On What Sorts of Thing There Are

Mind Association

On What Sorts of Thing There AreAuthor(s): Leslie StevensonSource: Mind, New Series, Vol. 85, No. 340 (Oct., 1976), pp. 503-521Published by: Oxford University Press on behalf of the Mind AssociationStable URL: http://www.jstor.org/stable/2253037 .

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On What Sorts of Thing There Are

LESLIE STEVENSON

A generation ago Quine attributed a curious simplicity to the ontological problem: that it can be put in three Anglo-Saxon monosyllables: 'What is there?" Those beguiling opening words already betray the assumption I want to attack, for the use of the phrase 'the ontological problem' presupposes that there is exactly one such problem.

Of course, Quine's main contribution has been to divide the problem into the two questions of what a theory says there is, and what theory we should accept. To answer the first question, he offers his famous criterion for the ontological commitment of a theory-paraphase it into the first-order predicate calculus, and look to the range of values of the bound variables. To answer the second, he claims that our assessment of an ontology is on a par with our assessment of scientific theories in general. Quine's emphasis on theories surely represents an advance over conceptions of ontology as the description (in a quite ordinary sense) of the general structure of the universe.2 But I am going to argue that Quine, and many of his critics, have blurred his insights by failing to separate three different meanings of that crucial semi-technical phrase 'the ontological commitments of a theory'.

i Three kinds of ontological problem

Let me first give examples of what I see as three different levels of dispute about what there is. At the first level, two people may

W. V. Quine, 'On What There is', in From A Logical Point of View (LPV) (Cambridge, Mass., I953), I.

2 See, for example, G. E. Moore: 'It seems to me that the most important and interesting thing which philosophers have tried to do is no less than this; namely: to give a general description of the whole of the Universe, mentioning all the most important kinds of things which we know to be in it. . . '-in Some Main Problems of Philosophy (London, 1953), i. Such conceptions are by no means dead; see N. Wolterstorff: 'Ontology, as I shall understand it and try to practice it, is a description of the most general structure of what there is. . ., I hold that we can know not only our conceptual scheme, but that to which our conceptual scheme applies'-in On Universals: An Essay in Ontology (Chicago, 1970), xii.

503



504 LESLIE STEVENSON:

disagree about whether there is a monster in Loch Ness, about whether there were more than three shots fired at Kennedy on that fatal day in Dallas, about whether there is a sub-atomic particle with a certain mass and charge, about whether there is an even number which is not the sum of two primes. In each case, what one side says there is the other side maintains there isn't, so the dispute may be said to be straightforwardly over the truth or falsity of a certain existential statement.

For an example at the second level, consider Davidson's claim that the logical form of 'Brutus stabbed Caesar with a knife' is a formula intprpreted as 'There was an event which was a stabbing of Caesar by Brutus and was done with a knife'. The claim follows from a general theory that the proper logical analysis of sentences about actions involves bound variables ranging over events and therefore requires that events be part of our ontology.1 An opponent of this theory, who denies that quantification over events is implicit in our ordinary talk of actions, need not disagree with Davidson about the truth of any particular action-sentence involving Kennedy or Caesar or anyone else. The dispute here is not over historical facts, but about the correct logical analysis of a whole class of historical statements. We can take two more examples of this second level of ontological question out of Quine's own mouth.2 He suggests that 'a theory might accommodate all rabbit data and yet admit as values of its variables no rabbits or other bodies but only qualities, times, and places'. When told that there is a rabbit in the yard, the adherent of such a theory (the immaterialist) need not disagree; in practice he will continue to talk of physical objects like everyone else, but he holds that in theory such talk must be analysed without use of quantification over bodies. Quine also suggests the case of 'someone who has for reasons of nominalism renounced most of mathematics and settled for bodies as sole values of his variables.... He will agree that there are primes between io and 20 when we are talking arithmetic and not philosophy. When we turn to philosophy he will condone that usage as a mere manner of speaking, and offer the paraphrase.' So the immaterialist and the arithmetical nominalist are not disputing the truth of any particular statements about bodies or numbers, but recommending paraphrase of all such I D. Davidson, 'The Logical Form of Action Sentences' in N. Rescher, The

Lgic of Decision and Action (Pittsburgh, I967). 2 Quine, 'Existence and Quantilication', in Ontological Relativity and Other

Essays [OR] (New York, I969), 98-IOO.



ON WHAT SORTS OF THING THERE ARE 505

talk into terms which do not require quantification over bodies or numbers.

Disputes at the second level are thus independent of disagree- nents at the first. But there is, I suggest, a third level of ontological question which is similarly independent of the first two. For consider two philosophers McX and McY who not only agree about all questions in zoology, history, physics and mathematics, but are also in accord about how the statements in these various disciplines are to be paraphrased into the language of first-order logic, that is, they agree about what predicates and what ranges of values of individual variables are required in such paraphrase. McX and McY will be happy to find that despite this rare unanimity they can still argue about whether the use of predicates commits us to the existence of corresponding properties, or if the truth of sentences involves the existence of corresponding facts. This third kind of ontological problem is, then, whether an adequate semantic understanding of first-order languages requires us to assign extra-linguistic correlates to other types of linguistic expression besides singular terms. It is clearly at an even higher level of generality than the second kind of problem, for it does not concern any particular subject-matter but is a matter of the semantics of any talk at all. The traditional ontological problem of universals must surely be located at this third level.

At this point someone will be sure to suggest that any differences between these three alleged levels of ontological question are only differences of degree, and not of any ultimate philosophical importance. For it could be argued that the disputes at all three levels can be represented as over the truth of the appropriate existential statements, e.g. 'There is a monster in Loch Ness', 'There are events', 'There are properties', so that the only difference is in the generality of the relevant terms, which is not a matter of logical interest. Indeed Quine himself has often expressed such an attitude, notably in his rejection' of Carnap's distinction between internal and external questions of existence, which is closely akin to our distinction between the first and second levels above. The fact that agreement at one level does not entail agreement at another (e.g. the nominalist who will admit that there are primes between io and zo when we are talking arithmetic, but not when we are talking philosophy), is perhaps some argument

I Quine, 'On Carnap's View on Ontology', in The Ways of Paradox and Other Essays [WP] (New York, I966).




that the differences are not just in the degree of generality of terms. But no doubt more than this will be needed to persuade someone who resolutely maintains Quine's holistic approach to ontological questions. In what follows I will argue that when we closely examine what Quine himself has said over the years, in the effort to clarify his notion of the ontological commitments of a theory, we will find that three more technical notions emerge, which correspond exactly with the three levels we have distinguished informally above.

2 The existential statements implied by a first-order theory

In this sense of 'theory', a theory is a set of sentences expressed in the first-order predicate calculus. Any theory worth talking about will be consistent, so it will not be closed under negation, but we need not refuse to call even inconsistent sets theories. We could insist that a theory be deductively closed, i.e. that it contain all the sentences entailed by any subset of its sentences, but we shall see that this does not matter for our purposes.' The important thing to clarify here is in what ways a set of sentences of first-order logic can be interpreted, for we are not interested merely in the syntactic properties of the logical formulas but in their being interpreted as formalizations of what we may want to assert. I'he standard Tarskian set-theoretic semantics, expounded in all the logic textbooks nowadays, specifies a basic domain as the range of values of the individual variables, and then assigns subsets of that domain to the predicates, and so on. Thus a domain of numbers would be assigned to an arithmetical theory, a domain of people to a bit of everyday gossip. But it is apparent that this is not what Quine has in mind, at least in some places where he talks of the ontological commitments of theories. For he says 'the variables of quantification, "something", "notning", "everything", range over our whole ontology, whatever it may be' [LPV, I3]

and 'such is simply the intended sense of the quantifiers "(x)" and "(3x)": "every object x is such that", "there is an object x such that"'.2 Quine thus wishes to follow Frege in having all I Quine sometimes defines a theory as deductively closed (see Ontological

Relativity, 5i) but elsewhere he does not require this (see his 'Replies', in Davidson and Hintikka, Words and Objections [WsOs] (Dordrecht, 1969), 309). Quine usually requires that a theory have no singular terms other than variables, but I need not insist on this for my purposes here.

2 WFord and Object [WO] (Cambridge, Mass., I960), 242; cf. The Roots of Reference [RR] (La Salle, Ill., I974), 98, I00.




objects together in one huge domain for quantifiers, but unlike Frege he realizes that it is a controversial matter what should go into this domain, since different people have conflicting views about what 'all objects' includes. What then of the predicates? In many places, Quine seems content to identify them with words or phrases of English, and uses a mixture of English and logic, e.g. '(3x) (x is a dog)'.

It is thus apparent that one of the ways in which Quine uses the word 'theory' is to mean any set of sentences with predicates of English, and with quantifiers whose range is unspecified except to say that it is the whole ontology, whatever that may be. He then proceeds to offer criteria for the ontological commitment of such a theory, in terms of what must be in the range of the variables if the theory is to be true. Thus in the first edition of From a Logical Point of View, p. I03, he says:

An entity is assumed by a theory if and only if it must be counted among the values of the variables in order that the statements affirmed in the theory be true.

This criterion makes ontological commitment a relation between a theory and an entity. It therefore suffers from two serious disadvantages. Firstly, we could not say that a certain theory is committed to a dubious entity like the Loch Ness monster without presupposing its existence ourselves, for if a relation holds at all there must exist that to which it holds. We would thus be entangled in 'Plato's beard', the doctrine that nonbeing must in some sense be, which is exactly what Quine wants to avoid [LPV, I-2]. Secondly, the criterion assigns no ontological commitment even to a theory which says '(3x) (x is a dog)', since there is no particular dog which must be in the range of 'x' for that sentence to be true.

Realizing this second point, Quine has more recently said: Of course a theory may, in this sense, require no objects in particular, and still not tolerate an empty universe of discourse either, for the theory might be fulfilled equally by either of two mutually exclusive universes. If for example the theory implies '(3x (x is a dog)', it will not tolerate an empty universe; still the theory might be fulfilled by a universe that contained collies to the exclusion of spaniels, and also vice versa [OR, 96].

Presumably this is why in the second edition of From a Logical Point of View [2nd ed., IO3], Quine changed the above criterion to:




Entities of a given sort are assumed by a theory if and only if some of them must be counted among the values of the variables in order that the statements affirmed in the theory be true.

We must assume, I think, that by 'sort' here Quine does not mean any-thing more mysterious than 'class'. Indeed, in a later formula- tion of the criterion he uses only the notion of class:

To show that a theory assumes a given object, or objects of a given class, we have to show that the theory would be false if that object did not exist, or if that class were empty [OR, 93].

This criterion still makes ontological commitment a relation between a theory and its objects, and therefore it is still entangled in Plato's beard, for how can we say that a theory which implies '(3x) (x is a unicorn)' is committed to objects in the class of unicorns without ourselves presupposing that the class is non- empty? If we try saying that the commitment is to the class, rather than to the objects in the class, then we fall foul of Church's point that commitment to unicorns is not the same as commitment to purple cows, even though the class of unicorns is identical with the class of purple cows, being the empty class.' Another defect of the last-quoted criterion is that it allows all manner of apparently extraneous entities into the relevant classes. Consider for example the class which contains all dogs together with the prime numbers between io and 2o: '(3x) (x is a dog)' would be false if that class were empty, but we would not want to say that it requires all the objects in the class, yet the criterion gives us no way of excluding the irrelevant members. To do this, Quine must say that a theory is committed to (all) the objects of a class if and only if that class is the smallest class C such that any range in which the theory is true must include some members of C. But in any case Cartwright has convincingly shown that we cannot eliminate the modal 'must' or the counterfactual 'would be' from the above criteria without getting unacceptable results.2

What we have to recognize is the irreducible intensionality of the notion of the ontological commitment of a first-order theory, as

I A. Churclh, 'Ontological Commitment', Yournal of Philosophy, lv (i958), IOI3 note.

2 R. Carfwright, 'Ontology and the Theory of Meaning', Philosophy of Science, xxi (1954), 36-325X




a stream of papers have argued over the last twenty years.' It is the sense of the predicate in '(lx) Fx', or of the singular term in '(3x) (x a)', which determines the ontological commitment. The commitment cannot be a relation to an entity or entities, on pain of getting entangled in Plato's beard. It can only be commitment to the truth of an existential statement. Quine recognizes this in his doctrine of 'semantic ascent', according to which we must formulate an ontological dispute not by talking about disputed objects (for that already gives away the game to the affirmative side) but by 'characterizing the statements' which are affirmed and denied [LPV, I6, the phrase 'semantic ascent is introduced in the last section of WO]. But what Quine does not seem fully to recognize, presumably because of his suspicion of all talk of meaning, is that it is hardly enough to characterize just the sentences, the concrete inscriptions and utterances, which are involved in an ontological dispute. For we surely want to understand what is being affirmed or denied-in particular, he who takes the negative side must understand what his opponent is asserting, for it is precisely the negation of what he says himself.

On this understanding of the matter, we can say that a theory is 'ontologically' committed to the truth of '(3x)Fx' or of '(3x)(x = a)' if and only if it implies '(3x)Fx' or '(3x)(x = a)'. And this shows why it does not matter whether we define a theory as deductively closed-if we do, then for 'implies' we can substitute 'includes' in the last sentence. The important point is that either way, the notion of entailment or logical implicatiLon is crucially involved. Thus the wlhole semnantical excursion through 'what must be in the range of the variables' just brings us back in the end to the truism that the ontological commitment of a theory is what it says or implies there is. Problems can be raised, however, about just how we should decide the existential implications of a theory.2 If a theory implies '(3x)(x is a bachelor)' does it therefore imply '(3x)(x is an unmarried male)'? If it implies '(3x)(x is a winired horse)' does it therefore imply '(3x)(x is a wing)'? At this

Cartwright, op. cit.; Church, op. cit.; N. Chomsky and I. Scbeffler, 'What Is Said to Be', Proceedings of the Aristotelean Society, lix (I958-9), 7I-82; T. Parsons, 'Extensional Theories of Ontological Commitment', journal of Philosophy, lxiv (I967), 446-450, and 'Various Extensional Notions of Ontological Commitment', Philosophical Studies, xxi (1970), 65-74; M. Jubien, 'The Intensionality of Ontological Commitment', Nous, vi (1972), 378-387; J. WV. Oliver, 'Ontic Content and Commitment', in R. H. Severens, Ontological Commitmnent (Athens, Ga., 1974). See C. S. Chihara, Ontology and the V7iciouis-Circle Principle (Ithaca, N.Y., 1973), ch. III, section 3.



5IO LESLIE STEVENSON:

stage, I think the clearest answer to these questions is to assume that each theory has a certain finite vocabulary of predicates, and to say that its implications are just those that hold in virtue of logical form alone. Thus a theory is defined as a certain set of sentences, and it implies p if and only if p is a logical consequence of that set in the first-order predicate calculus. So the above implications would hold if and only if the theory included or implied '(x)(x is a bachelor v x is an unmarried male)' and '(3x)(x is a winged horse) v (3x)(x is a wing)'. The question of regressing into a metalanguage will come up in the next stage of our analysis.

3 The range of variables of a first-order language

In one of his replies to critics in Words and Objections, Quine makes a crucial distinction which throws new light on his preceding thirty years of ontological lucubration:

My remaining remark aims at clearing up a not unusual misunderstanding of my use of the term 'ontic commitment'. The trouble comes of viewing it as my key ontological term, and therefore identifying the ontology of a tlheory with the class of all things to which the theory is ontically committed. This is not my intention. The ontology is the range of the variables. Each of various reinterpretations of the range (while keeping the interpretations of predicates fixed) might be compatible with the theory. But the theory is ontically committed to an object only if that object is common to all those ranges. And the theory is ontically committed to 'objects of such and such kind', say dogs, just in case each of those ranges contains some dog or other [WsOs, 315].

The last two sentences still fail to recognize the intensionality of ontological commitment. But the important point for us now is the distinction drawn between the ontology of a theory and its ontic commitment. (I assume that the change from 'ontological' to 'ontic' is merely an abbreviation.) In saying that the ontology of a theory is the range of its variables, Quine seems to be presupposing a rather different sense of 'theory' from that discussed above. For it looks as if a theory in this new sense must somehow involve a specification of the values of its variables, whereas in the former sense the range was left unspecified except to say that it




is the whole ontology, whatever that may be. And yet when Quine talks of reinterpretations of the range being compatible with the theory, it does not fit very well with his preceding sentence, for if a theory somehow specifies its range, to reinterpret the range is to change the theory. I think we have to conclude that this passage shows Quine hovering between two senses of 'theory'-first-order theories with ranges left unspecified (as discussed in Section 2 above), and another notion of theories with specified ranges. Much of Quine's ontological talk, early and late, makes sense only on the latter understanding of 'theory':

We may be said to countenance such and such an entity if and only if we regard the range of our variables as including such an entity [WP, 66]. The objects we are to be understood to admit are precisely the objects which we reckon to the universe of values over which the bound variables of quantification are to be con- sidered to range [WO, 242]. What there are, according to a given theory in standard form, are all and only the objects that the variables of quantification are meant in that theory to take as values.'

The notions of 'regarding', 'reckoning' and 'meaning' are surpris- ingly subjective-sounding to come from the mouth of a professedly extensionalist logician in his formulations of a crucial notion, but they fall into place as mere figures of speech if we assume that specifying the range of the variables is part of putting a theory into 'standard form'.

Indeed, we noted above that the specification of a domain for the individual variables is a basic part of the standard Tarskian semantics for first-order theories. But Tarski's work has shown us that discussion of the semantics of a theory must take place in a metalanguage distinct from the object language. A first-order theory can hardly specify the range of its own variables; the specification must be done in a metalanguage. This is surely the basic insight behind Quine's recent doctrine of 'ontological relativity':

We cannot require theories to be fully interpreted, except in a relative sense, if anything is to count as a theory. In specifying a theory we must indeed fully specify, in our own words, wh-iat s,entences are to comnrise the theory, and what things

I Philosophy of Logic [PL] (Englewood Cliffs, N.J., 1970), 89.




are to be taken as values of the variables, and what things are to be taken as satisfying the predicate letters; insofar we do fully interpret the theory, relative to our own words and relative to our overall home theory which lies behind them. But this fixes the objects of the described theory only relative to those of the home theory; and these can, at will, be questioned in turn [OR, 5I].

But much remains mysterious in this talk of theories and home theories. One thing that needs clarifying is the relation between theories and languages. A theory is surely a set of sentences within a language, and if the theory is consistent it can contain at most one of any pair of contradictory sentences; whereas a language can be said to consist of all the sentences which its grammatical rules generate, and is thus closed under negation. Now when we specify a range of variables for a theory, we ipso facto specify a range for the language in which that theory is expressed. For example, if our theory includes the sentence '(3x)(x is a monster & x is in Loch Ness)' and the range of 'x' is physical objects, then a theory which implies the negation of that sentence has just the same ontology of physical objects, for the negation of a quantified sentence must have the same range of values as the sentence itself. This is why I have given this Section the title it bears. And indeed, some of Quine's earliest formulations of his ontological criterion are in terms of languages rather than theories:

What entities there are, from the point of view of a given language, depends on wnat positions are accessible to variables in that language [WP, 68; see also 'Designation and Existence', J. Phil., xxxvi (I939), 708].

It seems, then, that it is theories which have ontological commitments, but languages which primarily have ontologies, although of course a theory whose range is specified can be said to have the ontology of its language.

What then of the metalanguage in which thne ontology of a language is specified? Obviously, it must contain the appropriate general term, e.g. 'physical object' for the language containing '(3x)(x is a monster & x is in Loch Ness)' 'natural number' for the language containing '(3x)(x is prime & x is between Io and zo)', 'event' for the language containing '(3x)(x was a stabbing & x was done with a knife)'. But it is required not just that there be the appropriate term, but that it have application; for it is an essential



ON WHAT SORTS OF T HING THERE ARE 5I3

feature of the Tarskian semantics for standard first-order theories that the domain specified for the individual variables be non-empty. Thus in saying that the ontology of a language is F's, we must not only use the term 'F', but must assert (or at least presuppose) that there are F's. This is the justification for Quine's talk of fixing the objects of the described theory 'only relative to those of the home theory'. It emerges, then, that ontological relativity is not so much a matter of needing a metalanguage to state the ontology of a theory, but of needing a metatheory to state the ontology of a language.

Does this mean that Plato's beard has grown again at this new level? Can we say, for example, that Davidson's analysis of action- sentences requires an ontology of events only at the cost of ourselves admitting that there are events? Such a result would make nonsense of many seemingly meaningful and important philosophical discussions. In the heydays of positivism and of linguistic philosophy this thought was a commonplace, but since then we have learnt caution in dismissing philosophical questions as meaningless. In the case of ontological problems of our second level, we think that we can say that a certain language requires an ontology of F's without thereby presupposing the existence of F's ourselves. But, in the light of ontological relativity, how is this possible? The answer is surely by a further 'semantic ascent'. For, to continue with the example of Davidson on actions, his analysis already involves two levels-he offers us a language into which to paraphrase action-sentences, and an interpretation of that language, whereby he says that events are the range of its variables. We, standing on neutral ground and wanting to understand what Davidson's theory involves before we commit ourselves to accepting it, must say that his metatheory affirms that there are events. Thus the ontology of the language becomes the ontological commitment of the metatheory. And, as with ontological commitment at the first level, we can surely characterize the commitment of the metatheory without having to accept it ourselves. Thus, as Quine says, the objects of the 'home theory' can, at will, be questioned in turn.

But the difference between ontological commitment and ontology is more than just the difference between theory and metatheory. For the existential statements to which a theory is committed can involve any kind of predicate or open sentence, e.g. '(3x)(x is a dog)', '(3x)(x is red)', '(3x)(x consists of water)',

I7




(3x)(x ceased to exist in I945)', '(3x)(y)(x is older than y)', etc. But to specify the ontology of a language, the ran-ge of values of its variables, we cannot just employ any predicate or open sentence at all. For a range for quantification must be clearly articulated or individuated into distinct objects, so that every identity statement has a clearly defined truth value. As Strawson puts it in Individuals [p. I6], 'that it should be possible to identify particulars of a given type seems a necessary condition of the inclusion of that type in our ontology'. In Word and Object [p. 236], Quine sees quantification and identity as two sides of the same objectificatory process:

We may be perceived to have posited the objects only when we have brought the contemplated terms into suitable interplay with the whole objectificatory apparatus of our language: articles and prono-uns and the idioms of identity, plurality, and predication, or, in canonical terms, quantification.

So it would not do to specify the ontology of a language as all water or all sugar, for mass terms do not divide their reference into distinct objects. Nor would it do to say that an ontology comprises everything red or everything ridiculous or everything more than fifty years old, unless one had already supplied a criterion of individuation for objects or things, for the predicates instanced do not supply any such criterion. To specify a range for quantification, we must use a 'sortal' term, i.e. a term which supplies a criterion of identity as part of its meaning.

This talk of identity in the context of ontological relativity raises the question of the relativity of identity. Quine says that identity is of a piece with ontology, and is thus involved in the same relativity [OR, 55]. Geach has also maintained a thesis about the relativity of identity,' and has recently tried to relate his thesis to Quine's.2 But a distinction must be made here between relativity within a language and relativity between languages. Geach, in claiming that it is possible for a to be the same F as b, and be a G, and yet not the same G as b,3 is maintaining the former, for the individual terms 'a' and 'b' and the sortal terms 'F' and 'G' are surely supposed to be all in the same language. A strong chorus

I P. T. Geach, 'Identity', Review of Metaphysics, xvi (I967), 3-I2. 2 'Ontological Relativity and Relative Identity' in M. K. Munitz, Logic and

OCntology (New York, I973), 3 Reference and Generality (Ithaca, N.Y., I962), 157.




of opposition has arisen against Geach's claim;' here I need only mention the basic point that it is incompatible with the standard logical law of the indiscernibility of identicals. Quine's view concerns the relativity of identity between languages. Within a given language, identity can be defined by exhaustion of predicates [PL, 63], but when we specify the ontology of a language, we do this in a metalanguage and it is open to us to say that the defined identity-relation in the language is to be interpreted not as identity but only as an equivalence relation in the metalanguage.

The next question is whether any sortal term will do for specifying an ontology, or whether further restrictions must be imposed. Normally, we would employ very general sortals such as 'physical object', 'event', 'natural number' rather than more specific terms like 'rabbit', 'battle', 'prime number'. But there does not seem to be any logical bar to using the latter for specifying ranges. Is this a case where the differences really are only of degree? Various philosophers have tried to argue the contrary, by distinguishing the high-level 'category' words in some way. Carnap suggested that 'C' is a 'universal word' if for any individual term 'a', the sentence 'a is a C' is either analytic or meaningless, i.e. if meaningful at all then it is necessarily true.2 The intuition was that sentences like 'Caesar is a natural number' or 'The number two is an event' are meaningless rather than necessarily false. In 'Empiricism, Semantics, and Ontology' Carnap envisaged using a many-sorted first-order language, with different sorts of variable for the different categories.3 We would then say that the ontology of such a language comprises several different sorts or categories of thing. More recently, Sommers has built an elaborate tree-structure of types and categories, which he claims reveals the ontology of natural language.4 But the trouble is that the structures of both Carnap and Sommers rest on the shaky foundation of an unexplained distinction between the meaningless and the necessarily false. Such a distinction is at least as controversial as that between the analytic and the synthetic. I D. Wiggins, Identity and Spatio-Temporal Continzuity (Oxford, I967),

Part One; J. Perry, 'The Same F', Philosophical Review, lxxix (I970), i8I-200; L. Stevenson, 'Relative Identity and Leibniz's Law', Philosophical Quarterly, xxii (I972), I55-I58; M. Dummett, Frege: Philosophy of Language (London, I973), ch. i6.

2 R. Carnap, The Logical Syntax of Language (London, 1937), section 76. 3 R. Carnap, 'Empiricism, Semantics, and Onto'Logy', Revule Internationlale

de Philosophie, iv (I950), revised version reprinted in R. Carnap, Mlleanling and Necessity, second and enlarged edition (Chicago, I956).

4 F. Sommers, 'Types and Ontology', Philosophical Review, lxxii (I963), 327-363.



5I6 LESLIE STEVENSON:

A different approach to a definition of categories lies through the notion of a criterion of identity. Frege first introduced this notion when he said that if we are to use the sign 'a' as a sign for an object, we must have a criterion for deciding in all cases whether a = b.1 And in saying that we can define what numbers are by stipulating a criterion of identity for them, Frege seemed to presuppose that there are different criteria of identity for different categories of object [ibid. ?63]. Such an idea appeals to our intuitions, for we are surely inclined to say of rabbits and dogs, battles and weddings, even numbers and odd numbers, that these are six sorts of things, but of only three categories or ultimate sorts. Such intuitions lead Dummett [Frege, 75-76] to define a categorial predicate as the most general term in a class of nouns all of which supply the same criterion of identity. And one can develop a formal logic in which sortal terms are distinguished from predicates in general, and within the sortals the ultimate or category terms are distinguished from the others.2 But all this rests on somewhat shaky foundations too, for what it presupposes is that we have a way of telling, in general, whether one sortal supplies the same criterion of identity as another, i.e. that we have a criterion of identity for criteria of identity.3 Yet it is not at all clear that we do have such a criterion, for there are many places where our intuitions become confused and uncertain. 'Same person', 'same animal', 'same organism'-do these phrases convey the same criterion of idelntity? Is there really a single criterion of identity for all physical objects, and a single criterion for all events, or are the genuine category terms rather less general than that? On the other hand, are events and material things to be unified into one huge category of four-dimensional objects [cf. RR ?34]. Unless and until we achieve a deeper analysis of the notion of a criterion of identity, it looks as if Quine must be right when he says in his latest work:

Putting our house in ontological order is not a matter of making an already implicit ontology explicit by sorting and dusting up ordinary language. It is a matter of devising and iMDosinlg rRR. 881.

I G. Frege, Fouindations of Arithmetic, trans. J. L. Austin (Oxford, 1950), section 62.

2 L. Stevenson, 'A Formal Theory of Sortal Quantification', Notre Dame 7ournal of Formal Logic, xvi (I975), I85-207.

3 Cf. L. Stevenson, 'Dummett on Frege', Philosophical Quarterly, xxiv (I974), 352,-3 59.




Should we conclude, then, that the difference between our first and second levels of ontological question is after all only a matter of degree? I don't think so, for our analysis has brought out the fact that individuation and identity are essentially involved in questions of the ontology of a language, whereas the ontological commitments of a theory can include any kind of existential statement at all. It is no accident that second-level disputes, for instance about the acceptability of an ontology of events or of propositions, so often take the form of seeking a criterion of identity for the disputed entities. With disputes at the first level, the relevant criterion of identity is not usually at issue, the question is whether there are entities of the relevant sort which satisfy a certain predicate or open sentence.

Now that we have examined the difference between ontological commitment and ontology, it is apparent, I think, that the main thrust of Quine's intention has been towards questions of the second level, although much of the attention of his critics has been diverted to the first-level notion of ontological commitment because of his failure (at least until recently) to make the distinction clear. What Quine has been concerned with overall is the logical regimentation of the whole of our truth-claiming discourse into a first-order language. Our total ontology would be the categories of object we find we need in such a conceptual scheme for the whole of knowledge.' This programme owes its ultimate inspiration to Frege, as has been well expressed by Dummett:

Frege's philosophy of language embodies the faith that it is only by representing the various linguistic devices belonging to natural language as constituting often far from transparent means of expressing sentence-forming operations of predicate logic that we shall attain an adequate semantics for our language [Frege, 478].

That this is not a charter for unemployed logicians to torture a logically innocent natural language into their Procrustean symbol- ism, but a necessary condition of our achieving theoretical understanding of the operation of the idioms we unselfconsciously employ every day, has been argued by Davidson, with his emphasis

It may be objected that we have already found reason to doubt whether the relevant notion of category can be adequately clarified; yet the natural tendency to use some such notion can be found even in Quine himself, when he describes his ontology as comprising both physical objects and classes (Word and Object, 267).




on the need for a semantics for natural language which can offer an adequate theory of truth-conditions.1

4 The extra-linguistic correlates of a semantic theory

But to accept the above programme, embodied in the tradition which runs from Frege and Russell through Quine and Davidson, and hence to accept that the associated ontological problem is what ranges of individual variables we need for an adequate systematization of everything we want to assert, still leaves completely unanswered a third level of ontological question. This is the question of whether an adequate semantics for first-order languages in general requires us to assign entities to other types of linguistic expression besides the singular terms. Realists about universals, from Socrates and Plato down to Bergmann in our own day,2 have maintained that we must acknowledge the existence of extra-linguistic and extra-mental realities corresponding to our general terms (or at least to some of them). Moore and Russell insisted that the world contains facts as well as things, and that facts cannot be named but are what correspond to true sentences.3 Wittgenstein even started his Tractatus by asserting that the world consists of facts rather than tlhings. Neither facts nor universals are new categories of object, they are not objects in Frege's sense at all, for they cannot be referred to by singular terms. It is important to see that the ontological questions about them arise even without the introduction of quantifiers binding sentence-variables or predicate-variables, for the question is whether an adequate semantics for standardfirst-order languages must somehow assign correlates to sentences and predicates.

Facts have taken a severe battering since their heyday in the time of logical atomism; perhaps they are still not quite dead,4 but I will not attempt either to revive them or flog them further here. Some comment on universals will, I think, be appropriate, but there is a matter of terminology which must be sorted out first.

Davidson, 'Truth and Meaning', Synthese, xvii (I967), 304-323, and subsequent papers.

2 G. Bergmnann, 'A Note on Ontology', Philosophical Stutdies, i (950), 89-92; 'Particularity and the New Nominalism', MIethodos, vi (I954), I3I-I47, reprinted in Vlleaning and Existence (Madison, Wis., i96jo)

3 Mloore, So,-ne MLain Problems of Phlilosophy, chs. XIV-XVI; Russell, 'The Philosophy of Logical Atomism' in R. C. Marsh, Lqgic anid Knowledge (London, I956). See also E. W. Hall, What is Value? (London, I952), ch. 4.

4 See Davidson, 'True to the Facts', Journal of Philosophy, lxvi (I969), 748-764.




For most of the time when Quine talks of 'the ontological problem of universals' what he means is the question of whether we should quantify over various ranges of abstract objects, such as numbers and classes. He thus uses the labels 'Platonism' and 'nominalism' to mean the acceptance or rejection of such quantification.1 But, if Frege is right,2 the reference of a predicate cannot be an object at all, not even an abstract object; it can only be what Frege called a concept, something which has a certain 'incompleteness' which mirrors the incompleteness of linguistic predicates. So, quite apart from the second-level question of quantifying over abstract objects, there is the third-level problem of whether we must understand predicates as referring to realities which are not objects. It is this latter problem which I take to be the problem of universals proper.

Now Quine has many times said that the mere use of predicates as meaningful components of sentences does not commit us to the existence of any corresponding entities, call them concepts, universals, attributes, properties, or what you will. Since we readily admit that other types of expression, conjunctions for instance, are thus 'syncategorematic', that they contribute to the meaning of sentences in which they occur without standing for any entities in their own right, this is an obvious line to take about predicates. But Dummett has reasserted Frege's standpoint against Quine as follows:

Our ontological commitment depends upon what expressions of our language (including incomplete expressions) have to be taken as forming logically significant units and therefore as having reference [Frege, 479].

Predicates are surely logically significant units, so Dummett therefore argues that they have reference and that Quine's assessment of ontological commitment is 'excessively parsi- monious'. There seems to be obvious room here for Quine to defend himself against Dummett by questioning the inference from being a logically significant unit to having reference, or at least to having reference in the sense of referring to a non-linguistic entity. Indeed Dummett himself, in his discussion of Frege's

I See, for example, Quine and Goodman, 'Steps Towards a Constructive Nominalism', Journal of Symbolic Logic, xii (I947), 97-122; TVord and Object, 233.

2 Frege, 'On Concept and Object' in Philosophical Writings, trans. Geach and Black (Oxford, 1952); cf. Dummett, Frege, 471 ff.




notion of reference earlier in the same book, is at pains to distinguish two strands in the notion-that of semantic role, and that of relation to an extra-linguistic entity. He documents in detail how when Frege generalizes the notion of reference from singular terms to predicates and to sentences, the two strands in the notion pull apart [ibid. 243, 427]. Surely then it is open to us to admit that predicates play a distinctive semantic role, but to question whether that role consists in standing for corresponding entities. But, Dummett says, it is in no way apparent that Quine 'has any alternative type of semantic account to offer, one that does not involve associating with a one-place predicate a concept or set' [ibid. 525]. Certainly, the standard Tarskian set-theoretic semantics assigns to each predicate a subset of the domain, which is to be understood intuitively as the set of those objects of which the predicate is true. But it is dubious whether this algebraic device gives any understanding of how our language works in practice. For we do not establish that John is bald by identifying the set of bald things, and then seeing whether John is among them; rather we first have to know whether John is bald before we can say whether he is a member of that hairless class.' Can we not say that the semantic role of a predicate consists in its giving us a rule, a criterion, for telling whether it applies to a given object? (It is not required that we are able to decide the question in practice- consider the predicate 'is 100,583,752 years old'-but only that we can understand what it would be to settle the question.) So the recursion clauses for predicates in a Davidsonian theory of truth for a language with a finite number of predicates can take the form, not of "'x is F" is true iff the denotation of "x" is a member of the denotation of "F"' but rather "'x is F" is true iff the denotation of "x" is F'. (It is not even required that the metalanguage include the object language-a clause could be: "'x ist blau" iff the denotation of "x" is blue'.) No doubt there is more to be said here; I do not claim to have disproved the existence of universals, I have only criticized one argument for them, and brought out how the issue is quite distinct from any at our first two levels.2

I Cf. Stevenson, 'Dummett on Frege', loc. cit., 355. 2 No doubt Bergmann would say that in emphasizing that predicates give a

rule or 'mapping', rather than relate to a concept or set, I am bringing out the nominalism which he claims is hidden behind Frege's apparently robust realism. See Bergmann, 'Frege's Hidden Nominalism', Philosophical Review, lxvii (1958), 437-459; reprinted in Meaning and Existence.




There are also those who make the opposite criticism of Quine, suggesting that his assessment of ontological commitment is over- generous, since even first-order quantification can be interpreted substitutionally, in terms of expressions rather than objects.' I do not have anything to add to the strong defence Quine and others have made on this point,2 the basic argument being that when we come, as we must, to give the truth-conditions of all the sentences in the language, we must surely make reference to the objects for which the singular terms (or at least some of them) stand. However, a substitutional reading of second-order quantification would come in very handy, if we can indeed explain the semantic role of predicates without appeal to corresponding entities. For we could then meet the challenge of how to account for the validity of inferences like 'John is foolish and Henry is foolish, so there is something which John and Henry both are' without appeal to references of predicates. We could thus draw the sting of the following argument for universals: 'To me it seems obviously true that if something is red, then it possesses the property of being red; and that if something possesses the property of being red, then there is such a property as being red, and then there is such a thing as being red. To me it seems plainly contradictory to allow that there are red barns and red stamps and red faces, and yet that there is no such thing as being red.' [Wolterstorff, On Universals, I23].

I have not settled any ontological questions here. My concern has been to show that they arise at three different levels, the differences between which are not just matters of degree. Talk of 'the ontological problem' is shallow. Perhaps even Quine's famous phrase 'the ontological commitment of a theory' has outlived its usefulness, for we need to distinguish the notions expressed in the titles of my last three sections.3

UNIVERSITY OF ST. ANDREWS

R. B. Marcus, 'Interpreting Quantification', Inquiry, (i962), 252-269; 'Quantification and Ontology', Nous, vi (1972), 240-250.

2 See, e.g., J. Wallace, 'On the Frame of Reference', Synthese, xxii (I970), I I7-I 50.

3 Ancestors of this paper have been read at the Universities of St. Andrews (at a meeting of the Scots Philosophical Club in MIay I972), Leeds, Glasgow, and Princeton, and I have learned from the discussions there, and from comments by W. V. Quine and Donald Davidson. I am grateful to the University of St. Andrews for a period of sabbatical leave, and to the Philosophy Department at Princeton University for electing me a Visiting Fellow for that period.



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On What Sorts of Thing There Are