Aequivocal

 My enterprise, in this paper, is to explore some of the questions which arise out of a fairly well-known cluster of Aristotelian theses. In Categories, I Aristotle distinguishes two sorts of case of the application of a word of phrase to a range of situations; one in which both the word and a single definition (account, logos) apply throughout that range, the other in which the word but no single definition applies throughout the range. In the first sort of case, he says, the word is applied synonymously, or (more strictly) to things which are stonma in the second it is applied homonymously. to things which are merely homonuma. Provision is also made for an intermediate class of cases, or (if you prefer it) for a subdivision of homonymous applications of a word into (a) cases of "chance homonymy" and (by cases of "other-than-chance homonymy", or as Aristotle calls them, cases of "paronymy". I shall label the second of these subdivisions cases of "Unified Semanic Multiplicay (USM). Prominent among examples of USM is the application of the word 'be'; according to Aristotic, "being is said in many ways"; and among further important examples of USM we find the word hgathón ("good") which according to Aristotle exhibits a multiplicity seemingly related to, and perhaps even dependent upon, that displayed by the word 'heing'; for in Nicomachear:

Ethics I, vi Aristotle remarks that "good is said in as many ways as being" The doctrine of the USM of 'being' is notoriously of great importance to Aristotle, since it is used by him to preserve the otherwise acceptable characterization of the science of Metaphysics as the study of being quabeing, which is threatened by the objection that the word "being cannot apply synonymously to all the items with which Metaphysics is concerned, and that there is, therefore, no more a genuine single science of Metaphysics thon there is (say) a genuine single science concerned with vices, somc of which (like dishonesty) are moral, and some of which (like clamps) are made of metal. This objection can, Aristotle hopes, he met by the reply that semantic multiplicity can be tolerated in the terminology specitying the subject matter of a single science provided that such

multiplicity is mified

Before 1 specify the questions with which in this paper I shall mainly be concerned, I should like to say a word about the nature of my interest in Arstotle and about the prospects of deriving from him a significant contribution to the enquiries which I have it in mind to undertake. First, I regard Aristotle as being, like one or two other historical figures, not just a great philosopher of the pass but as being a great philosopher; that is to say. I think of him as being concerned with many of the problems to which we today are, or at least sbould be, devoting our efforts. Furthermore, it is my view that once he is properly interpreted, he is likely found to have been handling such problems in ways from which we have much to leam. I subseribe therefore to a programme of trying to interpret of reconstruct his views (and 1 am not too fussy about the difference between these two descriptions) in such a way that, unless the text is totally probibitive, 1 ascribe to him views which are true rather than false, which are reasoned rather than unreasoned, and which are interesting and profound rather than dull or trivial. Second, I think that in the philosophical arca within which the topics of this paper fall there are specially strong reasons for Istening as attentively as possible to what Aristolle has to say. A definition of the nature and range of metaphysical enquiries is among the most formidable of philosophical tasks; we need all the help we can get, particularly at a time when ctaphysicians have only recently begun to reemerge from the closet, and to my mind are still hampered by the aftermath of decades of ridicule and vilification at the hands of the rednecks of Vienna and their adherents

The man questons to which I shall be addressing myself are three in number.

1. If. as Aristore suggests, at least some expressions connected with the notion of "being' exhibit semantic multiplicity, of which expressions is the suggestion true? More precisely which forms of the verb to be' and in what syntactical constructions is this suggestion most plausible? What cognates of the verb, if any, are similarly affected?
2. What link is there, if any, between unity, semantic multiplicity and jdentity or difference of meaning!
3. In what different wags may semantic multiplicity become unified?

In addition to these three main questions there are two further questionswhich might on occasion profitably engage our attention. (a) What considerations, il any, confer upon the availability of a single definition of special pride of place among possible criteria for identity of meaning? Can this suggestion be argued for, or is it just a matter of intuition! How, if at all, can the availability of such a definition be confirmed?

(b) Is Aristotle's classification of the ways of unifying semantic multiplicity exhaustive, are its components mutually exclusive. and which form of unification applies to the semantic multiplicity connected with

"being"?

I1. Being and Semantic Multiplicity

A. Existential Being and Semantic Multiplicity

The first question to be faced with regard to the possible semantic multiplicity of 'being' (or of cinai (to bo) or dò & (what is)) is a not very subile question of interpretation: in what range of employmcats of the word 'be' (or of an appropriate Greek: counterpart) is semantic multiplicity to be looked for. From a standard viewpoint (to which I do not in fact wholly subscribe) there will be at least four possible locations of such semantic multiplicity: (i) in the word 'be' taken as meaning 'exist', (i) in the word 'he' taken as a copula in a predicational statement, (in in the word 'be' taken as expressing identily, and (iv) in the word "heing" considered as a noun and as roughly equivalent to 'object' or 'entity.

Some of these vatiants are not really independent of one another. Since an object or entity seems to be anything which is or exists, it is rcasonable to suppose that semantic multiplicity would altach to such a noun as 'entity' if, and only it, it also attaches to the word 'exist. Furthermore, if we accept the commonly received view that 'exist may be paraphrased in terms of self-identity (Julius Cocsar, for example, exists if and only if Julius Cacsar is identical with Julius Casar), then any semantic multiplicity in the phrase "is identical with" will go hand in hand with a corresponding semantic multiplicity in the word 'exist'. We are then left with two possibly independent candidates for semantic multiplicity, 'be' (understood as meaning 'exist') and "be' (understood as meaning a copula).

G.E.L. Owen in Aristotie on the Snares of Ontology (ASO) opts for the supposition that semantic multiplicity attaches to 'be' (meaning 'exist'): and, as I tor a long time shared this belief, I shall consider it first. Since 1 wish to attribute a view to Aristotle only if I can find in his work or altematively invent on his behalf, a reasonable plausible argument to support it, 1 shall ask. whether we can find of devise such an argument in this instance. I offer the following.

Argument A1

(1) [Topics 121al7-15, cf.121b5-7] Being (existence), like unity is predicated of everything. This statement certainly implies that the word

'exist' is truly applicable to every object; it may also imply that the universal signined by 'exist' (or, it there is a plurality of such unircrsals. that one or another of the universals signified by 'exist') is instantiated by every object. But let us be cautious, and let us not assume that the second implication holds.

1. |De Inierpretatione, chapters 2-GJ Every simple declarative sentence [propositionalj contains a hréme (verb phrase) which signifies something said of something else (16b6), the 'something che' being signined by a noun phrase, Indeed the divisibility of declaratire sentences into kaapináseis (assertions and ipopirseis (denials), which respoctively allira or deny something about something (17a25| suggests that the noton of the exhibition of 'subject-predicate fon' enters into the definition of the concept of a declarative sentence or proposition. Existential sentences propositions) are no exception to this thesis, and they even tolerate quantilicational modifiers (19b15-19J.
2. From (1) and (2), it follows that existential propositions attribute universals to subject items.
3. Il 'crist' signified a single universal il would signily a gencric universal, since, as is shown by category-differences, there are different ways of existing which would le species of existence. [This step has been supplied by me.l

(S) Being (existence) is nol a genus, and so is not a generie universal.

This is argued in Metaphysies W98620-28, and the detals of this argument will be turther examined by me in an appendix lo my presentation of argument A1. A different account therefore, has to be found of what are naturally thought of as ways of existence.

1. From (4) and (S) it tollows that being (exist' does not signily a singic universal.
2. From (3) and (6) it follows that 'exist' signifies now one, now another, of a plurality of universals.
3. If 'exist' signifies a plurality of universals, that plurality should satisty two conditions: first, (a) it should be as small i plurality as possible (by an intuitively acceptable principle of economy), and second, (b) each of the elements of the plurality should be an essential property of items of the kind to which it attaches: the removal of such a property from any bearer belonging to that kind should deprive that bearer of existence, more brietly, with respect to each kind, cach element property should be entailed by the concept of existence.
4. The only set of universals which would satisfy both of the conditions which are specified in (8) is the set of category-beads themselves (as the most general list of essential properties one of another of which every

objeet possesses); so the category-heads constitute the required plurality.

(10) So exist by virue of signifying a plurality of universals, exhibits semantic multiplicily.

Appendiz to Argument Al

The argument given by Aristotle in favour of the contention that being is not a genus is, to my mind, obscure; it rests on the thesis that a genus cannot be predicable of a differcutia of one of its species, and if being were i genus it would have to offend against this probbition, since being is unisersally predicable. The following is my speculative expansion of this argument. Il Sis a species of a genus G then it must be the case (1) that G belongs essentally to Sand is therefore in the same category as S; (2) that S is differentiated, within G, by some universal D; and (3) that D is categorially difterent from, and (so to speak) "categorially inferior to" $ and G (in that no item in the category of § and & may attach essentially to, and so be predicabie of. D. Tio-footed, for example, it a difterentia of ern, will difles in category from man and animal (will loe a quality rather than a substance) in such a way that acither mars not animal can be predicable of it; secondaty substances are not predicable of qualities, even though it may be the case that necessarily anything which has a cenain quality is a certain sort of substance. But if being were a genus, since being is uneversally predicable (see step (1) in Argument Al), it would be predicable of any differentin of any of its species.

To show that exist possesses not merely semantic multiplicity, but unified semantic multiplicity, we shall need a further igument which 1 shall endeavour to supply.

Argarer A2

1. By the preceding argument A1, an item exists just in case it belongs te some particular category C (c.g., Substance, quality, quantity, eic.)
2. If category C is a catogory other than a substance, then an item x can be a C (fall under C) only if x is a C of some substance y. This thesis can be seen as an application of a version of the doctrine of universalia in se. a version which demands that the existence of a universal requires not just the possibility but the actuality of an item which instantiates that universal This thesis, though not my justification of it, seems to be enunciated in Metaphysics IV. ii. 1003a7.
3. Being a C of some substance y which instantiates C entails being a C of something y which exists in that sense (interpretation) of 'exist which is appropriate for substances. By hypothesis, for a substance to exist is for it to be a substance.
4. So substancial existence' is prior to, and presupposed by, cach forni of 'non-substantial existence'

(3) So the set of ways in which 'esistence is said are united byapproprate relanon to primary (substantial) being, and so "exist' exhibits unified semantic multiplicity.

I hope that the twin arguments, which I have presented hase both a recognizable allinity with philosophical positions which Aristotle is known 1o have lickd, and also at loast a superficial charm. They do, however, have their drawbacks both from a historical and from a conceptual point of vicw. My cument thoughts with regard to the first of these two aspects have been greatly influenced by my colleague Alon Code.

A crucial passage for consideration is Metapitysics V, vi (4 7), 1017a23-31, part of the chaptes devoted to what is (being) in the

"philosophical lexicon" contained in the Metaphysics. 'There, Aristolle says, it seems that whatever things are signilied by the "foms of predication" (i.e. presumably the categories), are said to be in themselves (per se, kath' auta); 'being' has as many significations as there are forms of predication. Since predieates sometimes say what a thing is, sometimes what it is like, sometimes how much it is, (and so on) there is a signification of 'being' corresponding to each of these. He concludes with the remark that there is no difference between "man walks (flourishes)" and "man is walking (Gourishing)".

(a) The obvious interpretation of the last remark is that the appearance of vert-forms like "walks' or 'Bourishes' create no difficulty, since they con be replaced by expressions in canonical for like 'is walking' or "is flourishing'; and if the latter expressions are regarded by Aristoile as canonical in form it is because the uses of eindi ("being') whose multiplicity he is at least at his point discussing are not existential but copulative. Owen, though he recognizes [ASO p. 82 n| that Aristotle does on occasion admit categorial variation in the sense of the copulative 'is. evidently is unwilling to allow that Anstotle is primarily concerned here with the copulative "is'; so he rather strangely interprets, the last remark (1017a27-30) as alluding to semantic multiplicity in the copula as being (supposedly) a consequence of semantic multiplisity in the existential 'is'.

This interpretation seems difticult to detend.

(b) When Aristotle says that predicates sometimes say what a thing is, sometimes what is it like (its quality), sometimes how much it is (its quantity) and so on, he seems to be saying that if we consider the range of predicates which can be applied to some item, for example to a substance like Socrates or a cow, these predicates are categorially various, and so the uses of the copula in the ascription of these predicates will undergo corresponding variation. But in the immediately preceding sentence, Aristotle has connected the semantic multiplicity in the copula not with variation between predicates of one subject, but with variation between essential (per se) predications upon different (indeed categorially different) subjecis (such predications as "Socrates is a man", "Cambridge blue is a colour (a blue, a blue colour) *). A desire to hannonize these statementsleads me to wonder whether Aristotle may be maintaining not only that the copula exhibits semantic multiplicity which corresponds to categorial differences between different statements about one subject, for example, Socrates, but also that dis semantic multiplicity is attributable to a multiplicity in the notion of essential being; the signification of 'is varies between (i) "Socrates is a man" (ii) "Cambridge blue is a colour" (ili) "A weight of two pounds is in magnitude". To voice my suspicion more explicitly: it might be Aristotle's view that if (a) "Sociates is F" is an occidental (non-essential) predication, (b) "F" signifies an item in category C, and (c) "has" expresses the converse of Aristotle's relation of inherence (presence in), deen the logical form of the proposition Socrates is F may be regarded as expressed by "Socrates has something which is. F" where 'is'. represents a sense of 'is' (of 'is essentially') which correspoads to category

C. The copula in such cases expresses the logical product of a constant relation expressed by 'has' and a categorially variant relation expressed by

'is' ('is essentially').

These predominantly scholarly murmurs agoinst the 'reccived' vicw that Aristotle regards existential statements (propositions) as the habitat of semantic multiplicity are not the only possible kinds of dissent. A different kind of complaint, against the viability of the position which I have been treating so far as if it were Aristotle's rather than against the suggestion that he in fact held it, would urge the untenability of the thesis, supposedly a foundation of his position that existentials are a particular type of subject predicate statements. 11 is possible (1 am not certain) that Owen voices something like this charge in ASO when he distinguishes single star and double-star existence. One form of such an objection would be that

"goats mumble"

, whether treated as a way of saying "goats always

mumble" or saying "goats usually mumble", or of saying "goats sometimes mumble", or as being indeterminate between these alternatives, has to be supposed to presuppose the existence of goats. This will be attested both by intuition, and by a need to extend to all interpretations a feature which is demanded for universal and particular statements, in order to escape ditficulties which arise in connection with the Square of Opposition. To suppose "goats exist" to be analogous to "goats mumble", would be to suppose that "goats exist" presuppose that goats exist; or to put it another way, the truth of "goats exist" is a necessary precondition of its being enher tre or faise that goats exist. This is an absurdity.

It seems to me that Aristotle can be defended against this attack. To begin with, the invocation of a semantic relation of presupposition is not the only recourse when one is faced with troubles about the Square of Opposition; one might, for example, try to deploy a pragmatic notion of presupposition which would not generate the alleged absurdity. But a more sericus defence might suggest that Aristotle has more than one method of handling existentials; that there are indeed two such methods,both subject-predicate in character, which when combined avoid the churge. In Metaphysics VIII, in; 1042h100., where the primary topic seems 10 be what kinds of attributes are constitutive of and differentiate between sons of sensible things, Aristotle argues the range of such crudal teatures is much larger than Democritus allows, and indicates ways of giving quasi definitions of a variety of sensible objects, such as threshold and ice, which contain analogues of genus and differentia. At this point, almose parenthetically, he gives a pattern of analysis for existentials about such things: the pattern consists (it seems) of the sequence some + genus* + l: + differentia*; c.g., "Some water is frozen" (an analysand for "ice exists") and "A stone is situated in threshold position" (an analysand for "a threshold exists"). We have, then, for certain existentials a definiens in subject-predizate form which by utilizing the elements in definitions, eliminates the word 'exists' altogether. I would suggest, on Aristotle's behalf that this climinative form could be employed lo analyst general existentials, like "ice exists" , "gonts exist", while the category citing forms.

like Socrates is a substance could be used to analyse singular existentials, like "Socrates exists".

B. Copulative Being and Semontc Mutiplicity

My strategy for an attempted presentation of in argument in support of the hypothesis that unified semantic multiplicity is to be located in the copula (or in a sub-tange of examples in which "be' is used as a copula, viz., cases of acedental predication) will be to put forward as a preliminary a partial sketch of a theory of categories, which I rogard as being in the main Aristotelian, to comment on some points of interest in that sketch, and finally to use it as a basis for the proposed argument. My sketch will depast from Aristotle's own position in one or, two respecis, thereby depicting. I think, i somewhat improved theory, and it will incorporate what seems to be a conspicuous excusion of his theory, though one which, so far as I can see, he might well have accepted without detriment to his account. My main hope is to put forward an outline of an account of categories which is overtly more systematic than the assemblage of dicta which one may extract from Aristotle's writings

(L) I start, much as Aristotle did in Caiegories, by distinguishing two Capital Predication Relations. My relations, which I shall call "izzing' and

"hazzing', are approximately the converses, respectively, of his relations being said of and being in (a subject); x izees (hazzes) y approximately iff y is said of (y is present in) x. I shall use the upper case letters 1 and 11 10 symbolize these relations, I shall begin by listing some of the formal properties which I wish to assign to these relations. I may remark that in one or two cases there seems to be options. Izzing is reflexive (Vxix izzes

x), Non-symmetrical (symmetry-neutral), and transitive. Hazzing, on theother hand, is ineflexive, either intransitive or transitivily-neutral (depending on which view is taken of an operation which I shall mention in a moment), and (i think) asymmetrical. In all cases, if an individual x izzes y, then y is essential to x in the sense that it x were not to izz y, then x would not (or would no longer) exist. It is, however, certainly not true in all cases that if x hazzes y, its hazzing y is essential to its existence; indeed, I am inclined to think, though 1 am not wholly confident that this is not truc in any casc. I am disposed to accept the following "mised" law. (0) 11 x I y and y H z, then x Hz; the acceptability of this law would depend on the idea that a non individual y hazzes something z ilt [of necessity] every individual falling under y (that is every indivicual that izzes y) hazzes 2. 1 am not disposed to accopf the "mixed" law. (ii) If x H y and y lz, then x Il z, since I would like to espouse the idea that a subject a (in any category other than that of x) harzes only individuals (in a somewhat technical sense of individual explained below); in which case, l might also espouse the idea that the copula can be analyzed in terms of the disjunction of & l y and x H something z which I y. But this procedure could easily be relaxed.

(2) Sone definitions can now be given.' It will be noted that, unlike Aristotle, 1 hare made izzing reflexive, so some of my definitions must differ from his, since I cannot claim, as le did in Caregories 3a7, that nothing tzzes an individual substance. The debnitions will run as follows:

1. I is an individual iff nothing other than x izzes x
2. x is a primary individual iff x is an individual and nothing hazzes x.
3. x is a primary substantial (x is in the category of "substance") iff sune primary individual izees x.
4. x is il secondary substance ig & is a primary substantial but not an individual.
5. x is identical with y iff x izzes y and y izzes x.
6. y is predicable of x iff either x izzes y or & huzzes something z which izzes y. (We may compare this last definition with my carlier suggestion of the analysis of the copula.)

(3) And y will be a primary element in some category other than that of substantials just in case there is a primary individual x [an individual which is a primary substantiall which hazzes something z which in tum izzes y (this allows for the possibility that z may be identical with y); but obviously, in the case of such 'forcign' predications a nethod will be needed for determining which 'foreign' category is involved as being the category of the predicated item y. Here it must be admitted that Aristotle's offering is less than fully satisfactory. We can atiempt to make use of the diflerent one-word interrogatives which can be extracted from

' An extended treatacot of my views about izzing and hazzing can te lamd in Alan Code, "Aristotie: Essence and Accident" in Richard Grandy und Richard Wiarner (eds.).

Pludosophicol Grounds of Rationality: Insentions, Calegories, Ends (Oxlord: Oxford

University Y'ress. 1966).Anstotle, with the supposition that items in a particular category may be suitably invoked to provide answers to just one of the kinds of questions asked by each of such interrogatives; but it is not clear that such a list of interrogatives is sufficiently comprehensive (relatives, for example, secm to escape this programme), nor is it clear what the rational basis would be for such a list of questions. And while Aristotle says much that is interesting about some particular categories, his attempts, for example in the cases of quantity and quality, to pick on primary distinguishing marks are neither clear nor clearly correct. Fortunately, however, for my present purposes, such shortcomings do not matter; it will be sufficient for me to assume the availability of some discriminating procedure (perhaps some furtirer development of the 'interrogatives method) since my main oracern is with the consequences of a scheme involving some procedure of such a cort

(4) At this point my sketch incorporates the previously mentioned extension of Aristotle's thcory of categories. I assume that there is an operation (which I shall call "substantialization) which, when appled directly to individuals which belong to a con-substantial category, relocates them (or counterparts of them) in a non-primary division of the category of substantials, thereby instituting or licensing the iclocated items as further subjects of hazzing; the items hazzed by them will inhabit non-primary divisions of categories other than that of substantials. Qualities of substances, for example, might be relocated as non primary substantials, thereby becoming subjects which hazz. (soy) fusther qualitatives of quantitatives, or whatever: that is to say. inhabitants of a non-primary division of this or that non-substantial category. So the category of qualitatives may include qualities of substances, qualities of substantialized qualities (or substantialized quantities) of substances, and so without any fixed limit. The scheme, as l envisage it: (a) would, provide for substantialization with respect to some, but not necessarily to all, items which initially belong to some non-substantial category; some categories, however, might be inebigible for the application of substantialication, and in other categories it might be that only sub-categories would be eligible for substantialization; (b) would ensure that substantialization went hand-in hand with beooming a subject of hazzing; but (e) would not guarantee that substantialiced items would hazz further items in every non-substantial catessory.

The scheme as 1 have set it out is absirace of 'mathematical' in character: and it would be necessary to make sure that it could have application to concrete cascs. It might also, even if concretely applicable, be oaly partial in character; it might, for example, provide for one kind of category (say

"logical categories'), but leave other kinds of categories, like sensory categories, unprovided for. But if some version of it were to prove viable, that would generate several philosophical dividends.(l) The scheme would leave room in more than one way lor sub. categorial diversities within a given overall entegory, (a) There might be distinctions ictween, for cxample, qualities of substances, qualitics of quantities of substances, qualities of quantities of actions of substances, and so forth. All of these specifie classes would fall within a general category of quality: and there would be opportunity to legislate (if that should be desirable) against any item's belonging to more than one sub-division. (b) Within an already discriminated category or sub-category there might be a categorial distinction between substantializable and non-substantialicable items.

(2) There will be room (again should it seem otherwise desirable) 1o adopt a cruerion of realiy distinct frem the perhaps increasingly cedious Quinian condition of being "quantifiable over"

* One might, for example,

insist that reality attaches, or full reality attaches, only to items which besides being izzers, being izzed, and being huzzed, are themselves haziers (that is, are susceptible to substantialication).

(3) Since it cannot be assumed that a non-primary substantial will receive predicables in every non-substantial category, there is room for distinctions of richness between the range of categories from which predicobles apply to one huzzer, and that from which predicables apply to another; and these variations in predicationable richness could be used as a measure of degree of reutty (the richer the realer, with primary substantials at the topi.

III. Semantic Multiplicity and Mulliplicity of Meaning

It is now time to take stock. I have discussed two different suggestions about the possible location of semantic multipticity associated with the notion of being. One would lie ta the range of maximally general specitications of the notion of existence (of the use of the verb to be' to signify existence); the other would lie in the use of the copula to signify different predication relations. Both suggestions seem to have solid Aristotelian foundations; the categorial multiplicity of the term 'exist' and the distinction between different fonns of predication relations are both well-established Aristochian docirines. So far, then, there might seem little room for a preference of one suggestion to the other. There are, however, two lines of reflection which in one way or another might upset this equilibrium. The first line of reflection would allow that Aristotle or an Aristotelian might have good reasons for secking two, rather than merely one, predication-relation, reasons perhaps conaected with intuitively acooptable restrictions on the scope of transitivity, and with a desire to block such unwanted inferential moves as "Socrates is white, white is a colour, so Socrates is a colour". But it will remain true that nocharacterization hos been given of the concept of a predication-relation; and though certain formal properties may have been assigned to izzing and hazzing, it is not clear that these formal properties would by themselves be adequate guides for someone wanting to be told how to apply the terms izzing' and luzzing' in particular cases. Nor is it clear whot extra formal supplementation could he provided, one would hardly suppose, for example, such relational terms to be susceptible of ostensive definition. It may then be that these relations do not (and presumably cannot) have a readily discernible character, a fact which if not a blemish at least creates a problem. It is possible then that despite initial appearances the notion of a predization-relation is not well-defined, and indeed that apparent examples of such relations are illusory. This line of reflection then, might confer better survival chances upon the first of the two suggestions here dstinguished. I am not sure how seriously to take this line of reflection.

The second line of reflection, however, is one which I am certainly inclined 10 take seriously. Unlike the first, it would not lavour the attribution to Aristole of one rather than the other of two viens about the location of a cortain semantis multiplicity. It would rather suggest. or conjecture, that the attribution to Aristotle of either view would involve a misconception of Aristotle's position, unless it wore accompanied by a recognition of a certain not immediately obvious distirction. It would be a mistake to suppose Aristotle to be holding that the existential "is signites a plurality of distinct universals and that therefore the existential 'is' bos a plurality of meaning; it would also he a mistake to attribute to Aristotle the view that the copulative 'is may signify one or another of lWo precication relations therchy signifyiog a plurality of universals, with the consequence that the copulative "is' has more than one meaning. What Aristole is really proposing is a separation of the question what universals ure, or may be, signified by a particular capression, from the question how many meanings that expression possesses. He is suggesting the possibility that a particular expression may have only one meoning and yet be used on different occasions to signify different universals. It is no doubt trus that historically universals were admitted to the realm of philisaphical disonurse in order to be itens in which the meaning of particular expressions might consist; but this historical fact does not establish an indissoluble connection between universals and the meanings of linguistic expressions; and it should be modified or abandoned should subsequent rational reflection provide reasons for adopting such a ovurse.

Universals and Meaning

I am aware that the suggestion, whether advanced on behalf of Aristotic or independently, that a distinction should be made between, on the onc hand, the universal or universals, which either in general or on a pasticularoccasion are signified by the expression, and, on the other hand, the meaning or meanings of the expression in question, which is likely to give rise to a sense of shock; 1 think, moreover, that susceptibility to this sense of shock will be independent of the question whether the person who feels it is friendly or unfriendly towards universals. Let us consider first the reaction of one who is friendly to universals. He will be liable to take the view that the reason for introducing universals in the first place was primarily, indeed exclusively, to equip ourselves with a range of items, cach of which would serve as that which was meant, or as one of the things that was meant by significant expressions. This is what universals do, and it is what they are supposed to do, and they do it perfectly well; it is not therefore in order te propose a severance of just that connection with meaning which gives universals a raison d'être. One who is unfriendly to universals can hardly be expected to be more sympathetic to the proposal, such a person might be unfriendly to universals either becausc, like Quine, while he is prepared to describe each of a multitude of expressions as being meaningtul, be is not prepared to count as legitimate specifications of what it is that a caningful expression means, or he is not prepared to allow that two distinct expressions may each mean the same thing. These denials are plainly linked; if it is legitimate to ask of two meaningful expressions, what it is that each mcans we can hardly preveat it from being the case, sometimes, that what each means is just the same as what the other means. Alternatively the enemy of universals might not wish to eliminate specifications of mcaning or the possibility of synonymy; his position is rather that an adequate account of the full range of meaning-concepts can be provided without resort to universals. But the enemies of universals, from whichever camp they come, may well insist that one who, unlike them, is disposed to bring in universals is not at liberty to contemplate divorcing them from that connection with meaning which he will have to allow as underlying their claim to existence.

I am not sure that such hostility to the general idea of divorcing the signification of one or more universals from the possession of one or more meanings is as solidly founded as initially it appears to be. If I ask someone whether he knows the birth place of Napoleon, he might reply in two quite dilferent ways. He might say "Certainly I do; he was born in Corsica." Altematively he might reply "I am afraid I don't. Napolcon was born in Corsica, 1 am afraid I have never been able to get to Corsica so I don't know the place at all." The obvious difference between these two distinct interpretations of the question seems to me to be plainly connected with the functioning of certain pronouns as (a) indirect interrogatives (b) as relatives; in my example, the first reply claims knowledge where Napoleon was born, the second claims ignorance of that place where (in which) Napoleon was born.

There are other ways of looking at the linguistic phenomenon presentedby my example, which are not incompatible with the way just outlined. and indeed which may tumm out to be uscful complementaries to it. One might draw attention to a distinction between knowledge of propositions and knowledge of things, suggesting that what the first respondent claims is propositional knowledge, whereas, what the second respondent disclaims is thing-knowledge; the second respondent exhibits a certain bit of propositional knowledge but professes substantial ignorance concerning the item to which his propositional knowledge relates. There is of course no reason why these two states should not coexist. While we are directing our attention to this approach, we night bear in mind that one kind of knowledge might be dependent on the other. It might, for example, be the case that knowing a thing a consists in the possession of a perhaps indefinitely extended supply of pieces of propositional knowledge, all of which are cases of propositional knowledge which relates to x; or alternatively, knowledge of x might consist not in an indefinite supply of pieces of propositional knowlcdge about x, but rather in the possession of a foundation or a base from which such propositional knowledge may be readily generated. Yet a further idea to be considered begins with the recognition that definite descriptions like many other kinds of phrases may, within a sentence occupy either subject position or predicate position; as some might prefer to put it, "the birth place of Napoleon" may be used either referentially or predicatively. It might then be suggested that in the mouth, or at least in the mind, of the first respondent the phrase "the birth place of Napoleon" occurs predicatively, whereas in the case of the second respondent it occurs referentially, as, potentially at least, a subject expression. If we suppose the phrase to occur predicatively in a given cose, it will be necessary that one should be able to point to a mentioned or unmentioned item to which the predicate in question might apply: then, in the case of the first respondent in normal circumstances there will be some particular item which he thinks of as, or believes to be, the birth place of Napoleon.

The relevance of this discussion to the topic of meaning and universals is that it may with some plausibility be alleged that those who have invoked universals as the items in which the meaning or meanings of significant expressions consist are guilty of representing such a phrase as "knowing the meaning of the word 'watershed " as referring to knowledge of an object or thing, as knowledge of "that which" the word watershed' significs or means (where the pronoun "which' is a relative pronoun); whereas, in fact, the phrase plainly refers to knowing what the word

'watershed means where the pronoun 'what' is indirectly interrogative rather than relative. The theory of universals as meaning, then, rests on a syntactical blunder; that this is so is attested by the fact that in principle at least the caning of an expression E, may be identical with the meaningof the expression Ez but plainly to know the meaning of E, is not the same as to know the meaning of Ez

This attack on the historical genesis of universals as the focal elements in a certain kind of anti-nominalistic theory of meaning, might encounter the following response. It might not be denied that the kind of syntactical blunder, which I have been attempting to expose, is in fact a blunder and has indeed been committed by some who have championed the cause of universals. It is, however, a remedial blunder which can be rectified, ultimately not only without damage, but even with advantage to the view of universals as the primary constituents of meaning. Once universals are admitted, they can be, and should be, thought of and accepted as being those items which are the meanings of this or that element of language. In the end, then, knowing the mcaning of an expression E would emerge as knowing what E mcans, that is, as propositional knowledge connected with interrogative pronouns rather than as thing-knowledge connected with relative pronouns. So everything comes right in the end; and the tie between universals and meanings cannot be put asunder.

This delence of the inviolability of the link between universals and meanings may be ingeniously contrived, but is not, I think, irresistible. If the specification of meanings were to provide not merely a useful mode of employment for universals once they are recognized as being around, but rather the sole justification and raison d'ete of the supposition that they are around, the specification of meaning would have to be not merely something that can be commodiously done with universals, but rather something which cannot be done or fully done without universals. To my mind this stronger requirement cannot be mct. There are, I think, some cases of expressions E such that knowing the meaning of E cannot comfortably be represented as knowing, with respect to some acceptable entity that it is that to which the description "the (a) meaning of E" applies. I offer two examples:

(1) If I were to say "The wind is blowing in the direction of Sacramento", any norally equipped English speaker would know the meaning both in general and on the current occasion of the phrase *in the direction of Sacramento; that is to say he would know both what in general the phrase means and what 1 mcant by it on the occasion of utterance. But such cxamples of knowledge of the meaning in general, and also the meaning relevant to a particular occasion, of a particular phrase, so far as 1 can sec, neither requires, nor is assisted by, the specification of an admissible entity which is to be properly regarded as that to which the description *the meaning of the phrase 'in the direction of Sacramento'" applics, cither senceally or on this occasion. It is unlikely that there is such an admissible entity, the phrase 'in the direction of Sacramento' does not seem to be one which applies to any particular entity; and even if it were possible to justifythe claim, such a justification scems hardly to contribute to one's capacity for knowing what such a phrase means.

(2) By a precisely parallel argument I may know perfectly well what is meant by the phrase the inducement which I otfer you for looking after my garden', even though I am neither helped nor hindered by the presence or absence of any thought to the effect that there is some admissible item which satisfies the description "the meaning of the phrase 'the inducement which I offer you for looking atter my garden' "

Before leaving this topic, I should make two comments: first, the fact that the concction between universals and meanings may not be inviolable does not dispense someone who wishes to modify it from obligations to make clear just what changes he is making; second, if a theory of meaning should fail to provide an indispensable rationale for the introduction of universals, it might turn out to be incumbent upon a metaphysician to offer an alternative rationale. But this question will have to wait for another occasion.

IV. Modes of Unification of Semantic Multiplicity

Let us for the moment retain an open mind on the nature of Aristolle's views about the connection between the unification of semantic multiplicity and the prescnce or absence of identity of meuning. Aristotle lists a number of modes of this kind of unification which I shall consider one by one. As one embarks on this enterprise one might well bear in mind the possibility that the list provided by Aristotle might not be intended to be exhaustive; and that the number and proper characterization of the modes which do occur in Aristotle's list is sometimes uncertain. Alistotle refers to cases in which a general term is applied by reference to a central item or type of items as ones in which there is a single source for a contribution to a single end. It is not clear whether he is giving a single general description or a pair of more specific descriptions each of which applies to a different sub-class of examples. I know no way of settling this uncertainty. The modes of unification actually listed by Aristotle consist in (a) what 1 shall call recursive unification in which the application of each member of a range of predicates is determined by the conditions governing the application of a primary member of that range, (b) what I may, with deference to G.E.L. Owen, call focal unification (unification which derives from connection with a single central item), (c) analogical unifiestion, in which the applicability of one predicate or class of predicates is generated by analogies with other predicates or classes of predicates, I shall consider these headings in order.Recursive Unification

The cases of recursive unification are primarily, though not exclusively. mathematical in character; they are also cases in which what one might call the "would-be" species of a generic universal stand to one another in relations excmplifying priority and posteriority. The Platonists, so Aristolle tells us, regarded such priority and posteriority as inadmissible between fellow species of a single genus. Aristotle does not explicitly subscribe to this view, but he does not explicitly reject it and is liable to act as if he accepted it. Why should priority and posteriority stand in the way of being different species of a single genus? Why should not different numbers be distinct species of the genus number? In the case of numbers, End. Eih. (121%aff.) attempts a reductio ad absurdum: if there were a form (universal) signified by "number" it would have to be prior to the first number, which is impossible; this argument might be expanded as follows: consider a sequence of "number-properties" (Pl, p?..., e.g., 2-ness, 3-ness ...): such a sequence satisfies, inter alia, the following conditions.

1. For any x and for any n 1, x instantiates Pi entails x does not instantiae pa-' (nor indeed any P').
2. For any x and for any n * 1, x instantiates P" entails something y (* x) instantiales pr-/
3. If P™ = P'
   , no counterpart of (a), (b) holds; so Pl is the first

number.

If the fulfillment of the abore conditions is to be sufficient to establish a sequence of properties as a sequence of number properties, then there cannot be a universal number; if there were, it would, like any genus, be prior to each of its species, and so prior to Pl; but since P' is the first number it cunnot have a predecessor and so nothing ean be prior to it.

There seem to be two objections.

1. It is by no means clear that the above conditions are sufficient to guarantee that a sequence of properties is a sequence of number-properties.
2. Even if they were, one part of them would not be fulfilled in the case of Pl and being a number; if x instantiates Pl (viz., 2-ness), x, not something other than x, will instantiate being a nuenber, a set whose cardinality is 2 itself instantiates being a number (as a cardinality)

If this route to a denial of the existence of a generic universal number fails there are two further possibilities.

(1) One might attempt to represent conformity to a "standard" genus-species-differentia model as being not just an acceptable picture of situations in which a more general universal has under it a range of subordinate universals which are its specializations, but as being constitu. tive for such examples of the existence of the more general universal. The slogan might be "For there to be a universal U, with specializations U,, U,, ..., U,, U has to be the genus of those specializations with all that that entails" (or, more bricfly, "no specialization without species"). The justification for such a claim will not be casy to find. While, intuitively. one might be prepared to accept the idea that a more general universal must be independent of its specializations in that the non emptiness of the general universal should be compatible with the emptiness of any particular specialization (though not of course with the emptiness of all specializations), it does not seem intuitively acceptable to make it a condition of the existence of U that any pair of specializations U, and U2 should be in this sense independent of one another.

(2) One might try a simpler form of argument. If the special cuses for the application of a general term E, that is to say, the universals U, ... U, are united by a single ordering relation R into a series 5, the elements of which [U, ... U.] cover every item to which E applies, and only such items, then we do not need a gencric universal U; its would-be species U, ... U, are already unified by membership of the series S. The expression

"being an instance of some universal in the series S" is of course applicable to anything to which E is applicable; but this expression does not even look like the name of a gonus.

Focal Unification

The second mode of unification to which semantic multiplicity may be susceptible, that of focal unification, is discussed at length in Metaphysics IV, i (T, ii) 1003a32f., there Aristotle brings up two of his favourite examples, the applications of the adjectives "healthy' and 'medical'. He states that everything to which the word "heulthy' applies is related to, in one way or another, the focal item of health, "one thing in the sense that it preserves health, another that in the sense that it produces it, another in the sense that it is a symptom of health, another because it is capable of it." Similar considerations apply to applications of the adjective 'medical',

"that which is medical is relative to the medical art, one thing being called medical because it possesses it, another because it is naturally adapted to it, another because it is a function of the medical art." On the most obvious interpretation of this passage Aristotle will be suggesting that standard semantic theory will be right in supposing the applicability of certain adjectives to particular items depends on a relationship of such items to an associated universal, but wrong in supposing that the relationship in question is invariably that of instantiation; other sorts of relationship are frequently involved. There is, however, a less obvious position which Aristotle might have been taking up; this position would maintain with respect to universals, that the only way in which individual items may be related to universals is that of instantiation: that there will beOther entities which will indeed be general entities though not universals; to them individual items may be related in a variety of ways which are distinct from instantiation. The rolative merits of these two ideas will be a matter for debate.

This mode of unification is of special interest in my present enquiry since Aristotle states quite plainly that this is the mode of unification which applies 10 the semantic multiplicity connected with being. Categorially cifferent sorts of things may all be said to be by virtue of different kinds of connections which they have to the focal item, which will be intimately connected with the notion of substance. This central item might be an individeal substance or, more likely, might be the notion of substantal type: any items which 'izzed' this type would be an individual substance and so would exist. But non-substantial items could also be said to be by virtue of their relationship (different in different cases) to the same central item; some things may be said to be because they are affections of substanee, others because they are a process towards substance, and su forth.

It is evident that Aristotle habitually thinks of the focal item as being a universal, or at least some kind of general entity; but such restriction is not mandatory, nothing prevents the focal item from being a particular.

Consider the adjective "French" as it occurs in the pluases, "French citizen", "French poem", "French professor". The following features are perhaps signilicant: (1) The appearance of the adjective in these phrases is what I might call "adjunctive" rather than "conjunctive" (or "attributive").

A French poem, is not as I see it, something which combines the separate eatures of being a poem and being French, as a fat philosopher would simply combine the features of being fat and of being a philosopher.

"French" here occurs, so to speak, adverbially. (2) The phrase "French citizen" standardly means "citizen of France", while the phrase "French poem standardly means "poci in French"; but it would be a mistake to suppose that this fact implies that there are two (indeed more than two) meanings or senses of the word "French". The word French" has only one meaning, namely "of or pertaining to France"; it will, however, be what I might call 'context senstive"; we might indeed say, if you like, that while "French" has only one meaning or sense, it has a variety of meanings-in-context; relative to one context, "French" means "of France" as in the phrase "French citizen", whereas relative to another context

"French" means, "in the French language" as in the phrase "French poem". Whether the focal item is a universal or a particular is quite irrelevant to the question of the meaning of the related adjective; the medical art is no more the meaning of the adjective 'medical', as France is the meaning of the adjective 'French'. As a concluding observation I may remark that while the attachment of the context may well suggest an interpretation in context of a word, it need not be the case that suchsuggestion is indefeasible. It might be for instance that "French poem" would have to mean "poem composed in French" unless there were counter indications; in which case, perhaps, the phrase might mean "poem composed by a French competitor" (in some competition). For the phrase

"French professor" there would be two obvious meanings in context; and disambiguation would have 10 depend on a wider linguistic context or on the cireumstances of utterance.

Analogical Unilication

I turn now to what is possibly the most baffling of the ways explicitly suggested by Aristotle as being those in which what I am calling USM may arise. These will be cases in which the application of an epithet to a range of objects is accounted for by analogy detectable within that range; more explicitly to analogies between the specific universals which determine the application of the epithet, or (perhaps) berween the exemplifications of those universals by this or that type of object. More explicitly to analogies between the specific universals U, and Uz etc., which determine the application of the epithet, or (perhaps) between the exemplifications of U,, Uz ete., by items of the sorts ly. lo etc., The puzzling character of Aristotie's treatment of this topic arises from a number of different factors. First there are two things which Aristotle himself might have done to aid our comprehension. He might have given us a firm list of examples of epithets, the application of which to a given range of objects is to be accounted for in this way; alternatively, he might have given us a reasonably clear characterization of the kind of accounting which analogy is supposed to provide, leaving it to us to determine the range of application of this kind of accounting. Unfortunately he does neither of these things; he offers us only the most meagle hints about the way in which analogy might unify the various applications of an epithet; we are told, for example, that as sight is in the eye, so intellect is in the soul with the implicit suggestion that this fact accounts for the application of the word 'see' both to cases of optical vision and cases of intellectual vision, and he also suggests that analogy is responsible for the application of the word 'calm' both to undisturbed bodies of sea water and to undisturbed expanses of air. Such offerings do not get us very far, furthermore, not surprisingly, where Aristotle seems to fear to tread the commentators are most reluctant to plant their own feet. Perhaps the least unhelpful suggestion comcs from Ross who suggests as Aristotle's view that the application of the word 'good' is attributable to the fact that within onc category things which are good are related to things in general belonging to that category in a way which is analogous to the way in which good things in some second category are related to the general run of things which belong to that second category. Apart from obscurity in thepresentation of this idea, Ross's suggestion takes for granted something which Aristotle himself does not tell us, namely that the application of the epithet 'good' is one exemplification of unification which is the outcome of analogy: Ross's suggestion about 'good' would, moreover, be at best only a description of one special case of analogical unification, and would not give us any general account of such unification. I might add that little supplementary assistance is derivable from those who study general semantic concepts; such persons seem to adhere to the principle that silence is golden when it comes to discussion of such questions as the relation between analogy, metaphor, simile, allegory and parable.

So far as Aristotle himself is concerned it seems fairly clear to me that tie primary notion behiad the concept of analogy is that of 'proportion'.

This notion is embodied, for example, in Aristotle's treatment of justice. where one kind of justice is alleged to consist in a due proportion between return (reward or penalty) and antecedent desert (merit or demerit) but it remains a mystery how what starts life as, or as something approximating to, a quantitive relationship gets converted into a not-quantitive relation of correspondence of allinity. It looks as if we might be thrown back upon what we might hope to be inspired conjecture.

I take as my first task the provision of an example, congenial to Aristotle, of the unification by analogy of the application to a range of objects of some epithet. I shall expect this to involve the detection of analogical links between the exemplifications of the varicty of universals which the epithet may be used to signify. My chosen specimen is the verb grow. In this case a number of different kinds of shifts might be thought of as possessing an analogical unification. One of these would be examples of shifis in respect of what might be termed syntactical metaphysical category. A substance, indeed a physical substance like a lump of wax or a mass of metal, might be said to grow; and it would be tempting here to suggest that the relevantly involved universal, that of increase in size or getting larger, provides the toundational instance of the signitication of a universal by the word "grow'; we have here, so to speak, the 'ground-floor' meaning of the verb. But not only the physical substance itself but the various accidents of the substance may also be said to grow; not only the piece of wax but its magnitude, some event or process in its history, its powers or causal efficacy and its aesthetic quality (beauty) might each be said to grow; and it seems not unplausible to suggest that though growth on the part of these non-substantial accidents might be different, and more or, again, less boringly connected with growth on the part of the substance, there will always be some kind of correspondence or analogical connection between growth in the case of a non-substantial item and growth in the case of a substantial item. Another and different kind of calegorial variation may separate some of the universals which the word

"grow' may be used to signify from others; these will be connected withdifferences in the sub-categories within the category of suistance within which fall different sorts of entitics which may be said to grow; different universals may be signified by sonicone who speaks of a plant as growing and by someone who speaks of a human being as growing, and the confection between these diverse realizations of growth may rest on analogy. In what is called the growth of a plant, internally originated increase in size may occupy a prominent place, whereas in the case of a buman being the kind of development which may be involved in growth may be much more varied and comples; the link between the two distinct universals which may be signified might be provided by analogy between the roles which such changes fulfill in the development of the very different kinds of substances which are being characterized. No doubl many further kinds of analogical connection would emerge within the general practice of attributing growth.

My next endeavour will be an attempt to supply some general account of the way in which the presence of analogy may serve to unify semantic multiplicity; and if such an account should be found to offer prospecis of distinguishing analogy from other concepts, particularly metaphor which belongs to the same general family, that would be a welcome aspect of the account. It is my idea that in metaphorical description a universal is signified, which though distinct from that which underlies the literal meaning of an epithet is nevertheless recognizably similar to that literal signification

I come now to the notion of analogy itself. I shall start by considering items any one of which may be called an S,; I shall initially suppose that being an S, consists in belonging to a substantial type or kind, S,. though that supposition may be relaxed later. My first move will be to assume that being an S, consists in being subject to a systern of laws which jointly express the nature of the type or kind Si; and further that these laws, which furnish the central theory of S,, will all be formulable in terius of a finite set of S,-central propertics (let us say P, to P,); each law will involve some ordered extract from the central set, and their totality will govern any tully authentic Sy. This totality may well not include all the laws which apply to S,: but it does include all the laws which are relevant to the identity of Sy, all the laws which determine whether or not a particular item is to count as an 5,-

Let us next consider not merely things each of which is an S,, but also things each of which is an Sz; it is to remain at least for the moment an open question whether or not the typeS, is identical with the type S1. 1 assume that, as in the case of S,, membership of S, is determined by conformity to a system of laws relating to properties which are central to S2. I shall symbolize these properties by the devices Or ... Q.. We now have various possibilities to consider. The first is that every law which is central to the determination of Sz is a mirror image of a law which iscentral to S,; and that the converse of this supposition also obtains. To this end we shall assume that the properties which are central to being an $, are the properties O, through Os; and that if a law involving a certain ordered extract from the set P, through P, belongs to the central theory of Sto a law involving an exactly corresponding ordered extract from the set O, through , will belong to the contral theory of Sa; and that the same holds in reverse. In that case, we shall be in the position to say that there is a perfect analogy between the central theories of S, and Sz; and in that case, it may also be tempting to say that the types S, and S, are essentially identical. We should recognize that if we yield to this temptation we are not thereby forced to say that Sy and S, are indistinguishable, they might, for example, be differently related to perception, only one of them (perhaps) being accessible to sight; we shall only be forced to allow that essentially, or theoretically, the types are not distinct; how that is to be interpreted will remain to be seen.

The possibility just considered is that of a total perfect analogy between the central theories of S, and Sa. There is also, however, the possibility of a partial pertect analogy between S, and Sz. That is to say pait of the central theory of one type (say S,) may mirror the whole of the central theory of Sz, or again may mirror some part of a central theory of Sz. In such circumstances one might be led to say (in one case) that the type S, is a special case of the type S,; or (in the other case) that the types S, and S, both fall under a common super-type, determined by the limited area of perfect analogy between the central theories of S, and Sz. A third possibility will be that no perfect analogy, either total or partial, exists between the two central theories; the best that can be found are imperfect analogies which will consist in laws central to one type approximating, to a certain degree, with the status of being analogues of laws central to the other.

At this stage, I would propose a relaxation in the characterization of the signification of such symbols as 'S!', 'Sz etc., which till now I have been regarding as signifying substantial types or kinds, reference to which is made in more or less regimented discourse of a theoretical or scientific sort. I shall now think of such symbols as relating to what I hope might be legitimately regarded as informal precursors of the aforementioned substantial types, as expressing concepts of one or other classificatory sort, concepts which will be deployed in the unregimented descriptions and explanations of pre-theoretical. Examples of such unregimented classifica-tory concepts might be the concepts of an investor, a doctor, a vehicle, a confidante, and so on. I would hope that in many ways their general character might run parallel to that of their more regimented counterparts.

In particular, one might hope and expect that their nature would be bound up with conformity to a certain set of central generalitics (platitudes, truisms, etc.); to be an investor or a vchicle will be to do a sufficientnumber of the kinds of things which typically are done by investors or vehicles. One might expect, however, that the varicty of possible forms of generalization might considerably exceed the meagre armament which theoretical enquirers normally permit themselves to employ. One might also hope and expect that the generalities which would be expressive of the nature of a particular classificatory concept would be formulable in terms of a limited body of features which would be central to the concept in question. This material might be sufficient to provide for the presence from time to time of analogy, at least of imperfect analogy, between scucralities which aro expressive of distinct classificatory concepts. When they occur, such analogies might be sufficient to provide for semantic unity in the employment of a single epithet to signify dilferent classificatory concepts; and this semantic unity, in turn, might be sufficient to justify the idea that in such cases the expression in question is used with a single lexical meaning.

Conclusions

I conclude the presentation of my suggestions about the interpretation of the notion of analogy as a possible foundation for semantic unity with two supplementary comments. The first is that there scems to be a good ease for supposing that anyone who accepts this account of analogy-based unity of meaning is not free to combine it with a icjection of the analytid synthctic distinction. The account relies crucially on a connection between the application of a particular concept and the application of a system of laws or other generalities which is expressive of that concept, and, this in tum, relies on the idea of a stock of further concepts, in terms of which these laws or generalitics are to be formulated, being central to the original concept. But it seems plausible, if not mandatory, fo suppose that such contrality involves a non-contingent connection between the original concept and the concepts which are said to be central to it, a connection which cannot he admitted by one who denies the analytic/synthetic distinction. So either one accepts the analytic/synthetic distinction or one rejects at least this account of analogy-based semantic unity. I make no attempt here to decide between these alternatives.

Ihe second comment is that matcrial introduced in my suggested claboration of the notion of unalogy, particularly the connection between concepts and conformity to laws or other generalities, may serve to provide a needed explanation and justification of the initial idea that the applicability of a single defining formula, couched in terms of the ideas of genus, spocies, and differentia is a paradigmatic condition, if not an indispensable condition, for identity of meaning. We might, for a start, agree to treat a situation in which the applicability of an epithet to an item i, rests on a conformity to exactly the same laws or generalities as does itsapplication to item iz, as being a limiting case of partial perfect analogy.

Situations in which no icinterpretation at all is required may be treated as limiting cases of situations in which, though reinterpretation is required. one is available which ochieves partial perfect analogy. As one might say, a law is perfectly analogous with itself. Situations, then, in which an epithet applies to a range of items solely by virtue of the presence of a single universal, and so of a single set of laws, may be legitimately regarded as a specially exemplary instance of a kind of unity which is required for identity of meaning.

V. Some Larger Issues

Both a proper assessment of Aristotle's contribution to metaphysics and the theory of mcaning and studies in the theory of meaning themselves might profit from a somewhat less localized attention to questions about the relation between universals and meaning than has so far been visible in my rellections. I have it in mind to raise not the general question whether, despite the Nominalists, a theory of meaning requires universals (to which I shall for the moment assume an affirmative answer), but rather the question in what way universals are to be supposed to be relevant to meaning.

1. Consideration of the practices of latter-day lexicographers, so far from supporting a charge that, at least on my interpretation of him, Aristotle has proposed an illegitimate divorce between universals and mcaning suggests that it would be proper to go a deal further than did Aristotle himself in championing such a divorce, There will be many different forms of connection between the varicty of universals which may be signified by a non-equivocable expression beyond that countenunced by the tradition of Theory of Definition, and even perhaps beyond the extensions to that theory envisaged by Aristotle himself. These will include some forms of connection like those involved in metonymy and synecdoche, recognized by later grammatical theorists, and no doubt others as well. It would, I suggest, be a profitable undertaking to study carefully the contents of a good modem dictionary, with a view to constructing an inventory of these various modes of connection.
2. Such an investigation would, I suspect, reveal both that in a given case the invocation of one mode of concction may be subordinate and posterior to the invocation of another, and also that there is no prescribed order or limitation of order which such invocations must observe.
3. I suspect, also, that it might emerge that the question whether variations of meaning are thought of as synchronie or diachronic has no beating on the nature of the uniting connections. The same forms of connection will be available in both cases, and these in turn may well befound to correspond with the range of different figures of speech which conversational practice may typically cmploy.

   (4) Should this conjecture turn out to be correct, the underlying explanation of its truth might, I would guess, run along the following lines.

   Rational human thought and communication will, in pursuit of their various parposes, encounter a boundless and unpredictable multitude of distinct situations. Perhaps unlike a computer we shell not have, ready made, any vast altay of forms of description and explanation from which to select what is suitabie for a particular occasion. We shall have lo rely on our rational capacities, particularly those for imaginative construction and combination, to provide for our needs as they arise. It would not then be surprising if the operations of our thoughts were to refleet, in this or that way, the character of the capacities on which thought relies. I have to confess to only the haziest of conception bow such an idea might be worked out in detail.