.e. 'some'. Wetherefore can infer 'someone is a detective'from 'Sherlock Holmes is a detective', eventhough Sherlock Holmes does not exist. Asa matter of strict logic, then, it is neverpossible to infer existence from anything(except existence itself, of course), not evena sentence of partial quantification.

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'objects of thought'. When we use the word inthis kind of context all suggestions ofexistence are cancelled. If I speak of theobject of your search as the fountain ofyouth, there is no implication of existencehere. It is the same with 'some': most of thetime the implicature is in force, sincegenerally we mean to be speaking of existentthings, and this is common knowledgebetween us; but the general implicature can

in principle be cancelled, and then 'some'shows its true semantic colours as a deviceof pure quantification, with no existentialentailments.23 This is why we can quitehappily say, 'some objects (of thought) do notexist'. On this view, it is not that when 'some'occurs without existential force it is alwayssomehow embedded in an intentional contextwhich erases its customary existential punch;rather, it packs no such punch as a matter ofits semantics (as opposed to its pragmatics)but serves purely to express quantity orproportion—just like 'all'. If you want to getexistence semantically into the picture youhave to say so. This is why it is notpleonastic to say 'some tame tigers exist',and not contradictory to say 'somesuperheroes do not exist'. In other words, thelinguistic appearances are a true guide tosemantic reality: 'some' does not in factcontain 'exists', implicitly or explicitly, whichis just how it appears. Accordingly, we need'exists' in the language in addition to 'some'—which is exactly what we find. Whatquantifier words do is abandon singularity;what 'exists' does is attribute the property ofexistence to objects that are either denotedor quantified over. It invites confusion to tryto merge these two functions together into asingle primitive symbol ' x'. The phrase'existential quantifier' obscures this point:think how odd it sounds to call 'all' theexistential quantifier just because you

23 Imagine teaching a literature class inwhich various fictional characters are beingdiscussed (I do this quite often). You say,'some of the characters in Lolita aredespicable', and go on to discuss theirpersonal failings. This is perfectly goodEnglish and clearly the context excludesexistential implications. Now imagineswitching to a context of real criminalinvestigation; here it will be assumed thatyou are talking of real people when you

say, 'some of these car thieves are prettysmart'. But surely the word 'some' does notshift its literal meaning from one context tothe next; it is simply a matter of theimplicatures carried by the context ofutterance.

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believe, as some have, that it too impliesexistence. To label 'some' the existentialquantifier is not simply to describe itsfunction but to impose a tendentious theoryupon it, a theory that we have seen to befalse to the linguistic data. Matters would bemuch clearer if we spoke of the universalquantifier and the partial quantifier. We can,of course, just define an expression ' x' thatcontains both notions, as we have in effecttraditionally done; but we should be aware ofwhat the correct semantic analysis of such astipulated expression consists in—and weshould be wary of taking this symbol totranslate the natural language 'some'.

The topic of non-existence engages morepurely metaphysical concerns, and it is truethat the topic can quickly generatebewilderment and confusion; truisms turn intoabsurdities in the blink of an eye. Theproblem, put crudely, is to make sure thatthings that don't exist don't end up existingafter all. The predicate 'exists' fails to apply tosome things—what we have to ensure is thatthese things don't turn out to exist in someattenuated or second-class way: they simplydon't exist. I think it is essential, in avoidingthis danger, to acknowledge a crucialasymmetry between existence andnon-existence, namely that non-existence isrepresentation-dependent, while existence isnot. That is, the complement class of 'exists'is purely intentional—its esse is concipi. TheMeinongian ontology of non-existenceimplicitly denies this, holding that merelysubsistent entities could have Being even

though they have never been conceived. ButI want to say that there are nomind-independent non-existent entities—though there are plenty ofmind-independent existent entities. Comparea predicate like 'blue': there can be bluethings we have not encountered cognitively,but there can also be non-blue things wehave not encountered—and similarly forevery other ordinary predicate. If we think ofthe complement class of 'exists' in this way,then we will hold that there could be objectsthat don't exist and have not been thought of,since their nature does not consist in theirbeing conceived. But this strikes me as afundamental misconception: there are nonon-existent things that transcend ourcognitive acts;

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all non-existent things are objects of thoughts,as a matter of necessity.24 And this marks adeep contrast with typical predicates. Not thatthis shows that 'exists' is not a predicate afterall, but it does tell us something importantabout how the concept works. When we saythat an object does not exist we are ascribingnonexistence to a purely intentional object;indeed this is precisely what itsnon-existence consists in. If it were any othertype of object, then it would have existenceafter all.

This raises the question of the relationbetween existence and possibility—inparticular, whether merely possible objectsexist. It seems wrong to insist that all possibleobjects must be conceived, because thismakes possibility into a mind-dependentmatter; yet in some sense merely possibleobjects are ontologically lacking. So arepossible objects non-existent and yetmind-independent? And are not fictionalobjects at least possible objects? Here I side

with Saul Kripke's view of non-existententities like unicorns and Sherlock Holmes:these are not genuinely metaphysicallypossible objects.25 The central problem withthe possibility interpretation of talk aboutunicorns and Sherlock Holmes is that thereare too many such possible objects, all theones that answer to the descriptions given inthe stories—and which of these is reallyHolmes or

24 The fundamental reason for this is thatnon-existent objects are individuated onlyby the ideas we associate with them. If weare told that a particular something doesn'texist, we need to know which thing is beingsaid not to exist—we need a suitableindividual concept. The notion of an entitynot existing that has no individual conceptassociated with it is ill-defined: what is it,precisely, that does not exist? Fictionalcharacters are the paradigm here: SherlockHolmes only comes not to exist because heis a character created by Arthur ConanDoyle—it is not that there was awell-defined fact of Holmes's non-existencebefore Conan Doyle ever created thecharacter. As it were, thought and languageare what bring non-existent objects intobeing. Even in the case of generalstatements of non-existence, such as 'tigerswith ten legs do not exist', we cannot saywhich particular such tigers suffer fromnon-existence without invoking someconceptual individuation. In the case ofunconceived existent objects the object itselfoperates to individuate it, but in the case ofalleged unconceived non-existent particularobjects there is simply nothing to give themindividuation conditions—there is nothingspecific that fails to exist in such a putativecase. This is why particularizednon-existent objects are always intentionalobjects.25 Naming and Necessity, 156-8.

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the unicorns? But this only tells us thatfictional entities are not metaphysicallypossible entities; it does not tell us whetherthere are other possible entities that arenon-existent and also mind-independent,contrary to the principle I laid down earlier.To this I reply that merely possible entities,such as the younger sister I might have had,really do exist, and did exist before I everformed the concept of them—though they donot actually exist. Such entities exist in therealm of the merely possible; their ontologicaldeficiency consists just in the fact that theirexistence is not actual. When we think thatthey fail to exist we are confusing existencewith actual existence, and it is their want ofthe latter that explains their difference fromordinary objects like the people around me.But I think that fictional entities, like SherlockHolmes, are not correctly viewed as possibleobjects analogous to the possible people thatwould have actually existed had thereproductive facts been different. Of course,such non-existent objects are epistemicallypossible, but they are not metaphysically so.So nonexistence is an essential property ofHolmes and unicorns, while it is not anessential property of my possible sister. Onthe other hand, existence is not an essentialproperty of Venus and Clinton. Thisasymmetry shows that existence, though agenuine property, is different from propertiesin general: generally, if Fness is a contingentproperty of objects, then so isnon-Fness—but not so in the case ofexistence. In sum, then, genuinely possibleobjects do exist, though not actually, whilegenuinely non-existent objects have thatstatus necessarily.26

26 I am not intending here to persuade thereader that it is correct to view possibleobjects as existing; I am simply stating what

I take to be a familiar view. My purpose is toindicate how the representation-dependence of non-existence can be madeconsistent with the mind-independence ofpossibilia—namely, by recognizing thatpossibilia exist. There may be an element ofstipulation in this way of talking, but itserves to protect what otherwise seems acompelling thesis, namely the identificationof nonexistent with merely intentionalobjects. Note that none of this is directlyrelevant to the question of whetherexistence is a property; the representation-dependence of non-existence is a logicallyseparate thesis.

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It might help if I restate my position byconsidering three different theories of thetruth conditions for 'Vulcan does not exist'.First, it might be held that 'Vulcan' stands fora possible object and that possible objectsdon't exist. Second, it might be held that'Vulcan' stands for a possible object and thatpossible objects do exist, and what thestatement is really saying is that this existentobject does not actually exist—thus 'theexistent possible object Vulcan is not actual'.Third, it might be held that 'Vulcan' stands forno possible object at all and that thepredicative part of the sentence simplyascribes non-existence to this non-existentobject. My proposal, then, is to go with thisthird view, thus cleaving to the thesis that allnon-existence is representation-dependent.Possible objects are not counter-examples tothis thesis since they involve existence.

But is impossibility a counter-example to thethesis? It might be thought both thatimpossible objects don't exist and that theyare not representation-dependent. Roundsquares don't exist, it may be said, but theyare not necessarily objects of thought. Didn'tround squares fail to exist in the universe

before thinkers ever came along to conceiveof them? Aren't there many impossibleobjects that we have never thought about?This is a puzzling and subtle issue, but I aminclined to take the following line: impossibleobjects, like possible objects, do exist, butwhat they lack is the possibility ofactuality—they are existent entities that couldnot be actual. They have the property ofexistence but they have it in such a way thatthey could never have this property actually.Their essence is to exist in modal limbo,necessarily closed off from actualization.This explains our sense that they arefundamentally lacking ontologically, but it isnot because they have no existence—it isbecause their existence is necessarilynon-actual. Nor could anything like themactually exist, whereas in the case of Holmesand the unicorns, though they lack existenceentirely, at least things like them could exist.Distance from actuality, as measured bymodal status or dissimilarity to actual things,is not the same as non-existence. Impossibleobjects are not, then, counter-examples

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to the thesis that non-existence is alwaysrepresentation-dependent.27

It may now be asked how we can ascribeany properties to purely intentional objects,including the property of non-existence. Herewe need to heed carefully the way weactually talk and not impose misleadingmodels on our concepts. For we simply doascribe properties to non-existentobjects—we make remarks about them. Thuswe say that Pegasus is a horse not a pig,that Zeus is the senior god, that SherlockHolmes is a brilliant detective. Thesestatements are all true and they containpredicative expressions; so, yes, we canpredicate properties of non-existent entities.

Not all predication involves referring to anexistent entity and ascribing a property to it;sometimes we take a non-existent entity andascribe a property to it.28 This, asWittgenstein would say, is what we do. Ourtheories

27 Again, I do not expect to persuade thereader of this conception of impossibleobjects, and the issue is certainly highlydebatable. By way of nudging intuitions,think of a conversation about whether thereare impossible objects as well as possibleones: no one in the conversation has everthought of such things as round squares,and then someone says, 'yes, there areimpossible objects—think of objects that areboth round and square!'; there followsgeneral agreement among the discussantsthat indeed there are such things, after all.Haven't they just agreed that impossibleobjects do exist, though it was hard to thinkof any examples for a while? These objectsare certainly not merely fictional, since theimpossibility of round squares obtainedindependently of anyone conceiving ofthem or telling a story about them.This raises the question of whetherSherlock Holmes might be such an existentimpossible object. I have said that Holmes isan impossible object, now I say suchobjects exist, so might not Holmes be onesuch? My answer is that impossible objectscome in two varieties: the existent and thenon-existent. We already know that Holmesdoes not exist, and his impossibility doesnot disturb this knowledge; but in the caseof round squares the matter is up fordiscussion, and there seem to be groundsfor allowing existence to these entities. Weat least know what it would be for roundsquares to exist—they are well-definedentities. But in the case of fictional entitieswe have the problem, noted by Kripke, thatthere are too many candidates for being

Holmes in the space of possible (andimpossible!) worlds—his individuation is toounderdetermined by the content of thestories. So: some impossibilia exist andsome do not. (Of course, I am aware thatthese are very delicate issues, and that it isnot altogether clear what to say about them;I am presenting what seems to be the bestoverall conception of the ontology of thesematters.)28 Compare ascribing properties to merelypossible objects: my possible sister Edith(the one that would have resulted from thecombination of a particular sperm and egg)has the property of being female. So it isnot only actual objects that have properties.In the case of fictional objects the originand foundation of their properties is thestory that refers to them; hence we can sayquite correctly that Holmes is a detective,thereby predicating a property of Holmes.And clearly the predicate 'detective' is notambiguous in factual and fictional contexts.

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need to respect this fact not deny it. And ifso, there is no bar to ascribing the propertyof non-existence to some of the things we talkabout. Just as Zeus fails to be mortal, so hefails to exist; just as Vulcan fails to be acactus, so it fails to exist; just as unicorns failto be two-horned, so they fail to be exist.Imagine someone overhearing aconversation you are having about Vulcanand wondering what you are talking about.'What is this Vulcan thing anyway?' they ask,and you reply, 'Oh, Vulcan is a planet thatsome astronomers mistakenly thought toexist.' 'So it's not a cactus you're referring towith the name "Vulcan"?' 'Definitely not,Vulcan is a planet not a cactus—andmoreover it doesn't exist.' Here we seeproperties asserted and denied of anon-existent entity, among them existenceitself. As a general rule, intentional objects

have just those properties our mental actsconfer on them; this is why it sounds so oddto suggest that Pegasus is really a fluffypoodle not a winged horse.

But there is another approach to assertionsof non-existence, which might be promptedby disquietude at the idea that nonexistentobjects can be genuine subjects ofpredication, at least in a primitive way. Wewant to ask what it is for an object to fail toexist; we want some analysis of this. To existis to have the simple property of existence,but non-existence seems to be a matter ofour failed intentionality, if I may put it thus.Given that non-existence is representation-dependent, we should be able to explain it inthose terms. Thus we might suppose thatthere is some complexity in such statements,and that they make reference to cognitiveacts in some way. There are two main casesto consider: fiction and empirical postulation.The idea, then, is that when I say, 'Holmesdoes not exist' I am saying something likethis: 'it is just a fictional pretence that Holmesexists'; and when I say, 'Vulcan does notexist' I am saying something like this: 'it wasa mistaken postulation

end p.42

that Vulcan exists'. In these paraphases'exists' occurs only in its positive form, andthe denial of existence is carried by theimplication that cognitive acts ofmake-believe or mistaken postulation haveoccurred. Putting both together, the basictruth condition of the negative existential isthat there was only an entertaining ofexistence. And we cannot further explain thisby saying that the object of the entertainingdoes not exist; the end of line comes with thestatement that this was a case of mereentertaining. Nonexistence is essentially andconstitutively failed intentionality, whereas

existence is not definable as successfulintentionality. Existence is having amind-independent property, but nonexistenceresults from the occurrence of a certain kindof mental act—a pretence or an erroneouspostulation of existence. Assertions ofnon-existence really are statements aboutmental acts, just as the representation-dependence thesis suggests.29 This makesnon-existence very different fromnon-squareness, say: to assert

29 When I say this I do not mean to beasserting that statements of non-existencemean the same as statements about failedintentionality; I am speaking rather of thebasic truth-maker for negative existentials.Analogies are always potentially misleading,but we can compare this to the secondaryquality conception of colour: what makes ittrue that an object is red is that it isdisposed to look red to perceivers, but it isnot that 'red' means (is synonymous with)'disposed to look red'; rather, the dispositionis what redness ontologically consistsin—or redness supervenes on such adisposition (see my 'Another Look at Colour'on this). Similarly, the non-existence ofHolmes depends upon the occurrence ofcertain creative mental acts that have notarget in the real world; if you like, suchnon-existence is supervenient on mentalacts that have no real world reference. Thisview is quite compatible with acknowledgingthat the concept of failed intentionality mustbe analysed by invoking the concept ofnonexistence—failed intentionality isprecisely a case in which the intentionalobject does not exist. In the case of colour'looks red' contains the word 'red', but thatdoes not show that redness is notsupervenient on dispositions to look red. Myclaim about nonexistence is not that failedintentionality is conceptually prior tonon-existence; it is the claim that facts of

non-existence obtain in virtue of failedintentionality, in the sense that there is nonon-existence without failed intentionality.This marks the difference betweenexistence and non-existence, sinceexistence is not supervenient on successfulintentionality. Existence is like a primaryquality; non-existence is like a secondaryquality. So we don't have to regard thenon-existence of an object as a bedrockfact with no further articulation; we can saywhat is involved in an object's (so to speak)coming not to exist.Alternatively, we could stick with the simpleidea that non-existence is just primitivelyone of the properties that Sherlock Holmeshas in addition to being a detective.

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that an object is not square is not to assertthat it was mistakenly taken to be square,since that may not be so and anyway is notwhat the statement means. There is noallusion here to erroneous mental acts. But tosay that an object does not exist is to alludeto mistaken suppositions or acts ofmake-believe. I think this asymmetry isentirely intuitive: non-existence really doeshave a lot more to do with misfirings of themind than do other kinds of property lack. Isuspect that it is the nature ofnon-existence—its difference from otherkinds of property lack—that is at the root ofthe old feeling that existence cannot be aproperty like any other. The negation ofexistence works differently from the negationof other properties, because of theunderlying representation-dependence ofnonexistence; but we should not infer fromthis that existence itself is not a simplefirst-order property of objects. Thus we canexplain the feeling that existence is a peculiarsort of property while not withdrawing theclaim that this is nevertheless what it is. To bea peculiar or even unique kind of property is

not to fail to be a property.

There is a further reason someone mighthave for doubting the predicate view, whichis epistemological in character: namely, thatexistence is not a perceptible property ofobjects. If we hold to the empiricist principlethat the only properties of objects areperceptible properties, at least in principle,then we get the result that existence isn't aproperty, at least on some plausibleassumptions. (Russell, of course, wasstrongly empiricist in his general outlook, sohe may well have been influenced by thisconsideration: where in my sense-datum of atable, he might have asked, is the quality ofexistence?) Why is existence not aperceptible feature of objects? Becauseregardless of whether or not an object existsit will still present the same sensoryappearance: hallucinated pink rats look anawful lot like existent pink rats. A non-existentobject can appear just as an existent objectdoes. Being blue, say, makes a difference tohow something looks, so that blue rats lookquite unlike pink ones: but existing makes noqualitative difference—there is noimpression of existence (as Hume in effectsaid). This is really why

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scepticism about the external world ispossible: you can never build existence intothe appearances, so it must always beinferred or assumed. If existence were likecolour, you could know that the external worldexists just by inspecting your sense-data: butthat is exactly what existence does not allow.I know that my current intentional object isblue and circular, but I have nothing sensoryto guarantee that it also exists.

The right response to this point aboutimperceptibility is to concede the premiss butdeny that the conclusion follows: true,

existence is not a perceptible property, but itdoes not follow that it is not a property—it isjust a rather special property. Is self-identitya perceptible property of objects, or logicaland modal properties? Apparently not, butthen why should existence be? Empiricism ofthis kind is just mistaken, a misguidedassimilation of everything real to theperceptible. To deny that existence is aproperty on account of its imperceptibility isjust a hyperbolic reaction to its specificcharacter. It is a property that is universal towhat exists, whose complement class isrepresentation-dependent, and which is notperceptible: that is its nature. So there is nocogent objection here to the view thatexistence functions as a first-order propertyof objects.

I now want to consider three specificcontexts in which the concept of existence isessentially invoked; my purpose is to showthe superiority of the predicate view over theorthodox view in handling these contexts.

(i) The Cogito. Consider the statement 'Iexist': how should we analyse it? On the faceof it, this is a subject-predicate statementconsisting of an indexical singular term and aterm that ascribes a property to the referentof that indexical (in a context). And I maintainthat this is precisely what it is, logicallyspeaking. This is the default position, barringarguments to the contrary. But how does theorthodox view handle it? It needs to find apredicate for 'exists' to attach to; but no suchpredicate apparently figures there;

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so one has to be contrived. Thus we arepushed towards a description theory of 'I',which will enable us to say that theproposition that I exist is equivalent to theproposition that a description D has a uniqueinstance. But there are well-known problems

with this, since any natural description will failto have the force of the indexical.30 I canknow, for example, that the description 'theauthor of The Mysterious Flame' has aunique satisfier without realizing that I amthat author, so indexical and description donot mean the same.31 The only remotelyworkable description will be metalinguistic,like 'the referent of this (token of) "I' ", so thatthe Cogito is saying in effect that 'x is areferent of this (token of) "I' " is uniquelyinstantiated. Now that does not look much likewhat the original statement says: the Cogitois less convoluted than that; it is notmetalinguistic; it could be stated by someoneincapable of semantic ascent; it has atransparent certainty the paraphrase lacks.But there is also a clear logical problem,because we are now referring to twothings—the self and a token of 'I'—and bothhave to exist for the statement to be true. Sowe are presupposing the truth of 'this tokenof "I" exists', which contains an indexicalreferring to a word token—and how is that tobe analysed? We will need another definitedescription: but that will either contain anindexical or it won't. If it does, then we needanother description to explain the existenceof its referent; if it does not, then we fail toproduce something with the semantic forceof the original, since indexicality cannot becaptured non-indexically. The same pointapplies if we replace 'I' with 'the bearer ofthese mental states',

30 What about invoking self-identity again inthe shape of the predicate ' I'? Then wecould say that 'I exist' means '( x)(x I)',which latter inherits the semantic propertiesof the original indexical. But, again, thispresupposes my existence, since the term'I' must be taken to refer to an existent entity—me—in the context ' I'. We do not explainwhat it is for me to exist by stating thatsomeone is identical to me. Nor, intuitively,

is this what I mean when I say that Iexist—where is the identity sign to be foundin that sentence? And there is also the pointI made at the beginning, that the idea of aninstance of ' I' already builds in the notionof existence, since Sherlock Holmes cannotbe allowed to count as an instance ofself-identity if this is to be sufficient forexistence.31 See John Perry, 'The Problem of theEssential Indexical'.

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referring to my own mental states: thispresupposes the truth of 'these mental statesexist', and this cannot be analysednonindexically. The point here is that theirreducibility of indexicals, especially the 'I' ofthe Cogito, is inconsistent with the orthodoxanalysis of singular existentials in terms ofdescriptions. If the only way to preserve thespecial semantic properties of 'I' is tointroduce some new indexical, then we needto explain the corresponding existencestatement, which presents the sameirresolvable dilemma. So the case is evenworse here than for existence statementscontaining proper names. The lesson is thatthe Cogito cannot be formulated using theorthodox analysis of existence; it needs thepredicate treatment.

(ii) Essentialism. A natural way to expressessentialist claims employs the notion ofexistence: for Clinton to be necessarily aman is for it to be the case that Clinton couldnot exist without being a man. Generally, 'x isessentially F' means 'necessarily, if x exists,x is F'. Now let us ask how the orthodox viewwould analyse this latter sentence. There aretwo possibilities: either we use 'F' itself as thepredicate to which existence attaches, or weintroduce a new predicate. Suppose we use'F' itself: then we get 'necessarily, if x is an

instance of Fness, x is F'. This would be away of formulating the claim that (say) everyman is such that, necessarily, if he exists, heis a man; and it says that every man is suchthat, necessarily, if he is an instance ofmanhood, then he is a man. But this, ofcourse, is a plain tautology, which theoriginal statement is not—so they cannotmean the same. We thus need to find somepredicate distinct from that which is beingdeclared essential to the objects in question.That will not in general be impossible to do:Clinton, say, satisfies the predicate 'USpresident in 1999'. This raises Kripkeanproblems about whether we can preservemodal status under such an analysis, but thepoint I want to make is different and parallelsthe point I made earlier about bare existence.It is that the orthodox doctrine now entailsthat nothing can have an essential property Funless it instantiates other properties (notincluding existence). But is that really ametaphysical necessity?

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Couldn't an object have just one property andhave it essentially? More to the point, is thedenial of this something that an essentialistclaim entails? Is it contradictory to say 'x isessentially F and x has no properties otherthan F'? I don't see that it is, but the orthodoxanalysis implies that it must be, once thetautological translation is ruled out. If we take'exists' to be a predicate, on the other hand,then we can say simply that for Clinton tohave the property of existing he must alsohave the property of being a man, and this isneither tautologous nor committed to the ideathat Clinton must have some further property.But if we take existence to attach to aproperty, in the orthodox way, then we arecommitted to Clinton having properties otherthan that of being a man. He does, of course,but my point is that this is not something that

the essentialist claim should logically imply,since it is not contradictory to say that anobject is essentially F and yet has no furtherproperties. I therefore conclude that theorthodox analysis cannot properly handle theuse of existence in expressing essentialistclaims, while the predicate view has notrouble with this.

(iii) The Ontological Argument. The standardobjection to the ontological argument (OA) isthat it assumes that existence is a property.Clearly, I am committed to saying that this isa bad objection; so the question for me iswhat to say about the claim that the definitionof God implies his existence. Now I think itwas always suspicious to pin the fallacy ofthe argument on treating existence as aproperty instead of as a second-orderconcept, as if we just hadn't noticed that'exists' is logically on a par with 'numerous'.That is like saying that the argument dependsupon a scope confusion or affirming theconsequent or some such logical howler. Butsurely the argument is more interesting andsubstantive than that diagnosis allows; it isnot some simple logical fallacy—pleasant asit might be to think this. Second, it seems tome quite unclear that the argument cannot bereformulated using 'exists' in thesecond-order way. Thus we can ask whetherit is part of God's definition that his attributesmust have at least one instance. Does 'beingall-powerful and all-knowing and all-good'have to have an instance?

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For if it did not, then wouldn't it fail to expressthe concept of the most perfect being? Theconcept 'being a perfect being' has to havean instance or else it would not be theconcept it purports to be. Third, we shouldnote that the argument can be deployed inthe opposite direction to prove the

non-existence of the most imperfect being.Call that being 'Satan': then Satan cannotexist because he is the most imperfectconceivable being, and existence is one ofthe perfections. To exist and be imperfect isto be less imperfect than a maximallyimperfect being who fails to exist. Thus themost imperfect conceivable being cannotexist. Whatever is wrong with thesearguments is independent of whetherexistence is a property; the logical status of'exists' is irrelevant.

How can the OA and its Satanic counterpartbe resisted? I don't need to answer this inorder to defend the property view ofexistence, but I will make some observationsabout it anyway. One might think that theweakness lies in the assumption thatexistence is a perfection and non-existencean imperfection. That is certainlyquestionable on any natural interpretation ofthe notion of perfection. But actually we canformulate the argument without using thispremiss, by appealing to other aspects ofGod's definition. He is also the mostimpressive and most powerful being, bydefinition. But surely, it will be argued, youcannot be the most impressive and powerfulbeing conceivable if you fail to exist; anotherbeing who was just like you but did existwould have to be more impressive andpowerful. Thus existence is part of God'sdefinition by virtue of these attributes and notmerely by virtue of the notion of perfection.Equally, we can prove that the leastimpressive and powerful being conceivablecould not exist (he will not be the devil, astraditionally conceived), since if a being isdefined as the most minimally impressive andpowerful being conceivable he could not existgiven that existence augments one'simpressiveness and power. It is true that thisargument sounds strange and sophistical, butit is hard to put one's finger on what exactly

is going wrong.

My own suspicion, which is outside thescope of the topic of existence, so I won't tryto pursue it here, is that the fault lies in

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taking notions like 'the most perfect,impressive and powerful being conceivable'to be well-defined. We can make sense ofbeing the most perfect being that exists, andwe know what conceivability is, so we thinkwe know what is meant by combining them.But we are lapsing into disguised nonsensehere, analogous to the idea of (say) the mostperfect conceivable triangle or piece ofmusic or meal. Here too we may know what itis to be the most perfect triangle to exist(construed as an actual drawing), or the bestpiece of music, or the best meal—and wealso know what it means to conceive of oneof the things as being superior to another.But it does not follow—and it lookspeculiar—to say that there is then awell-defined concept of the most perfectconceivable item of any of these types.Suppose I call the most perfect mealconceivable 'Bill': can I infer that Bill existsbecause if it did not then there would have tobe a meal that was conceivably better thanBill? We just don't know what it would be tobe the most perfect conceivable meal orpiece of music. Similarly, the notion of, say,the most powerful conceivable mouse makeslittle sense; or the most impressiveconceivable daisy. This seems to me theplace to look for the error in the OA, not insome supposed mistake about the logicalcharacter of existence. We can let God havethat property so long as his definition reallywarrants it—but that is what is not at all clear.The problem with the OA, then, is that ittrades on notions of the maximal forms ofcertain attributes, particularly perfection, that

are inherently ill-defined.

I conclude that 'exists' is a predicate and thatit expresses a property just as otherpredicates do (whatever properties are andwhatever it is for predicates to express them).There is no good objection to this view, andthe alternative to it is full of difficulties. It is aword we can correctly apply to individuals,which is just what the surface form of ourexistential sentences suggests. It has itspeculiarities, of course, but they merely tellus what kind of property it is. As so often, theway a word is semantically turns out to be theway it appears to be syntactically (compareproper names).

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This is quite compatible with maintaining that'tigers exist' says that 'tiger' has instances,since the relevant notion of instance is simplythat of an object that has the (first-order)property of existence. The orthodox view hasinflated a correct point about generalstatements of existence into the incorrectdenial that existence is a property. So wecan keep all that is good and wholesome inthe logical tradition while not rejecting theobvious. By all means analyse generalstatements of existence in terms of the'existential quantifier', but do not make themistake of inferring that existence is not apredicate just because this analysis works.The existence of tigers consists in the factthat tigers severally have the property ofexistence; this is what grounds the fact thatthe concept tiger has instances and hencemakes true '( x)(x is a tiger)'.32

32 Thus singular existential facts are basicrelative to general existential facts, as wegenerally suppose for singular and generalfacts: 'a is F' is what makes true 'somethingis F'. The Russellian doctrine, by contrast,does not allow this obvious parallelism with

singular and general facts in general.end p.51

3 PredicationAbstract: The extensional view thatpredicates are general terms that referseverally to the members of a set of objectsthat satisfy them is rejected. Instead, it isargued that predicates refer to properties,and are thus singular terms like names. Thedistinction between names and predicates isupheld, but it is argued that what accountsfor it is not the spurious distinction betweensingularity and plurality of reference, butrather grammatical position, and theontological type of the reference.

Keywords: indeterminacy, names, pluralreference, predicates, predication, Quine,singular reference, Tarski semantics

Colin McGinnPredicates, we are taught, haveextensions—the class of objects of which thepredicate is true. That seems hard to deny,putting aside special issues like vagueness: ifpredicates can be true of objects, then thereought to be a set of objects of which thepredicate is true. But a stronger claim iscommonly made: that these extensionsconstitute a semantically relevant feature ofpredicates. A sentence formed from apredicate and a name is said to be true ifand only if the object referred to by the nameis a member of the set that forms theextension of the predicate (and similarly forother types of sentence structure). Thus itbecomes natural to say, as Quine does, thata predicate has 'divided reference' or'multiplicity of reference': it refers in a pluralmanner.1 As a name refers to a singleobject, so a predicate refers severally to the

members of a collection of many objects.Predicates refer to each of the many objectsthey are true of; so there are as manyreferences for a predicate as there areobjects of which it is true. The sense of apredicate may possess a unity or singularity,but its reference is a scattered and multipleaffair. Since a predicate is true of manydispersed things, its reference is adistributed totality. On this conception, then,a predicate is not a singular term in Quine'ssense: 'a singular term names or purports toname just one object. . . while a general termis true of each, severally, of many objects'.2Predicates are classified as general termsprecisely because they do not refer uniquelyto a single entity but generally to a range ofentities. It is the multiplicity inherent inpredicate reference that is held to markpredicates off from names and other properlysingular terms.

1 See Quine, Word and Object, 90 ff.2 Ibid. 90-1.

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This conception has become so ingrainedthat we are not apt to notice that it is in fact asubstantive theory about the semantics ofpredicates and their distinction from namingdevices. But there is another way of lookingat predicates that gives a very differentpicture of their semantics, namely thatpredicates refer singularly to properties. Thepredicate 'red' refers to the property of beingred, not to the many red objects the worldhappens to contain. Iventureto suggest thatthis is the natural way to conceive ofpredicates, as opposed to the standardextensional view. On this natural view, then,predicates are taken to refer to properties orqualities or attributes—universals in thetraditional sense. These properties are not tobe identified with extensions: they are notsets of objects but the attributes that form

such sets. Thus 'red' refers initially to theproperty of redness, and those objects thathave this property constitute the set of redthings. According to this conception, apredicate does not divide its reference at all,since its reference is a property that is justas 'singular' as the object referred to by aregular name. The truth conditions of simplesubject-predicate sentences are givenaccordingly: a sentence of the form 'Fa' istrue if and only if the object referred to by thename has the property referred to by thepredicate. There is then no reason towithhold the title of singular term frompredicates: they name (refer to, designate)just one entity—the property they are used toascribe to objects. There is no multiplicity ordivision of reference here—just a uniqueentity of the universal kind. Predicates do notrefer to what they are true of, but to theproperties that are instantiated by the thingsthey are true of: the 'true of ' relation and the'refers' relation are distinct relations.

Which of these two views is preferable?3 Itmight well seem that the standard view hasthis advantage—that a predicate at least has

3 It might be said that we do not need tochoose: predicates refer both to theproperty they express and to the membersof their extension. But, as I will argue below,we could say the same of names, andhence could equally claim that names have'divided reference', thus losing theirsemantic distinctness from predicates. Inany case, once we allow properties asreferents we hardly need to reckon withextensions. This is why the two conceptionsof predicate reference are traditionallytaken to be rivals—considerations ofsemantic redundancy.

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an extension distinct from any other

reference it might be supposed to have, whilea name has no extension over and above theobject it refers to. So, putting asideontological worries about properties for now,the semantics of predicates differs cruciallyfrom that of names: even acceptingproperties as the reference of predicates,there is another semantic level that needs tobe acknowledged—the extension of thepredicate. With names there is just thenamed object (and possibly also the sense ofthe name), but with predicates there is thenamed property and the class of things thathave this property. So predicates differfundamentally from names in virtue of themultiplicity inherent in their extensions. Quineis right even if predicates refer to properties,since there are still extensions to reckon with;he has still put his finger on what markspredicates off from names. Suppose weagree that predicates express senses andrefer to properties; then there is still theirextension left over as an extra layer ofsemantic reality. But in the case of names, itappears, once we have distinguished theirsense and reference we have exhausted theirsemantic description.4 Herein lies the basicdistinction between the name and thepredicate. And if we need extensions anywaywhy bother to invoke the properties thatallegedly mediate between a predicate andwhat it is true of?

I am going to argue against this position.Ultimately, I wish to defend the naturalproperty view against the standard extensionview; but my immediate aim is to underminethe argument just offered. My strategy will beto show that names have the same kind ofsemantic duality that predicates are taken tohave, once the matter is viewed impartially.To establish this I shall present what may welllook like a formal trick, using this to arguethat the entire

4 Thus names have a two-level semantic

analysis corresponding to sense andreference, while predicates are taken tohave a three-level analysis, correspondingto sense, reference, and extension. InFregean terms, predicates are taken toexpress a sense, refer to a (first-level)function ('concept'), and have an extension.I shall be arguing that this commondistinction between two- and three-levelsemantic analyses, held to distinguishnames from predicates, is arbitrary andunmotivated.

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standard framework of extensional semanticsis unmotivated and deeply flawed. We havebeen hoodwinked by a prejudice, not seeingwhat is really an arbitrary stipulation for whatit is. I intend to loosen the hold of somefamiliar and unexamined assumptions bysetting up an alternative semantic frameworkin which the usual picture is totally inverted.

Take the name 'Bertrand Russell': this namerefers to a certain concrete individual, nowdead, who is customarily reckoned to be theextension or reference of the name. Thisobject is taken to be the 'semantic value' ofthe name—the entity invoked in giving thetruth conditions of sentences containing thename. Now consider the propertiesinstantiated by that object—everything thatholds of Russell. Form the set of theseproperties, and then assign this set to thename, calling the assigned set the'second-level extension' of the name.Evidently there is such a set, assuming thereare properties at all (we shall return to this),and clearly there is a function that takeseach (non-empty) name and yields such aset for that name. If the first-level extensionexists (Russell, in this case), then thesecond-level extension also exists (the totalityof properties of Russell). Now consider asentence formed using this name, say

'Russell was bald', and interpret the predicateby assigning a property to it, viz. baldness.Then we can say that the sentence is true ifand only if the following condition holds: theproperty assigned to the predicate is amember of the set that forms the second-levelextension of the name. That is to say: 'Russellwas bald' is true if and only if baldness is oneof the properties Russell had. It is quiteevident that this truth condition is correct andis in some sense equivalent to the standardtruth condition formulated in terms of objectsand predicate extensions. If Russell belongsto the extension of 'bald', then baldnessbelongs to the second-level extension of'Russell'. But the two truth conditions employquite different ontologies; in particular, theextension of 'bald' is not referred to in thenew style of truth condition. Instead ofobjects and sets of objects we have

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properties and sets of properties. We have,in effect, inverted the usual rule forconstructing truth conditions, now treating thepredicate as having a singular reference andthe name as having a multiple extension. Andthe implicit question I am thus posing is: whyis this new way not just as good as the oldway? Why do it with regular extensionsrather than with our newfangled second-levelextensions? Why not treat the predicate asmaking specific reference and the name ashaving a referential plurality, referringseverally to each of the properties thatconstitute its second-level extension?

An immediate reply from those of Quineaninclinations will be that the new truth conditioninvokes an ontology of properties, and theseare 'creatures of darkness'. I have nosympathy for this rejection of properties, forreasons I will not discuss here, but theimportant point for present purposes is that

such an ontology is quite incidental to themoral I am after. We could, if we like,stipulate instead that our sentence is true justif the predicate 'bald' is a member of the setof predicates true of the referent of 'Russell',thus dispensing with properties; we simplytake the second-level extension of the nameto be a set of linguistic items. Then again, wecould also proceed as follows: take theextensions of each of the predicates true ofRussell, assign these to the name, andformulate the truth condition thus: theextension of the predicate 'bald' should be amember of the set of extensions (themselvessets) assigned to the name. Suppose one ofthese extensions is the set of bald things;then the sentence would be true, since thepredicate 'bald' has an extension that isidentical to one of the extensions assigned tothe name. Though this truth condition issomewhat less intuitive to grasp, it will beseen on reflection to be equivalent to the truthcondition stated in terms of properties—forthe simple reason that each property has itscorresponding set of objects that instantiateit. So we can ask again: why not use thisstyle of truth condition instead of thestandard one? Actually, it is simpler in onesense to do it this way, since we are nowdealing with a uniform ontology of sets at allpoints in the semantics. We

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need sets of objects under the Quineandispensation anyway, so why not do thewhole thing in terms of such sets?

It may also be complained that thesecond-level extension of a name is notknown or grasped by the speaker—is notpart of his understanding of the meaning ofthe sentence in question. That is true, sincesomeone who understands 'Bertrand Russell'is not required to know all of Russell's

properties; but it is equally true that thestandard extension of a predicate is notknown or grasped by the speaker either,since someone who understands 'bald' is notacquainted with all the things that are bald.Neither type of semantics meshes naturallywith speakers' understanding. The type ofsemantics that works best in this regard isthe type I am working towardsdefending—that in which we assign an objectto the name and a property to the predicate.My point at present is that the standardapproach enjoys no advantage in thisrespect over the contrived alternative I amconstructing. Both approaches are faulty formuch the same reasons.

Enthusiasts of Tarskian semantics mightmake the following point: the standard axiomsfor names and predicates differ in that theformer assign denotations to names, whilethe latter specify satisfaction conditionssimply by using the predicate (or itstranslation) in the metalanguage. Thus it isusual to have clauses like the following:" 'Hesperus" denotes Hesperus' for names,and 'x satisfies "man" iff x is a man' forpredicates. In the latter clause no entity isascribed to the object-language term, while inthe former this is the case. Doesn't thisfamiliar asymmetry support the denotationalview of names and undercut the parallel viewof predicates? The answer to this is that wecan easily invert the Tarskian treatment fornames and predicates. Nothing stops us fromwriting: " 'man" denotes the property of beinga man', and then formulating truth conditionsby saying, " 'Socrates is a man" is true iff thedenotation of "Socrates" has the propertydenoted by "man' ", using the denotationaxioms for name and predicate to derive thestandard truth conditions. Once we haveproperties to play with we can write suchthings as: 'x satisfies "man" iff x has the

end p.57

property of being a man' and 'x has theproperty of being a man iff x is a man'.These conditions are all logically connectedin the predictable way. There is nothing inTarski to preclude a denotational approach topredicates, even though the standard axiomtakes the familiar mention-use form.

But can we also give a non-referentialdisquotational axiom for names? The answeris that this is perfectly easy once we allow anontology of properties or sets. Let us say thata property P fulfils an open sentence of theform 'a_' iff Pa, for some name 'a'; or a set Xcompletes an open sentence 'a_' iff a is amember of X. For example, P fulfils'Socrates_', where the blank takes propertiesas values (or takes predicates assubstituends), iff Socrates has P; intuitively,a property fulfils a name 'a' just when a hasthat property. Here we have a treatment fornames that assigns them no reference,officially speaking, and works by employingan ontology tailored for a predicate variable.It is exactly parallel to the usual method thatemploys an ontology of objects and interpretspredicates by using them in conjunction withthis ontology: instead of saying 'x satisfies"man" iff x is a man' we say 'P fulfils"Socrates" iff Socrates is P'; in both caseswe just disquote the object-language termand attach it to the variable, therebyeliminating the semantic terms 'satisfies' and'fulfils'. The Tarskian scheme by itselfimposes very light constraints on the way weinterpret names and predicates, so it cannotbe invoked to justify the asymmetry inquestion. In point of getting the truthconditions right we can proceed eitherdenotationally or disquotationally, dependingon prior semantic convictions; just as we canget truth conditions right either by regularextensions for predicates or second-levelextensions for names. Truth conditions by

themselves underdetermine semantics.5 Myown view would be that we know antecedentlythat

5 I am thus opposing the whole (recent)tradition of trying to work back from truthconditions to semantic analysis: gettingtruth conditions right radicallyunderdetermines assignments of semanticvalues to terms. In particular, Tarskianconstraints can be fulfilled in far too manyways. Our conception of the semanticproperties of terms should dictate theassignment of truth conditions, not the otherway about.

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names denote objects and predicates denoteproperties, so we would want to write ourTarskian semantics so as to respect this fact.The illuminating and correct way to write anaxiom for a predicate is then: " 'man" denotesthe property of being a man', and we reachthe disquotational truth condition by using theprinciple that something has the property ofbeing a man iff that thing is a man. In anycase, there is no impartial way to motivatethe standard asymmetry deriving fromTarskian considerations.

Returning to first- and second-levelextensions, we can note a further symmetrybetween them. The extension of a predicatetypically varies over times and worlds, as newthings become bald at later times or exhibitbaldness in other worlds; but the same is trueof the second-level extension of a name,since new properties will hold of the individualas time goes by or as different worlds areconsidered. If extensions must be such as tovary with these parameters, then our newextensions pass the test just as well as the oldones. Indeed, they pass it for the very samereason that standard extensions pass it,namely that objects change their properties

with time and possibility. What does not varyin this way are the objects and properties thatnames and predicates are naturally taken todenote (they are rigid designators, temporallyand modally, of these entities). The name'Russell' invariably denotes Russell, while thepredicate 'bald' invariably denotes baldness.

Is there any reason to prefer the method ofsecond-level extensions? Well, there is if youharbour a certain kind of metaphysicaloutlook about objects and properties, to theeffect that objects are analysable as 'bundlesof qualities'. On such a view, Russell just isthe set of his properties, so the regularextension of the name is identical to itssecond-level extension as I am defining it.This metaphysical view makes propertiesontologically basic, and so it is natural toformulate truth conditions accordingly: theproperty expressed by the predicate isamong those that enter into the 'bundle' thatconstitutes the object denoted by the name.Of course, you can use this type of truthcondition even if you don't subscribe to thissort of ontology,

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but if you do it will seem the natural andobvious way to go. So it is not as ifsecond-level extensions have no conceivablemotivation in general ontology. Someone likeRussell himself, who disliked the notion ofsubstance or continuant particular, might wellfavour the property-based truth condition. Itis certainly there to be favoured.

It is easy enough to see that the new methodcan readily be extended to quantifiedsentences and other sorts of complexsentence. The variables now range over setsof properties and the truth conditions aregenerated in the same fashion as before: theset assigned to the variable (as its valueunder an assignment) contains the property

expressed by the predicate. The second-levelextensions do all the work that an orthodoxdomain of discourse can do. As far as I cansee, no purely formal test distinguishesbetween the two sorts of approach; and thisis not surprising in view of the power of theontology of properties (the usual logicaltheorems will surely go through, mutatismutandis).

If we were to adopt the new approach, wewould come to see names and predicates ina very different light. Where now we are aptto find singularity in the name and plurality inthe predicate, we would make the oppositedispensations under the revised framework.The predicate would have the job of pickingout a unique property, thus asserting itssingularity, while the name would beassigned a multiplicity of items—the manyproperties had by the object named—towhich it dividedly refers. The name would bedistinguished from the predicate by virtue ofits inherent semantic plurality. In our chosensentence, 'bald' would be the singular term,while 'Russell' would refer severally to themany properties had by that philosopher.Some might argue, on this basis, that wemay as well dispense with the ordinaryreference of the name altogether, rather asnow some dispense with the propertyexpressed by a predicate; after all, we don'tneed to mention it in stating truth conditions.We require only that the membership relationhold between the property expressed by thepredicate and the set of properties assignedto the name; the bearer of the name

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drops out, semantically speaking.6 (Ofcourse, we need to regard Russell as morethan the sum of his properties if we are toabandon him while embracing the set of hisproperties; just as we now regard a property

as more than the sum of the objects that haveit when we reject properties in favour ofextensions. Both distinctions are of coursecorrect; and the symmetry between them isinstructive: objects are no more bundles ofproperties than properties are bundles ofobjects.) Some may even go further andannounce that this gives the true ontologicalpicture of the world, since semantics is theroyal road to metaphysics: there are reallyjust sets of properties, despite our usualassumptions about the existence of objects.

What is alarming here is how close to certainstandard moves such arguments would be.The methodological point I am making is thatthere are far too many degrees of freedom atthe semantic level of truth conditions towarrant such inferences and constructions.But I shall pursue the question ofsignificance and morals after a briefmetaphysical interlude.

The world has a certain interlockingstructure, generated by the relation ofinstantiation. Take a single object, say mycoffee cup: it instantiates a number ofproperties—it is blue, cylindrical, fragile, etc.These do not exhaust all the properties thereare, obviously, since no object instantiates allproperties. Now take all the objects thatinstantiate the aforementioned properties—allthe blue things, all the cylindrical things, allthe fragile things. We obtain a largeexplosion of objects from this simpleoperation, but still not all the objects thereare. But now iterate the process andconsider all the

6 Can it be argued that we still need thebearer of the name to 'tie together' thevarious properties that compose itssecond-level extension? At an ontologicallevel that seems true, but semantically thebearer still does not need to be cited informulating truth conditions. And,

significantly, the same can be said aboutthe role of the property denoted by apredicate in 'tying together' the variousobjects that compose its extension. Again,there is no relevant asymmetry to justify theusual differential treatment of names andpredicates.

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properties possessed by all the objects inthese classes—a colossal number! Nowagain take all the objects that instantiate thishuge set of properties. And when you havedone that you can repeat the procedure andget all the properties instantiated by thatenormous class of objects. If you go on thisway you may not exhaust all the objects andproperties the universe contains, but you willcertainly generate a very large totality out ofjust a few iterations—and all starting from asimple coffee cup. Perhaps some traditionalmetaphysicians will see in this a sign of theessential Oneness of creation—theinextricable organic Unity of Being. Be thatas it may, what we do have is a branchingstructure that links objects and properties in achain (as you will see if you draw a diagramof the steps involved): there is a fanning outof objects and properties as we trace theinstantiation relation from the initial object outalong its axes.

I find this chainlike structure rather beautifulin its simplicity and power, but I do notmention it solely for aesthetic reasons (notthat these are insufficient reasons to mentionsomething). I mention it because it is thefundamental ontological structure underlyingthe equivalence of truth conditions I havebeen indicating. Just as we can move fromthe property expressed by a predicate to theset of objects that instantiate it, so we canmove from the object denoted by a name tothe set of properties that object instantiates.We are simply travelling in opposite

directions along the line of instantiation. Nodirection is any more legitimate than theother; both are written into the structure ofthe facts. In particular, there is nothingprivileged, seen from the metaphyscialstandpoint just adumbrated, about choosingthe extension of a predicate as the way tostate truth conditions (or conceive of thestructure of facts). The contrary method offorming second-level extensions simplyproceeds in the opposite direction—bystarting with the object and considering theproperties it instantiates. We could just aswell conceive of the structure of facts in thatway: every fact consists in the membershipof a property in some set of properties—instead of the membership of an object insome set of objects. Then, too, there is athird view, that facts consist in theinstantiation of properties by objects—the

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view I favour. Thus we could depict facts inthree different ways: [x, {x, y, z}]; [P, {P, Q,R}]; [x, P]. In the first, Quinean, way asingular fact is an ordered pair of an objectand an extension, a set of objects; in thesecond way such a fact is an ordered pair ofa property and a second-level extension, aset of properties (or we could do the wholething with extensions and sets of them); in thethird way a fact is simply an ordered pair ofan object and a property. My point is thatthere is no particular reason to prefer thefirst of these to the second, and the third isreally the natural view to adopt. When weappreciate what the underlying ontologicalstructure is we can understand why bothsorts of conception work—and how littlereason there is to favour one over the other.At the risk of sounding airily metaphysical,we can say that every unity (object orproperty) has its corresponding plurality (setof properties or set of objects)—with these

correspondences setting up a great chain ofinterlocking objects and properties stretchingas far as the eye can see. The chain allowsus to formulate our semantics in equivalentways, by selecting the sets we fancy andassigning them to the various parts of speechin ways that preserve the requisiteinstantiation relations. How we do this isessentially arbitrary, unless some furtherconstraints can be found and motivated. As itturns out, I don't think this is terribly difficult,but the necessary constraints rule out thestandard Quinean approach, and hencedetermine a quite different semanticconception of the function of predicates.Extensions will no longer be in the picture.

One possible response to the availability ofsecond-level extensions in formulating truthconditions is to declare deep semanticindeterminacy. A name indeterminatelyrefers either to its bearer or to the set ofproperties possessed by its bearer; apredicate indeterminately refers either to theproperty it expresses or to the members ofthe set of objects that instantiate thisproperty. There is simply nothing to choosebetween the standard approach and thealternative approach—no 'fact of the matter'.This would be quite a strong result, showingthat there is nothing privileged about thestandard

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approach and the conception of predicates itengenders; it really is arbitrary which way wechoose to go. Names can be treated ashaving multiple reference to properties (orsets of extensions), just as well as predicatescan be treated as having multiple referenceto objects. Either approach delivers semanticvalues that work to fix truth conditions.Presumably this would not please Quine,despite his predilection for indeterminacy

theses, since it undermines his generalconception of what a predicate distinctivelyis.7 But I can see how it might be temptingfor some to draw such a conclusion.

However, I don't think we are forced toaccept semantic indeterminacy here; thereare other constraints that can be mobilized.The obvious, and familiar, move is tointroduce epistemic considerations: roughly,we require that the speaker be acquaintedwith the semantic values that are invoked.This certainly rules out second-levelextensions as the semantic value of names,since a speaker cannot be expected to knowall the properties of the objects he refers to.But it also rules out regular extensions, sincethe speaker will not be acquainted with all theobjects that make up the extensions of thepredicates he understands. Such knowledgerequires, intuitively, knowledge of facts, notmerely semantic knowledge. What is notruled out by this constraint is the simple viewthat I prefer: that names denote objects andpredicates denote properties. When apredicate is understood what is known isprecisely the identity of the propertyexpressed by the predicate; just asunderstanding a name involves knowledge ofthe identity of its bearer.8

7 So two Quinean sentiments are in tension:a penchant for semantic indeterminacytheses, and use of the singular-pluraldistinction to distinguish names frompredicates. If what I have argued is correct,then that latter idea is nullified throughindeterminacy considerations. In a way it issurprising that the kind of indeterminacy Iam alluding to did not occur to Quine, givenhis ingenuity with contrived alternativesemantic schemes.8 The kind of view of name understandingdefended by Gareth Evans in The Varietiesof Reference, in which individuating

knowledge and causal relations areblended, could be extended to predicateunderstanding: we understand a predicatewhen we have individuating knowledge ofthe property it denotes, mediated by causalrelations in which that property is involved.Or again, Russell's idea that understandingpredicates involves acquaintance withuniversals mirrors the idea thatunderstanding a name involvesacquaintance with its bearer: see TheProblems of Philosophy, ch. 5.

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So we can construe what I have said so faras an argument along the following lines: ifyou don't accept this view, then you areforced to accept indeterminacy as betweenthe standard approach and the second-levelextension approach.

The simple view abandons extensions (ofeither sort) as semantically relevant andthereby relinquishes the idea that predicatesare general terms in Quine's sense—predicates do not have multiple reference butrather are singular terms denoting properties.In effect, the 'true of ' relation betweenpredicates and objects is not semanticallyrelevant. Of course, predicates are true ofmany things—but it is equally the case thatobjects satisfy many predicates: and we don'tsay that names of objects have pluralreference simply on account of this. Theunderlying ontological structure always givesus a plurality for any unity, no matter fromwhich direction we approach the instantiationrelation.

The singular term view of predicates isconfirmed by a well-known point, namely thatpredicates can be nominalized so as to giveterms that feature in subject position—as with'redness', 'mortality', 'baldness', etc. Herethey clearly do not designate extensions, and

so it is natural to assume semantic uniformityand take the corresponding predicates todesignate properties when occurring inpredicate position. Thus predicates are asmuch singular terms as their nominalizationsare. Of course, that is not to say that theyare names, in the sense of terms referring toparticulars; the entities they purport uniquelyto denote are properties or universals, notparticulars. The singularity consists in theirnot denoting the members of a set of objectsvia the 'true of ' relation; they do not 'dividetheir reference'. It is true that they aresatisfied by many objects, but these objectsare not components of their semantic value;just as a name refers to an object of whichmany properties hold without its semanticvalue being those many properties. Apredicate refers to a property with manyinstances; a name refers to an object withmany properties: that is all. The meaning ofeach category of term stops at its ordinaryreference without reaching out further intothe non-semantic world of

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property instantiation. Extensions of bothkinds are fixed by the facts of the world, notby the meaning of the terms. They are extra-semantic items.

The asymmetry between names andpredicates is not then a matter of singularityversus plurality of reference. Then what doesit depend upon? Two things: grammaticalposition and the ontological type of thereference. Predicates occur in predicateposition, ascribing properties to objectsthereby. But they also denote a special classof entities—universals. It is not the way theyrefer that marks them off from names butwhat they refer to—and the sententialposition they refer from. So it is not that noasymmetry can be found between 'Russell'

and 'bald' in the sentence 'Russell was bald'once the idea of multiple reference isabandoned. We can account for thedifference between subject and predicatewithout employing the singular-generaldistinction to do so.9

I would say that the idea of 'multiplereference' is a kind of oxymoron, once youreally think about it. An ambiguous word like'bank' or 'John' indeed has multiplereference, but an unambiguous word like'red' has a unique reference.10 We canalways ask 'What does that word refer to?'and expect to be given a single answer—thatis how the word 'refer' is used. Thecontortions of 'multiple reference' stem froma desire to avoid properties for (misplaced)ontological reasons; the notion has nothingotherwise to recommend it. It is certainly notthe case that 'refers' is synonymous inEnglish with 'true of '. Saying that 'bald' refersto the set of bald

9 Frege, of course, accounted for thedifference in terms of his notion ofincompleteness: names of objects arecomplete expressions, names of conceptsare incomplete expressions. He does notaccount for the difference between subjectand predicate in terms of singular versusdivided reference. I do not say his accountis unproblematic; I am simply pointing outthat rejecting Quine's account of thedistinction does not leave us withoutresources of other kinds.10 Of course, there are also plural nounslike 'The brothers Grimm' which havemultiple reference; but predicates like 'red'are not plurals, so there is no basis here fordeclaring them multiply referential. The ideaof non-plural terms having multiplereference is what strikes me asoxymoronic.

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people instead of to each bald individualseverally is no help in restoring a measure ofsingularity, since the predicate is clearly nottrue of the set of bald men (no set is bald!).The predicate is supposed to be true of themembers of its extension not of the extensionitself. The extension of a predicate (a set) isnot supposed to be the reference of thepredicate; rather, the extension is made up ofthe many objects that are each referred to bythe predicate. Quine's talk of division ofreference would not be appropriate if thereference were the extension, since thatobject is as singular as you could wish. If thereference were literally the extension, thenpredicates would be singular terms byQuine's own lights, purporting uniquely todenote a single object, a set. We need tokeep this distinction clear if we are toappreciate the force of maintaining that apredicate has plural reference: 'bald' refersseverally to this man and that man and theother man, according to the Quineanconception, not undividedly to the set of baldmen. My complaint then, once this point isclarified, is that this is not a natural use of theword 'refer', suggesting ambiguity wherethere ought to be univocity. Frege had it rightin not assigning a semantic role to extensionsfor predicates: he assigned only a sense anda reference, where the reference is afunction from objects to truth-values. Apredicate does not for him refer to theobjects of which it is true, but to the functionthat maps these objects onto the True and theFalse—something close to the notion ofproperty in the intuitive sense. For Frege apredicate is a name (singular term) for thisfunction, just as I am maintaining.11 TheQuinean idea of multiple reference isdistinctly unFregean, a product of conflatingthe 'refers' relation with the 'true of ' relation.

11 Predicates are also rigid designators forme, as they cannot be if taken to designate

their extensions, since these vary fromworld to world. I say that 'red' designatesthe property of redness in every possibleworld, as 'Bertrand Russell' designatesBertrand Russell in every possible world.Here again names and predicates aresemantically analogous. See my 'RigidDesignation and Semantic Value'.

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The general upshot is this: semantics shouldnot employ the relation of set-membershipbetween objects and extensions, but ratherthe relation of instantiation between objectsand properties. A singular sentence is truewhen an object (or sequence of objects)instantiates some property, not when objectsare members of certain sets. Set theory istherefore not the right format for statingsemantic truths. Semantics is not aboutclasses of objects unless it appears to be, aswhen we speak overtly of classes. In effect,Quine brought classes into semantics inorder to oust properties, but he failed to seehow far this could be pushed, notably in thedirection of second-level extensions and theirset-theoretic counterparts. The lesson, Isuggest, is to return to the naive view of howpredicates work: they function to ascribeproperties to objects. This view of predicatesis to the Quinean view what the usual view ofnames is to the second-level extensionview—the natural precursor of monstrousoffspring. Extensions are creatures ofdarkness; or at least lumbering monsters lostin the semantic wilderness.

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4 NecessityAbstract: The view that modal expressionscan be successfully paraphrased by meansof quantification over possible worlds is

rejected on the grounds that such translationsare either circular or inadequate. It is arguedinstead that modal expressions function as'copula modifiers', specifying whether anobject instantiates a property in the'necessary mode' or in the 'contingent mode'.The chapter concludes with a briefexamination of some metaphysical issuesabout modality, including whether itconstitutes a sui generis ontological categoryand whether it is causally efficacious.

Keywords: copula modifier, modal truth,modality, naturalismnecessity, possibleworld semantics, possible worlds,predicate modifier, supervenience,Tarskian semantics

Colin McGinnPhilosophers have been infatuated with thequantifier. Understandably so, sincelogicians showed the power and elegance ofthe predicate calculus. And it is alwaystempting to want to put shiny new tools touse. If we can translate some idiom of naturallanguage into quantifier form we feel weknow how it works; we feel we have tamed it.This is notably so for idioms of existence, asI discussed in Chapter 2: to make anexistence statement is to make anexistentially quantified statement; the word'exists' disappears into its quantificationalparaphrase. But I rejected such a view ofexistence, arguing that existence is bestexpressed as a first-order predicate.Similarly, it has been attractive to many toregard identity as definable quantificationally,by means of Leibniz's law: identity statementssay that every property of x is also aproperty of y, and vice versa. Apparentlysingular statements thus get recast inquantificational form. I also rejected this viewof identity, taking identity to be a primitiverelation expressed by a two-place predicate.

In the case of modal idioms we find a similarappeal to the quantifier, in the standardpossible worlds semantics. To make astatement of necessity is to say that allworlds are thus and so; to make a statementof possibility is to say that some worlds arethus and so. Thus 'Socrates is necessarily aman' translates into 'in every world, Socratesis a man' and 'Socrates is possibly a wiseman' translates into 'in some world, Socratesis a wise man'. Again, what look like singularsentences turn out to be general quantifiedsentences. In the case of identity andexistence the corresponding idioms of naturallanguage have the grammar of predicates,two-place and one-place respectively, whilein the case of modality the idioms involvedlook adverbial or operator-like. But they allturn

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out to be quantificational in their underlyinglogical form. Not surprisingly, I shall also berejecting this view of modality. The infatuationhas gone on too long.

According to possible worlds semantics, wecan replace any occurrence of a modal wordwith a suitable quantificational translation.1We take what looks superficially like anoperator and interpret it by means of anexistential or universal quantifier over 'worlds'—however exactly these entities are to beconstrued. Most of the debate has then beenover what sorts of entities worlds are. But theobjection I want to make to this is that such atranslation is either circular or inadequate;specifically, we need to use the modal notionbeing translated in order to get the translationto come out right. The point is parallel to oneof my arguments against the quantificationaltreatment of existence in Chapter 2, namelythat the required notion of 'having instances'has existence built into it in an unanalysed

form. So let us consider some proposition ofthe form 'possibly p': this is meant to go overinto 'there is a world in which p' or 'for someworld w, p in w'. Now the question I want toask is: does the notion of 'world' here invokedinclude or exclude impossible worlds?Suppose it includes them. Then 'possibly p'will be true if 'p' holds in an impossible world.But that is clearly not the truth condition of'possibly p': a proposition that is necessarilyfalse is true in some impossible world! If Isay 'possibly water is not H 2 O' or 'possibly2 2 5' I speak falsely, but the embeddedstatements are true in some impossible world.So clearly the notion of 'world' must be takento exclude impossible worlds. There seem tobe two and only two ways in which this resultcan be ensured. First, we might say outrightthat 'possibly p' is equivalent to 'in somepossible world, p' or 'for some w, w ispossible and p in w'. But this now

1 I will be limiting myself to this semanticclaim in what follows; nothing I say here willbear on the use of an ontology of possibleworlds for other purposes. The idea I will becriticizing is just the idea that modalexpressions can be successfullyparaphrased by means of a quantifier overworlds. Nor do any of my criticisms dependupon which specific ontology of worlds isadopted; they are intended to apply to allsuch semantic theories, from the most'realist' to the most 'constructivist'.

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contains an explicit use of the word 'possible',which we claimed to be reducing to aquantifier over worlds. In effect, we are nowtreating 'possibly' as a predicate of worlds,not as a quantifier over them. We are notreplacing 'possibly' with a suitable quantifierbut using it to limit the scope of the quantifier.So no analysis has been given of the force of

the modal notion concerned. It might bethought that this is no problem, since we canalways translate the offending occurrence of'possibly' into quantifier form. So let's do that:'w* is a possible world' now becomes 'forsome w, w* w', where 'w' is simply a variableover worlds and 'w*' is a name of someparticular world; we are saying that w* ispossible iff it is identical to some world w. Butnow the problem is whether w is a possible oran impossible world. If the latter, then thetruth conditions are wrong; if the former, thenwe have a new occurrence of 'possible' thathas not been analysed. And obviously it won'thelp to bring in a new variable over worlds toexpress that w is a possible world. Theunderlying point here is exceedingly simple:when we say that 'possibly p' is true we mustbe saying that 'p' is true in some possibleworld, but then we have the quantifier 'someworld' and the word 'possible'; it is not that thelatter has vanished into the former—on thecontrary, the former needs the latter. Whatwe really have in the standard variable 'w' isa restricted quantifier embedding the word'possible', analogous to 'some man' (whichclearly does not analyse the notionexpressed by 'man'). We cannot allow theworld variable 'w' to remain neutral betweenpossibility and impossibility, on pain ofmaking the truth conditions of modalsentences come out wrong. We have tomean possible world or else there will be nonecessities and too many possibilities.

The second way to rule out the impossibleworlds objection is to append to our truthcondition the stipulation 'there are noimpossible worlds'. Then we will be sayingthat 'possibly p' is true iff 'p' is true in someworld w (not explicitly stipulated to bepossible) and there are no impossible worldsin which 'p' might be true. There are twoproblems with this. First, we are again using

a modal term that we have not analysed, viz.'impossible'. We are taking

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'impossible' to be a predicate of worlds andthen saying that it has null extension. But thequestion is what this use of 'impossible'means for a possible worlds theorist forwhom all modal terms are analysable asquantifiers. If we have to take it as primitive,why don't we do the same for modal idiomsgenerally? The second problem is that thesuggested truth condition fails to capture theforce of the original proposition: it is no goodsaying that 'possibly p' is true iff 'p' is true insome world, neutrally understood, and as amatter of fact there are no impossible worlds.That does not give us the idea that 'p' isgenuinely possible, since it leaves open thethought that 'p' might hold in some impossibleworld; and that thought is not closed off bysimply saying there are no such worlds. Thatjust makes the proposition true by a kind ofmetaphysical accident; and it is no lessaccidental if we add 'and there could not beany impossible worlds', as well as introducinganother unexplained modal term 'could'. No,the obvious point is that we must be meaningpossible world when we say that 'possibly p'is true iff 'p' is true in some world, or else thiscondition does not add up to what we need.We have to be ruling out the case in which'p' holds impossibly. Of course, we get thesame kind of problem for 'necessarily': if wesay that 'necessarily p' is true iff for all worldsw, 'p' is true in w, we again have the questionwhether we are including impossible worlds.If we are, then the condition is too strong,because no necessary proposition is trueeven in the impossible worlds: even '2 + 2 =4' is not true in the impossible world in which2 + 2 = 5—but it is a necessary truth nonethe less.2

The point becomes even clearer if we switch

from 'world' to 'state of affairs' or 'maximalstate of affairs', since these terms wear

2 This is assuming that in the impossibleworld in which 2 2 5 it is not also true that 22 4, so that this world is at least consistent.In any case, if there is a world in which it isnot true that 2 2 4, then that proposition failsto hold in all worlds. Similarly, if there is animpossible world in which 2 2 5, then thatproposition comes out possible under thestipulation that possibility is truth in someworld, possible or impossible—which itplainly is not. Obviously, then, we mustrequire that our world quantifier range onlyover possible worlds.

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their neutrality on their sleeves. If we say that'possibly p' is true iff 'p' is true in some stateof affairs, we immediately invite the questionwhat kind of state of affairs—are weincluding a state of affairs in which, say,water is not H 2 O? We have to mean'possible state of affairs', but then we areusing that modal word again. We havebecome so accustomed to using 'world' asshorthand for 'possible world' that we don'tnotice that the notion we need must beconstrued this way: but then the problem isthat we can't explain this occurrence of'possible' by means of a quantificationalparaphrase—there is always a residualoccurrence of 'possible' that refuses to betranslated into the 'for some w' quantifier.Ironically, it is the very use of 'possible' in thecontext 'possible world' that resists thepossible worlds treatment. And notice that mypoint here is not that this treatment takesmodality as primitive and that this isobjectionable per se; my point is that thequantificational approach claims not to betaking modal words as primitive and yet in theend it has to. Just as the quantifier treatment

of existence claims to be able to give anaccount of the notion of existence wherever itmay occur, so the quantifier treatment ofmodality claims such coverage. But in bothcases it is only a disguised use of the verynotion in question that gives the would-beanalysis an appearance of working. Thelocution 'has instances' must mean 'hasexistent instances' and the locution 'in someworld' must mean 'in some possible world'.And the question is what these words meanin these occurrences, with the threat ofregress that ensues.

The standard parallel with temporal discoursemasks this problem for the quantificationaltreatment of modal terms. Suppose we saythat 'occasionally p' is true iff for some time t,'p' is true at t, and 'eternally p' is true iff for alltimes t, 'p' is true at t. Then certainly we areusing the notion of a time here in a way weare not analysing; but that is no problem,since that notion is neutral with respect to thenotions of 'occasionally' and 'eternally'—andthe claim is not that we can always replacetemporal locutions such as 'a time' byquantifiers. The trouble with the modal caseis that we have the notion of impossibility tocontend with, which forces us

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to reintroduce the locutions we are trying toparaphrase; there is no analogue for this inthe temporal case. It is not as if we have tosay 'for some occasional time t' in analysing'occasionally p'. But we do have to say that'possibly p'is true iff 'p' is true in somepossible world. The point about excludingimpossible worlds simply makes vivid theneed to speak of possible worlds inspecifying modal truth conditionsquantificationally; the supposedly neutralword 'world' cannot do the job. To be modallyneutral in the use of 'world' simply leaves it

open whether 'p' is really possible.

This objection has nothing to do with theontological status of possible worlds—whatkind of entities they are, whether they aremerely useful fictions, and so on. It appliesno matter what view of possible worlds youchoose to adopt. It is a strictly semanticobjection concerning the project oftranslating all occurrences of modal wordsinto quantifiers. And as far as I can see, it isconsistent to hold that there are possibleworlds in as strong a sense as you like andalso accept my argument, so long as youdon't go on to hold that modal terms arereducible to quantifiers over such worlds.3The semantic role of modal terms cannot bethat of quantifiers, since such terms have tobe taken as unanalysed even given thequantificational paraphrase. As so often inphilosophy, the price of sufficiency iscircularity.

What alternative might be offered? Thereseems little prospect of a straightforwardpredicate treatment of modal expressions,since this is not how they function in naturallanguages; they seem far more adverbial oroperator-like. One approach that has beendeveloped is that modal words function aspredicate modifiers, like

3 So David Lewis can keep his possibleworlds, so far as my argument isconcerned, just as long as he does notemploy them as the domain for quantifiersintended to translate modal expressions:see his On the Plurality of Worlds. Andthere are clearly other uses to which anontology of possible worlds may be put. Fora further critical discussion of this ontologysee my 'Modal Reality'.

end p.74

'large'.4 I think this approach is on the right

lines, but I want to modify it in a small butcrucial respect. Consider 'Socrates isnecessarily a man'. On the predicatemodifier theory, the logical form of thissentence is that the modal adverb operateson the predicate to produce anotherpredicate, as with 'Socrates is a large man'.Modal words express functions fromproperties to properties: they take anon-modal property as argument, and theyproduce a modal property as value. Just asthere is the property of being a man, so thereis the property of being necessarily a man orcontingently a man. Accordingly, we can saythat our original sentence means somethinglike 'Socrates has the property of necessarilyhaving the property of being a man'. Inaddition to there being all the usual propertiesthere are the modal properties that can begenerated from them. Now I am a littlesuspicious of there being all these extramodal properties in addition to the usualones—this seems like an extravagant way tohandle the data—but I do not want to objectto the predicate modifier treatment on thatground alone. My objections have more to dowith explanatory adequacy. First, I believethere is another treatment that bettercaptures the intuitions behind the predicatemodifier treatment, which I will outline soon.Second, I don't think the predicate modifiertreatment quite captures the intended forceof the sentences it sets out

4 See David Wiggins, 'The De Re "Must": ANote on the Logical Form of EssentialistClaims'. There are also operatorapproaches that treat modal expressions asone-place sentence operators, modelledupon the operators standardly employed inmodal logic: see, for example, ChristopherPeacocke, 'Necessity and Truth Theories'. Iwon't have much to say about this approachhere, except to indicate later why I find theview I favour preferable. Let me just remark

that there is nothing sacrosanct about theformulas of modal logic as a framework fora theory of the semantics of naturallanguage, or as the basis of a goodmetaphysical account of modality. In fact, Ithink that modal logic, modelled as it is onthe sentence operators of propositionallogic, distorts our understanding of modalthinking. We should certainly notautomatically suppose that the structures ofmodal logic properly represent the nature ofmodal thinking; they embody a theory likeany other. Similarly, the standard treatmentof 'not' as a sentence operator is itself atendentious theory of the semanticfunctioning of 'not'; it is not the inviolabletouchstone for the correctness of any othersemantic proposal about negation. (I say allthis to loosen the hold of any prejudices thatmight come naturally to someone steeped inthe forms of classic propositional calculus.)

end p.75

to analyse—and which the other viewcaptures perfectly. So I am going to modifythe predicate modifier treatment slightly,while sticking to its general spirit. The reasonthe predicate modifier treatment does notquite capture the force of a modalproposition like 'Socrates is necessarily aman' is this: it leaves open the way in whichSocrates has the property predicated of him.What we are told is that Socrates has theproperty of being necessarily a man, wherethe copula here is modally neutral: that is,Socrates is said to have a modal property ina modally neutral fashion. So we canintelligibly ask whether Socrates has thismodal property necessarily or contingently.But the original statement looks as if italready settles that question: Socrates hasthe property predicated of him in the mode ofnecessity.5 But on the predicate modifiertreatment the sentence says merely thatSocrates neutrally has a certain (modal)

property. As it were, the modality of thepredication gets absorbed into the modalityof what is predicated. But, intuitively, that isnot how it is with the original sentence; itdoes not leave open the modality of theascription. What this suggests is that'necessarily' modifies what precedes it in oursample sentence and not what follows it—thecopula 'is', not the predicate 'a man'. Bymodifying only the predicate the modality ofthe ascription is left open, but by modifyingthe copula the modality of the attribution

5 My point here is not that 'necessarily'implies the iterated 'necessarilynecessarily'; it is that 'Socrates isnecessarily a man' settles the question ofthe mode of instantiation of manhood inSocrates. The predicate modifier treatmentlimits the scope of the modal expression tothe predicate term that it modifies andleaves the copula unaffected; whereas theapproach I favour brings the copula into thescope of the modal expression, thus settlingthe question of mode of instantiation. On myapproach, the predicate itself isn't strictlywithin the scope of the modal expression atall, any more than the name is; we couldtherefore as well write 'concerning Socratesand the property of being a man, the formernecessarily has the latter'. Of course, if thepredicate modifier position is interpreted tomean that the predication, including thecopula, is what is modified, then the view isvirtually indistinguishable from the copulamodifier theory. What I am opposing is theidea that modal expressions modifypredicates, i.e. property terms, as 'large'surely does. The lambda abstractionnotation clearly suggests this latter type ofview, since 'necessarily' here operates on asingular term (definite description) of aproperty, as in 'Nec[(λ x)(Man x)]': seeWiggins, 'The De Re "Must": A Note on theLogical Form of Essentialist Claims'.

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is pinned down. If we indicate the scope ofthe modal modifier with a dash, then we canparse the sentence either as 'Socrates isnecessarily-a-man' or as 'Socratesis-necessarily a man'. The first way ofparsing it ascribes a modal property toSocrates but in a neutral way, while thesecond ascribes a non-modal property in amodally committed way. Thus the secondparsing settles what the first leaves open, andhence corresponds more closely to thesense of the original. My proposal, then, is todevelop the approach that settles what oughtto be settled by any good paraphrase. Thisapproach I shall call the copula modifiertheory, as opposed to the predicate modifiertheory.

I can sum up what I just argued by sayingthat in a modal sentence the copula is notmodally neutral. And isn't this exactly the waywe read such sentences? Don't theyprecisely say that a property is had in themode of necessity or in the mode ofcontingency? We start by remarking thatSocrates is a man and then, when ourthoughts turn modal, we want to knowwhether this property inheres in Socrates inthe necessary way or in the contingent way:how is he a man? What we are interested inis mode of instantiation. Modals are modes.To say that modal words modify the copula isthe linguistic counterpart of the ontologicaldoctrine that modality is a matter of thestrength of the instantiation relation: does theobject in question instantiate the predicatedproperty only accidentally or is this a matterof logical or metaphysical necessity?6 Thus,according to the copula modifier theory, wedo not work with an ontology of modalproperties; rather, we take the stock ofnon-modal properties and think of them aspossessed in different modes. If you like, the

instantiation relation is the only thing thatgives rise to modal properties—the propertiesof being instantiated necessarily orcontingently. There are two modes ofinstantiation and a fund of non-modalproperties

6 What of 'a is possibly F', where this canbe true even though the object doesn'tactually have the property? In this case,obviously, we cannot be saying in whatmode the object has the property, since itdoesn't have it. Instead, we are saying thatthe object possibly instantiates the property,where again the modal expression modifiesthe copula, as in 'Socrates possibly-is aman'.

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instantiated in these two modes, instead ofthere being a collection of specifically modalproperties corresponding to the originalnon-modal properties. On this conception,modality is really not like 'large' and otherpredicate-modifying adjectives and adverbs.These expressions do not work by modifyingthe copula but by generating new properties.It is not that 'that is a red kayak' is tantamountto 'that reddishly instantiates being a kayak';rather, the former means something like 'thathas the property of being a red kayak'.Similarly for attributive adjectives like 'large':they don't tell us how something instantiatesthe property they modify; they tell us what(complex) property something has—as itmight be, the property of being a large bee.The metaphysical picture here is that thereare objects and their properties, includingbeing a red kayak and a large bee, and thenthere is the modality with which theseproperties are possessed. The copulamodifier theory is meant to answer to thispicture.

There is clear linguistic support for the

theory, since grammatically we often expressmodal claims precisely by modifying thecopula. Thus we say 'Socrates must be aman' and 'Aristotle could be a farmer' and'Plato happens to be a philosopher'. But thereare no parallel constructions for 'large' and'red' etc. When we convert 'is' to 'must' weincorporate the modality right into the copulagrammatically, and this is the natural way toexpress modal claims outside of stiltedphilosophical usage. Just as we expresstense by copula modification, as with 'was'and 'will be', so we express modality this way.The ease and naturalness with which we dothis is evidence that modality is conceived asmode of instantiation. Incidentally, this alsoshows that the copula is not semanticallyredundant, since it exists in surface structureto be modified: given that there are modalwords in the language, we would expect thatpredicative copulation would rise to thesurface to serve as a lexical item to bemodally qualified—and this is exactly what wefind. We have the modally neutral copula 'is'and alongside it the modally committedcopula words 'must', 'could', etc. Naturallanguage is thus in favour of the copulamodifier theory and the metaphysical pictureit implements.

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It might be objected that this account workssmoothly enough for de re uses of modalwords, but how does it handle de dicto uses?What about 'it is necessarily true thatbachelors are unmarried males' and 'thestatement that 2 2 4 is necessary'? Surely inthese sentences the modal word is notfunctioning to modify the copula in the de restyle. My answer to this is that all such usesshould be taken as modifying the copula as itattaches to the truth predicate. The canonicalform of these uses is: 'the proposition that pis necessarily true'—consisting of a singular

term for a proposition, the copula, thecopula-modifying modal, and a predicate'true' ascribed to the proposition denoted.The logical form of this is exactly the same asthat of 'the teacher of Plato is necessarily aman'; the difference lies in the kind of entitydenoted—individual or proposition—and thenature of the predicate. So on this account'necessarily' works in exactly the same wayin de re and de dicto occurrences. When wesay of a proposition that it is necessary weare predicating truth of it in the mode ofnecessity; just as when we say of anindividual that it is necessarily thus and so weare predicating a property of that individual inthe mode of necessity. The difference issemantic ascent, with the accompanyingneed for the truth predicate. Truth is aproperty that can be possessed bypropositions in the mode of necessity orcontingency, just as regular properties caninhere in ordinary objects in these twomodes. I think this is intuitively right and itunifies the de re and de dicto in a pleasingway. In a certain sense both uses come outas de re, since they serve to attributeproperties to objects in different modes—it isjust that in the case of de dicto necessity theobject is a proposition and the property istruth. There is only one 'must', but it cangovern different types of property; in allcases its logical function is copulamodification. Thus we can say of theproposition that bachelors are unmarriedmales that it has the property of being trueessentially—where this gets glossed ashaving the truth property in the mode ofnecessity.

It follows, of course, that such uses of modalwords do not work as sentence operators.Superficially operator-like occurrences get

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translated into one or other of the two forms

mentioned, most likely into themeta-propositional form with the attachedtruth predicate. Syntactically, we can stillemploy modal words as if they weresentence operators, functioning like negationin classical logic, but semantically they arecopula modifiers always. I take it the neededtranslations are readily produced and entirelynatural. Indeed, it is hard to know what itcould mean to say that necessarily bachelorsare unmarried males except that thecorresponding proposition is necessarilytrue—and this lends itself directly to thecopula modifier treatment. There is a clearsense, therefore, in which the standardformulas of modal logic, with their one-placesentence operators, are not a goodrepresentation of natural languagemodality—if the present account is on theright lines.7 Not only are modal words notquantifiers over worlds; they are notoperators on open and closed sentences—unless this is taken to be semanticallyequivalent to the copula modificationtranslations I have proposed. We certainlyshould not simply assume that the sentenceoperator treatment of modality enshrined inmodal logic is sacrosanct—that is a theory ofnatural language like any other. However, thetwo theories are clearly similar in spirit, atleast as contrasted with the quantifier theory;I view the copula modifier theory as a moreexplicit and fine-grained expression of theintuitions that also encourage the sentenceoperator theory.

According to the view I am defending,instantiation comes in modes, the necessarymode or the contingent mode. It is alwaysone or the other, though a predicativestatement might be neutral about which it is.If I just say 'Socrates is a man' I do notcommit myself to the mode of instantiationinvolved—the copula is modally neutralhere—but the instantiation itself is always

either necessary or contingent.

7 Note that Quinean worries about opacity,quantification, and modal operators aresidestepped on the present approach, sincemodal expressions never generateintensional contexts—they never havescope over terms or predicates orsentences, even for so-called de dictomodality. Only the copula is governed bymodal modifiers. Treating modality in termsof sentence operators obviously does courtthese objections, however.

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The statement is well-formed and truth-evaluable, despite its modal neutrality. Thuswe can say two things here: (a) it is not that'is' is an incomplete symbol when it occursunmodified, since the sentences in which itoccurs have perfectly determinate truthconditions; but (b) instantiation itself comesin (at least) two forms, depending upon themodality involved. This may remind us of thetopic of identity, where it has been held that ''is an incomplete symbol and that identityitself (the relation) does have many forms. Irejected both of these doctrines aboutidentity in Chapter 1, but it would not beincorrect to say that I hold a version of thelatter doctrine for instantiation. Whereas, asFrege said, identity is given to us in such aspecific way that various forms of it are notconceivable, it seems to me that instantiationis given to us in such an open-ended waythat various forms of it are conceivable. If weare told that x instantiates F, we can alwaysask how x instantiates F—in what mode. Themode is, as it were, internal to theinstantiation. Instantiation is a kind ofdeterminable whose determinate forms arethe modal modes. The linguistic counterpartof this is the fact that the copula admitsmodal modification in the form of 'must' and'could be'. The identity sign admits of nothing

corresponding to this.

I have suggested that modal words functionas copula modifiers: but how does this workout in the semantics? What kind of semanticsis appropriate for this general conception?More specifically, how do we contruct aTarski-style semantics for this view? (I amnot saying that the proposal stands or fallswith the availability of such a semantics, but itis worth asking what the general form of aTarskian semantics might be.) Withoutundertaking a rigorous treatment, I think it isclear enough what the general form of theaccount will look like. The basic shape of theaxiom will be simply this:

x satisfies 'is necessarily F' iff xnecessarily satisfies 'F'.

And the axiom for 'possibly' will follow suit.Just as with the standard axioms in a truththeory, we simply disquote the object-language expression and then use it in themetalanguage in the same way it is used inthe object-language, except that now it iscombined

end p.81

with semantic vocabulary. Given the methodsthat have been developed to handle modaloperators disquotationally, as well aspredicate modifiers, there seems no difficultyof principle about extending these methods tothe copula modifier account.8 Basically, weuse the disquoted modal words as copulamodifiers in the metalanguage, combinedwith the semantic term 'satisfies', in order tointerpret the object-language modal terms.This is really the easy part. The problems, ifthere are any, lie with the Tarskian paradigm—particularly, whether it is revealing enoughabout the idioms it seeks to interpret. But myaim is not to defend Tarskian semantics, onlyto show that the present theory can be slotted

into this general framework.

Finally, what should be said about theiteration of modal locutions? Evidently it iswell-formed to say such things as 'Socratesis necessarily necessarily a man' and'Socrates is necessarily possibly aphilosopher'—and indeed these sentencetypes exemplify the characteristic axioms ofmodal systems. I have said that modalexpressions modify the copula, but is thistrue of iterated modal expressions? Well, ifwe take the view literally, then we would haveto say that each iteration requires its owncopula to modify—as in 'Socrates isnecessarily is necessarily a man'. But this ispatently ill-formed; so we had better not takethe view quite so woodenly. The naturalamendment, then, is simply that the modalword most proximate to the copula modifiesit, while the iterated modal words modify theresult of this modification—as in 'a necnec-is F'.9 This is essentially the sameconception that is standard for the sentenceoperator view of modal words, except now weare applying it to the copula modifier view.We regard the embedded modal words aswithin the scope of the outer modal words, sothat changes of scope can induce changesof truth-value. So far as I can see thesemantics is straightforward and theunderlying conception sound. In fact, there isvery little to choose, in the present respect,between

8 See Peacocke, 'Necessity and TruthTheories'.9 If we view the initial 'necessarily' asforming a modal copula, as with 'must', thenwe can still say, simply, that all modalexpressions modify the copula, since a newmodal copula is formed by successiveiterations of 'necessarily'.

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this view and the predicate modifier view;

both will handle iterated modalities in thesame general way.

I now want to address some moremetaphysical issues about modality, usingthe view just sketched as background. Sincemy aims in this book are primarily logical andsemantic, I shall not pursue these broaderquestions at any length; but I think it is worthalluding to the implications for metaphysicsand epistemology, so that we don't run awaywith the mistaken impression that the presenttopics are cut off from broader concerns.For the most part, I shall simply state, withoutmuch in the way of argument, what I think thebroader implications are.

(i) According to the present view, modalitybelongs to a special ontological category: itconsists neither in objects (unlike thepossible worlds theory) nor in properties(unlike the idea of modal properties that goeswith the predicate modifier view), but ratherin items I have called modes. Intuitively,these modes are ways of binding objects totheir properties, where the binding can behard or soft, rigid or pliable. So an inventoryof the 'furniture of the world' needs to includethese sui generis items and not insist thatthey belong to antecedently recognizedcategories of entity. There are objects,properties, and modes in which objects haveproperties. Presumably, these modes areneither mental nor physical, but rather'logical', for want of any better term. Wemight say they are topic-neutral, like causalrelations, though this is not to say very much.They are logical in somewhat the way identityis logical—highly general, not specific to anyparticular category of objects. And of coursethey are the subject-matter of what we callmodal logic. They are as logical asinstantiation itself, the ontological counterpartto predication. They are also objective, in thesense that they do not depend upon minds

for their existence (there were essential andaccidental properties before human mindsever existed). Modes are objective, logical,real: they are what they are and not someother thing.10

10 See my 'Modal Reality' for more on themetaphysics and epistemology of modality.

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(ii) These modes give rise to epistemologicalperplexity. How do we know that a property isnecessary or contingent? We can know thatSocrates is a man by ordinary empiricalmeans, but how do we come to know that heis necessarily a man? We certainly do notcome to know this by sensory perception ofthe necessity in question. Such knowledgeappears a priori if any knowledge is, andhence a problem for empiricist (and causal)epistemology.11 There are many ways ofresponding to this problem, which I will notattempt to go into; what is clear is thatmodality is a prima-facie threat to the usualkind of naturalistic-causal-empiricist theoryof knowledge. This is not, however, in itself areason to doubt that modality is real; it simplylocates a genuine gap in our understandingof human knowledge.

(iii) Do the modal modes have a hiddenessence, in the way natural kinds like waterdo? I think it is clear that they do not—anymore than identity and existence do. It is notthat modal words pick out modalities bysuperficial marks, so that we might go on todiscover what their underlying essence is.Modes are not natural kinds in this sense.They are transparent in the sense that theirnature is given in the concepts we have ofthem. We might be able to go on and give ametaphysical account of their nature, but wecannot go on to give a scientific account ofit: we are not going to discover the truth of'necessity X', for some empirical essence X,

in the way we have discovered the truth of'water H 2 O'. Modal concepts are not labelswaiting for an empirical theory of theirreference. This is generally the case for thelogical concepts investigated in this book.

(iv) Modal truths seems to be supervenient onnon-modal truths. If x and y are exactly alikein all non-modal respects, and x isnecessarily F, then y is also necessarily F.For example, if x is necessarily human, andy is non-modally indistinguishable from x(say, a molecular duplicate with the sameevolutionary origin),

11 On the analogous problem in philosophyof mathematics see Paul Benacerraf,'Mathematical Truth'; also my 'A Priori andA Posteriori Knowledge'.

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then y is also necessarily human. And thisholds as much for de dicto modality as for dere modality, since the logical form andconceptual content of a propositiondetermine its modal status. Any propositionindistinguishable from 'bachelors areunmarried males' in non-modal respects isalso a necessary truth. The modal is notreducible to the actual, but it is stronglydependent on it. In this respect, the modalresembles the moral, where we have acomparable supervenience of the evaluativeon the descriptive. This means that there isno analogue in the case of the modal for thealleged possibilities of zombies and invertedspectrum in the case of the mental. That is,we cannot conceive of a non-modallyspecified duplicate y of a modally endowedobject x that wholly lacks any modalproperties, and we cannot conceive of sucha duplicate that inverts the modal propertiesof its non-modal twin. For example: therecould not be a duplicate of me with noessential properties at all, given that I have

many such properties; and there could notbe a duplicate of me that was (say)contingently human and necessarily aphilosopher, given that I am actuallynecessarily human and contingently aphilosopher. So there can be no'conceivability argument' for something like'modal dualism': here supervenience iswritten into our understanding of theconcepts.12 We reel at the thought that themodal might float free of the actual in theseways. And such supervenience is quitesurprising when you reflect on it, since themodal is no mere restatement of the actual;modal truths are genuinely a new class oftruths.

12 There is thus no Kripke-style argumentsuggesting some sort of contingent linkbetween modal and non-modal facts, unlikewith the link between mental states andbrain states: see Naming and Necessity,144 ff. When God created the non-modalfacts he thereby fixed the modal facts too.For example, when God created me ahuman being it was already settled that I benecessarily a human being; he could notmake something of a certain natural kindand then be free to decide whether being ofthat kind is to be necessary or contingent.This is analogous to creating a situation withcertain descriptive characteristics andasking about the moral characteristics ofthe situation: once God does the non-moralwork he is not free to decide what the moralstatus of the situation is—any more thancreating bachelors leaves him free todecide whether bachelors are unmarried ornot. In these cases, supervenience seemsassured a priori.

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There is no possibility of reduction here, butthe supervenience looks solid as a rock,scarcely in need of argument.

(v) From a causal point of view, modality isepiphenomenal. My weighing 146 lb. affectsmy causal powers in obvious ways, butwhether I weigh 146 lb. necessarily orcontingently makes no difference at all to mycausal powers. Thus the modality cannotmake any contribution to the explanatoryforce of my having that weight. And similarlyfor all my other properties. Only the actualcan be causal.13 In this respect, also, themodal resembles the moral. Anyone who tookcausal potential to be a test of reality wouldtherefore have to declare modes unreal;better, I think, to abandon that test. It is anobjective fact about me that I am necessarilyhuman, but that fact makes no difference tomy causal profile; so some objective factsare non-causal. The modal is not part of thecausal order, though it is no worse off forthat. And this is the underlying reason thatmodalities are not perceptible: they cannotcause themselves to be sensorily perceived.

(vi) Given all this, it is not surprising thatmodality is often suspected of being'non-natural' and hence a potential candidatefor 'elimination'. Without trying to argue thepoint here, my own position would be thatmodality is simply a counter-example to thistype of naturalism, so that the project ofelimination is unwarranted. The 'queer' ishere, and we need to learn to live withit—even if we may not be able to bringourselves to love it.14 Modalities are part ofwhat there is, problematic as they may be tocertain philosophical perspectives.

13 What about dispositions? Aren't theymodally characterized and yet causallyefficacious? This is a difficult question, but Iam not intending to take a stand on it here; Iam discussing so-called metaphysicalnecessity. My claim is that which of myproperties is essential to me makes nodifference to how the world works causally.

14 For this general point of view, as appliedparticularly to ethics, see my Ethics, Eviland Fiction, chs. 1 and 2. My position here,as elsewhere, is that certain phenomenagenerate mysteries that we have no inklinghow to solve—but that this is not a sufficientreason to deny their existence. It may bethat the mystery stems simply from ourconceptual and theoretical limitations: seemy Problems in Philosophy, especially ch.6.

end p.86

5 TruthAbstract: Taking disquotation to be theessence of truth, this chapter argues thattruth is that unique property of a propositionfrom which one can deduce the fact statedby it. This position is called 'thickdisquotationalism', for though disquotationalin nature, truth is nevertheless a robustproperty. The chapter concludes with a briefdiscussion of the metaphysics of truth: truthis a primitive, non-natural property thatsupervenes on the facts and is constitutive ofreality.

Keywords: definition, disquotation,disquotationalism, inference,supervenience, theory of truth, truth

Colin McGinnDisquotation is the essence of truth. Thismuch is widely accepted.1 It is less clearquite what this tells us about the concept oftruth. My aim in this chapter is to articulateexactly what the disquotational insightimplies, and does not imply, about what it isfor a proposition to be true—what followsfrom it and what it reveals about the innernature of truth. I think the disquotationalproperty of truth has been widely

misinterpreted, and that the correctinterpretation of it shows truth to be a farmore interesting concept than has beenrecognized. Specifically, I am concernedwith the question of whetherdisquotationalism entails something deservingthe label 'deflationism'. The view I shalldefend, which I call thick disquotationalism,holds that there is something importantlywrong about the deflationary interpretation.Truth is a more robust property thandeflationism allows, despite its disquotationalessence.

Truth can be predicated of both linguisticitems (sentences) and what they express(propositions). This difference will notconcern me in what follows. For convenienceand purity I will take truth to apply tointensional items like propositions or beliefs,so that the

1 See Quine, Philosophy of Logic, 10 ff. AsQuine famously writes: 'No sentence is truebut reality makes it so. The sentence "Snowis white" is true, as Tarski has taught us, ifand only if real snow is really white. Thesame can be said of the sentence "DerSchnee ist weiss"; language is not the point.In speaking of the truth of a given sentencethere is only indirection; we do better simplyto say the sentence and so speak not aboutlanguage but about the world' (pp. 10-11).Many writers have given voice to the samesentiment: Frege, Wittgenstein, Tarski,Ramsey, Strawson, and others. For a usefulcollection of readings see Simon Blackburnand Keith Simmons, Truth. I will glide lightlyover this large literature in this chapter,assuming that the reader is familiar with thegeneral shape of it.

end p.87

question of their semantic interpretation isirrelevant. Given this, 'disquotational' isn't

quite the right word, since only words can bequoted or disquoted: 'dis-intensional' or'dis-representational' might be moreaccurate. But I will stick with 'disquotational',warning that it must not be taken too literally.Using roman 'p' as the name of a proposition,then, we can express the disquotationalproperty of truth in the following familiar way:'p is true iff p', i.e. 'the proposition that p istrue iff p'. Thus the truth predicate takes usfrom something referring to a proposition tosomething referring to what that propositionis about. Analogous general principles canbe formulated for satisfaction and reference,as in: 'F is true of x iff Fx' and 'a refers to biff a= b', where again the roman letters referto concepts. My question, then, is exactlywhat the significance is of the truth—indeedthe analytic truth—of these biconditionals:what do they tell us about truth, satisfaction,and reference? Focusing on truth, what isthe concept of truth such that thedisquotational principle holds of it? What is itabout truth that makes disquotationalismtrue? But before I get to this, I want to makea few remarks about competing theories oftruth and how they run afoul of thedisquotational property of truth.

It can be quickly seen that the classiccoherence and pragmatist theories of truthare committed to idealism of some sort by thedisquotational character of truth, andidealism is not something one wants to becommited to just by virtue of one's analysis ofthe concept of truth.2 This is because it isfacts about beliefs or desires and actions thatconstitute truth according to these theories.Thus the coherence theory says that p is trueiff the belief that p coheres with other beliefs,and the pragmatist theory says that p is trueiff the belief that p leads to the satisfaction ofdesires or to successful

2 I mean here, not the nature of truth, but

the meaning of the word 'true'. Possibly, assome have argued, notably MichaelDummett, the nature of truth dictates an'antirealist' conception of the world. I am notintending to rule this out here (though I havecriticized it elsewhere: see my Knowledgeand Reality); my point here is that theordinary sense of the word 'true' should notdictate an idealist philosophy—on pain ofmaking idealism excessively easy toestablish.

end p.88

action. But now if we substitute in thesebiconditionals the disquoted sentencelicensed by the disquotation principle we getthe result that facts about the world areconstituted by beliefs and desires. Forexample, we start by saying: 'the belief thatsnow falls from the sky is true iff the beliefthat snow falls from the sky coheres withone's other beliefs'. Then, by disquotation,we can substitute to derive the following:'snow falls from the sky iff the belief thatsnow falls from the sky coheres with one'sother beliefs'. But this makes snow's fallingfrom the sky consist in something aboutone's beliefs—which is a form of idealism.Snow could surely fall from the sky even ifthere were no beliefs in the world to coherewith each other. So the biconditional cannotpossibly express an analytic truth, and itneeds to if it is to claim to be a definition oftruth. Similarly for the pragmatist theory: itmakes snow's falling from the sky consist in afact about human desires and actions—which it does not. To say that snow fallsfrom the sky is not, failing idealism, to saythat the corresponding belief coheres withother beliefs or that it leads to desiresatisfaction. There is simply no analyticconnection here.

That was the simple way to make the point,but it is open to a natural reply: why not make

the two theories conditional on the existenceof beliefs and desires? Thus we might say:'given that there is the belief that snow fallsfrom the sky, that belief is true iff it cohereswith other beliefs', and similarly for thepragmatist theory. Then we only get the resultthat, given the existence of an appropriatebelief, snow falls from the sky iff the beliefthat it does coheres with other beliefs—andthis does not commit us to idealism. Nolonger are we making the existence of thefact depend upon the existence of thecorresponding belief. But this only postponesthe problem, because we are still saying thatsnow's falling from the sky consists in thecoherence of beliefs, or the satisfaction ofdesires—and these are still mental facts. Weare still committed to supposing that snowcannot fall from the sky unless there iscoherence among beliefs or satisfaction ofdesires—even though we have made thedisquotational biconditionals conditional onthe

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existence of beliefs and desires. Of course,proponents of these theories often had anidealist agenda; what I am saying is that thisis built right into their theory of truth, once wetake notice of disquotation. And we surelydon't want idealism to follow directly from ourdefinition of truth alone.3

The correspondence theory has a differentkind of problem. Suppose we say, 'p is trueiff p corresponds to the fact that p'. Then thequestion is why it is only the fact that p that pcorresponds to, and not, say, the fact thatnot-p. For example, we naturally say, 'theproposition that snow falls from the skycorresponds to the fact that snow falls fromthe sky', taking the correspondence relationto relate that proposition to that fact and tothat fact alone. But why not say that there is

another correspondence relation that relatesthe proposition that snow does not fall fromthe sky to the fact that snow does fall fromthe sky? There surely is such a relation: it isthe relation, not of truth-maker, but of falsity-maker. For any truth-makingcorrespondence relation there is a falsity-making relation—the one that maps factsonto the negations of the propositions thatthey make true. So we can say that theproposition that snow does not fall from thesky corresponds to the fact that snow doesfall from the sky—in the sense that there is amapping from fact to proposition accordingto the making-false rule. Just as there is afunction from facts to true propositions, sothere is a function from facts to falsepropositions. But clearly that is not thecorrespondence relation we need when weaffirm the correspondence theory of truth: weneed the correspondence relation that takesus from propositions to their truth-makers,not their falsity-makers. So let us amend thetheory as follows: 'p is true iff p correspondsto a fact that makes p true (not false)'. But ofcourse now this is blatantly circular, since ituses the concept of truth on the right-handside. The trouble is that the neutral notion ofcorrespondence lets propositions and factsstand in the wrong kinds of

3 In any case, my main point is that suchtheories of truth are committed to idealism,like it or not.

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relations to serve the purposes of thecorrespondence theory; but if we tie thecorrespondence relation down in the rightway we have to stipulate that it is the relationthat holds when a fact makes a propositiontrue—which uses the concept of truth again.Correspondence has to be understood astruth-making correspondence or else it won'twork. This explains the air of triviality that

surrounds the correspondence theory, andhence its apparent undeniability: it implicitlybuilds the idea of truth into the notion ofcorrespondence. Of course, if we read thecorrespondence theory as simply a windyway of asserting disquotationalism, thenthere is no problem; but if the notion ofcorrespondence is to do real work then wecannot avoid the question which sort ofcorrespondence—and it will have to bedefined as the truth-making kind.4 But thereis no interest in a theory that says 'p is trueiff p corresponds to the fact that p in such away that that fact makes p true'. To put thepoint more generally: if we say that p is trueiff pR x, for some relation R and entity x,then we need to know that R maps p onto theright x, since there are many relations thatmap propositions onto entities (e.g. theproposition that snow falls from the sky mapsonto the fact that I am sitting at my desk,since there is the relation of being typed by aperson sitting at a desk that relates thatproposition to that fact). But what is it thatselects the relation that intuitively constitutesthe truth of the proposition in question? If wesay it is the truth-making relation, we have acircle; but it is hard to see what else we cansay to avoid this circle. Certainly thecorrespondence theorist owes us an answerto this question or else his theory is quiteunexplanatory.

4 Other types of theory have advertisedthemselves as correspondence theories—those that make use of a notion ofrepresentation, by way of either thereference of terms or the expression ofstates of affairs by whole sentences. I amnot trying to dismiss all such theories bymeans of the argument given in the text; Iam speaking only of correspondencetheories that invoke a correspondencerelation between sentences and facts in theway specified. I have no objection to

invoking reference relations in giving truthconditions; nor am I objecting to theoriesthat say such things as that a statement istrue if and only if the world is as it isrepresented as being.

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In the light of these problems, and manyothers I have not mentioned, but which areonly too familiar, we do well to explore theprospects of the disquotational theory.Maybe registering the disquotationality oftruth is all we need to say about truth to havea satisfactory account of its nature. This is aview that has been widely held and I am verysympathetic to it; but I think that the realimport of the view has never been properlyarticulated—the task to which I now turn.

There has been a standing tendency tosuppose that the right and left sides of 'p istrue iff p' express the same proposition, thatthey say the same thing. This has fuelled anumber of conceptions of truth that go bysuch names as 'the redundancy theory', 'thereassertion theory', 'the pseudo-property/predicate theory', 'thedisappearance theory'. The thought behindthese slogans is obvious: if 'p is true' and 'p'express the same proposition, then theformer expresses no more than the latter,and the latter contains no predicatewhatsoever that is applicable to propositions.The concept of truth gets swallowed up bythe proposition to which we apply it. Thus weget the idea that to apply this concept to aproposition is simply to affirm the proposition,that 'true' is redundant, that it does notexpress a genuine property, that itdisappears under analysis. To use theconcept of truth is just an indirect way to saysomething you can say without it—somethingnot about propositions but about whatpropositions are about. When I say that theproposition that snow falls from the sky is

true I am simply saying something aboutsnow, namely that it falls from the sky; thereference to a proposition cancels out, asdoes the impression of a special kind ofproperty expressed by 'true'. Truth is simplya way to go from outside a proposition toinside it (so to speak)—a device of semanticdescent: disquotation entails disappearance.My argument will be that this thesis ismistaken: disquotation does not entaildisappearance. If we call the disappearancethesis 'thin disquotationalism', then my ownposition

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can be called 'thick disquotationalism':disquotation with a robust truth property.

What I primarily want to claim is that the leftside expresses something logically strongerthan the right side, so that they cannot besynonymous. The first reason for saying thisis straightforward and I think uncontroversial,though its implications are sizeable (as I shallargue): the logical form and ontologicalcommitments of the left are different fromthose of the right. The left side has the logicalform 'F a', a one-place predicate 'true'attached to a singular term for a proposition(or other truth-bearer); whereas the right—though it may have this logicalform—typically does not. The left refers to aproposition and thus is ontologicallycommitted to such, while the right makes nosuch reference and has no suchcommitment: it refers to snow and whitenessand suchlike things.5 Therefore they cannotexpress the same proposition: for ifpropositions p and q have different logicalforms and different ontological commitments,then they cannot be the same proposition.The plain fact is that the left side ascribes aproperty to something that the right does not;as I would put it, the left contains a predicate

that denotes a property that the right does notcontain, even implicitly. Thus the left hasentailments that the right does not have; it islogically stronger in that it entails the rightwhile entailing other propositions that theright does not entail. And this already showsthat adding the truth predicate to a languageexpands the expressive power of thatlanguage; it increases the entailments of thelanguage. As Tarski would put it, the

5 What about formulating the disquotationalbiconditional with an operator-like truthconcept, as in 'it is true that p iff p', where'true' does not (allegedly) occur as apredicate at all? Two problems with this: (i)it is not clear that 'true' fails to be apredicate here, since 'that p' is naturallyinterpreted as a singular term; and (ii) weneed a grammatical truth predicate tocapture general statements about truth, asin 'everything the Pope says is true'. If wewant to view instances of the truth schemaas instances of such generalizations, asthey seem to be, then we need a suitablepredicate. Besides, the predicate version ofthe schema is clearly just as correct as the(putative) operator version.

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metalanguage is always logically strongerthan the (truth-free) object-language.6

Second, there seem to be cases in which theright side does not entail the left. Take anyexample of a proposition that suffers fromtruth-value gaps, according to yourphilosophical predilections—fictionalpropositions, counterfactuals, ethicalpropositions, vague propositions. Now it isnot that I am myself particularly wedded totruth-value gaps for these types ofpropositions; my point is that the veryconcept of a proposition does not seem toimply that substituting it into the truth schema

yields a truth.7 Consider the sentence 'theproposition that Sherlock Holmes is adetective is true iff Sherlock Holmes is adetective'. Can't we quite comfortably affirmthat Holmes is a detective without having tobe committed to the claim that thisproposition is true? For it to bestraightforwardly true, 'Holmes' would have torefer to something real, but it does not, so theproposition cannot be true. There is nothingto make this proposition true, but it stillseems to be a proposition; even if it cannotbe properly asserted, it can at least occur asthe antecedent of a conditional, so it canfunction propositionally. Or consider the viewthat 'the king of France is bald' is neither truenor false and yet expresses a proposition; ifso, what propositions bearing the propertiesof truth or falsity does this proposition imply?It seems to imply nothing about the truth orfalsity of itself; certainly it does not imply thatit is true—if it did it would imply its ownfalsity, since it is not true (and not falseeither)! Propositions suffering fromtruth-value gaps cannot entail that they aretrue propositions, so they cannot entail theleft side of a truth schema in which theyoccupy the right side. Most propositions aretrue or false, so this disparity does not showup in their case—we can

6 Note that Paul Horwich, for one,unhesitatingly accepts this point about thelogical form of the truth schema: see Truth,38. Whether he sees that admitting thiscasts doubt on minimalism is less clear;witness his remark: 'it is not part of theminimalist conception to maintain that truthis not a property' (p. 38).7 Dummett makes this point abouttruth-value gaps and the disquotationalschema in 'Truth'.

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generally say 'if p, then p is true'. But this

does not seem to be guaranteed by the veryidea of a proposition, so it is not analyticallythe case that, for all propositions p, if p, thenp is true. The notion of truth is moredemanding than the mere notion ofproposition—of what can be intelligibly said.We want to leave conceptual room for theidea of propositional speech acts that fail oftruth and falsity. Calling a proposition trueelevates it above merely uttering it. So thereis no entailment from the right to the left of anarbitrary instance of the truth schema.8

Let us agree, then, that the left side is richerexpressively than the right; and let us agreethat 'true' really does express a property, justas much as any other meaningful predicateexpresses a property. The truth predicate ofa language is a genuine semantic predicate,ascribing the property of truth to whatinstantiates it. Now the point I want to insistupon is that this is consistent with the thesisthat truth operates disquotationally. I want toput together these two claims—that truth is arobust property, and that it is disquotationallydefinable—and ask what conception of truthemerges. Here, then, without further ado, isthe essence of the concept of truth: truth is aproperty whose application conditions can bestated without making reference to thatproperty—moreover, it is the only property ofwhich this can be said. Let us accordinglysay that truth is a self-effacing property inthe foregoing sense. The first part of theclaim that truth is self-effacing is easy tograsp: the right side gives a necessary andsufficient condition for truth to apply to aproposition but it makes no referencewhatever to the property of truth—theapplication conditions of 'true' are givenwithout alluding to the property this predicatedenotes in any way. We must be careful tounderstand this claim correctly: the

8 There is, however, an entailment from the

left to the right, which I take to be the heartof the disquotational analysis of truth. Butsince the entailment is only one way(though analytic in some sense) theschema cannot express an equivalence orsynonymy, and hence cannot be used tounderwrite a redundancy theory of truth.My overall position could be put by sayingthat the left-to-right entailment is whatcaptures the essence of truth, once this iscombined with the admission that the left isstronger than the right—that is what I meanby 'thick disquotationalism'.

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claim is not the trivial one that the applicationconditions of 'true' can be given in otherwords or in other concepts. Obviously, wecan give the application conditions of'bachelor' in other words, like 'unmarriedmale', and obviously too we can give theapplication conditions of 'water' by using theconcept H 2 O. But in these cases we are stillreferring to the same property we started outwith, though using other words to refer to thatproperty. My point is not that 'true' can benon-circularly defined—for that is true ofmany concepts. It is that truth can be definedwithout even making reference to theproperty 'true' denotes—or using anypredicate equivalent to it. That is what isspecial about the disquotation principle: itexplains truth without referring to it in anyway, under any description.9 As we mightput it, a shade paradoxically, truth applies toa proposition in virtue of something otherthan itself. I also claim, and will soon argue,that only truth is self-effacing in this sense,so that we can define truth as 'theself-effacing property' and pick it outuniquely. More exactly, I will argue that noother property sustains disquotation: onlytruth allows the kind of semantic descent itwarrants.

I am now in a position to spell out the

essence of the disquotational nature of truthas I see it. There are two parts to this: First,truth is a property of a proposition fromwhich one can deduce the fact stated by theproposition.10 Second, it is the only suchproperty.

9 This is quite unlike the classic coherence,pragmatist, and correspondence theories,which all seek to analyse 'true' by means ofsome predicate deemed to be intensionallyor extensionally equivalent to 'true'. That iswhy the right side of such analyses alwayscontains a reference to the propositionmentioned on the left side. Seeing that thisis the wrong format to explain truth is reallythe central insight of the disquotationalconception: this conception differs in thelogical form of its analysis, not just in thesubstance of it.10 This is shorthand for: truth is a propertyof a proposition from which one candeduce that the state of affairs representedby the proposition is a fact. Of course, notall propositions state facts, since not all aretrue. Rather, if a proposition is true, thenthe state of affairs it represents is a fact. Noheavy ontology of facts is intended by thisformula; it is just a convenient way to saythat if p is true then one can deduce that p,for any proposition p. To say that one caninfer from the truth of 'snow falls from thesky' that it is a fact that snow falls from thesky is just to say that from that premiss onecan infer that snow falls from the sky. Thisis what I mean by talking of inferring factsfrom propositions with the aid of truth. I ammerely locating the disquotational propertyof truth in an epistemic context.

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Together: truth is that (unique) property of aproposition from which one can deduce thefact stated by the proposition. In other words,

truth is the only property of a propositionwhich entails the fact that makes theproposition true. Propositions can have manyproperties—they can be believed, justified,denied; they can entail other propositions;they have constituent structure—but none ofthese properties entails the very fact statedby the proposition. They entail other facts, tobe sure, but not the fact stated. This point isreally quite self-evident: If you know that p istrue you can thereby deduce that p. But ifyou merely know that p is believed or justifiedyou cannot deduce that p—though you maybe able to deduce some other proposition q.It is as if the property of truth enables you tolook through the proposition right to the fact itstates. In saying that truth is disquotationalwe are saying that it is reality-implying in thissense.11 By knowing that truth applies to aproposition you come to know, not just factsabout propositions, but facts about the world.And this is a remarkable thing once onetakes the measure of it: who would havethought that there is a property propositionshave that points beyond them to the extra-propositional facts? All the other properties ofpropositions stay at the level of propositions—whether they are believed or justified orentail other propositions or what elementsmake them up. But there is this one propertythat takes us outside propositions and downinto the world beyond them. And this isdirectly related to the self-effacing characterof truth: because its conditions of satisfactionmake no reference to it, but only to objectsand properties in the world, via thenon-semantic right side of the truth schema,we can infer worldly facts from theapplication of 'true' to propositions. If thesatisfaction conditions of this property werecorrectly stated by referring to it, then wewould still be at the level of propositions; butbecause it is self-effacing in the way it is wecan

11 This is my gloss on Quine's 'No sentenceis true but reality makes it so', quoted in n.1. As he later remarks, 'By calling thesentence ["snow is white"] true, we callsnow white' (Philosophy of Logic, 12).

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move from its application to a proposition to afact about the world. It is not that 'true'expresses no property, so that 'p is true'means 'p'; rather, it expresses a genuineproperty that has the characteristic of beingself-effacingly fact-implying. This is not thena trivial result of a synonomy, as it would beif we thought both sides of the schema saidthe same thing, but a substantive fact about areal property.12

How does it work with falsity? Falsity is not,strictly speaking, disquotational: we have theschema 'p is false iff not-p', and the right sideis not a disquotation of the left, since itcontains 'not' and p lacks this word. But wecan easily modify the rule to accommodatethis: if a proposition has the property offalsity, then you can deduce its negation—ifyou know that p is false, then you therebyknow that not-p. Falsity is simply disquotationplus negation. When you know that aproposition has this property you can deducethe opposite fact to the one it states—so wehave the same semantic descent and world-directedness for falsity too. And we cansimilarly assert that falsity is the onlyproperty of a proposition that licenses theinference to the negation of the fact it states(or purports to state).

Let us now consider some alleged counter-examples to the uniqueness claim. Weshould note that this claim is crucial if we areto have defined the notion of truth, since iftruth is not the only disquotational propertythen this property does not individuate truth.(No one ever seems to concern themselves

with establishing the uniqueness claim, beingcontent to show that truth isdisquotational—but this is clearly not enoughif we are to have succeeded in fixing uponwhat distinguishes truth from all otherconcepts.) Consider then the concept ofknowledge: we have it that if x knows that p,then p. So knowledge disquotes: you caninfer the fact stated by a proposition from theproperty a proposition

12 Clearly, if the two sides weresynonymous, then the inference wouldsimply be an instance of 'p entails p'—wecan infer a proposition from itself. I amsaying, quite differently, that if we know thatp is true we can infer that p, where premissand conclusion are distinct propositions.

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has of being known. Similarly for theproperty of following from something true, orthe property of being believed by an infallibleGod. These are all distinct properties fromtruth, it may be said, but they all license theinference I am saying is distinctive of truth:so how can truth be uniquely disquotational?I take it the answer to this question isobvious: each of these properties includes orembeds the notion of truth, and it is thisembedded truth element that is doing all thedisquotational work. Knowledge,omniscience, and entailment-by-a-truth allimply that the proposition in question is true.So these are no more counter-examples tothe uniqueness claim than the property ofbeing both true and written in red ink is.13

Yet it does not seem self-evident that noother property could license disquotation.Take the property of being intelligible asapplied to propositions. Certainly we cannotinfer that grass is green from the fact that theproposition that grass is green is intelligible.But what about a proposition that says of

itself that it is intelligible—the propositionexpressed by the self-referential sentence'the proposition expressed by this sentence isintelligible'? This proposition does have theproperty of intelligibility (just about!), andfrom its having that property we can infer thatit is intelligible—but isn't that exactly what itsays? So we can deduce that thatproposition is intelligible, which is what itsays, just from the fact that it has theproperty of intelligibility—we can thereforededuce the fact stated by the propositionfrom the property ascribed to the proposition.The proposition states that it has the propertyof intelligibility, and we can infer this factfrom the knowledge that it has the property ofintelligibility. Or consider the sentence 'thissentence is written in English'. That sentencehas the property of being written in English,so we can trivially infer that it is written inEnglish: but that is what the sentence says;so we

13 Indeed, these alleged counter-examplesare all analysable as conjunctions in whichtruth is one conjunct; truth is a necessarycondition for each of the complex conceptsin question.

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can infer the fact it states from the knowledgethat it has the property of being written inEnglish. Or suppose I have a belief that isrealized in my brain by state S, and supposethis belief has that very content—that it isrealized in my brain by state S. Then the factstated by the proposition I believe can beinferred from the property my belief has ofbeing realized by state S. So here we havethree cases in which there is a convergencebetween the property possessed by aproposition and the fact it states.

But I hope it is obvious that these contrivedcases are extremely special and do not really

threaten the claim I am making. My claim isthat for any proposition truth licenses theinference in question; no matter whichproposition you choose you can alwaysmake this move. But the properties justcontrived are not such that for anyproposition they permit the move—the moveworks only in these strange self-referentialcases. It is not in general true thatintelligibility, being-written-in-English, andbeing realized by a particular brain stateallow one to infer the fact stated by thepropositions or sentences with theseproperties. In the vast majority of cases suchan inference would be lamentably off themark.14 So these are not counter-examplesto the general claim I am making—that truthalways permits the inference and nothingelse has this power. Still, the putativecounter-examples may serve to indicate whyit is that my claim may not seem totallyself-evident, since there is a kind of localviolation of it in special cases ofself-reference. The uniqueness claim is nottrivial, though it is I think virtuallyunassailable. In fact, I think it is sufficientlyobvious that no one (to my knowledge) hasever thought to defend it before—or even toformulate it explicitly. But it does need to bemade explicit and evaluated, as I have donehere, if we are to

14 Obviously, establishing the truth of aproposition generally requires more thanscrutinizing the proposition and employinglogical reasoning; we have to investigate thesubject-matter of the proposition. So theexamples cited in the text are quite differentfrom standard cases. Truth is reality-implying because knowledge of truth isreality-involving, one might say.

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assure ourselves that we have captured theessence of what truth distinctively is.

It might help to bring out the role of theconcept of truth if we try to imagine doingwithout it. Imagine being a member of acommunity of propositional beings who thinkand communicate but have no concept oftruth. Someone says something to you andyou register it, but you cannot apply theconcept of truth to what is said. It seems, inthese circumstances, as if you are in noposition to form beliefs about the world as aresult of what people say to you: all you knowis that the speaker said that p, not that p istrue. You cannot disquote on p and henceform beliefs about the world as a result oftestimony, since you lack the device ofdisquotation that is the essence of truth. Butnow suppose you suddenly acquire theconcept of truth, perhaps with the help of afriendly alien. All at once you can apply thisconcept to what people say and hence inferfacts about the world. If you take whatsomeone says to be true, then you can inferthat p, for some p—you can acquireknowledge of facts. Of course, you can alsocome to know facts about the world directlywithout deploying the concept of truth, aswhen you simply see (say) that grass isgreen; in such cases there is no detourthrough other people's speech acts. But ifyou are to acquire knowledge of the world onthe basis of testimony, then you need thetruth concept. Truth thus comes into its ownwhen we start using other people's beliefs toacquire knowledge of the world. This is thepragmatic side of the disquotational propertyof truth; it explains why we care about thisproperty, what it does for us. Without theconcept of truth we could not learn fromothers; no truth, no education.15 Education isone long exercise in

15 When I speak of 'learning' here I meanmaking a rational inference from belief-expressing speech acts to propositionalknowledge of the world; I don't mean the

kind of learning that results from imitation orconditioning or some such. We canimagine having a mechanism in our headsthat causes us to form knowledge of theworld as a mere causal upshot of hearingspeech acts, where the concept of truthplays no cognitive role in this process; butthis would not be a case of rationalinference from speech act to knowledge.My claim is that this latter is what requiresdeployment of the concept of truth.

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disquotation, using the teacher's beliefs toacquire knowledge of the world, this beingmediated by the concept of truth. Withouttruth we would be condemned to be completeautodidacts.16

From this point of view, truth is essentially adevice of inference. When I learn that a birdis yellow by seeing it I learn something aboutthat bird, and what I might infer from this isincidental to acquiring that knowledge. Butwhen I learn by testimony that a propositionis true the interest of this lies in what I caninfer from this knowledge, namely the factstated by the proposition. When I learn bytestimony that the proposition that a certainbird is yellow is true what I learn is somethingI infer from this, namely that the said bird isyellow. I make a transition from proposition toworld, and this transition is the whole point ofthe notion of truth. In saying that truth is adevice of disquotation, then, we are alsosaying that it is a device of inference—inference to the disquoted form. It is notthe mere fact that a proposition is true that isinteresting; it is what can be inferred fromthis about how the world is that is important.Truth is essentially a method for deducingfacts from propositions.

To bring out how special the inferentialpowers of truth are, let us formulate these

powers abstractly. Suppose you are told thatthere is a certain property P such that whenP applies to an object x it is logically impliedthat some other object y has some distinctproperty Q; and further that this property P isa non-relational monadic property. Thiswould be like being told that the property ofbeing yellow is such that when it holds of anobject x it logically follows that some otherobject y is (say) square. That would

16 Let me not be misunderstood: I don'tmean autodidact in the sense of someonewho is self-taught from books instead offrom actual teachers; I mean the idea ofacquiring all one's knowledge first-hand,from direct investigation of the world.Obviously, learning from books is aninstance of education in the intendedsense, and involves the usual process ofdisquotation: one reads the sentence,predicates truth of it, and then forms thecorresponding belief about the world. Youcan pick up quite a lot of useful knowledgethis way, and most of it has nothing to dowith words and books at all. (I hope myreader has been engaged in thedisquotational act steadily throughout thisbook.)

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seem like a very remarkable claim: how canthis object's being monadically P possiblyimply that that object is monadically Q?Surely that is impossible: what has thecondition of the one object got to do with thecondition of the other, logically speaking? Butthis is precisely how truth works. From thefact that one object, say the proposition thata certain bird is yellow, has the property oftruth we can deduce that another object, aparticular bird, has the property of beingyellow: we can jump between entities andproperties using truth as our springboard.Moreover, we are moving from properties of

abstract or linguistic entities to properties ofconcrete things: and that sounds like sayingthat the number 2's being even logicallyimplies that a particular bird is yellow! Butthat is precisely what truth allows: from thefact that an abstract proposition has a(non-empirical) property, viz. truth, we candeduce that the world of concrete objectsinstantiates certain empirical properties. Thisshould strike us as more remarkable than itdoes; we are so familiar with this property oftruth that we fail to appreciate howanomalous it is. Truth is not just a device ofdisquotation; it is a device of ontologicalleapfrog—or rather, that is what disquotationreally amounts to, properly understood. Truthforms a logical bridge between the world ofpropositions and the world of objects andproperties; it enables us to travel frompropositions to the objects and propertiesthey are about.17 No other concept cancross this ontological and deductive gap;truth is the only disquotational concept.

In the light of all this we can now state a'definition' of the concept of truth, i.e. acondition that truth and only truth satisfies.

17 Of course, reference is what mediatesthe link that takes us from proposition tofact. What truth does is enable us to movefrom a sentence to a fact by way of thereference of the terms in the sentence: ifwe know what 'snow' refers to and what'white' refers to, then we can put thistogether with the knowledge that 'snow iswhite' is true in order to derive theconclusion that snow is white. Withoutreference we wouldn't know which fact toinfer from a sentence's truth. And of coursethe involvement of reference here makesthe leapfrogging power of truth perfectlyunmysterious (though still remarkable).

end p.103

Truth is to be defined as that property of a

proposition that entails the fact (purportedly)stated by the proposition. This definitionfocuses on the disquotational aspect of truthand is intended to be a reformulation of thatidea. But we can also define truth byemploying the related notion ofself-effacement introduced earlier: truth is tobe defined as the self-effacing property, i.e.that unique property whose applicationconditions can be stated without reference tothe property. Thus we can say 'p is true iff phas the self-effacing property' and offer thisas a definition. These definitions do notcompete with other definitions, say Tarski's;rather, they home in on certain features oftruth, features that distinguish truth fromother concepts. But the definitionsthemselves are far less important thangrasping the unique (and remarkable) waythat truth operates: it performs the miraculousfeat of taking us from language and thought,on the one hand, to the world of objects andproperties, on the other. No other concepthas this power: truth is the adhesive thatbinds mind and world, to put it metaphoricallyand portentously. More soberly, when abelief has the property of truth (as opposedto any other property it might have), then theworld is guaranteed to be a certain way, theway the belief represents it as being. If thisremystifies the concept of truth, then so be it.

I shall now discuss the metaphysics of truthmore directly. Again, I will be brief anddogmatic. The concept of truth seems simplein the following sense: it has no conceptualdecomposition, and no empirical essence ornature.18 We cannot analyse it intoconceptual constituents, and we cannotexpect to discover a hidden underlyingempirical structure for it. Truth is primitive, inthis sense (which is not to say that nothingilluminating can be said about the concept).In this respect, I would say it is like the otherlogical concepts investigated in this book:

identity, existence, predication, necessity.These concepts form a conceptual bedrock;they stand, as it were,

18 See Horwich, Truth, especially ch. 1.end p.104

underneath all our other concepts. They haveno analysis.19 But, despite theunanalysability of truth, it is possible to give anon-circular definition of the concept. This ispeculiar: one would have thought that if aconcept was simple and unanalysable thenno account could be given of it in otherterms. One would think, that is, that all wecould say about 'true' is that it applies to aproposition iff that proposition is true. That issurely what one would say about 'blue' if onetook this concept to be analogously primitive:'blue' applies to an object iff that object isblue. But the peculiar thing about truth is thatwe can define it by means of the disquotationprinciple, even though it is primitive. Truth isa simple unanalysable property that can bedefined: that is to say, non-circularnecessary and sufficient conditions, of ananalytically warranted kind, can be given forthe instantiation of this property by aproposition. This is because truth isself-effacing: its application conditions canbe given without referring to it under anydescription, and so its primitiveness does notstand in the way of providing theseconditions. Truth is thus both definable andprimitive (in the sense of having noconceptual decomposition and no underlyingempirical nature). It is as if blueness couldbe the simple property it is and yet haveapplication conditions given by reference tosomething quite other than blue objects. Putsimply, the primitive property of truth appliesto the proposition that snow falls from the skyin virtue of the fact that snow falls from thesky—and not in virtue of the propositionmeeting some condition

19 I mean this in the specific sense thatthese concepts have no sort of conceptualdecomposition; this is not to say that wecan have no theory of them, and indeed Ihave offered theories of all these conceptsin this book. What I am denying is thatthese concepts can be defined in anyilluminating non-circular way. Similarsentiments are expressed by DonaldDavidson in 'The Folly of Trying to DefineTruth', 320: 'Let me suggest a diagnosis ofour aporia about truth. We are still underthe spell of the Socratic idea that we mustkeep asking for the essence of an idea, asignificant analysis in other terms, ananswer to the question what makes this anact of piety, what makes this, or any,utterance, sentence, belief, or propositiontrue. We still fall for the freshman fallacythat demands that we define our terms as aprelude to saying anything further with orabout them.'

end p.105

that analyses (or simply reuses) the conceptof truth. The predicate 'is true' holds in virtueof a condition not specified by the use ofsome (intensionally or extensionally)equivalent predicate. Yet it is still itself agenuine predicate standing for a realproperty—as much as 'blue' is. Therein liesthe essential character of the truth concept,making truth an oddity in our conceptualscheme. Truth is really a very exotic propertyindeed, when viewed in the right light. And itis precisely the disquotational aspect of truththat lies behind this oddity. To call thedisquotational view 'deflationary' thereforestrikes me as wide of the mark: truth turnsout to be very interesting in its workings, notthe banality some people suppose.20 Ofcourse, it would be fair enough to use theterm 'deflationary' if one held that 'p is true'says nothing different from—is synonymous

with—'p', but we have seen that that is thewrong way to interpret the disquotationalcharacter of truth. Truth becomes interestingprecisely when one accepts this principleand yet recognizes that 'p is true' sayssomething stronger than merely 'p'—inparticular, that the former refers to a propertythe latter does not refer to. This is why I callthe view I am defending thickdisquotationalism, unlike the thindisquotationalism implied by the synonymythesis. Truth is a substantial, robust property,as thick as any property, not thedisappearing pseudo-property it issometimes said to be. Or, putting the point inthe formal mode, 'true' is as genuine apredicate as 'blue' or 'square'. What makes itunique is that it is a predicate that applies toan object (a proposition) in virtue ofsomething other than a predicate of thatobject.

Does any version of supervenience hold fortruth? I think it does: if you fix all thenon-semantic facts, and you fix all thepropositions, then you fix the application ofthe truth concept, analytically so. That is, iftwo possible worlds are exactly alike in thefacts obtaining in them, and they contain thesame propositions (which on reasonableassumptions they will), then exactly the same

20 On the doctrine of deflationism see AnilGupta, 'A Critique of Deflationism', andHartry Field, 'Deflationist Views of Meaningand Content'.

end p.106

propositions must be true and false in the twoworlds. This is indeed a simple consequenceof the disquotational biconditional, read fromright to left. If snow falls from the sky in aworld, and there exists the proposition thatsnow falls from the sky in that world, then thatproposition must have the property of being

true in that world. In short, the truths aresupervenient on the facts. Here,supervenience is trivially assured. Yet itwould be a mistake to say that truth is nothingover and above the facts on which itsupervenes. Truth does not collapse intofacts and propositions, since it is anirreducible property—though one whoseinstantiation is fixed by conditions that makeno reference to it. Such supervenience mayremind us of a familiar position with respectto moral goodness. G. E. Moore tookgoodness to be simple, unanalysable, andnon-natural, but he also took it to superveneon the descriptive and natural.21 I would saythe same of the concept of truth, and I wouldadopt the same kind of realism about truththat Moore adopted for goodness. The truthproperty is a constituent of reality as muchas blueness or electric charge or goodnessis (though it is what we have been calling alogical property). It is a primitive constituentthat nevertheless supervenes on facts that donot involve the notion of truth.22 But there is asignificant disanalogy with goodness, namelythat there is no counterpart to the naturalisticfallacy for truth. We cannot deduce thatsomething is good simply from informationabout its non-moral properties—there isalways a logical gap here. There is always an'open question' as to whether something isgood, given that it has such-and-suchdescriptive properties. But nothing like thisholds of truth with respect to itssupervenience base: you can deduce that pis true given the information that p and theexistence of p. There is no logical gapwhatsoever here, thanks to the disquotationalbiconditional. So the irreducibility of truthdoes not result from a

21 See Principia Ethica; also my Ethics,Evil and Fiction, chs. 1 and 2.22 Compare the modal and the actual,discussed in Ch. 4. I defend a similar view

of colour as supervenient yet primitive in'Another Look at Colour'.

end p.107

non sequitur analogous to the naturalisticfallacy—there is no fallacy involved ininferring truth from fact. And yet the propertyof truth is not reducible to its superveniencebase.

Where there is still an analogy with goodness(and the other concepts discussed in thisbook) is on the 'non-natural' status of truth.Truth is not a property that has causalpowers or can be perceived by means of thesenses; it is an object of intellectualcognition. It flouts naturalistic epistemology. Itis 'queer'. But, as I remarked earlier,sometimes we just have to learn to live withthe 'queer': denial and denigration are notsensible responses. What does seem clear,in the light of this non-naturalism, is that'deflationism' is not remotely the right wordfor the kind of thick disquotationalism I havedefended, if this is taken to imply that thisview of truth is philosophically unproblematicor somehow 'tame'. If anything, myconception of truth deserves to be labelledinflationary. As I am conceiving it, truthraises many ontological and epistemologicalperplexities—but I do not regard this as anobjection to the view I am defending. It is justthe way things are.23 Often the right view inphilosophy is the one that identifiesaccurately just where the problems lie;evading real problems can never be the routeto philosophical understanding.

This book has sided with what might be called'logical realism', though that has not been theprime focus of my enquiries. Generallyspeaking, the concepts I have discussedhave turned out to be more primitive andfundamental than has commonly beensupposed. Reality has its logical properties

too—basic, irreducible, real properties. Thisposition raises many questions, ontologicaland epistemological, but I believe they arethe right questions.

23 I take the same kind of view of ethicalproperties in Ethics, Evil and Fiction, andthe general metaphilosophy behind the viewis set out in Problems in Philosophy.Ontological diminishment or evasion is notin general the right response tophilosophical perplexity.

end p.108

Bibliography

Benacerraf, Paul, 'Mathematical Truth', inPaul Benacerraf and Hilary Putnam (eds.),Philosophy of Mathematics, 2 nd edn.(Cambridge: Cambridge University Press,1983), 403-20.

Blackburn, Simon, and Simmons, Keith(eds.), Truth (Oxford: Oxford UniversityPress, 1999).

Davidson, Donald, 'The Folly of Trying toDefine Truth', in Blackburn and Simmons,Truth, 308-23.

Dummett, Michael, Frege: Philosophy ofLanguage (London: Duckworth, 1973).

——'Truth', in P. F. Strawson (ed.),Philosophical Logic (Oxford: OxfordUniversity Press, 1967), 49-69.

Evans, Gareth, The Varieties of Reference(Oxford: Clarendon Press, 1982).

Field, Hartry, 'Deflationist Views of Meaning

and Content', in Blackburn and Simmons,Truth, 351-91.

Frege, Gottlob, Basic Laws of Arithmetic,trans. Montgomery Furth, 2 vols. (Berkeleyand Los Angeles: University of CaliforniaPress, 1967).

—— Foundations of Arithmetic, trans. J. L.Austin (Oxford: Basil Blackwell, 1950).

——'On Sense and Reference', in P. Geachand M. Black (eds.), Translations from thePhilosophical Writings of Gottlob Frege(Oxford: Basil Blackwell, 1980).

Geach, P. T., Logic Matters (Oxford: BasilBlackwell, 1972).

Gupta, Anil, 'A Critique of Deflationism', inBlackburn and Simmons, Truth, 282-308.

Horwich, Paul, Truth (Oxford: Basil Blackwell,1990).

Kripke, Saul, 'Identity and Necessity', in M.Munitz (ed.), Identity and Individuation (NewYork: New York University Press, 1971),135-64.

—— Naming and Necessity (Cambridge,Mass.: Harvard University Press, 1972).

Lewis, David, On the Plurality of Worlds(Oxford: Basil Blackwell, 1986).

McGinn, Colin, 'Another Look at Colour', inMcGinn, Knowledge and Reality, 298-313.

end p.109

McGinn, Colin, 'A Priori and A PosterioriKnowledge', in McGinn, Knowledge andReality, 36-49.

—— Ethics, Evil and Fiction (Oxford:Clarendon Press, 1997).

—— Knowledge and Reality (Oxford: OxfordUniversity Press, 1999).

—— 'Modal Reality', in McGinn, Knowledgeand Reality, 65-110.

—— Problems in Philosophy (Oxford: BasilBlackwell, 1993).

——'Rigid Designation and Semantic Value',Philosophical Quarterly, 32/127 (Apr. 1982),97-115.

Moore, G. E., Principia Ethica, rev. edn.(Cambridge: Cambridge University Press,1993).

Peacocke, Christopher, 'Necessity and TruthTheories', Journal of Philosophical Logic, 7(1978), 473-500.

Pears, David, 'Is Existence a Predicate?', inP. F. Strawson (ed.), Philosophical Logic(Oxford: Oxford University Press, 1967),97-102.

Perry, John, 'The Problem of the EssentialIndexical', Nous, 13 (1979), 3-21.

——'The Same F', Philosophical Review, 79(1970), 181-200.

Quine, W. V., Philosophy of Logic, 2nd edn.(Cambridge, Mass.: Harvard UniversityPress, 1986).

—— Word and Object (Cambridge, Mass.:MIT Press, 1960).

Russell, Bertrand, 'The Philosophy of LogicalAtomism', in R. C. Marsh (ed.), Logic andKnowledge (London: George Allen & Unwin,1956).

—— The Problems of Philosophy (Oxford:Oxford University Press, 1912).

Wiggins, David, 'The De Re "Must": A Noteon the Logical Form of Essentialist Claims', inGareth Evans and John McDowell (eds.),Truth and Meaning (Oxford: ClarendonPress, 1976).

—— Sameness and Substance (Cambridge,Mass.: Harvard University Press, 1980).

Wittgenstein, Ludwig, Tractatus Logico-Philosophicus, trans. David Pears and BrianMcGuinness (London: Routledge & KeganPaul, 1961).

end p.110

Index

analysis of orthodox view of existence22-3 ,24-5

problems of27-8

asymmetry between names and predicates66

'bare existence'28-30

basicness of identity9-10 , 11-12

classic coherence theory of truth88-9

Cogito45-7

copula modifier theory76-9 , 80 , 81

correspondence theory of truth90-1

criteria of identity5-7

definability of identity7-9

definition of identity7-9

deflationism87

disquotationalism87-9 , 92 , 106disquotational biconditional107

distinction between sub-types of identity2-3

distinctness and identity11 , 12-13

entertaining of existence43

epiphenomenality of modality86

essentialism47-8

excluded middle, law of11

existence:the Cogito45-7

definitional thesis (Russell)20

essentialism47-8

existential quantifier20 , 23 , 32-7interpretation offormula33

and use of 'all'/'some'36-7

and imperceptibility45

and impossibility40-1

of individuals25-6

negative existential43

non-existence32 , 37-8

not perceptible property ofobjects44-5

objections to orthodox view21-30'bare existence'28-30

instantiation21-6

proof that it cannot begeneral analysis of notionof existence24-6

sentences that resistorthodox paraphrase26-8

Ontological Argument48-50

ontological status of17

ontological thesis (Russell)19

and possibility38-40

as a property15 , 16

semantic/logical thesis(Russell)19-20

'exists':complement class of37

as predicate16-17 , 37-8, 50-1

two sorts of interpretationof26-8 see alsofirst-order property view

extensionssee names; predication

falsity98

fictional entities38-40 , 42-4

first-level extension of names55-6 , 59

first-order property view30-1

end p.111

Frege, G.:and existence20 , 21

and identity1-2 , 4 , 6 , 8 , 12 , 13

and predication67

God48-50 , 99

goodness108property of6n11 , 107

Horwich, Paul94n6

Hume, David44

idealism and theories of truth88-90

identicals, indiscernibility of6 , 8 , 9

identity:basicness/fundamentality of9-10 ,11-12 , 14

challenge to Fregean thesis2-7

criteria of5-7

definability of7-9

denying that it is unitary5-7 , 13

and distinctness11 , 12

fundamentality of11-12 , 14

indefinability of9 , 14

is unitary1-2 , 6 , 9 , 14

Leibniz's law3 , 4 , 7 , 8 , 9 , 69

logical properties of2

as logical relation13-14

necessary and contingent3n5

notion of property identity7-8

numerical2

propositions13

as psuedo-relation12

qualitative2 , 8

self-identity31

sortal relativity of statements of4

statements9

ubiquity of12

universality of9-10

identity indispensability of12

imperceptibility45

impossibility:and existence40-1

including/excluding impossibleworlds70-4

indeterminacy, semantic64-5

indiscernibility of identicals6 , 8 , 9

indispensability of identity12

individuals, existence of25-6

instantiation of properties17-18 , 21-3 , 61-3interlocking structure of world61-3

mode of77-9 , 80-1

intelligibility, property of99-100

intentional entities17

irreducibility of truth107-8

iteration of modal locutions82-3

Kripke, Saul38 , 47

Leibniz's law3 , 4 , 7 , 8 , 69

make-believe, cognitive acts of43

Meinongian ontology of nonexistence37

mistake, characteristic of a31

modality69-70 , 73-4copula modifier theory76-9 , 80

de re and de dicto use of modalwords79

epiphenomenality of86

iteration of modal locutions82-3

modal truth84-5

modes83-4

predicate modifier treatment74-7

in special ontological category83

modes83-4

Moore, G. E.107

multiple references66-7

names:asymmetry between names andpredicates66

non-referential disquotational axiomfor58-9

second-level extensions of56-7

end p.112

singularity and plurality60-1 seealso predication

necessity69modality69-70

quantifiers69-70

use of term 'necessarily'75-7

negation and pseudo-relation12

negative existential43

non-contradiction, law of11

non-existence32 , 37-8 , 42-4

non-referential disquotational axiom fornames58-9

'object', use of word35-6

objects:conceivable31-2

purely intentional41-2

Ontological Argument (OA)48

ontology:logical14

Meinongian33 , 37

of properties56 , 58 , 60 , 62

'p is true iff p'92-6

plurality of objects10-11

possibility:

and existence22 , 38-40

making a statement of69

postulation, mistaken42-4

pragmatist theory of truth88-90

predication:asymmetry between names andpredicates66

'Bertrand Russell' as example55-7

denotational approach topredicates57-8

identity and distinctness in10-11

natural property vs. standardextension view53-5

predicate modifier treatment74-7

predicate reference52-3

predicates and extensions52 , 54

properties53

semantics of53

singular term view ofpredicates65-6

singularity and plurality60-1

truth87-8

universal predicates31 see alsonames

pronominal anaphora11

property:of all existent things28-30

first-order property view30-1

identity of7-8

instantiation of17-18 , 24-5

of intelligibility99-100

logical properties31

name 'Bertrand Russell' asexample55-7

notion of15-16

and purely intentional objects41-2

self-effacing95-6

of truth95-6

uniqueness of a29-30

proposition, truth as property of a96-8 , 104

quantifiers69-70intentional33-4

interpretation of existential32-7

quantificational treatment of modalterms73-4 see also individualquantifiers e.g. 'some'

Quine, W. V.10 , 52 , 63 , 64 , 65 , 67 , 87n1

references for predicate52-3multiple66-7

reflexivity of identity2 , 6

relativity of statements of identity, sortal4-5

Russell, Bertrand:structure of existential fact18-21 ,25

three sub-theses of19-20

'same', meaning of term4

end p.113

Satan49

second-level extension of names56-7 , 59-60, 62 , 63-4

second-order variables7

self-identity31

semantics:epistemic considerations64-5

extensional55-7 , 64 , 68

indeterminacy64-5

modal words as copulamodifiers81-2

possible worlds70

Tarskian57-9 , 82

sentences:quantified60 , 69

sentence operator theory79-80

that resist orthodox paraphrase(existence)26-8

singular statements, analysis of9 , 18

'some', use of term34-7

sortal dependence of identity4-5

'state of affairs', use of term72-3

supervenience106-7

symmetry of identity2 , 6

Tarski, A.57-9 , 82 , 93-4

topic-neutrality13-14

Tractatus Logico-Philosophicus(Wittgenstein)12

transitivity of identity2 , 6

truth:classic coherence theory of88-9

correspondence theory of90-1

counter-examples to uniquenessof98-100

'definition' of concept of103-4 , 105

as device of inference102-3

and disquotationalism87-9 , 96-8 ,105-6

essence of concept of95

and falsity98

irreducibility of107-8

metaphysics of104-8

modal84-5

pragmatist theory of88-90

role of concept of101-2

and supervenience106-7

theories based on proposition 'p istrue iff p'92

unanalysability of105

uniqueness of97-101

truth condition:availability of second-levelextensions63-4

disquotational59 , 87-9

and impossible worlds71-2

inverted rule for55-6

ontological structure underlyingequivalence of62

of singular propositions22-3

ubiquity of identity12

uniqueness:problem of securing24

of truth97-101

universality of identity9-10

universality of property of existence16

variable-binding11

Wittgenstein, Ludwig12 , 41

'world', use of term72-3

end p.114

end p.115

end p.116

end p.117

end p.118

end p.119