Essays in Linguistic Ontology 0809310449

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E�says zn Linguistic Ontology JACK KAMINSKY

Southern Illinois University Press Carbondale and Edwardsville

Copyright © 1982 by the Board of Trustees, Southern lllinois University All rights reserved Printed in the United States of America Edited by Karen S . Craig Designed by Bob Nance, Design for Publishing Library of Congress Cataloging in Publication Data Kaminsky, Jack, 1922Essays in linguistic ontology. Bibliography: p. Includes index. I. Analysis (Philosophy) 2. Ontology. I. Title . B808.5.K35 Ill 81-14411 ISBN 0-8093-1044-9 AACR2

In Memory of My Beloved Son Eric

Contents Preface

1. Language, Form, and Ontology

IX

1

2. Logical Form and Formal Languages

39

3. Construction and Interpretation

61

4. Individual and Predicate Terms

76

5. Linguistic and Traditional Ontology

92

6. T he Linguistic Criterion of Ontology

114

7. Is the Number of Planets 9?

137

8. Individuals

148

Bibliography

183

Index

193

Preface The issues in this book are derived mainly from an analysis of certain kinds of terms that are very important in the construction of formal language systems but whose ontological implications are frequently either inadequately explained or simply ignored. Thus I am concerned with what an individual variable is, what a predicate is, and what it means to speak of the values of a variable. These issues lead directly into a critical analysis of Quine's definition of ontology as the study of the values of the quantified variable. Except for the chapter on Quine's paradox, (chapter 7), the book deals pri­ marily with various aspects of ontology as they relate to formal systems. In each chapter I have usually tried to examine one particular problem in some detail, although I have sought to avoid, as much as possible, any use of the standard logical symbolism that, I believe, very often serves to obfuscate rather than to clarify an issue. Since few ontological problems can ever really be divorced from one another, the chapters often overlap. Thus it is difficult to see how one can try to state what a predicate is without also immediately trying to state what a name is. And, if names are discussed, one must eventually be led into an examination of Russell's theory of descriptions and Kripke's attempt to refute it. It has sometimes been argued that contemporary analytic views of ontology are different from traditional views. Traditionally, ontology was a separate, indepen­ dent study divorced from any particular interest in logic, language, or the natural sciences, even though, of course, elements of these disciplines often contributed to ontological analyses. Many contemporary philosophers take ontology to be a resultant product of formal language systems. The inquiry into the nature of in­ dividuals, properties, and classes arises because they seem to be the designata that are required to define the substituends, that is, the linguistic terms that re­ place the individual and predicate variables. Thus there would seem to be a dis-

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Essays in Linguistic Ontology

tinction made between the way ontology is studied by many contemporary phi­ losophers and the way ontology was studied in the past. But in an important sense the problems are similar. The tradition is concerned with what an individ­ ual-a substance-is and how its properties relate to it. The contemporary view is concerned with thing-words-names or constants or definite descriptions­ and how predicates are associated with them. The tradition posits monads and simple substances and sense data, and then proceeds to ask how worlds are con­ structed out of them. The contemporary philosopher posits domains of individu­ als and then proceeds to ask how much of the world can be described with such domains. There is more language emphasis in contemporary approaches to on­ tology, but the underlying issues are not so dissimilar. Thing-words still seem to require explanation in terms of individuals, and predicates are still said to allude to properties and classes. The terminology of substance and essence is no longer in fashion, but whether names are replaceable by clusters of predicates or by lists. of definite descriptions is an important contemporary issue. In fact, with the ad­ vent of Kripke's rigid designators-expressions that refer to the same entity in every possible world-a new interest has arisen in the nature of essential proper­ ties, since these seem to be necessary for the identification of such entities from one possible world to the next. And, finally, "exists" has been replaced by the existential quantifier, and therefore it is no longer taken to be a predicate. But the quantifier has its own odd problems, and those expounding a "free" logic have refused to connect existence to quantification. My own view that I attempt to present and to argue for in this book is that our commitments to what exists, that is, our ontological commitments, come, first, not only from the values of the variable, but also from the linguistic framework in which these variables are embedded. It is the framework that tells us what kind of entities will be found if there are any entities at all. Thus, for example, in the framework of Principia Mathematica, we are not being told what entities there are, but we are being told that, whatever they are, they will be individuals having monadic or dyadic properties. The framework, like a Wittgensteinian arrange­ ment or a Kantian set of categories, exists in the same way that the objects them­ selves do. Second, it is important to recognize that linguistic frameworks are not simple arbitrary stipulations that one creates by fiat. They are derived from a nat­ ural language that itself has a certain basic categorial structure, and it is this structure that is incorporated into the construction of formal languages. In inter­ preting a pure logical calculus, a great deal of natural language is eliminable, but it is questionable whether such concepts as "being a member of" or "having a property" or "being a part of" can also be omitted from the interpretation. By using a formal language, we can reformulate and transform a great deal of natu­ ral language so that the often implicit presuppositions of a sentence are made explicit. But it is always a matter of degree. Make the changes too incisive and

Preface

XI

suddenly the language becomes unintelligible. It might be possible to eliminate names in favor of descriptions, but there must still be a commitment to individu­ als as distinct from properties and classes that satisfy the descriptions. I have much to say about individuals, properties, and fictitious entities. Of individuals my conclusion is that there cannot be bare particulars such as those postulated by Bergmann and his school. Postulation of such entities poses the same difficulties as those involving \Vittgenstein's simple objects. But something can become an individual if it plays a certain role in the construction of man­ made objects. By thinking of individuals in this way, I also find the solution of how to treat fictitious entities. Pegasus and Hamlet do exist; and by this I do not mean that they exist in some strange, subsistent Meinongian world or that they are members of one of Kripke's possible worlds. They exist in the real world we know and experience just as the sculpture of David in Florence exists. We con­ stantly think of individuals in terms of natural entities and thus overlook the ob­ vious fact that much of the world we encounter is man-made. We create build­ ings, chairs, and art structures. They are man-made objects fabricated out of steel, cement, wood, and paint. But we also create things out of words, and these creations exist in the same sense as our other human creations. Hamlet and Pegasus are verbal constructions just as David is a marble construction. All three exist, and they and the other man-made objects are the designata of our so-called nonreferring terms. But I also indicate that it might be difficult to apply this anal­ ysis in all contexts, since certain objects can be constructed only as possible ones, for example, some of those in science fiction. The verbal construction of possible entities leads directly to Quine's modal paradoxes. I should like to thank Max Black and Rom Harre for taking the time to read and criticize portions of this book. But, of course, neither Black nor Harre is in any way responsible for the various ways I have used their views and criticisms. Finally, I should like to thank my wife, Alice, without whose constant encour­ agement this book would not have been written.

Cortland, New York 19 fune 1981

JACK KAMINSKY

E�says zn Linguistic Ontology

1 Language, Form, and Ontology Some philosophers, such as Quine and others, have argued that the study of ontology is to be defined as the study of what exists, as distinct from what does not exist or what only seems to exist, and is a study that cannot be divorced from the language that is being used. Sometimes the argument is presented in the fol­ lowing way: if we wish to know what we are ontologically committed to, that is, what we acknowledge as being actual rather than illusory or mistaken to be ac­ tual, we observe what we are willing to assert, that is, what sentences we are willing to insist upon as true. If we are willing to assert that there are dogs, rather than to question whether there are dogs or to hypothesize that there are dogs or to speak of dogs in some Kripkian possible world, then to us the universe, that extra­ linguistic domain of our language, is populated by at least one dog, regardless of whether it is Lassie, Rover, Rin-tin-tin, or Pluto; and this dog is at least one part of our ontological commitment. (It is only one part, since most people, includ­ ing philosophers, usually make more than one existence claim and therefore at­ tribute existence to more than one entity.) Similarly, if we are willing to assert that there are golden mountains and if the assertion is not being made facetiously or as an exercise in logical symbolization, then for us there is at least one golden mountain or, in more technical terms, there is at least one entity that is golden and is a mountain in the domain of the designata of our linguistic expressions; and golden mountains are, therefore, a part of our ontology. Or, finally, if we assert that there are numbers or sets that are not mere groups or aggregates or "virtual" eliminable classes, in Quine's sense, then we are committed to the exis­ tence of such entities as numbers or sets. 1 1. For Quinc's discussion of "virtual classes," by which we seem to be talking of classes "without talking of anything of the kind," sec W V Quine, Set Theory and Its Logic (Cambridge, MA: Har­ vard Univ. Pr., 1963), pp. 15-21.

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Essays in Linguistic Ontology

This view of ontological commitment combines elements of plausibility and implausibility. It seems to have a degree of plausibility in that it focuses attention on the need to consider questions of ontology in terms of the language in which such questions are posed. It indicates that ontology must be identified with on­ tological commitment in a language, that is, that what there is cannot be di­ vorced from the particular language, with its particular rules and idiosyncrasies, which is used to state what there is. So that, to consider the problem of substance and attributes, it becomes necessary to think of it in terms of the relation among names, predicates, and definite descriptions. It is not difficult to see how the con­ temporary issues of whether names are eliminable in favor of some cluster of predicates and whether definite descriptions are synonyms for names are directly connected to the issue of whether substances are no more than clusters of properties. Still, there is much that is implausible about this view. First, we ought to keep the historical record straight. Traditionally, ontology is not the study of what there is, but of what there must be. When Webster's Second International Dic­ tionary defines ontology as "the branch of knowledge that investigates the nature, essential properties, and relations of being, as such," it is stressing the important fact that, at least in terms of the traditional definition, ontology is not concerned simply with what is or with what one is committed to in a language, but with what must be if there is anything at all. If A promises to do X for B, then A has made a commitment to undertake X. A has an obligation. But obligations are very often broken; promises are sometimes not kept. It would be quite a misuse of the word's traditional connotation to call it an ontological commitment. Sim­ ilarly, if one says "There are elm trees," then, in contemporary usage, even if the sentence is tenseless, there is an ontological commitment here to whatever en­ tities "elm tree" is or was applicable. These are the so-called values of the vari­ able. But elm trees might exist only for today or for this year. In fact, blight has destroyed a good number of the elm trees in the United States and elsewhere. The statement "There are elm trees," if it is true, entails a commitment to one or more objects to which "elm tree" is applicable. Why should this be an onto­ logical commitment? In the traditional sense what we have here is a presupposi­ tion or an implicit acknowledgment of the existence of certain entities if the statement is true. But not all presuppositions or implicit acknowledgments in­ volve ontology. Now, it may very well be that, in terms of the tradition, we have discovered that there are no true statements involving ontological commitments. It may be that, despite Kripke's arguments to the contrary, there are no essential properties and no necessary statements except those analytic ones of pure, uninterpreted logical calculi. But then it ought to be stated quite clearly that the definition of

Language, Form, and Ontology

3

ontology is being changed, or perhaps it simply ought to be asserted that there are no ontological commitments. There arc simply commitments. Second, aside from the peculiar ambiguity in "ontological commitment," there are other serious difficulties in the view under consideration. It is implausi­ ble in that it makes it seem as if ontology is not a commitment in a language, but a commitment made by a person's use of the language, so that as a result there may be as many ontologies as there are users of the language. It would make it seem as if one who said "There are elves" and who insisted vehemently on its truth or used it in some important way, for example, to make a child eat break­ fast, would be just as ontologically committed as one who denied its truth. But in actual cases a distinction is always made between what a specific person might claim or how a person might use a sentence and what is taken to be true because of the grammatical, logical, and truth rules of the language. As various linguists, especially Chomsky, have been telling us, every language that purports to de­ scribe or convey information about some extralinguistic domain has some crite­ ria, no matter how vaguely formulated, for proper grammatical construction and for proper use of "true" and "false." 2 Perhaps these rules are not as ironclad as Chomsky would sometimes seem to want us to believe; nor need they have the explicitness and clarity of those proposed by Tarski and Carnap. They are, nev­ ertheless, rules of some sort by which even the most primitive tribes can evaluate the correctness or incorrectness of assertions by individual members. As one so­ ciolinguist puts it, although the uses and values of making truth claims vary from culture to culture-the Navaho Indians, for example, believe that telling the truth is very important within their own tribes, but of little importance when dealing with outsiders, whereas for the Burundi truth is a value under all condi­ tions-the concept of truth, that is, the employment of some criteria, even if they are not explicitly expressed, by which true claims are distinguished from false ones, seems to be "highly uniform." 3 Thus it is not what any one individual asserts about what there is that determines an ontological commitment, but how well what is asserted squares with the rules of truth, grammar, and logic in the language. We might assert "There are elves" or "The square root of 1 is blue," but if the criteria of truth and well-formedness of sentences, criteria that no mat­ ter how inadequately stated permit the application of "true" or "well-formed" to 2. Noam Chomsky, Language and Mind (New York: Harcourt, 1972), cnl. ed. Sec also E. H. Sturtevant, An Introduction to Linguistics (New Haven, CT: Yale Univ. Pr., 1947), p. 53; Francis Whitfield, "Glosscmatics," in Linguistics Today, ed. Archibald A. Hill (New York: Basic Books, 1969), p. 257; Suzette Haden Elgin, What is Linguistics? (Englewood Cliffs, NJ: Prentice-Hall, 1973), p. 32; John Ly ons, Noam Chomsky (New York: Viking, 1970), p. 110. 3. Ethel M. Albert, "Culture Patterning of Speech Behavior in Burundi," in Directions in So­ ciolinguistics, ed. John J. Gumperz and Dell Hymes (New York: Holt, 1972), p. 100.

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Essays in Linguistic Ontology

some sentences, but not to others, do not permit "true" to apply to 'There are elves" or "well formed" to "The square root of I is blue," then the former is false and the latter is ill-formed regardless of who utters them. Thus we can assert anything at all, but whether or not it entails, in the contemporary sense, an on­ tological commitment, whether or not it is an assertion about what exists, de­ pends on the status of the sentence in the language. Only if certain basic criteria, implicit or explicit in the language, have been met is an ontological commitment attributable. A more important reason for denying the plausibility of connecting ontologi­ cal commitment to assertion-one of major philosophical significance-is that it makes it seem as if what there is can be clearly and easily discerned if one is careful about what is stated and how it is stated, that is, if one avoids, as much as possible, obvious and perhaps even not so obvious logical, linguistic, and truth­ rule violations. Thus it is probably true that if one is careful some of the obvious logical fallacies can be avoided, and one will think twice before hypostatiz­ ing such abstract expressions as "freedom," "democracy," and "the class of all classes." But it is a mistake to think that ontological commitments are easily come by. The Wittgenstein of the Tractatus seemed, at least at times, to believe that language, regardless of whether it is ordinary or formal, immediately re­ vealed what it was meant to symbolize-presumably, objects in configuration.-+ This is surely wrong. It is very often not clear, even to the most fastidious and discerning utterers, exactly what is being asserted when they assert that there are, say, dogs. Are they saying that there are objects that are members of the class of dogs and that, therefore, what exists are individuals as well as classes of which such individuals are members? Or are they saying that there are objects that have certain properties by virtue of which we call these objects dogs and that, there­ fore, there are both objects as well as properties of objects? Or are they saying that there are all three-objects, properties, and classes? Nor ought we to ovedook the possibility that they are saying that there are only objects as presumably as­ serted by Wittgenstein or that there are only properties as asserted by Hume and, more recently, by Goodman or that, since individuals can be defined as unit classes, there are only classes as stated by Quine. 5 (And perhaps we ought not to overlook the possibility that they are saying none of these. ) Furthermore, if we 4. Thus Wittgenstein says, "All propositions of our colloquial language are actually, just as they are, logically completely in order" (Tractatus 5.553); and also "Every possible proposition is legit­ imately constructed (Tractatus 5.4733). But there is also evidence that Wittgenstein may have really been speaking of a more formal language. See I. Copi, "Objects, Properties, and Relations in the 'Tractatus,'" in Essays on Wittgenstein's 'Tractatus,' ed. I. Copi and R. W Beard (London: Routledge and Kegan Paul, 1966), pp. 167-69. 5. Tractatus 2.0232. See also the discussion by Copi, "Objects,'' pp. 184-86. More specifically, Goodman's objects are bundles of qualia, whereas Hume's are collections of simple ideas; see David Hume, A Treatise of Human Nature, bk. I, sec. 6, and Nelson Goodman, The Structure of Ap-

Language, Form, and Ontology

5

follow the standard interpretation of existentially quantified sentences when we say "There arc dogs," we arc not simply talking of this or that clog. We are saying "Pluto is a dog or Fido is a dog, etc.,'' where "etc.'' is a way of informing us that there may be, and probably arc, other entities called dogs. Then implicit in this use of "etc." is the notion that the objects indicated by "Pluto" and "Fido" either are elements of a class or partake-in perhaps some less controversial sense of "partake" than that specified by Plato-of some property which is extendable to others. It might be possible to avoid these sudden moves from an apparently innocent statement such as "There are dogs" to the rather abstract statements "There are properties that dogs have in common" and "There are classes of which dogs are members" by asserting "There is this," and then picking up a dog, and "There is that," and then picking up another dog. In this way we might believe that we have avoided any controversy concerning exactly what we are asserting. We are committing ourselves solely to what we call attention to with the use of "this" and "that." But even if we overlooked the various difficulties that Dewey, Russell, and Wittgenstein raised about how such egocentric particulars as "this" and "that" can be used to refer to such a diversity of objects or even to a single object, since signs that must be accompanied by physical gestures can always be misinter­ preted, 6 we would still surely be justified in asking "Well, what is this?" or "Well, what is that?" And the answer "This is a dog" or "That is a dog" would lead directly back into the original problem of trying to clarify exactly what we are asserting that there is. For 'This is a dog" or "That is a dog," just like "There are dogs," can be taken as a way of asserting that there is a concrete entity that I am holding in my hands and it is a member of the class of dogs or it has the proper­ ties that characterize what I call a dog. The question that now arises is this: would we be better able to understand what our existential commitments are if we made explicit the rules that, it has been maintained, govern the construction and employment of our sentences? These rules would presumably not only uncover the deep form that is very often obscured by the surface form of a sentence, but also would tell us what semantic categories the language permits, that is, individual, class, property, relation, cause, and so forth, as well as how the truth of a deep-formed sentence is deter­ mined. Thus, given any sentence in the language, we can uncover its basic form, that is, the structure from which we can unpack all the existential claims pearance (New York: Bobbs-Merrill, 1966), 2d ed., pp. 189-94. Individuals for Quine become con­ verted to unit classes; see his Methods of Logic (New York: Holt, 1972), 3d ed. , p. 254, and Set Theory and Its Logic, p. 31. 6. John Dewey, Logic, The Theory of Inquiry (New York: Holt, 1938), pp. 53-54; Bertrand Rus­ sell, An Inquiry into Truth and Meaning (New York: Norton, 1940), pp. 134-43; Wittgenstein, Phil­ osophical Investigations, trans. C. E. M. Anscombe (New York: Macmillan, 1953), p. 253.

6

Essays in Linguistic Ontology

of the sentence. If 'There are A and B" is shown to be well formed, and if A and B must be class terms, in accordance with the semantical rules of the language, then we can say that, if the rules of truth permit "true" to be applied to the sen­ tence, then this commits us to ( I ) classes, ( 2) the classes A and B in particular, and (3) individuals who are members of these classes. Our ontological commit­ ments would become explicit. Sentences, however, are very often ungrammatical, ambiguous, and, as we have seen, misleading in regard to their existential claims. How then are we to discover the genuine form of a sentence? How are the ultimate existential claims of a sentence to be determined? We could argue, following another assertion of Wittgenstein, that the ultimate form of a sentence, the final resultant analysis of a sentence by which we can truly decide what our existential commitments are, is to be found when all expressions, including syntactic ones, have been fully defined. -; Thus, if we defined the terms of a given sentence and then proceeded to define the terms of the resultant definitions, and so forth, we would eventually obtain a set of atomic sentences designating some series of simple objects config­ ured in a certain way. These atomic sentences would be the only ones exhibiting form, and their conj unction would be the final form of the original sentence. In Wittgenstein's terms we would then have the logical, rather than the grammati­ cal, form of the sentence. We would have a form that would immediately ex­ hibit, or show, its logical properties and whose terms would immediately desig­ nate the ultimate existential objects that were only implicitly designated in the original sentence. Thus, once I have fully defined "There is a broom in the cor­ ner," I should obtain the logical form that is implicit in this sentence, and this logical form would tell me exactly what my existential commitments are when I assert this sentence. But the problem arises about what the logical form of a Witt­ gensteinian atomic sentence is. Presumably, if we follow one acceptable inter­ pretation, it consists of a predicate followed by one or more proper names. But neither the predicate nor the proper name is of the usual variety encountered in natural- or even formal-language contexts. Wittgenstein's predicates do not designate or in some way allude to properties or classes or characteristics or qualities. They are not labels for primitive colors or some other basic observa­ tional phenomena. Nor are they simply Quinian general terms that have no exis­ tential counterpart, but are simply true or false of some entity. On the contrary, they simply indicate the structuring or arrangement of objects. Thus the func­ tion F ab does not indicate a dyadic property involving the two objects a and b. Nor does it specify a class consisting of two objects. Rather, it indicates two ob­ jects, a and b, arranged or structured in a certain specific way. 8 There are no 7. Tractatus 2. 0201. 8. " Instead of, The complex sign " a R b" say s that a stands to b in the relation R,' we ought to put " ' That " a " stands to b i n a certain relation says that a R b" ( Tractatus 3. 1432); in this way Wittgen-

Language, Form, and Ontology

7

existent properties of objects or existent relations connecting different objects; there are merely the objects themselves, with the predicates being merely a spe­ cial conventional linguistic device of our language to indicate the various ar­ rangements these objects can and do take. Similarly, Wittgenstein's proper names are not to be equated with "John Smith," "Robert Jones," and so forth, since these designate complex entities and genuine proper names must only designate simple entities. Furthermore, the proper names of a natural language are always definable by means of descriptions-at least if we accept the views of Russell and Quine, although not that of Kripke-whereas genuine proper names cannot be further defined. Nor must we equate Wittgenstein's proper names with Russell's logically proper names. For Russell a logically proper name is one that imme­ diately denotes an object with which we are directly acquainted. But with no stretch of the imagination can we ever say we are directly acquainted with Witt­ genstein's objects. Thus there is a decided strangeness about Wittgenstein's use of names and predicates. Still, we might argue that with all their strangeness perhaps predicates do indi­ cate no more than arrangements, and perhaps the usual proper names of ordi­ nary language, on close analysis, are reducible to names that designate simple entities . After all, Quine has maintained that most predicates are merely general expressions that either apply or do not apply to individuals; no properties need be posited. 9 Bergmann and others of his school of metaphysics have argued strongly that we must eventually understand sentences as designating, among other things, bare particulars with which we can never be acquainted. Even Kripke has spoken of a name as an expression that denotes the same entity in all possible worlds-an entity that can be said to be present even if every description of it were to turn out to be false. 1 0 And surely such an entity, which has no intrinsic connection to any description of it or to any cluster of properties, is just as myste­ rious as Wittgenstein's elusive object. Thus we might say that the kind of sen­ tence that results after constant redefinition has reached only indefinable terms or only terms that in some way allude to conceptual, as distinct from perceptual, objects-that kind of sentence with its particular linguistic form-gives us the true picture, the logical, noncontradictory picture, of what exists. That kind of stein distinguishes the signs a and b, which do designate objects, from the sign R, which does not. For further discussion see Copi, "Objects"; E. Stenius, Wittgenstein's Tractatus (Oxford: Basil Black­ well and Mott, 1960), pp. 61- 63; George Pitcher, The Philosophy o{ Wittgenstein (Englewood Cliffs, NJ: Prentice-Hall, 1964), pp. 112-30; Max Black, A C ompanion to Wittgenstein's 'Tractatus' ( Ithaca, NY : Cornell Univ. Pr., 1964), pp. 103- 07; Garth Hallett, A C ompanion to Wittgenstein's "Philosophical Investigations" ( Ithaca, NY : Cornell Univ. Pr. , 1977), pp. 115-20. 9. Quine, Methods of Logic, p. 80. 10. Saul Kripke, "Identity and Necessity," in Naming, Necessity, and Natural Kinds, ed. Stephen P. Schwartz ( Ithaca, NY: Cornell Univ. Pr., 1977), p. 83.

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Essays in Linguistic Ontology

sentence, and no others, exhibits the basic ultimate form and immediately shows us to what we are ontologically committed. However, even if we overlooked the obvious problems of explaining how a "picture" is to be understood here and what it means to say that a sentence can "show" us what exists, there are more serious difficulties with this modified view. First, it would seem that this kind of analysis would lead to certain significant logical violations. Since monadic predicates do not, at least on their surface, ex­ press an arrangement of objects-we normally think that "John is pale," for ex­ ample, refers to John and to one of his properties-all monadic predicate forms would have to be translated into polyadic predicate forms. Only a multiplicity of objects, not a single one, is arrangeable. But the logical tradition has it that only in some few instances, that is, as in the change of " x is a brother" to "x is a brother of y," is translation of monadic into polyadic predicates possible, and Carnap, at least, believed that the difference between the two kinds of predicates was fundamental. 1 1 The essential difference is easy to show. Consider a simple monadic sentence, " a is red." We can show that this sentence cannot be changed into a possible polyadic one such as "a is as red as b." Undoubtedly there could be a possible world in which one and only one object is red. In such a case "a is red" would be true, but "a is as red as b" would be false. Moreover, if " a is red" must be changed into "a is as red as b," then what is surely logically possible would seem to become logically impossible, namely, a domain with only one entity. If descriptive sentences must eventually reduce to atomic sentences de­ scribing relations among objects, then it follows that for Wittgenstein a world with one and only one object is, if not logically impossible, then surely inde­ scribable. But this conclusion would be incompatible with both mathematical and logical theory. In both mathematics and logic, a null domain is logically possible, and we can describe it in ordinary quantificational terms quite simply as (x) - (x = x). A domain with two entities and only two entities is also logically pos­ sible, and we can describe it as (3 x)(3 y)(x:¢: y. (z)(z = x. v. z = y)). In a similar way it is logically possible to have a domain with one and only one entity, and it is describable as (3 x)((x = x). - (3 y)( y:¢:x)). Wittgenstein clearly could not deny that there could be a possible world with one and only one entity and that it makes sense to speak of describing that world. It might be argued that the descriptions that we have given of both the null domain and the nonempty domains consist only of logical connectors and individual variables and that such descriptions are not disputed by Wittgenstein. Descriptions whose nonlogical terms are either in­ dividual constants or individual variables are, according to the Tracta tus thesis, 11. R. Carnap, The Logical Structure of the World, trans. Rolf A. George (Berkeley and Los An­ geles: Univ. of California Pr., 1969) , p. 20.

Language , Form, and Ontolog�'

9

satisfactory. Only the use of predicate terms that arc not polyadic is to be pro­ hibited. Thus statements about properties of objects arc to be redefined as state­ ments about relations of objects. But I think that it can be shown that statements that attribute a property to some objects cannot be eliminated. Consider the sen­ tence " a is red and b is red and c is red. " For Wittgenstein this would require a restatement into " a is as red as b, and b is as red as c," with the understanding that "is as red as" is both transitive and symmetrical. But if "is as red as" is taken as both transitive and symmetrical , then it must also be reflexive . In other words, given that a is as red as b, and b is as red as c, then we can infer that a is as red as a , and b is as red as b, and c is as red as c. What this means is that from a polyadic predicate involving three objects we can infer a relation about each ob­ ject separately. But a relation involving one object means that we are attributing something to the object that cannot be defined in terms of more than one object. But what is it that is attributable to a single object if not a property? Perhaps an exception to this is the identity relation that attributes a relation to the same ob­ ject-a is identical to a, or a is identical to b-but does not seem to lead to the notion of identity as a property of the object. But identity is often taken to be not a two-term relation, but rather an abbreviation for a claim about properties. In other words, the statement of identity reduces to an affirmation about the (non­ relational) properties of objects: " a is identical to b" if and only if whatever prop­ erties a has b has. So if Wittgenstein is trying to tell us that we must always deal with polyadic predicates, he is wrong, because even in the logic of relations we must be willing to countenance domains in which properties are attributable to single objects. Furthermore, even if such translation were possible, there would still be difficulties. Consider a polyadic form, F ab, where a and b designate Wittgensteinian simple objects. If the objects are simple, then they have no parts. And since there are no properties, they have no properties. Nor do they have any other relation besides that specified by F. (Although technically for Wittgenstein there are no relations either; there are only objects configured in certain ways.) But if this is the case, if there really are simple objects, then we must ask how F ab is to be distinguished from F ba. Since the objects are simple and without properties, nothing distinguishes one from the other, and F ab turns out to be equivalent to F ba-a violation of the rule of symmetry. We might try to modify Wittgenstein's view by asserting that his objects are elements of a space­ time system so that, even though simple objects without properties cannot be qualitatively different, they can be numerically different. Objects would be iden­ tifiable by their space-time positions. However, for Wittgenstein space and time were themselves configurations of objects, so that it was not sensible to speak of objects in space or in time. Space and time, like other properties, were really no more than resultants of objects arranged in various intricate designs. Thus to

10

Essays in Linguistic Ontology

speak of one object here and another there was to speak of their configuration in a certain pattern, but it did not serve to distinguish one from the other. Space­ time predicates were simply incorporated into F so that Fab still turned out to be indistinguishable from F ba . Furthermore, even if we were willing to posit rela­ tions and to speak of objects in space and time, identification of individuals does not occur merely by the introduction of space-time relational predicates. "A is to the left of B at time t" is asymmetrically distinct from "B is to the left of A at time t" only if A and B are identifiable as different from one another. Otherwise A must be taken as identical to B and the asymmetry cannot be sustained. The differentiation is made by the admission of a property that A has but that B does not. Properties, then, cannot be translated into arrangements without a loss of identification of objects. Second, we have been speaking of simple, or basic, entities as if they were perfectly intelligible. But Wittgenstein himself was undecided about what they were and how they were to be identified. He regarded the search for them as an "empirical" matter without explaining how we empirically go about discovering them. 1 2 Most commentators are fairly convinced that Wittgenstein was not sim­ ply thinking of the atomic particles of physics, but if the objects are not such particles then what are they? What are the objects that are being arranged? If they are objects of a metaphysical nature such as the monads of Leibniz or the "bare particulars" advocated by Bergmann and Allaire, then how are we to conceive of the arrangements of such entities? 1 ' How do we give structure to nonphysical unpropertied objects? Wittgenstein might be taken to mean that in any definition of terms we will eventually reach ultimate perceptual sense data or qualia that cannot be further defined so that his simple objects are the designata of Carnap's basic observation predicates. But Wittgenstein apparently disallows this. Simple objects are mutually independent. Otherwise, if they did in some way influence one another, then each would have at least the one property of influencing some other object. But this would destroy their simplicity. The color green is incom­ patible with the color red; that is, both cannot be simultaneously elements of the same fact. Therefore, these colors and colors in general cannot be simple ob­ jects. In fact, Wittgenstein specifically refers to color words as predicates, and, 12. Thus Norman Malcolm writes, " I asked Wittgenstein whether, when he wrote the Tractatus, he had ever decided upon anything as an example of a 'simple object.' His reply was that at the time his thought had been that he was a logician; and that it was not his business, as a logician, to try to decide whether this thing or that was a simple thing or a complex thing, that being a purely empirical matter!" (Ludwig Wittgenstein: A Memoir [London: Oxford Univ. Pr. , 19 58] , p. 86). 13. Cf. Edwin B. Allaire, "Bare Particulars," in Un iversals and Particulars, ed. Michael J. Loux (New York: Doubleday, 1970), pp. 2 3 5- 44; Gustav Bergmann , "Russell on Particulars," in The Metaphysics of Logical Positivism (London: Longmans, Green , 19 54), pp. 197-2 1 4. For a fuller dis­ cussion of Bergmann's position, see The Ontological Turn, ed. M. S. Gram and E. D. Klemke (Iowa City: Univ. of Iowa Pr. , 1974).

Language, Form, and Ontology

11

therefore, we must assume that he docs not want them to be regarded as the ultimate proper names, those expressions that do designate simple objects. i ➔ Finally, it is not at a l l certain that there must be ultimate simple objects. It could well be that just as it is possible to move from the positive numbers "down" through the negative ones without ever reaching the final negative number, so also Wittgenstein's absolute simple objects may never be attainable. The search for simple objects may real ly involve the same dilemmas as the search for final causes. Both may be as intelligible or unintelligible as the acceptance of infinite regresses. In formal languages it is usually irrelevant whether the domain consists of simple or complex individuals. And more recently Rolf A. Eberle has shown that formal calculi can be constructed that could be given nonatomistic inter­ pretations in the sense that they would fail to imply that every individual must consist of atomic parts. 1 5 There could be individuals, for example, human be­ ings, that are more than the sum of their parts. And if we think, as Wittgenstein did, that a domain of entities can include facts, then there is a serious question as to whether facts can be fully explicated by their atomic elements. In any event, so far as Wittgenstein is concerned, we are left without any clear understanding of what the basic form of a sentence is, since we do not know what the ultimate components of such a form are and what, if anything, they were meant to designate. If Wittgenstein's analysis of a sentence is not satisfactory, he, at least, may have been on the right track. Contemporary linguists have argued that sentences ought to be analyzed in terms of their surface and deep structures. It is the deep structure that really reveals the implicit categorial structure to which one is com­ mitted in the assertion of a sentence. The surface structure can only confuse us and cause us to think that its commonality with the surface structure of other sentences reveals the basic form. Thus, given the sentences "John is pale," "Mary is happy," and " Hamlet is sad," we might mistakenly infer that the grammatical arrangement these sentences have in common, namely, subject-verb-predicate, constitutes the form of the sentences. And then we could conclude that this form is the ultimate one from which all our existential commitments can finally be derived. But, even though what we have here may well be a display of common grammatical categories, it does not at all follow that the basic form of these sen­ tences has been revealed. For if the form is the same in each instance, then we should expect similar logical rules to be applicable. But, whereas existential quantification is satisfactory with "John is pale" and "Mary is happy," it would be false when applied to "Hamlet is sad." There is also an interesting example, given by Chomsky, of the two sentences "John is eager to please" and "John is 1 4. Tractatus 3 . 3 2 3 . 1 5 . Rolf A. Eberle, Nomi nalistic Systems (New York: H u manities Press, 1 970).

12

Essays in Linguistic Ontology

easy to please," which might be taken to have the same form. 16 But to maintain that identical logical or grammatical rules are applicable to both is a mistake, for from "John is easy to please" it follows that it is easy for someone to please John or that pleasing John is easy, whereas from "John is eager to please" it does not make sense to say that what follows is that it is eager for someone to please John or that pleasing John is eager. A commonality of surface form may have little if any logi­ cal or ontological significance. A more interesting example of how commonality of surface form may lead to unwarranted existential inferences can be found in the Wittgensteinian analysis of sensation, in which a sentence such as "Another person cannot have my sen­ sations" can seem to be a perfectly legitimate assertion comparable in form to "Another person cannot have my shoes." Once we assert that both sentences have the same form, it seems to be a fairly easy move to regard "my shoes" and "my sensations" as syntactically identical and open to the same syntactical rules. Thus since, except under very special conditions, a nondeviant negative sen­ tence means that its corresponding affirmative sentence is also nondeviant, we can also assert both "Another person can have my shoes" and "Another person can have my sensations." But we can see what has gone wrong here. We have mistakenly come to believe that, because the surface structures of the two sen­ tences are the same, therefore the same rules are applicable to both. It is like maintaining that "Everyone goes home" has the same form as "Everyone go home" and insisting that the logical derivations that could be made from the former could also be made from the latter. But, of course, this would be to con­ fuse the logic of imperatives with that of declaratives. Instantiation, for example, in the logic of imperatives, unlike in the logic of declaratives, is not a deductive inference. Thus, when we look to the linguistic contexts in which each sentence func­ tions, we find that what can be asked of one sentence cannot necessarily be asked of other sentences seemingly identical or very similar in linguistic arrangement. Wittgenstein makes the point that, if we were to try to make derivations simply from the surface form of sentences, then it becomes perfectly sensible to ask the question "Which shoes are the shoes that I claim cannot belong to anyone else?" and then to ask the same question with "shoes" replaced by "sensations." But is it possible to discriminate among sensations those that are mine and those that are not mine? Can I say of a sensation as I might of a shoe "Ah, this sensation is really mine"? For Wittgenstein such questions would be as absurd as asking "Which pains are my pains?" 1 7 16. Noam Chomsky, "Remarks on Nominalization," in The Logic of Grammar, ed. Donald Da­ vidson and Gilbert Harman (Encino, CA: Dickenson, 1 975), pp. 264-67. 17. Thus Wittgenstein say s, "Another person can't have my pains," and he replies to this, "Which are my pains?" ( Ph ilosophical In vestigations, p. 253). His point here is that both the statement and

Language, Form, and Ontology

13

It should be noted that Wittgenstein may be incorrect. There may be abso­ lutely nothing wrong with the idea that another person has my sensations . I might be able, at some far future time, to tap your nervous system into mine and then discover that. v.·henever your finger is pinched, I always received a certain unpleasant sensation . Thus there might be a legitimate reason to think that I am having your sensation or that at least we are both having the same sensation. (Sameness, as Wittgenstein was prone to point out, is not always a matter of iden­ tity. ) Or perhaps my visual system might some day be capable of being tapped into yours so that, whenever you saw a picture that was not shown to me, a sud­ den image of the picture appeared to me. Here also it might make sense to say that I am having your image or that we are both having the same image-espe­ cially if we both describe the picture in the same way. The important point in the Wittgensteinian analysis is that we cannot rely on derivations made from sur­ face form. The moral of the story, then, is quite clear: even though at first analysis a sen­ tence may have a clear and familiar form, the clarity and familiarity may be only on the surface. Because the language may permit the inclusion of a sentence such as "I have a pain," it does not follow that we are automatically committed to the existence of certain things called pains, just as we might believe ourselves to be automatically committed to the existence of certain things called dogs if we said "I have a dog." This does not mean that we are speaking falsely or saying something meaningless when we say "I have a pain"; it means that we have to be wary and critical about what we think exists when we make such a statement. We ought not to think that, because we can speak of a pain and also of a dog, both pains and dogs are existential entities. The surface form, or, as grammarians are prone to call it, the grammatical form, of "I have a dog" may be the same as that of "I have a pain." But this does not at al l entail that we are dealing with the basic form of the sentence. In fact, since sentences usually have other sentences as synonyms, or at least performing the same linguistic function, it is often not clear what the surface form itself is. "I hurt," "I am in pain," "I feel pain," "I am hurting" serve the same function as "I have a pain ." Each of these sentences belongs to a class of similarly formed sentences. Thus "I hurt" can be classified with "I run," "I see," "I talk," and so forth. But each class has its own peculiar characteristics. "I hurt" exhibits a set of categories different from that of "I have a pain." Since both perform the same function, which surface form is to be se­ lected? The choice is important, since the logical derivations that can be made the reply are spurious, since my has a function only as far as it can be used in relation to what is not mine. But how does one distinguish those pains that arc mine from those that arc not mine? Sec also the discussion by John W Cook, "Wittgenstein on Privacy," in Wittgenstein: The Philosophical Inves­ tigation, ed. George Pitcher (New York: Doubleday, 1966), p. 304; Hallett, A Companion to Witt­ genstein's "Philosophical Investigations," pp. 314, 333.

14

Essays in Linguistic Ontology

from " I hurt" are quite distinct from those that can be made from " I have a pain." Only the latter, apparently, permits quantification over pains. Ought we, then, to turn to the linguists, especially those such as Chomsky and his school, for they make the claim that every sentence has its own unique deep structural form and that this form is often common to a group of sentences that are markedly different in grammatical construction? This deep form would pre­ sumably be the basic one that would indicate the genuine designators in a sen­ tence and how such designators are related to one another. In brief, we would finally have information that wouid permit us to show the ontological claim of a sentence. We might begin by considering a sentence given by Chomsky, "The man hit the ball." 1 � What is the form of this sentence? According to Chomsky, this is a recognized, acceptable nondeviant sentence, in the sense that we would not re­ gard it as peculiar in the way we would "Man the hit ball" or the less deviant but ambiguous "The ball the man hit." Chomsky's problem arises in trying to deter­ mine why "The man hit the ball" is taken to be a perfectly acceptable English sentence whereas the other two are not. What he will try to show is that "The man hit the ball" is acceptable as nondeviant because it exhibits certain formal structures that are not present in other, unacceptable sentences. Chomsky appar­ ently assumes that there is a relation between acceptability and form. He believes that acceptability is more than a mere psychological or socially conditioned reac­ tion to a set of words or sentences. In his view acceptability reflects an inherent, perhaps genetic, competence in the use of language and an intuitive awareness of the form that can be derived from some yet undiscovered set of linguistic rules. But, of course, it should be pointed out that "acceptability" is a notoriously ambiguous expression. What is an acceptable sentence to a student is often not an acceptable sentence to his English professor. " Universals exist" is an accept­ able sentence to some philosophers, unacceptable to many others, and, proba­ bly, to the average individual totally incomprehensible. Thus acceptability is not a very reliable criterion for demarcating deviant from nondeviant sentences. Still we might wish to agree with Chomsky that some sentences-if we can call them sentences-are simply extreme deviations from those that we normally use. Except in some highly abstract poetic contexts, "Man the hit ball the" would not be an allowable arrangement of words. Thus, although the criterion of ac­ ceptability is not precise, still some sentence structures would not be acceptable under any circumstances, and Chomsky's problem could be one of determining why some structures are adequate for communication purposes while others are not. In fact, we might regard Chomsky's notion of acceptability as an initial re­ sponse that is refined as we learn more about sentence structure. Just as Quine 1 8.

Syntactic Structures

(The Hague: Mouton, 1 9 57), p. 26.

Language, Form, and Ontology

I5

speaks of the notion of "similarity" as a primitive attempt at classification that becomes more and more refined as scientific data is accumulated, 1 9 so also for Chomsky "acceptabil ity" is the first classifying principle of demarcation. Gradu­ ally, classi fication procedures are made more precise so that acceptabil ity is re­ placed by grammatical ity, which, in turn, is replaced by the fundamental l in­ guistic rules of generative grammar. W hen we think of acceptability in this way-as an initial response in classifying sentences-then it becomes clear why Chomsky is not concerned with the motivations, intentions, or personal reasons involved in uttering a sentence. These are not explanations for sentence forma­ tion or for sentence meaning. Such attempts to understand sentences are "pre­ analytical" and must give way to explanation in generative terms. Just as we be­ gin our explanation of atomic reactions by speaking in terms of affinities and attractions that are gradually replaced by more sophisticated terminology, so also acceptability is the primitive psychologistic explanation that is gradual ly replaced by more objectively oriented terminology that indicates why our sentences are usually acceptable. For this reason Chomsky rejects the arguments of Grice, Searle, Alston, and others who have concentrated on the perocutionary and il­ locutionary effects of a sentence in order to explain its meaning. 2 0 A sentence is still a sentence with its particular meaning regardless of what its effects may be or what a person intends by it. As Ziff has put it, in his own inimitable way, "W hat would a person intend to effect by uttering the sentence ' Snow is white and snow is white and snow is white and snow is white and snow is white'? I conjecture that a person uttering such a sentence would be either a philosopher or a l inguist or an avant-garde novel ist or a child at play or a Chinese torturer. W hat people would intend to effect by uttering such a sentence would most l ikely have nothing whatever to do with the meaning of the sentence. " 2 1 For a similar reason Chomsky rejects the Gricean analysis of meaning in terms of intentions. W hat we might intend in using a sentence can be, and very often is, quite different from what the sentence actually means. Just as understanding what an auto­ mobile is and how it operates requires a knowledge of the structure and the inter­ relations of its parts, so also for Chomsky sentences can be understood only by a knowledge of those basic mental istic rules-both syntactical and semantical­ that govern words and their many diverse combinations. These rules make up what is known as generative transformational grammar. We shall shortly see how Chomsky's rules of transformational grammar deal 19 . W V Quine, Word and Object (New York: Wiley, 1960), pp . 14 -17. 20 . Sec his criticism of John Searle, H . P. Grice, P. F. Strawson , and W P. Alston in Reflections on Language (New York: Random House, 1975), pp. 53- 77, 194 -95. 21 . Paul Ziff, "On H. P. Gricc's Account of Meaning," Analysis 28 (October 1967): 7 . Also re­ printed in Readings in the Philosophy of Language, ed . Jay F. Rosenberg and Charles Travis (En­ glewood Cliffs, NJ: Prentice-Hall, 1971 ), pp . 444 -50 .

16

Essays in Linguistic Ontology

with the ordinary English language sentence "The man hit the ball." But we might first inquire why certain sentences are taken to be deviant. W hy not say that "The square root of 4 is red" is simply false and not deviant? Square roots of 4, l ike brain cells, just happen not to be red. But, if a sentence is fa lse, then it is either analytically or synthetically false . If it is analytically false, then we are as­ serting that either it is a contradiction or it is a priori false . But clearly 'The square root of 4 is red" is not a contradication. It is not a substitution instance of p and p. Well , is it a priori false? If by "a priori false" we mean necessarily false, not through logical contradiction but through meaning or definition, then it is not a priori false, since "the square root of 4," neither in its definition nor in its meaning, entails that it cannot have color properties. "Not being red," l ike "not being sweet," is not included in the dictionary or mathematical definitions of "square root of 4." "A triangle has four sides" is necessarily false, because the definition of "triangle" requires the property of three sides and, therefore, not of four sides. But "the square root of 4" has nothing in its definition about colors. Thus 'The square root of 4 is red" is not a priori false . Shall we then say that it is synthetically false? But this also poses problems, since it would imply that there can be possible worlds in which it is true to say that the square root of 4 is red. Surely there cannot be a possible world in which such an assertion would be true. Colors are just not applicable to numbers, although they could be appl ica­ ble to numerals. It does make sense to say that the numeral 4 is printed in black or blue or red, or that the word "four" is written in red. But numbers, l ike ideas, thoughts, feelings, and the meanings of sentences, cannot be black or blue or red. (Although we can speak of feeling blue or having black thoughts, this does not mean that feelings are colored blue or that thoughts are colored black. ) And the reason for this is that numbers are not material, and color predicates apply only to material entities. W hat we have here are basic categorial distinctions that are violated in the assertion of certain kinds of sentences. We do not accept as a legitim3te sentence "The square root of 4 is red" because we implicitly recognize a violation of categories. Unfortunately, Chomsky does not take the time to tell us exactly how we come to recognize that certain sentences are deviant while others are not, either through intuition or through some faint gl immering of what the basic rules and categories of the language are or through inductive and analogical inferences based on prior sentential experiences. Probably some form of intuition is present, just as we intuitively grasp the Platonic universal among particulars, since Chomsky unhesitatingly rejects the view that we already explic­ itly know-even in some partial form-the rules governing sentence formation or that we have made inductive or analogical inferences from our past acquaint­ ance with certain l inguistic structures. 22 There is some play on the verb "know" 22. At one point Chomsky suggests we distinguish "knowing" from "cognizing"; we might "know" some scattered chaotic subpart of the coherent structure that is finally "cognized" ( Reflec-

Language, Form , and Ontology

17

here, since, according to Chomsky's analysis, we apparently do "i mplicitly" know the rules , whatever they may be, even though we do not "explicitly" know them. The rules are there, operating in the same way hidden, unconscious motivations may be operating within us . The very fact that our language perfor­ mance is normally so successful reveals our inherent linguistic competence. The linguist-at least the Chomskian kind- is there to uncover for us the basic lan­ guage structure that determ ines speech habits, just as the psychoanalyst is there to uncover for us the basic drives and complexes that determine our behavioral responses. The difference, however, is that, whereas the psychoanalyst regards the unconscious as formed out of experience-for example, our sexual and oedi­ pal complexes are due to traumatic sexual experiences or to aberrant filial rela­ tions-Chomsky considers his rules and categories as Kantian-they operate within all human beings in the same way regardless of personal experience, up­ bringing, or social condition. Presumably only the linguist, with his expertise in generative grammar, can eventually make us fully aware of what these rules and categories are. This view of implicit knowledge poses problems, since it immediately implies the existence of certain innate ideas, and innate ideas have not fared very well in philosophy. Serious questions arise as to what an idea is, for example, whether it is a particular arrangement of neurons, dendrites, and so forth, or whether it is a mental proposition or a picture. All of these possibilities have been very elabo­ rately criticized both in the past and in the present era. 23 Furthermore, Chom­ sky's innate ideas are not mere logical or mathematical truths whose necessity might conceivably support the view that the truths of some propositions are guar­ anteed simply by our contemplating them. (But it is never clear why any proposi­ tion should suddenly be taken as necessarily true or even as simply true merely by our contemplating it.) Chomsky's ideas are linguistic ones that, in Kantian fashion, give us the basic categories and rules that must be reflected in every language. This does not mean that all the rules of a given language are innate. Chomsky distinguishes between the internalized rules of a specific language and the innate rules that govern all languages. An internalized rule is one that hap­ pens to have evolved in the language. Thus in many languages noun endings have been dropped and word orders have changed. Modern English is consider­ ably different from Middle English and Anglo-Saxon. But change in any Iantions, p. 165). Chomsky's criticism of induction and analogy as ways of accounting for the human capacity to recognize and form new sentences appears in his many arguments against Quine; see, for example, Reflections, pp. 179-95; Words and Objections, ed. Donald Davidson and Jaako Hintikka (Dordrecht, Holland: D. Reidel, 1969), pp. 53-68. 23. For a major critique of theories involving "inner" concepts and innate ideas, including Chomsky 's views, see Norman Malcolm, Thought and Knowledge ( Ithaca, NY: Cornell Univ. Pr., 1977), pp. 159- 69.

18

Essays in Linguistic Ontology

guage has limitations, which reveal the innate structures of the language. Every language must include terms or more complex expressions that designate objects and perhaps properties of objects. But these limiting restrictions, these primary rules, are part of the mental makeup of human beings. In recent years, in spite of his commitment to mentalism, Jerrold Katz has posited these rules as ontological ones, free of any mentalistic connections. For Chomsky, however, they are both mentalistic and necessary, despite the fact that, as Wharf and other linguists have indicated, linguistic categories, that is, nouns, predicates, verbs, and so forth, and the linguistic rules that govern them do not have the kind of necessity that is attributed to logical and mathematical propositions. 24 Chomsky's general philosophy, then, seems to be bound to a complex form of psychologism and modality, and this may well be a morass from which he may never be able to extricate himself. But let us turn to the pure transformational theory itself and see how well it holds up in explaining what logical form is. Let us acknowledge the various demarcations Chomsky makes and proceed to exam­ ine how he obtains the generative grammar that presumably finally explains why we immediately make the kind of distinctions that we do. Is there some set of linguistic rules and categories such that from them we can derive only non­ deviant sentences, or, if we do derive deviant or ambiguous sentences, or both, we could show that they occur because of a confused use of the rules? Now, one very significant way in which "derivation" has been explained is in terms of recursive function systems best exemplified in formal languages. W hat we do in such languages is posit some set of marks that are categorized as predi­ cates or individual variables and combined into sentential forms by certain stipu­ lated recursive-formation rules. There could be an infinite number of such sys­ tems, but there is always an underlying assumption that the forms, when they are given interpretations, will turn out to be recognizable natural- or scientific­ language sentences. In a similar way Chomsky seeks to construct a recursive­ function system in which we should derive sentential forms that would be ac­ ceptable as natural-language sentences. We might begin, then, by introducing a set of categories and a set of rules from which we could recursively derive the simple sentence "The man hit the ball." These rules and categories make up what Chomsky calls a "phrase structure grammar":

( 1 ) Sentence --------------------llo N P + VP (2) NP

T+ N

(4) T (5) N (6) V

the (man, ball, . . . ) (hit, took, . . . )

(3) VP

V+ NP

24. Cf. John Lyons, Introduction to Theoretical Linguistics (London: Cambridge Univ. Pr. ,

Language , Form , and Ontology

19

In this grammar there are six categories and six rules governing the categories . The six categories arc Sentence, NP, VP, and so forth; the six rules are indicated by the arrows. Each arrow is to be interpreted such that the element to its right can replace the element to its left. Thus NP ("Noun Phrase") can be replaced by the combination of T ("the") and N (" Noun"; either "man" or "bal l," and so forth). Similarly, VP ("Verb Phrase") can be replaced by the combination of V ( "Verb"; either "hit" or "took," and so forth) and NP (any combination of T and N). Now, just as in a formal logical system, we can use recursive rules to derive well -formed formulas from the postulated elements in the system without any recourse to meaning, so here also we can derive "The man hit the ball " as a strict syntactical form by following the rules of the phrase-structure grammar. Begin­ ning with Rule ( I), we obtain N P + VP. Applying Rule (2) to N P of N P + VP, we obtain T + N + VP. We then proceed to use Rule (3) with VP and thus obtain T + N + V + T + N . Rules (4), ( 5), and (6) are then applied to give us "The + man + hit+ the + ball . " W hat we have derived, however, is not actua1 ly a sen­ tence, but rather a series of marks . By applying phonological rules to these marks, we transform them into the set of sounds that make up the English sen­ tence "The man hit the ball." We can then stipulate that the first noun phrase is the subject, while the verb and what follows it makes up the predicate. It is im­ portant to note that the rules of the phrase-structure grammar are followed con­ secutively. That is, we begin with Rule ( I) and then move through Rule (6). In this way, given the limited vocabulary we are al lowing in this grammar, we can determine whether a given set of expressions is a well-formed sentence in the language . Thus, if we wish to know why "The hit ball man the" is not a sentence in the language, we can demonstrate that this grouping of words cannot be de­ rived from the grammar without a violation of one or more rules. It violates Rules ( 1) and (2), which require a sentence to begin with NP, which in turn must consist of T + N . Since "hit" is an element of V and since T + V is not a permissi­ ble combination, "the hit bal l man the" is not a permissible combination in this grammar. We might ask whether there could be a set of rules from which we could derive "the hit ball man the. " Chomsky apparently believes that this would be impos­ sible, since the sentences that are derived must be ones that would also be accept­ able. Again, everything hinges on the purely psychologistic notion of accept­ ability. Furthermore, if acceptability is the first criterion by which sentences are distinguished, then it is possible that just as in a science two initially similar en­ tities are later classified as dissimilar-for example, as whales are no longer clasl 968), pp. 4 3 2 - 3 3; Judith Greene, Psycholinguistics, Chomsky and Psychology (Harmondsworth, Eng. : Penguin, l 974), p. 80.

20

Essays in Linguistic Ontology

sified as fish, so also an unacceptable sentence might become acceptable. Since Chomsky does not give us a criterion such as contradiction, which is used to show that some constructed logical systems are not satisfactory, we cannot rule out the possibility of a linguistic system in which "the hit ball man the" would be derivable. Sometimes the phrase-structure analysis can be given more picturesquely by the use of what Chomsky calls a tree diagram. Thus the derivation of "The man hit the ball" can be shown in the following way:

NP T/

I

tlie

--------

�N

I

man

Sentence �

/VP

V

I

hit

--------------NP T

/ �

t�e

I bal l

As in the previous derivation, this diagram shows that the sentence consists of two components, a noun phrase and a verb phrase, which are in turn reducible to T + N + V + T + N. The subject is the noun phrase that is directly controlled by the sentence, that is, the one on the left, while the predicate consists of the verb phrase . We thus have a way of showing quite clearly what the grammatical struc­ ture of a sentence is. We have, of course, only presented a very simple example using an almost primitive grammar. Not many other sentences could be derived from the phrase­ structure rules we have given. Unless we were willing to fill in the dots following "ball" and "took," we could construct only such sentences as "The ball hit the man" and "The man took the ball." Furthermore, more rules would be required; otherwise we could construct a deviant sentence, "The ball took the man . " For this reason Chomsky goes on to introduce rules by which Human nouns, those designating human beings, can be combined with non-Human nouns. 25 (It might be noted that at one time Chomsky believed that all linguistic rules can be formulated in strict syntactic terms, that is, without any reference to vague philo­ sophical or semantical concepts, but Human nouns require for their explication the semantical concept of Human. ) For deriving even more complicated sen­ tences, for example, ones involving synonymy of sentences and changes of tense, we would, first, require transformational rules by which we can, in the manner of transformational rules in a formal logical system, convert one sentence into another. Thus we would want to be able to say that the tree diagram for "The man hit the ball" is identical to the tree diagram for 'The ball was hit by the 2 5 . Aspects of the Theory of Syntax (Cambridge, MA: M . I . T Pr. , 1 965), p. 79.

Language, Form, and Ontology

2l

man. " We can do this by a passive-active rule such as "NP 1 + A ux + V + N P 2 is always replaceable by N P 2 + A ux + V + By+ N P 1 , " where "A ux" indicates the tense of the verb. This rule would accommodate many sentences having the specified form, but additional restrictions would be needed in order to avoid the move, say from "John stayed home" to "Home is stayed by John" or from "John cut his face" to "His face was cut by John." Presumably we would eventually reach a rule, in Chomsky's view, that would show us how all sentences can be translated from their active to their passive form. Second, we should also be required to distinguish the apparent subject of a sentence from the genuine one. Thus, in "John was persuaded by Harry to take up golf," the apparent subject, the one that seems to be the subject on first analy­ sis, is "John," but the real subject or "logical" subject, as Chomsky sometimes calls it, is "Harry," since a transformation rule changes this sentence into "Harry persuaded John that he (John) should take up golf. " Another rule, that of N P­ preposing, permits the move from "It seems that John is a nice fellow" to "John seems to be a nice fellow" or from "It is certain that John will win" to "John is certain to win. " 26 In both of these cases the subject in the embedded clause be­ comes the subject of the entire sentence. These rules, of course, still do not ex­ haust all that is needed in order to derive all the sentences that we take to be grammatically and semantically correct. As Chomsky points out, inquiry into generative transformational grammar is, like any inquiry, an ongoing process. 2 7 Just as new scientific theories are always being introduced and as old ones are modified in order to accommodate new data, so also the rules of transforma­ tional grammar are continually being either discovered or modified. But the basic point would seem to be the same. We should conclude with a structure that would distinguish for us what terms are nouns and verbs, and which of these are the "logical" subjects and predicates. Once we have explicitly shown which are the logical subjects and predicates of a sentence, then and only then can we fi­ nally state what ontological commitment it is making. It is as if Chomsky were telling us, in the manner of Russell, that only when we become aware that " Pegasus," for example, is not a noun, but rather a description or some other grammatical phrase can we determine what, if any, commitment to existence is involved in the statement " Pegasus was the winged horse of Bellerophon. " The question that arises, however, is what exactly is meant here by "logical" subjects and predicates. Has Chomsky presented us with a way of obtaining the 26. Reflections, pp . 86-87. 27. Thus Chomsky, arguing against Jonathan Cohen, asserts that any innate principle is revisable if, on further investigation, it is shown to be "violated elsewhere in the language or in some other language. In fact, proposals concerning universal grammar-hence . . . proposals concerning innate capacity-have repeatedly been revised on just such grounds" (Reflections, p. 207). Chomsky appar­ ently docs not recognize the peculiarity involved in a "revisable innateness. " If rules arc revisable both in principle and in practice, the innateness thesis becomes tautological and. therefore, trivial .

22

Essays in Linguistic Ontology

basic "logical" form of a sentence? It might be asserted that, once a sentence has been categorized and given structure in the way suggested by the linguist, espe­ cially the Chomskian linguist, then the basic implicit form of the sentence has been made explicit. Once we have discovered the true grammatical status of each expression, that is, that it i's "Harry" and not "John" that is the subject in the example above or that 'The man hit the ball" has as its genuine form T-N-V-T­ N, we have exhibited the genuine form of these sentences. Then and only then can we determine what commitments are being made to what exists. But why should the basic grammatical form tell us anything at all about our existential commitments? How are we to make the move from the word or the phrase or the sentence to what exists? Can we simply say that now we know ex­ actly what kind of existential claim is contained in the sentence "The man hit the ball"? The sentence is to be labeled "true" if and only if "the man" refers to a particular man, "the ball" to a particular ball, and "hits" to a certain relation between a man and a ball. But all of these ways of making the move to existence are suspect. Neither "the man" nor "the ball" refers to anything at all, since, as Russell has shown, if they did then we could not meaningfully speak of the pos­ sibility that there is no such man or that there is no such ball. Descriptions, un­ like (logically proper) names and demonstrative pronouns, do not designate an existential entity; they are satisfiable-to use the jargon of the logician--but they do not designate. And, of course, if "hits" refers to a relation, then our problems begin, for there is much controversy and confusion about whether relations can be said to exist. Thus the grammatical structures we obtain from transforma­ tional generative grammar seem to tell us very little about what our existential commitments are. Furthermore, Chomsky speaks of "logical" subjects and predicates as well as the "logical" form of a sentence. What makes his grammatical structures "logi­ cal" ones? If a sentence is logically formed, then we expect to be able to draw certain logical inferences from it. Just as from any mathematical sentence such as "There are four apples" we can derive, because of its mathematical compo­ nent, "There are at least four apples" and "There are less than five apples" and "There are two apples plus two more apples," so also we should be able to draw certain kinds of logical inferences from any logically formed sentence. \Ve should be able to recognize in the sentence that some of its expressions are quan­ tit1ers, others are names, and still others are predicates that are either monadic or polyadic, for these are the expressions that usually identify the logical form of a sentence. \Vhere do these devices appear in Chomsky's deep-structure sentences? Chomsky's deep-structure sentences seem to have the same difficulties as Witt­ genstein's basic sentences. If Wittgenstein's basic sentence is, as many believe, a concatenation of names, then how can such a sentence-if, indeed, we can ever call it a sentence-be linked to any known logical system? There are no "hooks,"

Language, Form, and Ontology

23

that is, logical connectors or other fami liar logical symbols, by which we can connect a basic sentence consisting solely of names to all the other logical ter­ minology with which we are acquainted. It is like thinking that, simply by pro­ ducing some set of numbers, we can automatically produce a mathematical sentence capable of being util ized in a mathematical system. But, of course, numbers, l ike names, have to be stated in certain forms before they can be uti­ lized. Simi larly, Chomsky's deep-structure sentence has no logical framework to which logical tools can be applied. I t does indeed make an improvement on W ittgenstein's atomistic form, since it does have a grammatical frame. But gram­ matical form is not necessarily logical form. We require logical "hooks" in a sen­ tence by vi rtue of which it can be l inked to a logical system. Could we then argue that, once we have the fundamental grammatical form, the deep-structure form that reveals the genuine grammatical status of all the expressions in a sentence, it is an easy matter to translate the sentence into some given logical system? Thus, for example, we could stipulate that, if a given noun phrase in a sentence is the first of two noun phrases, that is, the genuine subject that appears at the left of the tree diagram, then it is to be taken as the expression that replaces the first variable in such a form as Fxy of Russell 's or Quine's formal system. The verb is to replace F, and the second phrase is to replace y. In this way we have given the sentence entry into a logical system. How satisfactory is this procedure? If we determine the deep-structure gram­ matical form of a sentence, can some simple device translate grammatical into logical form? I think not. First, apparently the l inguist does not pursue the search for form with the needs of the philosopher in mind. The l inguist deals primarily with sentences as they are given in a natural language, so that for the l inguist form is a function of what is exhibited-either implicitly or expl icitly-in natu­ ral language. That is to say, the l inguist does not chal lenge the linguistic catego­ ries and the common l inguistic forms that appear in a language; they are simply what they are. They are the "raw data," so to speak, with which linguistic analy­ ses begin. They are the basic acceptable data whose construction must be ex­ plained by any set of grammatical rules that are finally adopted. Thus, for ex­ ample, if "Hamlet killed Polonius" and "Brutus killed Caesar" are acceptable sentences and exhibit the same deep structure form, that is, "x caused y to die" or "x caused the action that killed y," then each one can undergo the same gram­ matical transformation. If the active-passive rule is appl icable to one, it will be applicable to the other. Linguists are essentially concerned with the sentences, the specific set of symbols that are written or uttered. They are not concerned with whether a term acceptable in the language ought to be acceptable or whether the existential entities to which a l inguistic category commits them are free of logical paradox or contradiction. For this reason most l inguists speak spe­ cifical ly of linguistic categories·, deliberately avoiding any move that commits

24

Essays in Linguistic Ontology

them to any existential claim, for example, that nouns designate objects or that verbs refer to relations. But for the philosopher and the logician this is exactly what l inguistic analysis is al l about. They want to know how an expression relates to some domain, whether it denotes an entity or functions in some other way, whether a domain requires both material and abstract entities in order to account for the statements we take to be both meaningful and truth-functional. Thus, for the philosopher, since "Brutus killed Caesar" perm its and " Hamlet killed Polo­ nius" does not permit quantification and, therefore, does not give an existential status to Hamlet and Polonius, the philosopher rejects " Hamlet" and " Polonius" as names that can be appropriately categorized with such names as "Brutus" and "Caesar." The philosopher either substitutes for them definite descriptions as for­ mulated by Russell or introduces such oddities as null entities as referents in the way suggested by Frege and Carnap, or, as suggested by Strawson, characterizes sentences with nondesignative names as simply lacking truth values. Or the phi­ losopher might use a "free" logic approach in wh ich names can be vacuous, that is, devoid of any existential commitment, so that (3 x)( x = a), which is valid in classical predicate logic, will be an ordinary true or false premise . In other words, the ph ilosophical problem is not one of determining whether a sentence is gram­ matically and semantically correct. "Hamlet killed Polonius" is correct on both counts. It certainly does not seem to violate any syntactic rule, nor is it ambigu­ ous. But what are its referents? W hat kind of objects are required in order to give it a truth value? These are important questions whose answers will determine for us what we are to accept as real. Similarly, when Charles J . Fillmore argues that the deep structure of such a sentence as " Fred broke the lens" is " Fred caused the lens to break," he is making the interesting point that some verbs conceal the actual state of affairs that the sentence seeks to describe. 28 In this case "broke" must be translated into causal terms i n order to show the causal state that the sentence is being used to desc1 ibe. But Fillmore makes it seem as if the translation into causes has now given us the deep, the logical, form of the sentence. He apparently assumes that "cause" is a perfectly respectable term that is easily incorporated into a logical system. Of course, as Fillmore himself undoubtedly knows, "cause" has been one of the most controversial terms in both past and present philosophy, and, until we can use it in a formal system, we are simply jumping from the frying pan into the fi re when we make "cause" part of the ultimate deep structure of a sentence . We m ight note that this same lack of concern about the existential reference of terms and phrases is also exhibited in Fillmore's comment that the meaning of re­ semblance sentences is to be found by reference to memories. Thus the meaning 28. Charles J. Fillmore, "Subjects, Speakers, and Roles," in Semantics o{Natural Language, ed. Donald Davidson and Gilbert Harman (Dordrecht, Holland: D. Reidel, 1972), p. 4.

Language, Form, and Ontology

25

of "Your brother resembles a horse" is, for Fillmore, "Your brother as stimulus evokes in me memories of horses. " 2 () But, first, " a resembles b" is meaningful even if there is no one around to remember anything. Resemblance is defined in terms of overlapping of properties, not in terms of one's feelings or memories . Second, surely Norman Malcolm's critique of memories as explanatory devices cannot be ignored. ' 0 Malcolm has shown that even memory statements such as " I remember where I placed the key" need not depend at all for its meaning on my having something called a memory. I might ask someone while he is reading or studying, " Do you remember where you placed the key?" and he might auto­ matical ly point to a drawer. Although the action could be described as " He re­ membered where he placed the key," remembering need not entail the existence of some psychological event, that is, a memory. The main point is that l inguists, despite their detailed analyses and their refer­ ences to logical subjects and logical predicates, are still concerned with gram­ matical rather than logical categories. Linguists l ist the various grammatical cat­ egories that are displayed in a language, for example, nouns, verbs, and so forth, and then proceed to indicate the proper categorization of each word in a sen­ tence and the proper selection of subject and predicate. In this way linguists can legitimately distinguish deep from surface structure. But philosophers, in their search for logical form, argue that, even if it could be shown that in all contexts a given word really functions as a name or that in a given context it really functions as a subject, the question ought still to be raised as to whether the word ought to function in this way. Ought we to accept "cause" as a respectable word in the language? Ought we to acknowledge that there are memories or other psycholog­ ical entities because there are memory sentences? Ought we to take " Pegasus" as a naming expression because it always occupies a naming position in the language? Does this not raise havoc, as Russell indicated in his criticism of Meinong, with what we are wil ling to attribute to the domain of a language, even a natural one? Ought we to take " Hamlet killed Polonius" as having dyadic predi­ cate form comparable to that of "Brutus killed Caesar"? In one of his analyses, Chomsky gives us the "logical form" of "The pol ice know who the FBI discovered that Bill shot." The logical form turns out to be 'The pol ice know for which person x, the FBI discovered that Bill shot x." ' 1 The latter sentence has logical form because, as Chomsky tells us, there is a variable x and a quanti fier, "for which x," binding it. But is this all there is to logical form, finding a quanti fier expression and the variable it binds? W hat of "know" and 29. Ibid. , p. 12. 30. Norman Malcolm, Thought and Knowledge (Ithaca, NY : Cornell Univ. Pr. , 1977), p. 146. See also Malcolm's destructive analysis of both mcntalistic and phy siological theories of memory in Memory and Mind (Ithaca, NY : Cornell Univ. Pr. , l 977). 31. Reflections, p. 94.

26

Essays in Linguistic Ontology

"discovered"? Chomsky does not tell us how we are to treat these expressions, as simple polyadic predicates or as verbs taking oblique contexts. If they arc predi­ cates, then we ought to know whether they arc to be defined mentalistically or behaviorally. As philosophers well know, major difficulties accompany either al­ ternative. If "know" and "discover" take oblique contexts, then of course the problems quickly multiply. Can a quantifier in one context bind a variable in another? "For which person x" functions with "know," but the individual vari­ able that Chomsky wants to bind functions with "discovered" in another context. If we follow Quine and others, it is not by any means clear that a quantifier out­ side an oblique context can govern a variable within that context. ' 2 Since the introduction of intensions by Frege and Carnap, linguists such as Richard Montague, John Wallace, George Lakoff, David Lewis, and others have had few problems with positing intensions as designata for terms. B Since inten­ sions are nonextensional entities, terms that did not have extensions could have intensions. In one fell swoop abstract entities from meanings to ideas to proposi­ tions could now respectably enter the domain of any language, both formal and natural. And since Saul Kripke's formal interpretation of a pure calculus with modal operators in which possible entities along with actual ones can now be the referents of terms, these same linguists have had little difficulty with modal, oblique, or counterfactual sentences. These sentences do have designat3 , namely, objects in possible worlds. But, whereas linguists seem to be secure about these matters, philosophers do not. Both intensions and possible objects are philosoph­ ically suspect. Quine has asserted that both intensions and objects of possible worlds are "creatures of darkness" to which neither quantification nor the law of identity is applicable. From "I believe that John Smith is in the next room" it does not follow that there is someone in the next room who is called "John Smith." If we assume the normal interpretation of oblique and modal sentences, namely, that they consist of subsentences within sentences, then we cal lnot quantify into either oblique or modal contexts. From "It is possible that John Smith is in the next room" it does not follow that there is someone in the next room. Nor does it follow that it is possible that there is someone in the next room or that there is someone of whom it is possible that he is in the next room . Quan­ tification into modal contexts is opaque. Similarly, even if it is true that John Smith is the mayor of the city, ''I believe John Smith is in the next room" is not logically equivalent to "I believe the mayor of the city is in the next room. " The rule of identity that is applicable in nonoblique and nonmodal sentences is not applicable here. For this reason-that neither quantification nor identity seems 32. Cf. W V Quine, The Ways of Paradox (New York: Random House, 1 966), pp. 1 83- 94. Sec also the discussions of opacity as it affects both oblique and modal contexts in Reference and Modality, ed. Leonard Linsky (London: Oxford Univ. Pr. , l 97 1 ). 33. See the respective articles in Semantics of Natural Language.

Language, Form, and Ontology

27

to be appropriate here-it is not by any means clear what logical forms are at­ tributable to modal and oblique sentences. It is interesting that Chomsky seems to realize that there arc difficulties concerning words that create oblique sen­ tences, because he alludes to certain essential characteristics that we must be aware of \\'hen we use "know"-characteristics that, presumably, might settle these difficulties. H But nowhere does he tell us what these characteristics might be and how they would settle the questions at issue. In yet another discussion Chomsky maintains that he has given us the logical form of "John is certain to leave" when he shows that "John" is not really the subject at all. ' 5 Rather, the entire sentence must be transformed into "That John will leave is certain. " But he does not tell us exactly why this second sentence has logical form. Are we here dealing with a proposition that as subject takes "cer­ tain" as a predicate? Or are we dealing with a sentence as subject? It seems un­ likely that we are dealing with a sentence, since, first, "That John will leave" is not a sentence, and, second, even if it can be changed into a sentence, it imme­ diately runs into Alonzo Church's well-known translation argument. Translation of "That John will leave is certain" into French and German will be understood by a Frenchman and a German, respectively, but this will not be the case for " 'John will leave' is certain. " A sentence with a propositional element is not translatable into an identical sentence with a substituted corresponding senten­ tial element. In other words, " 'John will leave' is certain" is not identical and cannot be substituted for "That John will leave is certain. " We seem, therefore, to be dealing with a proposition that takes "certain" as a predicate. But are we sure that it is legitimate to introduce propositions and to speak of them as taking predi­ cates? When names take predicates we take it for granted, unless there is some special restriction, that we can quantify over these names. Yet, if we accept the analyses of Russell and Wittgenstein, propositions cannot be treated as names. Names obtain their meaning by denoting objects. But since propositions can be meaningful and false, denotation cannot be an essential element of their mean­ ing . Furthermore, when we quantify over a name, we are attributing existence to an object; at least this is the case when we are involved with classical predicate logic . Thus the rule of existential generalization, F y :J(3 x)Fx, states that given any name then it denotes some existent entity. But, then, if we quantify over propositional expressions, are we committing ourselves to the existence of certain odd, unverifiable and forevermore undiscoverable entities called propositions? Here we encounter important philosophical problems that make a sentence such as "That John will leave is certain" controversial and without a generally ac­ knowledged logical form . Yet for Chomsky the logical form is quite explicit once 34. Reflections, p. 88. 3 5 . Language a nd Mind, p. 1 04.

28

Essays in Linguistic Ontology

we have recognized that "That John will leave" is the subject. And what of "cer­ tain"? Chomsky finds no difficulty in calling it a "logical property," even though it is not by any means clear what a logical property is. 36 Does he mean a property that can in some sense be called analytic such as "red or not red" or one that is, in a Carnapian sense, a purely ostensive predicate such as "red"? Clearly "cer­ tain" is not a logical predicate in either one of these senses. In fact, it is not at all established that it ought to be treated as a predicate. Perhaps "certain" is defin­ able as "necessarily true" and ought to be used in conjunction with a modal oper­ ator or in relation to logically valid sentences. Perhaps it is a metalinguistic predi­ cate summarizing the evidence for a high-probability claim . In any event, the status of "certain" is not clarified by calling it a "logical property" or a "logical predicate." The linguist seems to leave the job of looking for logical form just at the point at which it begins to become most interesting and just as the philoso­ pher is getting started. It might be argued that the difficulties we have been indicating are due to the linguist's former sole preoccupation with syntax at the expense of semantics. Thus many of the questions we have raised might be answered by a semantical analysis of nouns, that is, an investigation of the verbal and written meanings attributed to nouns and their effect on syntactical relationships. We might then have been able to make a sharp distinction between "Hamlet killed Polonius" and "Brutus killed Caesar," since what might be attributed verbally to "Hamlet" and "Polonius" would not be attributed to "Brutus" and "Caesar. " "Hamlet," for example, is associated with the expression "fictitious," but neither "Caesar" nor "Brutus" is. Similarly, if we were acquainted with the semantical properties of "know" and "certain," perhaps Chomsky's reference to logical subjects and predi­ cates might not have been so objectionable. The questions that must now be raised are these: how is semantics introduced into linguistics and how much has it helped in the search for logical form? In their important and seminal paper, Katz and Fodor acknowledge that, in order to complete the projection problem, the problem involving the proper for­ mulation of the linguistic rules by which, from an understanding of a finite number of sentences, we can go on to understand any one of an infinite number of possible sentences that we may never use or encounter, every expression must u�dergo a semantic investigation. More specifically, since speakers can under­ stand so many more sentences than any they have ever used or encountered, it must be assumed that implicit in every expression, regardless of whether it is des­ ignative or purely syntactical, is a set of meanings as well as rules that determine under what conditions an expression can be legitimately used with other expres­ sions. 37 Only with this assumption can we presumably account for the fact that 36. Ibid. 37. Jerrold J. Katz and Jerry A. Fodor, 'The Structure of a Semantic Theory,"

Language

39

29

Language, Form , and On tology

the most unfam iliar, even outlandish , statement can be clearly understood by an average user of a language . Although probably no one has ever heard "The pur­ ple cat sat quietly by the rednosed elf who was eating marmalade," to the average user of the English language it would be a quaint, even absurd sentence that would still be understood . Thus Katz and Fodor tell us it is not sufficient that we be able to give a tree d iagram of "The man hit the bal l . " What the tree diagram gives us is a concatenation of morphemes, min imal classi fiable un its of a lan­ guage . The generative grammar shows us how we can construct certain com­ binations of these morphemes such as "The-man-hit-the-ball . " What we do not know is why this combination , unlike "H it-man-ball-the-the," is "acceptable" and considered to be "good" English . Having a machine that would produce "Ontogeny recapitulates phylogeny" and "The square root of 4 is red" as well­ formed groups of expressions would not mean that we know the mean ing of the words of the former or that we can account for the oddity of the latter. What is required is a semantic interpretation in wh ich each discrete morpheme is given a meani ng analysis. How are we to obtain this semantic interpretation? According to Katz the pro­ cedure is not too compl icated . 18 Assume that we have constructed a tree diagram for "Bachelors are unmarried men ." We can then take each term and , in turn , give it a tree diagram l isting the two important facets that explain its function i n a sentence: ( a ) its categorial status, whether i t i s a noun, verb, a n d s o forth; and (b) its different senses, that is, the different set of verbal expressions that are used to define it. Thus, for example, "bachelor" can be represented in the following way: bachelor (human�

noun

mal�

I (not young)

I .

(never married) I

�imal)

[one haLng academic degree conferred for completing first tour ars 0 f rie co e ] ?

(male) I ( you ng) l [ fur sea l w h en without a mate during breeding time] 4

-------

(young )

I

[knight who is serving under the standard of another] 2

( 1 963): 1 70- 2 1 0; reprinted in Readings in the Philosophy of Language, ed. Rosenberg and Travis, pp. 472- 5 14. 38. J. J . Katz, "Analyticity and Contradiction in Natural Language," in The Structure of Lan­ guage, ed. J . A. Fodor and J . J . Katz (Englewood Cliffs, NJ: Prentice-Hall, 1 964), p. 523.

30

Essays in Linguistic Ontology

Each branch from the categorial expression "noun" indicates a different path leading to a different sense. The four different paths, numbered I to 4, show that there are four different senses that are usually attributed to "bachelor." (Brackets are employed with senses that occur less frequently. ) These paths determine the different ways in which the expression can be used. The correct path for a given use of the expression is decided by the sentence and the context in which it ap­ pears. Thus, in "He is receiving a bachelor's degree at State College," the sen­ tence makes explicit the context in which "bachelor" is being used, and this tells us that sense 3, rather than I or 2 or 4, is the sense to be attributed to "bachelor." On the other hand, the context in which "All bachelors are unmarried" would normally appear-when we are speaking of men who are or who are not mar­ ried, rather than of knights or of seals-would indicate that sense I is being used. In a similar way ambiguities in a sentence are easily eliminable. Once we know the tree diagram of "bill ," we could quickly show and then eliminate the ambigu­ ity of such a sentence as "The bill is large." We should be able to recognize that the ambiguity arises because there are different paths, or senses, of "bill" and that to determine the correct one that is being used at any given time would require a more thorough knowledge of the context in which the sentence appears. Now, how much does this analysis help us to determine the basic form, the so­ called logical form, that Chomsky seems to be seeking and from which we would then be able to infer the genuine existential claim of a sentence? We ought to keep in mind that it is the existential claim of a sentence that is of major interest here. We wish to know what the ontological commitment of a sentence is, and this is determinable only if we can determine that we are not making a mistake in what we take to be the essential form of the sentence. If we believe that "Pegasus" is a name in the same way that "Sir Walter Scott" is a name, then the ontological commitment of "Pegasus was the winged horse of Bellerophon" would be far dif­ ferent from what we would conclude if "Pegasus" were a description or were to belong to some other linguistic category. Thus, if Katz and Fodor are right, then the linguist might now maintain that, with the tree analysis of words, we are in a position to know both the categorial status of these words and their various mean­ ings (senses). We can now know that "Pegasus" functions with such adjectives as "fabled" and "mythological ," unlike the name "Sir Walter Scott," and this infor­ mation will make us wary of ever thinking that "Pegasus" is similar to the names we ordinarily use. Similarly, we can show that none of the senses of "red" makes it attachable to a mathematical expression, so that "The square root of 4 is red" can be shown to be syntactically deviant because of semantic misinterpretation and that. therefore, we could not meaningfully attribute "blue" to a square root. Also, once we know the semantical properties of "know" and "think," we do not confuse the form of "The police know he is guilty" with the form of "The police think he is guilty," since the sense of "know" entails, while the sense of "think"

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31

does not, that he is guilty. By becoming aware of the syntax of a word and also of its different possible senses, we are now able to make explicit the sources of ambi­ guity that usually make it difficult to determine the logical form of a sentence. The question, however, that must be raised in regard to this elaborate linguis­ tic analysis is this: where do we obtain all this information that a given expression is a noun, that it has such and such senses, and so forth? Who tells us or where do we discover that "red' ' is not an appropriate adjective with "the square root of 4" or that "Pegasus" is defined or explained with such adjectives as "fabled" and "mythological"? Presumably this data is taken, first, from the phrase-structure grammar, with its transformation rules, and, second, from the dictionary. In fact, tree diagrams of expressions are often referred to as dictionary items, and Katz states explicitly that the formal representation of senses given in the tree diagram can be regarded as a device for indicating the information given in The Shorter Oxford E nglish Dictionary. 39 Thus the semantical tree diagrams serve to present more clearly and in a more organized fashion the information to be found in the dictionary. This procedure by which dictionary items are presented in a more "logical" organization undoubtedly gives us a quicker and better understanding of the grammatical status of a term and of the various meanings that are conventionally assigned to it. But the difficulty here is that neither the phrase structure nor the dictionary status of a term is necessarily its logical or philosophical status. "Bach­ elor" is a noun in the dictionary, but, in the formal languages developed by phi­ losophers and logicians it is a predicate. "Exists" is a verb in the dictionary, but at least since Kant most philosophers do not accept this categorization of the ex­ pression. (It should be noted that Kripke and those proposing free logics have reintroduced "exists" as a predicate. ) The dictionary calls "soluble" an adjective, but few philosophers believe that "soluble" can now safely be inserted into the same predicate slot normally reserved for "red" or "pale" or "large." Similarly, "possible" and "necessary" are modal terms that function in ways that usually are not even mentioned in the dictionary. For Chomsky, "must" and "can" are sim­ ply auxiliaries, 40 that is, supplements to the verb that are given scant analysis by linguists, but for the philosopher these expressions have posed some of the most controversial problems in the last forty years. Katz and Fodor make it quite clear that adjectives and nouns have various and often ambiguous meanings, and for this reason certain combinations of words make sense while others do not. But they seem to imply that, once we have clarified these ambiguities, once we have shown that one sentence is really a combination of two or more sentences be39. Katz, "Analyticity and Contradiction in Natural Language," p. 5 24 . 4 0 . Chomsky: Selected Readings, ed . J . P. B . Allen a n d P. Van Buren ( London: Oxford Univ. Pr. , 1 97 1 ), p. 3 1 .

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cause of the differing tree diagrams of the individual words, the new resulting sentences will show their logical form-they will reveal the genuine nouns, ad­ jectives, verbs, and so forth, and also the true subject and the true predicate. That they will do so has still to be demonstrated, I believe. "Soluble" is defined in the dictionary as "capable of passing into solution" and "capable of being solved or explained," so that if we say "The case is soluble" the particular sense to be used depends on whether we mean "case" as "case of sugar" or as "legal case . " This kind of clarification is important, but, once we have made this point, we are still nowhere near deciding the logical form of "The case is soluble" in terms of either interpretation. Philosophers are not at ail sure that "capable of passing into solution" and "capable of being solved or explained" are predicates. They are undecided about the status of "capable" and refuse to countenance it as an ordi­ nary predicate term. It is for this reason that philosophers have often translated dispositional predicates such as "soluble" into counterfactual or reductive ser:i­ tences. Even the ordinary determiners "a" and "the," which, unlike the catego­ ries of nouns and verbs, rarely even deserve mention in the indices of transfor­ mational grammar texts, are crucial logical devices, as Russell long ago attested, for revealing the logical form of certain frequently occurring descriptions such as "the boy next door," "the author of Waverly," and "the case. " It is important to be aware that linguists are not neutral in regard to philosoph­ ical issues. They do not make the claim that their search for logical form is to be divorced from the search made by philosophers. As is well known, Chomsky has insisted that linguistic study leads to an acknowledgment of innate ideas and uni­ versal concepts as well as to the acceptance of rationalism as a more plausible philosophical view than empiricism. George Lakoff has insisted that the deep form of a sentence will turn out to be equivalent to the philosopher's and the logician's notion of logical form. Jerrold Katz has argued that he has finally solved the thorny issue of analyticity. We might turn for a moment to examine the assertions of Lakoff and Katz. Lakoff has maintained that, once a sentence has been shown to be completely grammatical, that is, that its various ambiguities and grammatical violations have been eliminated, the resultant transformed sentence will turn out to be not only the deep-structure form of the sentence, but its logical form as well . Thus, for example, by the use of the adverb-preposing rule, Lakoff shows that we must be very careful about how we move adverbs in a sentence. 4 1 (A) ((I think Sam smoked pot last night" can be changed without any loss of meaning into (B) "Last night I think Sam smoked pot . " On the other hand, (C) "I mentioned that Sam smoked pot last night" cannot be changed into (D) "Last night I mentioned that 41. G . Lakoff, "Linguistics and Natural Logic," in Seman tics of Natural Language, ed. Davidson and Harman , p . 548 .

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Sam smoked pot. " What the examples show is that, whereas (A), (B), and (C) are grammatically correct, (D) is grammatically incorrect, since it violates the ad­ verb-preposing rule that specifically applies to such verbs as "mention" and "think. " As Lakoff tells us, such rules as the adverb-preposing rule not only filter out ungrammatical sentences, but at the same time also relate "the surface forms of sentences to their corresponding logical forms, while blocking any incorrect assignments of logical form to surface form." 4 2 In other words, if a sentence is not in violation of grammatical rules and presumably if its semantical ambiguities have been eradicated, then we can also go on to assume that it is now exhibiting its logical form. (0) lacks logical form because it is in violation of a grammatical rule. Now, serious questions arise here. First is the obvious question about the ad­ verb-preposing rule itself. Is it a convention? Is it an ad hoc rule simply pointing out how adverbs have operated with verbs such as "mention" and "think"? Could one foresee a possible language change in which the adverb-preposing rule no longer holds? Linguists very often tell us that the rules of language are conven­ tions, but, if they are and if a sentence is made grammatical by their application, then a logical form today need not be a logical form tomorrow. Logicians would surely deny that the rules of logic are of the same conventional flexibility as lin­ guistic rules. More serious questions follow. What does it mean to say that, at a certain point in the analysis of a sentence, its deep structure will finally be ex­ hibited? Assume that (A), (B), and (C) are not in violation of any known gram­ matical rules and are not ambiguous; then can we say that we are now being shown their logical forms? Why? For logicians, of course, neither (A), (B), nor (C) has logical form because, even though everyone seems to understand these sentences and to use them correctly, there is a serious problem-as we have al­ ready seen-about what the logical structure of an oblique sentence is. Further­ more, even if it were granted that (A), (B), and (C) were in logical form, we should be required to ask whose form it is. As Carnap has shown, oblique sen­ tences have been analyzed differently by Frege, Church, Quine, Russell, and Carnap himself. 43 So we must always ascertain which logical form we are talking about. Similarly, Lakoff analyzes some of the presuppositions of sentences. Thus "If I had realized that Harry had survived I'd have gone home" does presuppose that Harry had survived and that I did not go home. 44 Lakoff does not tell us exactly what kind of connective "presuppose" is, that is, whether it is to be taken as the ordinary material-implication sign or some form of entailment. Be that as it may, 42 . Ibid . , p . 549 . 43. R . Carnap, Meaning and Necessity (Chicago: Univ. of Chicago Pr. , 1956), enl . ed ., pp . l 3 3 - 44. 44. Lakoff, "Linguistics and Natural Logic," p. 575.

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it does nothing to tell us what the logical form of the counterfactual conditional is. W hat is unclear is what kind of conditional we have here. It is neither a logi­ cal nor a material implication. How then are we to treat this strange if-then sen­ tence? It is sometimes argued that the introduction of possible-worlds logic by Saul Kripke has settled all these questions. The subjunctive tense is really indica­ tive except that our domain is a possible, rather than an actual, one. Thus "If q were to occur, then r would occur" becomes "If q occurs in domain P (possible world), then r occurs. " Truth and falsity are applicable with the understanding that they function in a possible domain rather than in an actual one. Thus a molecular sentence can be given the truth value "true" in both possible and ac­ tual domains. But all this assumes that "true" in a possible domain is just as intel­ ligible as "true" in an actual one, and this is a major assumption! In A (the actual domain) we can determine whether a sentence ought to have "true" or "false" applied to it. How is such determination made in P? Some recent commentators seem to believe that the question of truth in possible worlds is no problem at all. They simply distinguish "nonactual (but possible) truth" from "actual truth. " 4 5 But this distinction is more confusing than ever. Are there also nonactual and actual falsehoods? Is "The golden mountain exists" a nonactual truth or a nonac­ tual falsehood? We can, of course, stipulate the truth value of a sentence whose domain is P, for Kripke has insisted that "possible worlds are stipulated, not dis­ covered." 46 If the truth of a counterfactual is stipulated, however, then the asser­ tion of such a sentence turns out to be trivial. We do not arbitrarily decide to stipulate the truth of "If I were to jump through this window (although I never will), I would fall 3 2 feet per second. " To label it "false" would be wrong. Our counterfactuals are relevantly, not trivially, true or false. Counterfactuals as well as the whole notion of possible worlds are still not fully understood. Quine believes that the use of modal operators leads to opaque con­ texts that make the application of quantification impossible; or else it leads to the postulation of enigmatic intensional entities. Linsky has argued that Kripke's no­ tion of rigid designators in all possible worlds is not intelligible unless we add a Fregean conception of sense to names. 4i But senses, like intensions, have their own enigmas and produce strange ambiguities when used in oblique contexts. For example, "John believes he should be given time off" requires, according to a Fregean analysis, that "John" and "he" have different denotations and senses. 48 The point of this excursion into the difficulties of the counterfactual is to indi45. 46. 47. 48.

R. Bradley and N. Swartz, Possible worlds (Indianapolis: Hackett, 1979), p. 12. Saul A. Kripke, Naming and Necessity (Cambridge, MA: Harvard Univ. Pr. , 1980), p. 44. L. Linsky, Names and Descriptions (Univ. of Chicago Pr. , 1977), pp. 67-74. For further criticism of Frege's views, see Carnap, Meaning and Necessity, pp. 129- 3 3.

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cate some of the issues that are usually ignored by linguists but that must be dealt with if counterfactuals arc ever to be given logical form. Lakoff is right about what is presupposed in his example, even though the notion of a presupposition remains unclear. But the search for logical form-at least for that form that will show us what our ontological commitments are-involves more crucial issues. Turning now to Jerrold Katz, we find that he has made the very specific claim that transformational grammar, with the addition of the semantic construction of tree diagrams for words, finally solves the major philosophical issue that has been with us since Kant-the issue of analyticity. And since a solution to this issue would indeed be of great contemporary consequence, we might pause to exam­ ine Katz's claim. If he is right, then philosophic speculation may well be even­ tually replaced by the investigations made by linguists. The solution Katz proposes is fairly simple and is implicit in what has already been said about tree diagrams. A sentence with two descriptive terms that have the same or very similar tree diagrams can be said to produce redundancy when the two terms appear, under certain conditions, in the same sentence. Thus a sentence consisting of noun phrase (subject term), copula, and noun phrase (predicate term) is redundant if both noun phrases have the same set of paths, that is, the same senses, or if the noun phrase in the subject contains within its tree diagram the senses of the tree diagram of the noun phrase in the predicate. "Bachelors are bachelors" is obviously redundant because of the repetition of tree diagrams; "Bachelors are unmarried" is also redundant because "bachelors" con­ tains all the senses that are attributable to "unmarried ." In Katz's words, "the sentence [ 'Bachelors are unmarried' ] is analytic because every semantic element in the path from the set of paths associated with the verb phrase is also found in the path from the set associated with the noun-phrase subject." 49 In other words, Katz is saying that a sentence, S, is analytic if the dictionary meanings of the subject (or antecedent if we are dealing with a conditional) of S is found to con­ tain the dictionary meanings of the predicate (or consequent). Thus it is because we have ignored the fact that words have dictionary meanings and that these meanings often overlap that we have had so much difficulty with analyticity. W hen we say "All bachelors are unmarried," we are really stating an implicit imperative: given that the sense of "unmarried" is one of the senses of "bachelor," then take it to be stated as true that if anything is labeled "bachelor" it will also be labeled "unmarried." That some universals, such as "All bachelors are bald," re­ late to the truth or falsity of some factual state of affairs does not mean also that all universals are required to undergo this kind of analysis. Some must be ana­ lyzed in terms of the overlapping of tree diagrams . 49. Katz, "Analyticity and Con trad ition in Natural Language," p. 5 3 1 .

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It would seem, then , that we have solved the problem of analytic statements. By using the tree-diagram notion of a term , we have clarified the oft-noted Kant­ ian ambiguity concerning the containment of one term in another. Terms are not contained in one another, but their dictionary items, thei r senses, as given in the tree diagram may overlap or be the same or be different. Katz's view does indeed seem to make more intel l igible the notion of contain­ ment stated by Kant and severely criticized by Quine. 5 0 However, it has one se­ rious flaw; it does not deal with the issue of analyticity in the way phi losophers have thought of it. Few have ever denied that "unmarried " expresses a sense or a meaning of "bachelors . " Perhaps there has not been expl icit reference to the dic­ tionary, but it has always been recogn ized that words do have meanings whose verbal izations are usuall y found in dictionaries. It has always been u nderstood that if one defined "bachelor" one would eventually come up with "unmarried" in the defin ition . What was not known , and what is still puzzl ing, is the element of necessity that seems to characterize analytic statements . "Crow" and "having lustrous black plumage" are two different expressions. Now, if we examined the tree diagrams of both these expressions, we should undoubtedly find that the se­ mantic paths of "having l ustrous black plumage" would also be part of the se­ mantic paths of "crow. " But no one would therefore conclude that "all crows are black" is analytically true. It is difficult to believe that we would deny crowhood to a nonblack crow, Similarly, in " Every man has a highly developed brain," we would undoubtedly fi nd that "man " and "highly developed brain'' have tree dia­ grams such that the former contains the paths of the latter. But again we do not take it to be analytically true that every man has a highly developed bra i n . There is no self-contradiction involved in thinking of a man without such a brain . What we have here are examples of synthetic sentences that ar_e enumeratively, not analytically, universa l . On the other hand, "bachelor" and "unmarried" are such that "Al l bachelors are unmarried" is analytically universa l . It is necessarily true. Why? Why should the overlapping of paths in "Al l bachelors are unmar­ ried" produce an analytic statement while it does not do so in the cases of "Al l crows are black" and "Al l men have highly developed hearts"? What Katz has done is confuse enumerative universals with analytic ones. Philosophers have always recognized that there are enumerative universals, and the analyses of these universals have not been without their problems, for example, whether the class referred to is eliminable in favor of general terms and whether instantiations are of a fi nite or an infinite number. But the crucial q uestion has always dealt with those curious u niversals that seem to be strictly analytic . How do we ac­ count for a universal sentence whose predicate term seems to be necessarily con50. W V Quine, From a Logical Poi n t of View (New York: Harper, 1 96 1 ), pp. 20- 2 1 .

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nected to its subject term, a n d vet the sentence is not a mere substitution in­ stance of a quantificational truth? It is this distinction between enumerative and analytic universals that is apparently completely ignored by Katz, and yet it is this distinction that marks the essential clement in any discussion of analyticity. Moreover, it should be noted that probably no dictionary lists "extended" as a predicate of "metals''; yet it is undoubtedly analytically true that all metals are extended. How does Katz's criterion for analyticity apply here if the dictionary does not give sufficient information? How are we to deal with the analytic char­ acter of ''Nothing is both red and green at one and the same time and in the same respect" if the dictionary does not specify that green is not red and that red is not green? And, finally, and perhaps most important, dictionary information is al­ ways open to change. As Morris Bishop, a contributor to the America n Heritage Dictiona ry, puts it, " Usage is the ruler, the governor, the judge of language . . . . Language, by its very nature, is a growing thing; and that whereas it may be culti­ vated, it cannot be 'fixed' without killing it. " " For example, a "shrewd" person was once regarded as "wicked, rascally"; now he is admired for being astute. A fixing of meaning cannot be a part of any dictionary definition; otherwise we can end up "killing" the language. But it is exactly this sort of fixing that characterizes analytic statements. It is surely necessarily true-a fixing of meaning-that "green" will never have the sense of "red" and that "round" will never have the sense of "square . " W hat Katz's analysis leaves out is the element of necessity that seems to distinguish analytic truths from all other kinds. It may very well be that necessarily every expression has a sense, but this does not serve to explain why some combinations of expressions result in necessary truths while others do not. These are some of the essential problems that are not answered in the linguis­ tic analysis. W hy do some terms with overlapping senses-in the linguistic view of having overlapping indexical paths-yield analytic truths while others do not? W hat is the kind of glue-linguistic or otherwise-that ties "bachelor" to "un­ married" and "red" to "not being green," but not "metals" to "conductors"? Nor would it help matters if dictionaries suddenly began to state that "red" has "not being green" as part of its definition (although we may question whether any primitive observation term such as "red" can be defined). We would still want to know whether it just happens to be the case that "red" has "not being green" as one of its senses or whether it m ust be the case that "not being green" is a sense of " red." And, indeed, if it m ust be the case, then what is the nature of this neces­ sity? In trying to answer this question we are led into more than a knowledge of tree diagrams or of rules in a transformational grammar. We are led into all the 51 . American Heritage Dictionary (New York: Amer. Heritage Pub. Co. and Houghton-Mifflin, 1 969), p. xxiii .

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difficult philosophical problems that center on such notions as modalities, es­ sences ) and synonymy. The linguistic analysis leaves the essential issues of ana­ lyticity untouched. The linguists, then, contribute to clarifying ambiguity and equivocation. They show us that we ought not to mistake a surface grammatical form for a deep grammatical form. But they tell us nothing about logical form and, therefore, nothing about what the ontological commitments of a language are. If we wish to know what kind of domain we are committed to by the use of a given set of lin­ guistic forms, we must look elsewhere, as this kind of knowledge is not made available to us in the linguistic critique.

2. Logical Fann and Fonnal Languages I n chapter one we saw that a traditional philosophical issue involved the ques­ tion of determining what the existential commitments of a sentence are. If we accept a given sentence as true, exactly what is it-if anything-that we are as­ serting about what exists? If "All men are mortal" is true, then does this commit its user to the acceptance of a domain of individuals, properties, and classes such that each of the individuals belonging to the intersection of the classes of men and mortals has the properties of being a man and being mortal? Or is the com­ mitment of an entirely different sort? The linguist has seemed to argue that the answers to these questions will be found once the deep form of a sentence and the various senses of its terms are made explicit. But this argument has been found to be unsatisfactory. The senses that a term might be given in the diction­ ary need not indicate anything at all about the fundamental issues that can arise when the term is taken to apply to some existential subject matter. Neither the grammarian nor the dictionary tells us of the problems entailed by taking desig­ native expressions to refer to properties or classes or individuals . Nor is the deep form the basic one-the logical one-from which existential commitments can be derived. I t may well be the case that we ought to understand "John is certain to leave" as " I t is certain that John will leave. " This oblique sentence may well show the deep form of the sentence. But once we accept this what move is then to be made in trying to relate this sentence to what exists? What do indirect sen­ tences designate? Let us assume that " I believe that it is going to rain" is a well­ formed deep-structure sentence. What is the designatum or the designata of this sentence? Are we committed to the existence of beliefs, or of intensions, or of cert2in Fregean senses? Or are we here dealing with an ordinary truth-functional sentence stating what someone said at some time and place? Or finally shall we

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say, in the manner of the early Wittgenstein, that basically there are no oblique sentences; there are only atomic sentences to which all oblique sentences must eventually be shown to be reducible. And this reduction will indicate to us what objects the sentence designates. In other words, all the problems of obliqueness that have plagued Frege, Russell, Carnap, and Quine remain to be settled. Sim­ ilarly, the dictionary tells us that "all" and "some" are adjectives, but it would be a serious mistake to think that when we say "All men are mortal" or " Some artists are shy" that we are speaking of an "all man" or of a "some artist" (although, of course, there is a colloquial sense in which a man can be "all man" and an artist can be "some artist! "). The dictionary gives us the grammatical status of an ex­ pression, but it tells us very little of how such an expression functions in a logical language. A Martian who was studying English by constantly referring to the dictionary would be easily disheartened if he thought he could find an "air' �an just as he could find a "pale" one. The dictionary also tells us that "exists" is a predicate, but again it would be a serious mistake to think that, just as we can find something that does not have the property of being pale, we can find some­ thing that does not have the property of existing. Finally, grammarians hesitate to become involved in semantics. Chomsky, in his early period, believed semantics could be completely avoided by the lin­ guists. 1 Thus for them "Pegasus does not exist" is a well-formed grammatical sen­ tence, and the difficulty of giving logical form to a sentence whose subject does not have a referent is simply irrelevant. If we are to understand what kind of existential claim such a sentence makes, however, we must ask how it can be formed without involving paradox or contradiction. In other words, we must think of it in terms of the logical form that makes such expressions as "contradic­ tory" and "noncontradictory" applicable. If the linguistic notion of form is not adequate, then what other alternative is there? The most obvious alternative is the one suggested by the logician and the philosopher. The logical form of a sentence is that form given to it when it be­ comes a member of a formal language . We can employ all the grammatical rules we wish in moving from the surface form of a sentence to its deep form. But, if th� deep form is not recognizable as a substitution instance of a form of some formal logical system, then there is no logical form. Lakoff sometimes speaks of a "natural logic," that is, a logic that is in some way different from the pure formal systems that have been constructed by logicians and philosophers. 2 Yet curiously enough none of this natural logic differs from the formal kind used by logicians. If a sentence does not fit into a formal scheme, then Lakoff does not look for some special logical rule that is to be found only in natural language. The senl . Cf. John Ly ons, Noam Chomsky (New York: Viking, 1970), p. 34. 2. G. Lakoff, "Linguistics and Natural Logic," in Sema n tics of Natural Language, ed. Donald Davidson and Gilbert Harman (Dordrecht, Holland: D. Reidel, 1972), p. 589.

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tence must be transformed until it can be fitted into a first- or second-order pred i­ cate calculus or into a modal system of the Kripkian kind. Transformations of a sentence must go on until the sentence has the familiar formal structure of a fam iliar logical system. At that point-when a sentence has been reached that "shows" a recognizable logical form-it can be said that deep structure has fi­ nally been revealed. Similarly, Katz agrees with Lakoff that natural language has its own logical structure, and he decries the traditional concern with artificial languages and purely formal calculi . ' By studying the meaning of expressions in their natural contexts, we discover the logical connections among sentences. Thus, by becoming aware of the semantic meaning of "believe," we discern that " Billy believes that Santa Claus is sick with the Au" entails "Billy believes that Santa Claus exists." 4 But Katz does not tell us what kind of entailment this is. Clearly, if x believes that y is F, it does not necessarily follow that x believes that y exists. I believe that Santa Claus is a jolly old man, but this does not mean that I believe that Santa Claus exists. Katz warns us that we are here dealing with a psychological verb, "believes," and it is therefore presumably in some psycholog­ ical sense that entailment occurs. But nothing in psychology can guarantee that a sentence of the form " p believes q" entails " p believes q exists." On the other hand, if we transform " I believe Santa Claus is a jolly old man" into " I believe there is a Santa Claus and he is a jolly old man," then " I believe there is a Santa Claus" follows. It follows not because of some hidden psychological or semanti­ cal rule, but from the familiar logical truth (p. q) ::Jp. The natural logic pro­ posed by Lakoff and Katz seems to require explication in terms of the formal logic they both deprecate. Logical form, then, is what we find in logical systems, and, since logical sys­ tems are themselves constantly being revised, there is no absolute logical form that a sentence can ever be said to have. A sentence in a Meinongian system could comm it us to existent entities, subsistent entities, and even contradictory ones. A sentence translated into the forms of a Fregean system would comm it us to individuals, individual concepts, senses, and null entities as well as to a Pla­ tonic entity called the True. The same sentence, using a form from Principia Mathematica, would commit us to properties, contextual kinds of classes, and individuals with which we must (eventually) be acquainted. If we were using Kripke's system, we should be committed to an infinite number of possible worlds, objects that exist in every world in which they are named and that are independent of any properties (except, perhaps, essential ones), and natural kinds that are similar to Aristotelian essences. These systems are not independent of one another. Russell's system eliminates notions of subsistent and contradic3. Jerrold J. Katz , Propositional Structure and lllocutionary Force (Brighton, Eng.: Harvester Press, 1977), p. 227. 4. Ibid . , pp . I 02 - 3.

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tory entities. Individual concepts and senses arc replaced by descriptions that are satisfiable or not satisfiable by objects. Kripke rejects Russell's conversion of ordi­ nary names into definite descriptions, arguing that Russell confuses the fixing of the meaning of a name with the fixing of its reference. Descriptions do not give the meaning of a name as, according to Kripke, Russell believed. If they did it would be contradictory to ask whether, for example, Aristotle might not have been the teacher of Alexander. Descriptions only fix the reference of a name. They are not synonyms for a name; they do not give the meaning of a name. They say that in a given possible world Aristotle is the same person that satisfies the description "the teacher of Alexander." In a different possible world, "the teacher of Alexander" might have been satisfied by someone else. Aristotle, nonetheless, would still have been Aristotle even if he had not been the teacher of Alexander. It is for this reason-that we distinguish between the individual and that which at a given time and place describes that individual-that descrip­ tions, not names, produce, according to Kripke, the de dicta- de re ambiguity. 5 "The teacher of Alexander must be a teacher" can be interpreted in two ways: ( 1 ) "Necessarily the teacher of Alexander was a teacher," which is de dicta true. Necessarily, if one is the teacher of Alexander, then he is a teacher; ( 2) "The teacher of Alexander necessarily was a teacher," which is de re false. Surely someone who is a teacher did not necessarily have to be a teacher. On the other hand, if we substituted "Aristotle" for "the teacher of Alexander," no ambiguity arises. "Necessarily Aristotle was a teacher" and "Aristotle necessarily was a teacher" are both false. Names are rigid designators and always name the same individuals. Definite descriptions are not rigid designators and are capable of being satisfied by many individuals. So Kripke's modifications of Russell's system causes an expansion of what our ontological commitments are. Both possible worlds and possible entities become elements of the domain. We find, then, that we are continually constructing formal languages incor­ porating logical systems, and it is by means of these languages that we give logical form to our sentences. The argument is that by means of this form ontological commitment is discovered. Grammarians find forms among different groups of sentences. They may discover that there are certain categories of expressions such as nouns, verbs, adverbs, and adjectives and that these categories usually combine in different ways. But these grammatical categories and arrangements do not give us any guarantee of a corresponding existent entity. An expression can be legitimately used as a predicate adjective in a sentence, for example, "sol­ uble" in "Sugar is soluble," and its meaning can be given in the dictionary as "capable of dissolving." What we are not told is what existential commitment is being made here when we apply "soluble" to an object called "sugar." Are we 5. SaulKripke, Nam i ng and Necessity (Cambridge, MA: Harvard Univ . Pr. , 1980), pp. 39 - 48.

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attributing a power to an object, o r an essence, or a disposition? And if we admit powers or essences or dispositions into a domain, how do they relate to the other entities that mav. alrcadv. be included as clements of the domain? Occurrcnt properties are open to observation , but can there be properties that are never ob­ servable? These are important questions in the construction of formal logical sys­ tems. The sentence "Sugar is soluble," by itself, even if we know the dictionary senses of its terms, does not tell us what our existential commitments are if we take the sentence to be true. For this reason Wittgenstein at first believed all sen­ tences must undergo analysis until the atomic propositions implicit in a sentence are made explicit; only the atomic propositions will tell us exactly what our com­ mitments are. Wittgenstein later recognized that the reliance on atomic proposi­ tions is not satisfactory, since there is no way of ever determining when an atomic proposition has been reached. How much definition of terms of "The broom is in the corner" is required before we reach the ultimate definitions-if there are any ultimate definitions? Wittgenstein thought that the only conclusion to be reached was that no proposition could be said to have implicit within it some ultimate logical form that the philosopher and the logician would finally un­ cover. But Wittgenstein's conclusion may be wrong. It may be true that no prop­ osition has implicit within it some specific form, but this does not mean that a proposition cannot be fitted with a form. This is the position usually taken by the formalist philosopher. A sentence is like some early vehicle that becomes shaped and is given form as new tools and new concepts evolve. We start with the propo­ sitions we have at any given time and we give them form in terms of the newest linguistic and philosophical tools that become available to us. "Soluble" may have led to the positing of powers or essences, but the philosophical examination of such entities has made it difficult to accept them without first resolving major dilemmas that arise with their introduction into a domain. Thus the argument here is that there is no ultimate logical form of a sentence. There is only that form we can attribute to a sentence on the basis of the logic we have available to us. More specifically, the logical form of a sentence is the form we think it would take if it were a member of a given formal logical language. It is this form that reveals to us the ontological commitments of a language, and for this reason it is really quite absurd to take seriously the Chomskian view that with sufficient study of language we shall some day find the universal grammar that permeates all lan­ guages. We shall presumably find the basic set of categories that every language exhibits in its deep structure. What would such categories be that would be in­ herently incapable of being revised or rejected? Would they be such categories as those specified by Fillmore, that is, Experiencer, Agent, Cause, and so forth? 6 6. Charles J. Fillmore, "Subjects, Speakers, and Roles," in Seman tics of Natural Language, ed. Donald Davidson and Gilbert Harman, p. 10.

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All of these are philosophically suspect. In fact, if we follow Rorty it may well be that the language of the future may even be without mental terms, since talk about mental entities may have become as untenable as talk about demons. 7 Thus those entities we take to be sacrosanct in describing a world may not be so sacrosanct after all. Today's notions of possible worlds and intensional objects that are so acceptable in contemporary linguistic analysis may very well turn out to be precisely what Quine has asserted they are-creatures of darkness. It may seem strange to think of natural-language sentences as potential mem­ bers of a formal language. We speak of tables, chairs, people, dogs, and so forth, without any apparent confinement to any particular logical system. The truth or falsity of "I see a human being" would certainly seem to be independent of any connections to some particular logical or even linguistic system. We say what we see and that is the end of the matter. But, as soon as we begin to ask ourselves what exactly it is that we claim to be seeing, then our prior commitments begin to come to the fore. Are we seeing something having the property of being a human being or something belonging to the class of human beings or something reflecting the essence of human being? Or are we seeing, in a manner once sug­ gested by Quine, a spatiotemporal series of parts all of which make up what we call a human being? 8 Or perhaps all these alternatives are incorrect, and we are seeing a grouping of actual and possible sense data, the whole of which we give the label "a human being." And, of course, we need hardly mention the ques­ tions that would arise with the introduction of sense data and possibilities. The point is that no statement-either in a natural or in a formal language-stands alone . It is connected either implicitly or explicitly to some logical framework that determines the general categories of our descriptions and that also deter­ mines the kind of inferences that can be drawn. And this leads us to the second observation that ought to be made in regard to sentences. Sentences are said to have many functions and many characteristics. They can be short or long; they can contain difficult as well as ''easy" words. Perhaps there could even be a language in which every sentence is unique so that no two sen­ tences are tokens of the same type. In any event, at least one feature that every sentence must be able to exhibit is that it is capable of inclusion in a system of inferences. We use sentences in order to infer other sentences and, in an impor­ tant sense, inference-whether it is deductive or inductive-is the crucial char­ acteristic of anything called a language. If we could not infer from one sentence 7. Richard Rorty, "Mind-Body Identity,_ Privacy, and Categories," in New Readings in Philosophi­ cal Analysis, ed. Herbert Feigl, Wilfrid Sellars, and Keith Lehrer (New York: Appleton, 1972), pp. 391-406; reprinted in Modern Materialism: Readings on Mind-Body Iden tity, ed. John O'Connor (New York: Harcourt, 1969), pp. 145-74. 8. W V Quine, Word a nd Object (New York: Wiley, 1960), pp. 51- 52. It ought to be noted, to be precise, that Quine's example relates to rabbits and not to men.

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to another, the prime purpose of a language would be lost. The language would consist of a list of descriptive expressions that would have little if any value for determining what we can expect on the basis of information we already have. It is only because we can use sentences to make inferences that, from " If there is a lion in the \rnods then we ought to go in the opposite direction" and "There is a lion in the woods," we can draw the rather important conclusion "We ought to go in the opposite direction." (I am here deliberately overlooking the difficulties of drawing inferences from premises that contain "ought" terms. ) Thus the logi­ cal connectors are a requirement in the use of any sentence. Although we move from sentence to sentence by means of logical connectors, logical connectors are not extrinsic to a sentence. What I mean is that, in order for a logical connector to function, its linguistic components must be formed in a certain way. It is be­ cause the antecedent of an implication has the form "All A is B" that the in­ ference "Some A is B" can be made. An implication sign without the appropriate formed sentence as antecedent and consequent has no function at all, so that if we wish to draw inferences in a language we are required to form our sentences in ways that will permit inference to occur. Thus, since "true" and "false" are essential to the inference process, sentences must be so constructed that they lend themselves to the application of truth or falsity. For this reason "Boy the store ran the to" is not a sentence in the English language, since its construction does not permit a truth value to become applicable to it. Similarly, "The boy eggled" is not a sentence, since "eggled" is not a legitimate word and, therefore, "true" has no application here. For the same reason we are not satisfied with the mere expression "Ouch!" We change it to "I have a pain" or " I am in pain," since we take it for granted that these sentences can be given truth values and thereby related to other truth-value sentences such as "If I have a pain, then I need a doctor" or " If I have a pain, then you must call an ambulance." With all the difficulties attributable to the analyses of pain sentences, we insist on molding them into forms that allow interconnections. And it is because some of these interconnections do not seem to be permissible-for example, the question arises as to whether we can infer "There exists a pain that I have" from "I have a pain"-that we have spent so much time searching for the appropriate form for pain sentences. Neither pain things nor mental entities in general have been ac­ ceptable elements in the domains of formal languages. Just as artists try to create pictures that have balance and good structure, so also the users of language try to make sure their sentences can be appropriately conjoined. The "appropriateness" is definable in terms of the truth-value systems that we construct. Finally, it is because of the inference requirement that we do not blithely ac­ cept the truth-value gaps permitted by Frege and Strawson, even though Frege did maintain that it was basically a defect in a language to have such gaps. For, if there were sentences to which truth or falsity could not be applicable, then there

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could be no way of logically connecting them to other sentences. If, for example, "Pegasus was a winged horse" could not be given a truth value because of the vacuity of "Pegasus," then no logical connection could be made to "Pegasus was winged" or "Pegasus was a horse" or "Pegasus belonged to Bellerophon," since nothing is attributable, one way or the other, to a nonexistent entity. (One might be able to say "Pegasus is nonexistent," but "nonexistent" is not a predicate. ) It would be a connectionless sentence that would be unable to play any role in the language game. From a truth-valueless sentence, nothing can be said to follow; nothing can be said to be connected to it either as consequent or as simple iden­ tity. For this reason Frege gave denotations to all terms including vacuous ones. Vacuous terms denoted the null entity, that is, the empty class of space-time points, or, if numbers were elements of the domain, they denoted the number zero. Nor should it be countered that modal sentences are not truth valued. They are not truth functional, but they are truth valued. A modal sentence must be capable of being labeled "true" or "false," even though, as I have indicated ear­ lier, serious problems arise in applying these terms in possible worlds. Except for the modal operators, the component parts of the modal sentence are the same elements used in the ordinary truth-functional systems. Even full truth tables, modified in order to permit partial truth tables that lack certain rows of true-false components, are parts of modal logic. Furthermore, even though modal systems are usually regarded as intensional, and truth-functional systems as extensional, all systems require "true" or "false" as predicates if they are to serve communica­ tive purposes. We may not favor intensional entities, and perhaps eventually they will be eliminable from modal systems (work has already been done to show that modality can be treated extensionally if we regard modal operators as predicates that designate properties of sentences or formulas), 9 but the main point is that anything we call a sentence, if we wish to uncover its ontological commitment, requires admission into a formal truth-value system. A modal sentence is not inherently committed to intensions. The system into which we translate it pro­ duces that commitment. Finally, we should reply to those who speak of meaning as having a logic of its own in which truth or falsity play no role at all. Thus from "I am having a night­ mare" I can infer, without any reference to truth or falsity, "I am having a dream. " The inference rests on the meaning of "nightmare. " Knowing that the meaning of "nightmare" in the particular sentence is "frightening dream," I can infer "I had a frightening dream" or simply "I had a dream. " But, first, we should note that, if neither "true" nor "false" could attach to "I am having a nightmare," 9. Cf. M. H. Lob, "Extensional Interpretations of Modal Logic," /ou rnal of Symbolic Logic 31 (1966): 23- 45; cf. also C. E. Hughes and M. J. Cresswell, An I n troduction to Modal Logic (London: Methuen, 1968), p. 291 n3 1 8.

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then no inference at all could be drawn. It is because I can say "It is true that I am having a nightmare" that I can go on to say "Therefore it is true that I am having a frightening dream. " If it were to tum out that, following Norman Mal­ colm , "I am having a dream" is not really a judgment at all, that is, not a gen­ uine proposition, since nothing can count in favor of its truth or falsity, then no inference is possible. 1 0 Second, nothing follows from any sentence or any word. Psychologically we can connect whatever we wish with any expression. But psy­ chological is not logical connection . "Bachelor" is normally connected to "un­ married man" as a synonym not because one word emotionally leads us to the other, but because we regard "All bachelors are unmarried" as true. Then, and only then, can we infer the truth of "x is unmarried" from the truth of "x is a bachelor." Thus truth-valueless sentences are not really sentences, even though they may be well formed in accordance with the rules of grammar or other rules or well­ formedness. A sentence in a language is both well formed and truth valued. Both characteristics are required. This does not mean that the dichotomy between le­ gitimate and illegitimate sentences is all that clear. Sentences that are only appar­ ently truth valued often surreptitiously slip in and out of the language. But we try to eliminate them or, as in the case of subjunctive and causal conditionals, to reconstruct them into truth-valued form. It is, therefore, not surprising that, if we use logical connectors in a natural language, we should expect that its sentences must have within them the kind of com mitments attributed to them by some logical system. If the logical system we employ is attributable to Aristotle or Thomas Aquinas, then " I see a man" will have an existential commitment to a class and an essence of man . But if the system is the one exemplified in Russell and Whitehead's Principia, then we will not be committed either to classes or to essences, but to properties or clusters of sense data. Thus the logical form of a sentence is the form we attribute to it, or, better, the form with which we fit it, on the basis of some given formal logical language. The search for the logical form of a sentence is simply the unjustified intrusion of Platonism into a language. It is important to recognize that inference terms in a language-the logical connectors-are also like mathematical terms. Both serve to make other func­ tions in the language more precise. Mathematics gives precise measure and quantity to designative terms; inference terms give precision to logical proce­ dures. The difference between the two is that inference terms are more crucial. We might have a language without mathematical terms, but we could not have one without inference terms . In most other respects, however, they function in a similar way. To discover the commitments made by the use of a mathematical 1 0. Cf. Norman Malcolm, Dream ing (London: Routledge and Kcgan Paul, 1 9 59), p. 37.

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term requi res the admission into the language of some interpretation of a mathe­ matical system in which the term has a formal status. Thus, for example, the assertion of "2 apples plus 2 apples equals 4 apples" in a natural language re­ quires the positing of a domain of entities called "apples" as well as entities whose existence depends on the specific arithmetical theory that is acceptable . And since there are different arithmetical theories-many of them inconsistent with one another, especial ly if one accepts and the other rejects transfinite postu­ lates-what exists will be relative to the arithmetical theory. If we accept a Fre­ gean analysis, then numbers will be defined in terms of concepts that character­ ize units and couples. If we accept Hilbert's view, then we are simply using mathematical symbols as strokes on paper. Or if we are speaking in the manner of Brouwer, then we are positing forms or constructions that we grasp intuitively. 1 1 In a similar way, as I have indicated earl ier, if we formalize a sentence in terms of the Principia, then we shall require a domain of properties, but not classes (o·r at least not real classes); on the other hand, if we employ the systems of Frege, Car­ nap, and Quine, we shall require such sundry objects as classes, properties, con­ cepts, and null entities. The important point is that the existential comm itments made by a sentence depend on the mathematical and inferential systems i mplicit in the use of the sentence . It is because "2," "if," and "or" are mere sounds or scratches on paper until their functions are exhibited in a formal system that the study of formal language is so important to an understanding of natural lan­ guage. It is in the formal language that we can wrestle with all the hard tasks of determining how nouns, verbs, and so forth, can function in a language whose logical framework is made explicit. The argument is then that only by trying to insert natural language sentences into formal languages can we determ ine what our genuine existential commitments are. We ought, therefore, to distinguish pragmatic from ontological comm itment. Pragmatical ly we are committed to whatever we are wil ling to say exists. \Ve can maintain that there are trees and chairs as well as ghosts and goblins and things that go bump in the night, but, when we speak of an ontological comm itment, we are asking what really and truly exists, and the way we discover this is by means of hard work. We require knowledge of how our terms would function in a context in which we are aware of all the paradoxes and logical absurdities that could arise if a term is incorrectly interpreted. Thus we think twice before we argue that from "I see a man" we can infer "There is a man," for we become aware of the difficulties in deriving an existential statement from a statement with a polyadic mentalistic predicate such as "see." Similarly, if we try to make the move from "I bel ieve there are ghosts" to "There are ghosts," we become aware of the complexities of oblique sentences. An existential statement, then, is not a l l . Cf. S . Korner, The Philosophy of Mathematics (New York: Harper, l 960), pp. l 78- 79.

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description of a present state-of-affairs. "There exists a chair" has as much exis­ tential status as "There exists an elf" until we try to fit these sentences into some formal language that commits us to a given domain with a given set of rules gov­ erning inference. In the terminology of Ryle, form is not given in a language; it is achieved. 1 2 This view, that the existential commitments of a sentence are not implicit within it, but are determined by the rules of the logical system in which it can be fitted, ought not to be surprising. In the ordinary questioning of what we say, we become immediately involved in relating the sentence to some-almost Pla­ tonic-ideal of what a language ought to be like. The very admission that we can be mistaken about meaning and reference implies that there are criteria for judg­ ing that a mistake has been made. Consider any arbitrarily selected natural lan­ guage sentence, for example, "It sure looks like rain today." To determine what this sentence means and what its designative terms might be referring to, we should begin by eliminating from it obvious idiosyncratic features. Probably we would change it into a more grammatical form:

( 1 ) It looks like rain today. But this sentence is still not satisfactory, even though by some rules of grammar it might be perfectly correct. There would still be a question involving the referents of "it" and "looks like." It is important to understand why this question arises. Why should there be this concern involving the referents of terms? The answer, I believe, is that we assume that a term may seem to have a referent when it does not actually have one and that there is a criterion by which this distinction can be made. In other words, the assumption is that there are rules that could deter­ mine exactly what existential commitments are being made by any given asserted sentence. This does not mean that there must be one final, eternal set of rules that, as Chomsky apparently believes, must be buried in the human psyche. That we can be aware that our statements about quasars and black holes pose problems does not mean that our determination to solve these problems will lead to final answers or to answers that in some odd Chomskian way are stored up in our unconscious. We simply require answers that fit into some coherent scien­ tific system-a system that is surely not innate within us. Thus, in the case of ( 1 ), we should inquire into "it" and "looks like," since "it" has no apparent refer­ ent and since "looks like" does not function here as it does in other contexts. In other contexts, in using "a looks like b," the rules of symmetry are applicable, so that logical transformations become permissible without any loss of sense. If " a 12. Cf. Gilbert Ry le, The Concept of Mind (London: Hutchinson's Univ. Library, 1949), pp. 149-50. Ry le introduces the notion of an achievement verb, but John Dewey refers to the existential proposition as the final judgment of the successful inquiry. Cf. John Dewey, Logic: The Theory of Inquiry (New York: Holt, 1939), pp. 121- 24.

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looks like b" is a legitimate polyadic predicate sentence, then " b looks like a" and " b does not look like a" as weH as " a does not look like b" wiH also be legitimate polyadic predicate sentences. But, in the specific case before us, it makes no sense at aH to ask whether rain looks like it or whether rain does not look like it. Our question relating to "looks like" derives from an implicit acknowledgment that this verb, like any verb, should be a permissible member of some system of logical connections. And, if it is not, then we do not know what it is to which the sentence commits us. For this reason, if someone asks what it is we are talking about when we assert ( 1 ), we give answers such as "There are clouds and this usual1y indicates that rain wiH fal] soon." The new sentence becomes one that is closer in form to one that might be formulated in a formal language. So it is not surprising if eventuaHy after further analysis we conclude with a statement such as the following: ( 2) Whenever weather conditions A, B, and C are present, then there is a probability, p, that rain wiH occur. Weather conditions A, B, and C are in fact present. Therefore, there is a probability, p, that rain wiH occur today. We see that ( 2) might be what ( l ) succinctly summarized. If the translation is adequate, then we have succeeded in fitting ( l ) into a logical system, since (2) can be given logical form by using the rules of Principia and Carnap's proba­ bility indices. Objections could be raised to the translation of ( I ) into ( 2). Other formulations might be more adequate. We might require to know how (2) relates to time. Is "whenever" a temporal variable so that quantification is permitted over time, or is it a temporal predicate by which (2) is to be read as "If A occurs at the same time as B and if B occurs at the same time as C, then there is a probability, p, that, etc. . . . "? In some discourses this might be an important consideration, since time as a temporal variable commits us to the existence of discrete mo­ ments, whereas time as an element of the predicate makes it a property of objects and therefore relativistic. " On the other hand, we might want to eliminate the time reference entirely, as Quine suggests, 1-+ and make ( 2) tenseless with time on a par with space. "Now" then becomes comparable to "here," with future and past related accordingly. Thus "Rain will occur" becomes " Rain occurs after now," where "after now" is comparable to "west of here." Further elaboration 1 3 . For a discussion concerning the problems of treating time as quantifiable, sec C. Bergmann, "Some Reflections on Time," II Tempo (Archivo di Filosofia, Padua: Ccdam , 1958); reprinted in Bergman n's Mea ni ng a nd Existence (Madison: Univ. of Wisconsin Pr. , 1959). Sec also the discus­ sion by Laird Addis , "Time , Substance, and Analysis," in The On tological Tu rn , ed. M. S. Cram and E. D. Klemke (Iowa City: Univ. of Iowa Pr. , 1 974), pp. 148-67. 14. Quine, Word a nd Obiect, p. 1 70.

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might also be needed concerning probability. But the main point would remain untouched. If we wish to know what the existential commitments of a sentence are, we are required to include it as a member of some formal-language system. In this analysis, translation becomes the major issue in determining the existen­ tial commitments of a sentence. If we have devised a formal system in which predicates are admitted only if they satisfy certain criteria and if "men" and "ra­ tional. , are such predicates, then we can determine the commitments of "Some men are rational." If our system is the one of Principia , then we can translate the sentence into (3 x)( M x. Rx), where M and R stand for "men" and "rational," re­ spectively. Once we have made this conversion, we can go on to claim that what­ ever satisfies the formal sentence, that is, (3 x)(M x. Rx), is what we are existen­ tially committed to. 1 5 In this instance satisfaction of the sentence can occur only if at least one of the instantiated disjuncts turns out to be true. That is, the logic tells us that any atomic sentence with an existential quantifier entails a disjunc­ tive series, M a . R a . v. M b. Rb. Rb. v. Mc. Re. v . . . . , where a , b, and c . . . are names or demonstrative pronouns of objects; and whatever sequence of ob­ jects makes at least one of these disjuncts true is what we are existentially com­ mitted to. The logical form tells us what specific entities as well as what specific kinds of entities we are required to accept if we use a given formal-language sys­ tem. Thus, if a , b, and c are constants in a system and if the designatum of b makes the disjunction true, then that designatum is our commitment; and, if quantification occurs only over the individual variable and not over the predi­ cate, then that designatum is an individual and not a property or a class or a relation. The logical form informs us of the entities that are in the domain and the kind to which they belong. It is important to note that fitting sentences with a formal structure does not entail an existential commitment. Rather, the argument here is that, if there is any existential commitment, then it will be found in the formalization. But there might be nothing in the domain at all. In the example given in the preceding paragraph, if all the disjuncts turned out to be false, then there would be no commitment. The domain is empty. Only the true atomic sentences are significant. Sometimes it is argued that it is not necessary to become involved in the prob­ lems of formalism and formal languages in order to determine what the existen­ tial commitments of a sentence are. In fact, the argument might be made that the search for form, especially by means of formal languages, can be pernicious in that it leads to an implicit acceptance that there are universal essences and forms that are reflected in language. But an examination of how language is 15. For a more elaborate analysis of how "satisfaction" functions in a formal sy stem, see Mark Platts, Ways of Meaning (London: Routledge and Kegan Paul, 1979), pp. 18-33.

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really being used reveals that there are no precise and certain l inguistic or logical forms, but only what W ittgenstein alluded to as a family of resemblances. 1 6 Sen­ tences are used in different ways, and a commitment in one context need not entail the same comm itment in another. This was W ittgenstein's point in the In vestigations, and it has been elaborately defended by Alston, Malcolm , and others. 1 7 But there is some ambiguity as to how we are to understand what is meant by the use of a sentence. Are we to think of a sentence as a mechanical object such as a hammer that can have one function in one context and another in a different context? Thus we could say that, just as we explain what a ham mer is in terms of its different functions, so also we explain what a sentence is by its different functions. But it ought to be noted that no instrument is si mply a set of functions! A hammer is not an "it" that is used to hammer or to extract nails or to do various other kinds of jobs. The hammer is its own thing, so to speak, with its own given size, shape, density, weight, and so forth. It is this entity that is then used to perform in different ways. Thus, amidst all the functions of the hammer, there is an identi fiable object with its own identifiable properties. And, if we are not aware of this object with its identifiable properties, then it makes no sense to speak of its functions. There is no "it" that performs functions. There is this hammer, that table, this chair. Similarly, sentences are not to be identi fied with their uses, at least not uses in the mechanical way suggested here. A]though a sentence clearly has many uses, it is still what it is with its own particular charac­ teristics that identify it amidst all the different contexts. When I say "I see a tiger," it would, in Austin's sense, clearly have different illocutionary force when I say it in a zoo from that when I say it on an African plain or in my backyard. But the sentence itself is still what it is, with its own governing rules that determine whether it is well formed and whether the designative terms involved are per­ m issible designative terms. These implicit rules decide what the existential com­ mitments of the sentence are. That "I see a ghost" could produce reactions very sim ilar to those that occur with the use of "I see a tiger" does not mean either that both sentences have the same meaning or that these reactions tell us what is being reacted to. It is still the sentence itself, with its particular form and descrip16. For a discussion of Wittgenstein's notion of family resemblances, see Garth Hallett, A Com­ panion to Wittgenstein's "Philosophical Investigations" (Ithaca, NY: Cornell Univ. Pr., l 977), pp. l 40-41, l 47-48; and Renford Bambrough, " Universals and Family Resemblances," and Haig Khatchadourian, "Common Names and 'Family Resemblances,' " both in Wittgenstein: The Philo­ sophical Investigations, ed. George Pitcher (New York: Doubleday, 1 966), pp. 186- 204, 205-30. 17. Cf. W P. Alston, "Meaning and Use,'' in Readings in the Philosophy of Language, ed. J. F. Rosenberg and C. Travis (Englewood Cliffs,. NJ: Prentice-Hall, 1971), pp. 403- 19; Norman Mal­ colm, "Wittgenstein's Philosophical Investigations,'' in Wittgenstein: The Philosophical Investiga­ tions, ed. George Pitcher, pp. 65-103. See also Malcolm's attempt to show how mentalistic terms function in ordinary contexts without any need to posit mental entities in his Thought and Knowledge (Ithaca: Cornell Univ. Pr. , 1977).

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tive terms that tell us what it is, that is producing certain consequences or permit­ ting certain uses. The fact that sentences ought to be distinguished from their uses does not mean that we are now committed to some essential state-of-affairs, some proposi­ tions as philosophers are prone to call them, that all identical sentences have in common. Wittgenstein was indeed correct when he argued against essences of this sort. Following Lemmon and others we ought to distinguish sentences from statements. 1 8 "John is revolting," said in a linguistic context that describes some of John's personal characteristics, is identical to the same sentence said in a con­ text describing John's independence. But, even though the sentences are identi­ cal, they are different statements. Lemmon regards them as different because they do not refer to the same proposition. But we need not introduce propositions at all. We can simply say that identity or lack of identity among sentences can be exhibited only once sentences have undergone investigation, that is, when a sen­ tence has reached the status of being a statement. It reaches this status only when we fit it with a logical form and give its predicates a formal analysis in which ambiguity and equivocation have been eliminated. Thus "John is revolting" is, as a set of expressions, identical to this same set of expressions regardless of where it appears. But these sets are not necessarily identical statements. Sentences are not automatically statements. They become statements when they are given logi­ cal form. I t is sometimes argued that, even if we are dealing with statements, this does not mean that we can avoid a commitment to propositions. "Le chien est brun" and "The dog is brown" may be perfectly proper statements. Yet to account for their identity would seem to require the need to posit a proposition to which they both refer. Why is there any such necessity here? We ought to ask why the trans­ lation from French to English, or vice versa, works? It surely is not the case that we hear both statements and suddenly obtain a certain kind of feeling that we take as evidence that the same proposition or some proposition is present. One does not immediately recognize that "Le chien est brun" and "The dog is brown" are identical statements. It takes time, effort, and much patience. But it has often been thought that the time, effort, and patience expended was directed toward the uncovering of the hidden proposition implicit in one or more sentences taken to have the same meaning. This would seem to mean that we must accept the existence of propositions. Well, we ought to ask in more specific terms how we get to this notion of a proposition. One answer is that, in order to know whether two sentences have the same meaning, we are required to discover whether they refer to or express the same proposition. How do sentences refer to or express propositions? How sentences express something is especially puzzling, and some18. E. J. Lemmon, " Sentences, Statements, and Propositions," in B ritish Analytical Philosophy, ed. B. Williams and A. Montifiore (New York: Humanities Press, 1 966), pp. 87-107.

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times the analogy is made with art, where paintings are said to express certain ideas or meanings. But, as any introductory text in aesthetics would tell us, it is no easy matter to explain how and what works of art express. Be this as it may, let us assume that sentences do express propositions and that these propositions are to be equated with the meanings of sentences. Some have questioned whether this understanding of propositions is legitimate, especially when we are dealing with indexical terms. Thus, if I say "I am ill" and if you, a Frenchman, say "Je suis malade," we are both expressing sentences with the same meaning, but the propositions are different. I am expressing the proposition that I, John Smith, am ill. You are saying that I, Jean LaFitte, am ill, a totally different proposition. But the difference in propositions seems to arise primarily with indexical terms. If we replace "I am ill" with "Snow is white" and "Je suis malade" with "La neige est blanche," then both meanings and propositions coincide. Indexical terms must be expanded to include proper names. Thus if "I am ill" must be expanded to "I, John Smith, am ill" and "Je suis malade" to "Je, Jean LaFitte, suis malade," both meanings and propositions coincide here as well . So perhaps it is true that the meanings of sentences are propositions. But there is something odd here. Con­ sider the example where one says that "Snow is white" means the same as "La neige est blanche." How do we know they mean the same? The answer is that they refer to the same proposition. But if we do not know what this proposition is, it tells us nothing to be told that both sentences refer to or express the same prop­ osition. So let us state what the proposition is. If we are English we say the propo­ sition is "Snow is white"; if we are French we say the proposition is "La neige est blanche." Now we go on to ask how we know that the proposition "Snow is white" is the same as the proposition "La neige est blanche." The infinite regress is obvious. It might be argued that propositions ought not to be stated as sen­ tences of any language, but as a set of concepts with a certain arrangement. But sooner or later we must ask which particular set of concepts with a certain ar­ rangement we are talking about as the proposition of a given sentence. And then we must use a sentence, a phrase, or some set of expressions of a given language, and the infinite regress appears again. My own view is that propositions are not needed. If we want to know whether two sentences have the same meaning, we can employ a technique suggested by Donald Davidson. 1 9 Davidson suggests that we transform " s means that p," which does commit us to a notion of propositions or to other intensional entities, to " s is true if and only if p," which requires only extensional analysis. Thus the sameness of meaning of s and p is expressed in terms of equivalence of exten­ sions-that is, their truth conditions are identical. Mark Platts has modified Da­ vidson's position to include what he calls a theory of force, which would show 1 9 . D. Davidson, "Truth and Meaning," Synthese 7 ( 1 967): 6.

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how linguists translate an object-language sentence, s, into a metalanguage sen­ tence, p. 20 No notion of a proposition is needed. Translation from s to p is done behaviorally, not by postulation of some entity that s and p have in common. Linguists make an inductive inference that the set of sounds, s, stated under cer­ tain linguistic, physical, and behavioral conditions, says what they, using the metalanguage, might assert under similar conditions. We then insert both sen­ tences into the Tarskian form, "s is true if and only if p," and proceed to indicate the formal truth conditions of s and p. No intensions, no propositions! Only lin­ guistic translations and formal extensional systems are required. The forms of sentences, therefore, are the forms they would have in a formal language. But, as I have been arguing, this does not mean that the discovery of logical form is an easy matter. Strawson and Ryle have been especially insistent on indicating the difficulties in identifying the ordinary use of "or," "and," "if," and "then," with their alleged counterparts in truth-functional logic . 21 The prob­ lems of formalizing "would," "can," and "make" sentences are well known. And, even though certain formalizations have become fairly well acceptable, some traditionally respectable analyses are still not all that secure. It took a long time to show how "All who draw circles draw figures" can be stated so that it would fol­ low logically from "All circles are figures." 22 There is still difficulty in determin­ ing the form of such sentences as "Some men are rational," since their transla­ tion into the formal quantificational language of, say, Principia Mathematica, leads to the absurd consequence that they are incapable of being falsified. In order to accommodate the number systems, the domain of Principia Mathe­ matica is required to be infinite. Hence existentially quantified sentences are re­ ducible to a never-ending disjunctive series to which a false truth value cannot be assigned. A similar difficulty arises with universally quantified sentences; they re­ duce to a never-ending conjunctive series to which a true truth value can not be assigned. Very serious problems arise also with proper names. 2 3 For Mill proper names have denotation but no connotation. For Frege and Carnap proper names have both a denotation and a connotation; even improper names such as "Pega­ sus" have denotation , for example, the null entity. For Russell proper names are 20. M. Platts, Ways of Meaning (London: Routledge and Kegan Paul, 1979), pp. 59- 61. 21. P. F. Strawson, In troduction to Logical Theory (London: Methuen, 1952), chs. 3, 8. See also P. F. Strawson, "Carnap's Views .on Constructed Sy stems Versus Natural Languages in Analytic Phi­ losophy," in The Philosophy of Rudolph Carnap, ed. P. A. Schilpp (LaSalle, IL: Open Court, 1963), pp. 503-18; Gilbert Ry le, "Formal and Informal Logic," in his Dilemmas (Cambridge: Cambridge Univ. Pr. , 1954); the discussions by P. F. Strawson, J. A. Faris, Franz Brentano, and W V Quine in Logic a nd Philosophy, ed. Cary lseminger (New York: Appleton, 1968), pp. 193-248. 22. Cf. W V Quine, Methods of Logic (New York: Holt, 1972), 3d ed., p. 138. 23. For a full and excellent discussion of proper names and how they relate to Russell's theory of descriptions and to Kripke's notion of rigid designators, see Leonard Linsky, Names a nd Descriptions (Chicago: Univ. of Chicago Pr., 1977).

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merely abbreviations for descriptions that, as incomplete symbols, have neither denotation nor connotation . In free logic proper names have no existential com­ mitment at all; an additional premise, stating that the name has a denotation , is required . More recently, Kripke has argued that proper names must be under­ stood in the larger context of modal logic, and this means that the domain of a language must be extended to take in possible worlds. 24 In each of these systems, therefore, sentences with proper names entail different ontological commit­ ments. But with all these difficulties-and there are many more in regard to counterfactual , oblique, and modal sentences-no one rejects the use of formal­ language systems in uncovering logical form, j ust as no one rejects the use of mathematical systems because of Godel's famous incompleteness proof. Now, if we think of logical form in the way that I have suggested , then several interesting consequences follow. First, it becomes clear that there are no onto­ logical commitments for sentences per se. They obtain comm itments only as they become formal ized , only as we become aware of how they function in a logical language. What are we committed to ontologically when we assert 'There are metals"? Are we committed simply to metals and that is all? Or are we also required to be committed to classes, since the logical system with which the sen­ tence may operate requires us to admit the existence of classes? But terms and the logical language in which they are embedded undergo change, and yesterday's designations may not be today's. Carnap takes the values of the variable as objects that are members of classes and that have properties. 25 Quine takes them to be j ust objects of classes, although usually they are merely objects that have general terms applied to them . 26 How do these commitments come about? Does Carnap have certain preconceptions that logical languages must have properties and classes in their domains? Does Quine have a preconception that only classes are to be elements of the domain? Perhaps. But we ought not to confuse psychologi­ cal with ontological commitment. Carnap's system requires the introduction of properties and classes (as well as individual concepts) in order to present a consis­ tent and clear account of modal statements, the Fregean paradoxes of identity, and certain antinomies that occur with names when they appear in oblique con­ texts. Carnap is not sympathetic to issues of an ontological sort and would be more comfortable without such entities as properties, individual concepts, and other intensional entities. But he requires them in order to explicate difficulties in his formal languages. Similarly, Quine may want to be a nominal ist, and he 24. See especially Saul Kripke, "Identity _ and Necessity," in Identity and Individuation, ed. M. K. Munitz (New York: New York Univ. Pr., 1971); "Naming and Necessity," in Semantics of Nat­ ural Language, ed. D. Davidson and G. Harman (Dordrecht, Holland: D. Reidel, 1 972). 25. R. Carnap, Meaning and Necessity (Chicago: Univ. of Chicago Pr. , 1956), 2d ed. , pp. 16-23. 26. Quine, Methods of Logic, pp. 235-37.,

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tries hard to show that some class expressions arc either general terms or simply expressions designating virtual classes-which are not really classes at all. How­ ever, in order to account adequately for the formulation of set theory, he must admit the existence of real classes. He begrudgingly admits his Platonistic as­ sumptions. Thus ontology comes about because of what is required in the expli­ cation of scientific, mathematical, and ordinary, commonsensical puzzles. We posit classes because they permit us to resolve certain kinds of issues, just as we posit neutrons and "charm" particles in order to explain dilemmas in our knowl­ edge of atomic theory. Thus-and this is the second interesting consequence-there apparently are no absolute ontologies. We may never be absolutely certain as to what the logical form of a sentence is, since the formal language into which the sentence is trans­ lated is itself constantly undergoing change or is simply one of a number of alter­ natives. It is this important point that Quine is making when he introduces his principle of indeterminacy of translation. 27 Language, formal or otherwise, is not static. The extensions of names and predicates as well as the syntax of logical frameworks are always open to possible modification. If there are no such absolute forms, are we then committed to a purely rela­ tivistic view of ontology? Must we then say that whatever existential claims we make are ephemeral, being rejectable at some future date? I should like to con­ clude this chapter by showing that we are not led to skepticism, but that we ought to think of ontology in the way scientists think of their own theories and hypoth­ eses, not as absolute, but as continually being made more warranted and more adequate. I should like to present the argument by means of a criticism of Witt­ genstein's theory of language games. If sentences operate only in language games, as Wittgenstein has asserted, then ontological commitment would seem to be meaningless, since an existence sen­ tence in one language game need not be an existence sentence in another lan­ guage game. And the reason for this is that the meaning of a word, just like the significance of a chess piece, depends on its "role in the game." Words, like any tools, find their functions in a context. Thus there is no essence designated by a descriptive term. If the designatum of a descriptive term is not necessarily the same in every discourse or if its rules of use can undergo change, then what is said to exist in one discourse need not exist in another. We have language games that can share family resemblances, but have no unique set of characteristics in common. However, it is surely not true that, at any given time, language games have 27. Quine, Word and Object, pp. 72-79. See also Jaako Hintikka, "Behavioral Criteria of Radi­ cal Translation," and Barry Stroud, "Conventionalism and the Indeterminacy of Translation," both in Words and Objections: Essays on the Work of W V Qu ine, ed. Donald Davidson and Jaako Hin­ tikka (Dordrecht, Holland: D. Reidel, 1969), pp. 69-96.

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nothing in common. W hatever the logic of the f u ture may be for us now, it is surely the case that all language games contain the logical connector "and" or some logically equivalent expression . It might seem possible to imagine a lan­ guage game in which there are no logical connections among sentences. But, first, the language games in which we normally indulge-social, political, eco­ nomic, scientific, athletic, psychological, and so forth-are all characterized by conjunctions, alternations, conditionals, and equivalences, that is, discourse containing logical terminology. Second, even though we might seem to be able to imagine a language game without any connectors among its sentences, it is not at all clear that such a language can actually be devised. We assume that any language must be more than a mere listing of sounds or a mere listing of either words or sentences. Just as chess pieces are not moved in a vacuum and have their fu nction in relation to other pieces in the game, so also words and sen­ tences have their function in relation to other expressions in the language. To say "This is a chair" and "That is a table" is to accept implicitly rules that indicate a distinction between "this" and "that" and that also identify the "a" phrase in both sentences as transformable in similar ways . ( In fact, we also implicitly accept the cross identity of phonemic structures in different sentences .) But these rules and relations can be expressed either in terms of Chomsky's transformational gram­ mar or in the connector expressions of logic. Thus all language games--if they are not mere pseudogames that really cannot be played at all-will have certain standard rules and regulations. It should also be pointed out that in every language game certain kinds of se­ rious questions arise. Thus it is perfectly legitimate to ask whether a given name or a given predicate ought not to be translated into a description, for otherwise we might be attributing existence to what does not exist. Adults and children talk seriously about Santa Claus, Rumpelstiltskin, Uncle Sam, and the Mass Man, but it would be ridiculous to believe that what is discussed must exist-in some sense-in order for us to be able to talk about it. Similarly, questions can be asked about the questions and answers in a given language game. Do the ques­ tions present a clear and legitimate range of alternatives? 2 Are the answers com­ plete so that the reply " 1 1 , 1 3, and 1 7" could be shown to be a false answer to "W hich primes lie between 1 0 and 20?" Are the answers distinct, so that "Cicero and Tully" would be counted as a false reply to "Who were the denouncers of Cataline?" Wittgenstein may have been right in pointing out that all sentences have their uses in language games, but the rules that govern such sentences are not exclusively within the game. There are rules of logical form that govern each sentence-either interrogative, assertoric, or imperative-and any violation of such rules invalidates whatever use is made of the sentence. It could be the case 2 8 . Nuel D. Belnap, J r. , and Thomas B. Steel , J r. , The Lo6 ic of Questions and Answers ( New 1;

Haven , CT: Yale Un iv. Pr. , 1 976), pp. 2 2 - 24 .

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that, in a gi,·en class of language games, sentences arc conjoined in such a way that the inferences are drawn in violation of modus ponens . But in such in­ stances use would not be its own justification . We should argue that, even if ev­ eryone used sentences in violation of modus ponens, it would still be wrong and that the use must give way to an affirmation of the rule . In brief, there are rules that tell us how to decide whether a given set of sentences is logically correct, and it is the language in which these rules are formulated-the urlanguage from which all the language games in a given language draw their basic grammatical constructions-that also decides what our ontological commitments are. It is the urlanguage that sets up the rules of syntax that determine the formal construc­ tions every language must incorporate if it is to be a game. The urlanguage is also the ultimate authority that governs the inclusion of designator expressions in any context. Whatever games we play a sentence is a genuine existence sentence only if it satisfies the truth conditions stipulated in the urlanguage. I have used the expression "urlanguage" as a way of indicating the general lan­ guage from which we draw our terms and expressions for use in the language games we play. I am not speaking here of an urlanguage in the sense of an U rsprache, the parent Inda-European language from which most European and Anglo-Saxon languages developed. The urlanguage, as I use it here, is not a his­ torical one, but rather that most logically adequate one into which, at any given time, our words and our grammatical constructions can be translated. Thus at an earlier time it could have been the Latin of Aquinas or the French of Descartes that served as the urlanguage in which all language games found their rules and restrictions. Or later it could have been the German of Kant or Hegel. And, fi­ nally, today the various formal languages have become the urlanguages that de­ termine the rules governing our contemporary language games. Any of these lan­ guages can serve the basic function of giving form and truth conditions for the sentences of any discourse. And so, by this analysis, we can gain some insight as to what it means to speak of an ontological commitment, for it may well be that one urlanguage is more adequate than another in that it leads to less ambiguity, has fewer paradoxical results, and makes explicit the rules of logical form. Per­ haps the only language in which an ontological commitment can be indicated with some degree of success is that urlanguage that is mos.t precise at any given time and which, within the limitations imposed on any system because of Go­ del's theorem, can show itself to be relatively free of inconsistency. It is that one about which no accusation can be made that a particular ontological commit­ ment arises because of an ignorance of how certain kinds of descriptive terms operate in the language or of how the syntax of the language functions. Thus, if there is any ontological commitment, it must always be thought of in terms of a highly sophisticated urlanguage that is cautious in its attributions of existence and whose existential statements cannot be shown to be disguised non-

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existential statements. Only in these languages can we legitimately speak of on­ tological commitments, since, first, as Strawson concedes, ordinary languages involve paradox and have "no exact logic," 29 and therefore presumably cannot be used to draw inferences about ontology, and, second, only formal languages per­ mit a precise formulation of what such commitments would be. Wittgenstein may have been right when he said that there is no common essence among lan­ guage games, in the sense that there is no common set of properties or even of objects. But it is not in the language games that ontology is to be sought. It is in the language that determines the form of the games that our commitments to existence are made explicit. The position of the formalist philosopher is strong and persuasive. It makes the study of ontological commitment a going concern, in the sense that we can be constantly looking for languages that avoid the paradoxes and shortcomings of other languages. We can presumably now ask how necessary it is to be committed to objects or to properties or to classes or to all those other entities that have usu­ ally been considered fundamental to theories of ontology and metaphysics. If there can be translation rules that change the interpretation of predicate terms into class terms, then properties need not be parts of the furniture of the world. If a language with individual variables can be translated into a language that does not require such variables, then it would not seem to be necessary to describe the world in terms of individuals. Thus the consequences of the formalist philoso­ pher's view can be very important. But strong objections have arisen , and in the following chapters we shall examine what these objections are and whether the formalist has succeeded in answering them. 29. P. F. Strawson, "On Referring," Mind 59 ( l 950): 344.

3. Construction and Interpretation The conclusion to be drawn from the preceding chapter is that the construction of formal systems leads us to deny that there can be more than relativistic on­ tologies, that ontology in the traditional sense of something necessary or of deal­ ing with what is necessary must give way to the modern sense of something con­ tingent and always open to possible change. Growth and development are as much a part of ontological systems as they are of any other systems. Ontological knowledge, like scientific knowledge, involves the constant attempt to become more adequate in its explanations. This does not mean that it is relative to a time, a place, and a culture. It is relative to its own internal requirement of logic and truth-valued adequacy. Although perhaps it is a truism that ontology, like other subject matters, grows in terms of knowledge and analysis, it has not been a truism to those positivistic philosophers and linguists who have rejected ontology as a legitimate study. They argue that all questions of what exists are best left to the sciences. Scientists, however, hardly concern themselves with the nature of individuals, properties, classes, and propositions or with what it means to speak of identity and self-identity. Few scientists and fewer linguists deal with counter­ factuals and their apparent commitment to possible worlds or to dispositional properties, or to both. But these are the issues that primarily concern philoso­ phers who deal with ontology. So only to those who are already involved in the analysis of ontological issues is it a truism that such analysis progresses. Furthermore, ontological relativity does not mean that there are no serious questions about those truths that seem to be necessary truths. How do the so­ called necessary truths square with the view that al l formal systems are open to further revision, that modal systems themselves are modifiable? It is possible to argue that not everything in a formal or modal system is modifiable; some parts must appear in every system. But such an assertion could be made only in a

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metalinguistic system about modal systems, and this could very well lead to an infinite regress of metalinguistic systems. If a sentence A in a metalinguistic sys­ tem serves to guarantee that a given part must appear in every modal system , what guarantees the necessary truth of A? Perhaps another, meta-metalinguistic system , and so forth? It has been argued, namely. by the early Wittgenstein and by Kripke, that there are truths that are true in all possible worlds. In every possi­ ble world nothing can be both red and green; nor can the number 2 be equal to the number 5 , nor can Tuesday in a given week tum out to be later than Wednes­ day. And, of course, what makes a pure logical truth logically true is that it is true in all possible worlds . All this presupposes that it makes perfectly good sense to speak of all possible worlds or that, somehow, even though there are serious in­ ductive problems in speaking about all objects, there is no problem in speaking about all possible worlds. But it does seem to be the epitome of presumptuous­ ness to make assertions about what may or may not be true in all possible worlds. No one ought to confuse inconceivability with ontological necessity. It was not too long ago that it was considered true in all possible worlds that the shortest distance between two points is a straight line or that parallel lines can never meet. We can stipulate, in the way Kripke does, that all possible worlds will des­ ignate the same entity when "Nixon" is used or that in all possible worlds water will not be water unless it is composed of hydrogen and oxygen. We can stipulate that this is how we understand "Nixon" and "water" when we use these expres­ sions . But the stipulation about how we understand expressions cannot be taken as a guarantee about what will exist in any future possible world that may become actual. If I say "All F are G," I mean that whatever F I encounter will also be a G. The universal unpacks to the instances "F a :::>Ga and F b :::> G b and F c:::>Gc etc. ," where a, b, c, and so forth, are constants designating objects in the domain. Knowing these instances and the function of :::> , we are given the conditions for the truth of "All F are G." But we can never guarantee its truth. \Vhether it will tum out that all instances are true is simply never realizable (except in the rare case where the domain is finite). Similarly, we can say that in every possible world the name "Nixon" will refer to the same individual we refer to when we use the name . This may help us account for counterfactual statements about Nixon. But such stipulations can never guarantee that, in some possible world that may become actual, "Nixon" may not have a different referent. How future societies-which for us are possible worlds-may use the name "Nixon" is not under our control. It is surely not logically impossible that at some future date "Nixon" may have become the name of a robot or of a well-trained presidential dog. In two hundred thousand years ·there might still be a society, and it seems incredible to believe that, if the name "Nixon" is used in that possible world, it must refer to the same man we refer to when we use the name. Similarly, those who try to explain logical truths by an appeal to all possible worlds seem to

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think that this is sufficient to guarantee the necessity of logical truths . Again, imagine the absurdity of claimi ng that in every logical system ever to be devised p or p must be true or that in every formal language in every possible world a will be identical to a . We already know that there can be many valued logics in which p or p is indeterminate, and identity has already been modified to ac­ count for falsehood when a is a definite description. There just is no guarantee about the possible worlds of tomorrow or about what future logical systems will be like . Modal systei ns do not tell us what must be true in every possible world. They tell us only that, in a given modal system, a statement is defined by the rules of the system to be true in all possible worlds. Thus the Barcan formula ( x)DFx� □ ( x)Fx, is true in all possible worlds in Lewis's S 5 modal system, but it is not true in all possible worlds in Lewis's S4 modal system or in the system propounded by Kripke. 1 In other words, in a given formal system, rules can be constructed so that they wil l define what the system takes to be true in all possible worlds. But the rules for induction hold here as well . No one can define into existence what futures must be l ike. And, since futures are possi ble worlds, no one can stipulate what must be in any possible world that will become actual . Our ontologies, then, are relative-relative to what we know about formal sys­ tems and the commitments they require. In this chapter I should l ike to examine in closer detail what a given formal language is and where the precise connection between ontology and formalism actually l ies . In the construction of a formal language, we can distinguish between a cal­ culus and its interpretation. A calculus is the form of a possible language, but is itself free of any commitment to any language. Thus Fx may be a well-formed formula in a given calculus, but, until it is given an interpretation, it is simply a combination of two letters, F and x. Calcul i can have Fx as a wel l-formed for­ mula, but they can also have xF or : or � or any other arrangement as well­ formed formulas . Nor need they have capital and small letters. A calculus could have xy or FG or FGHJ or xyzw or 1 2 3 or 2&9 or )-# or any combination of different marks as well -formed formulas . In brief, marks of any sort can be used in the construction of a calculus . As long as no interpretation is given to the marks, rules can be devised so that the marks, whatever they may be, can be arranged, rearranged, substituted for one another, or inferred from one another. Thus, given ), -, and # as marks in a calculus, we can devise a rule by means of which )-# turns out to be a well-formed formula, and the attachment of this formula to ) allows us to infer, that is, to place in an independent position or on a different l ine, the mark # . We could, if we wished, give this rule the name Modus Ponens, or we could simply cal l it Rule I. 1 . See G. E. Hughes and M . J . Cresswell, A n Introduction to Modal Logic (London: Methuen, 1 968), pp. 1 42-45, 1 70- 82.

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Our talk about the calculus is in what is normally called the metala nguage. The metalanguage contains not only names that name every mark in the cal­ culus, but also all the rules that govern those marks. Thus, following Martin, we could take rp to be a name for the mark ) in the calculus; vee could be a name for the mark V; tilde could be a name for -- , and so forth. 2 But instead of this proce­ dure we can use the marks themselves in the metalanguage. Thus, instead of "pee-vee-que" in the metalanguage (where the mark - stands for the concatena­ tion, or conjunction of p with v and then with q), we can simply write "p v q" as marks in the metalanguage representing the same marks in the calculus. The metalanguage is perhaps the most vital aspect of any formal language, since out of it comes the syntactical rules governing the well-formedness of vari­ ous arrangements of the marks of the calculus as well as rules of inference that state what marks can be further asserted from certain arrangements. Also from the metalanguage comes the semantical rules governing the kind of linguistic expressions to be attached to the marks. In this connection it should be under­ stood that the formula "p v q" is not to be construed as "p or q" or as a truth­ functional compound until and unless semantic rules are stipulated that permit such interpretation. Marks are not truth functional; they can become truth func­ tional if we so interpret them. If the metalanguage is elementary, then the semantics attributed to the marks of the calculus will be elementary; if it is rich, then this also will be reflected in the semantics. Thus, if the vocabulary does not have in it the sentences of atomic theory, then there can be no interpretation in which the domain consists of atoms. Similarly, if the metalanguage contains only monadic predicates, then dyadic well-formed formulas could not be interpreted. We could have a calculus with a finite or an infinite number of marks. And we could have certain recursive rules that permit various combinations of these marks but that do not permit other combinations. By employing recursive tech­ niques, we can make formulas short, long, or infinite, although questions arise about how very long or infinite formulas can be interpreted. The metalanguage can give an interpretation to Fxy or to F wxy or even to F wxyz. But how could it interpret a formula with F followed by 20 variable letters? Although it seems logi­ cally possible that there could be a metalanguage that could interpret a formula containing F followed by 20 variables, so far we have been unable to devise a metalanguage that could present an intelligible and utilizable interpretation. It might be possible to conceive of a self-generating relation that could take in a large--perhaps an infinite-number of variables. Thus Fx20 (F followed by 20 variables) could be interpreted as "x is the father of x 1 , who is the father of x2 , who is the father of x 3 etc." But this kind of self-generating function is no more 2 . R. M . Martin, Tru th a nd Denotation (Chicago: Univ. of Chicago Pr. , 1 9 58), p. 7 2 .

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than an abbreviated form for some series of dyadic predicate forms, that is, " x is the father of x 1 , and x 1 is the father of x 2 , and x2 is the father of x, etc." W hat seems difficult is to give an interpretation of Fx 211 where the reduction to another form is not possible. Thus an infinite number of calculi can be constructed, but not all of them can be given interpretations. In the usual construction of calculi, the marks are divided into different kinds. Some marks are individual variables; others are predicate constants or predicate variables; still others are logical constants. Strictly speaking, such division of marks is part of the interpretation of the marks; it is not, as Martin and others describe it, part of the syntactical metalanguage. When a mark is cal led an indi­ vidual variable, there is already a commitment that in the interpretation there wil l be a domain of individuals, for only individuals can be values of the individ­ ual variable. Similarly, to cal l a mark a predicate constant or a predicate variable is to presume that properties or classes will also be part of the domain. We might argue that only when quantification occurs is a commitment made to specific entities in the domain, and quantification might not occur over the individual or predicate variables. Even though this may be so, by naming the marks the way we do, we make restrictions on the kinds of domains that are possible. We are saying that the domain will contain either individuals or properties or classes or some combination of these. Although we are assuming beforehand that some of the marks wil l name in certain specified ways, such an assumption belongs tech­ nical ly not in the syntactical but, rather, in the semantical metalanguage, that is, in the metalanguage as it gives meaning to the marks, not as it simply stipulates formation rules for them. Similarly, we ought not to think of the logical con­ stants as part of the syntactical metalanguage, unless by a logical constant we mean no more than an abbreviated rule of formation or inference. Thus, for example, we need not think of "v" as a truth-functional connective, but rather as a mark that, combined with p and q in certain ways, permits us to move to another arrangement such as p -:J q or -( p. q), assuming, of course, that these other marks are permitted in the calculus. We might note further that, if the calculus contains marks such as (3 x), we cannot, without interpretation, call these marks the existential quantifier, since to do so already presupposes that (3 x) is a way of signifying what does or does not exist. At most we can stipulate a rule that the combination of marks (3 x), is to be used as an abbreviatory sign for some series of marks such as Fa v F b v F c v . . . , or as a way of signifying the marks which, according to some interpreta­ tion, will be those referring to entities in the stipulated domain. Thus ( 3 x)Fx might mean nothing or everything. It could be taken as no more than an abbre­ viation for Fa v F b v F c, where this is simply another kind of arrangement in the calculus. Or it could mean that it not only abbreviates certain formulas, but also shows, according to another interpretation, which marks are referential. Then a ,

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b , and c would be taken as referential, whereas F, which is not bound by some

set of marks, (3 F), is not referential. I think that this is the way Quine thinks of the existential quantifier. The marks with which it is used designate the referents of the system, that is, the ontology of the system. If it is not used with F, then F is, according to Quine, a schematic general term that does not refer and there­ fore makes no ontological commitment. Thus any set of marks can be converted into a calculus. F, x , a , b, c, 3, (, ), and v can all be combined in different ways without requiring that we regard them as anything else than the marks that they are. All that we need to change them into a calculus is a rule of well-formedness and a rule of substitution or a rule of transformation (in some calculi only a rule of transformation, that is, modus ponens, is necessary), ' or both, and a method for proving consistency and, perhaps, completeness. But now let us examine what it means to interpret a calculus. For it is the interpretation, not the formation, that produces ontological commitment . We have seen that a calculus, C, can be regarded neutrally. However, C is usually interpreted in such a manner that a formula in it, for example, (A) R u w, is defined in the following way: R is a predicate term that is a dyadic predicate constant or, under certain circumstances, a dyadic predicate variable; u and w are individual terms that are individual variables or, under certain circum­ stances, individual constants. (In some systems different letters are used to dis-• tinguish constants from variables. ) This is the primary interpretation of (A) . "Primary" means that there may be alternative ways of interpreting (A)-for ex­ ample, R, u , and w may all be predicate terms or they may all be individual terms or some of them may be syncategorematic terms or they may be terms of some unfamiliar kind such as action or event terms, which take actions or events as values. None of these alternatives can be said to be excluded until some crite­ rion is given that explicitly excludes them. In other words, every interpretation is allowable un]ess some criterion of rejection is stated and shown to hold for the interpretation-for example, it produces substitution instances of logical contra­ dictions or it leads to Russell's paradox or to other paradoxes or, perhaps, results in schemata that are nonsensical. (An interpretation that used the English lan­ guage as its metalanguage and that produced "Is are am" as a well-formed sen­ tence would not be an allowable interpretation. ) Thus there may be different in­ terpretations of a purely formal calculus. But the primary one is the usual one; 3. Cf. J. von Neumann in Mathematische Zeitsch rift 26 (1927): 1 -46 . Sec also Alonzo Church's system in his In troduction to Mathematical Logic (Princeton: Princeton Univ . Pr., 1956), pp. 148 - 49 .

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R is a predicate term taking properties or classes of n-degree as its values; u and w are individual variables taking individuals as their values. This division of terms is normally presupposed in the primary interpretation of the calculus that con­ tains (A). W hat is this presupposition? Why is it considered normal or usual for an inter­ pretation to be given in terms of predicate and individual terms? Is there some necessity or some basic consideration that requires the terms of a formal language to be excl usively of the predicate-individual variety or that requires u and w to be taken as individual rather than as predicate terms? Unless these questions are an­ swered adequately, there can be no determination of how serious the ontology is to which a formal system is committed . If, for example, it turns out that the need for predicate and individual terms is no more than a convention to which there are other viable alternatives, as Quine sometimes seems to believe, 4 then an on­ tology of individuals, properties or classes, or both, which are often taken to be the designata of individual and predicate terms, would lose the urgency it pres­ ently has for many philosophers. The problems of universals and classes that are taken to arise because of a commitment to properties and real, as distinct from virtual , classes would no longer be major philosophical issues . 5 Or, if it were to turn out that predicate variables are just as permissible in a formal language as individual ones are, then, as Quine has also demonstrated, quantification over such variables would become legitimate, and this would entail the stipulation of universals as existent entities. 6 Thus an inquiry into what the constants and vari­ ables of a formal system are and how they are to be interpreted is not of concern simply to the formal logician. The consequences of such an inquiry can be phil­ osophically very significant. One familiar answer to the question of why C is utilized with predicate and individual terms rather than with other kinds or combinations of terms is that every interpretation depends on the metalanguage that is employed. If that meta­ language, M, itself contains certain linguistic categories and certain formal ar­ rangements of these categories, then the interpretation of C will reflect these cat­ egories and their arrangements. More specifically, under this analysis R can be taken as a predicate term of n-places in C if M contains a category of such terms. Similarly, u (or w) is an individual term in C if M contains a category of these terms. And, finally, R uw is well formed or legitimately arranged in C if interpret4. Thus Quine say s that "someday . . . something of our present individuative talk may in turn end up, half vestigial and half adapted, within a new and as y et unimagined pattern beyond indi­ viduation" ( On tological Relativity [New York: Columbia Univ. Pr., 1969], p. 24). 5. The distinction between real and virtual classes appears in W V Quine, Set Theory and Its Logic (Cambridge, MA: Harvard Univ. Pr. , 1963 ) , pp. 15-21. 6. Cf. W V Quine, From a Logical Point of View (Cambridge, MA: Harvard Univ. Pr. , 1961) , 2d ed. rev., ch. 6.

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ing it as " u has the relation R to w" would result in a form that would be gram­ matically correct in M. Thus, if the English language is M, then Ruw can be taken as a well-formed formula consisting of a predicate constant and two indi­ vidual variables, since this kind of form is a grammatically correct form in En­ glish. In this analysis presumably criteria can be given for what specific expres­ sions can be legitimately introduced into the interpretation of C. Thus "is taller than" can be taken to be an appropriate substituend for R of (A), because "is taller than" is an instance of �he dyadic predicate category in M. "John" and "Robert" can be taken as appropriate substituends for u and w since these are instances of the individual category of M, and the substitution instance of (A), "John is taller than Robert," would be well formed because it is a substitution instance of a grammatically correct form in M. In other words, predicate and individual terms, arranged in certain specific ways, are used to interpret C because these are the major linguistic categories that appear in M. This answer, however, is not satisfactory. First, there is some question as to whether metalanguages are to be equated with natural languages. In a natural language predicates are, so to speak, on a par. No distinction is made between disposition and occurrent predicates. 'The fire hydrant is red" is no different grammatically from "The sugar is soluble." But the translation of these sentences into a formal system changes the latter into a reduction or a counterfactual sen­ tence, and the former into a normal subject-predicate sentence. Also in English "exists" is a predicate and "Pegasus" is a proper name. But these expressions are not carried over to become substituends for the predicate and individual terms, respectively, in the interpretation of C. Similarly, in English "Men are mortal" is a simple subject-predicate form of sentence; but, in the use of this sentence in C, both "men" and "mortal" are predicates of a molecular conditional form. Sec­ ond, even though metalanguages impose certain structural forms on C, C also apparently imposes certain structural forms on its metalanguage. Thus the natu­ ral-language combination of individual term and predicate term is presumably carried over into the structure of C . But if C is a calculus that has an expression that can be interpreted as a modal operator, and then if M is to yield an inter­ pretation of C, all adjectival forms of modality in M are required to be changed into quantificational forms. In other words, a reference to "possible" applied to an entity is required to be converted to a reference to "possible" applied to a state­ ment. Third, it is not at all certain that an interpretation of C must utilize proper names or constants of any kind. If the analysis of Russel l and Quine is accept­ able, then proper names are all reducible to descriptions, so that only individual variables and predicate constants are the descriptive expressions permitted in C. The individual variables have as their replacements not names but values, that is, the entities of the domain. In fact, some of these entities cannot be named.

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Thus, as Quine points out, "There are u nspecifiablc real numbers" is true , but the values here are not objects with names. 7 These objections , however, suggest a certain modification. It might be argued that only "a certain portion" of a natural language is used as the metalanguage and that the interpretation of C comes from this portion. W hat is this portion? R. M. Martin sometimes speaks of the metalanguage as a "very small part of Basic English" or as a language "closely akin to a very small fragment of English. " b But, as Martin himself recognizes, such characterizations of the metalanguage are much too ambiguous. Alonzo Church has suggested that the amount of a natural language that would be required for C would be (a) just that which is "sufficient to enable us to give general directions for the manipulation of . . . the symbols of the language" 9 and (b) a list of descriptive terms whose characterization as proper noun or common noun or adjective would permit such manipulation. 10 W hat Church apparently means here is that, if English, for example, were M, then its rules of grammar as well as certain basic descrip­ tive predicates would be incorporated into C, and all problematic expressions of the natural language would then be either eliminable or translatable by the rules into the predicates that are permissible. Thus what would be carried over into C would not necessarily be any particular expression, but rather rules that had been extrapolated from the English language and that would specify the categories into which all descriptive expressions would be required to enter. " Exists," then, could be rejected as a predicate, and " Pegasus" as a proper name, but this would not entail a rejection of a rule defining a well-formed formula of C as consisting of predicate and individual terms. The particular natural language of M would, in terms of this modification, still be the main basis for deciding how C is to be interpreted, but the determin­ ing factor now would consist of (a) the kind of syntactic forms that appear in M and (b) the particular requirements of the calculus. Since English uses as its pri­ mary syntactic form one in which individual terms are conjoined with monadic or polyadic predicates, it is not difficult to see why (A) of C would become inter­ preted as a dyadic predicate constant conjoined with two individual variables. The interpretation would simply reflect the basic categorial commitment in M. 1 1 Thus the rationale for giving a particular interpretation to a formal calculus is 7. Quine, Ontological Relativity, p. 95. 8. Martin, Tru th and Denotation , p. 63. 9. Church, Mathematical Logic, p. 47. 1 0. A. Church, "The Need for Abstract Entities," in Con temporary Readings in Logical Theory, ed. I. M. Copi and J. A. Could (New York: Macmillan, 1 967), p. 202. 1 1 . Thus Carnap say s, "The language B (the natural language) belongs to the world of facts. . . . The language B-S (the formal language), on the other hand, is something constructed by us. . . .

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now apparently quite clear. We look to the basic categorial commitments of the natural language that is serving as a metalanguage. These commitments are then reflected in the interpretation of the calculus. But now the question arises as to the status of these commitments. W hy do such categories appear in the meta­ language? W hy introduce one set of l inguistic expressions that refers to or desig­ nates properties or classes and another set that refers to or designates individuals? W hy make this distinction at all? Any answer to the last question would seem to be fraught with great difficu lties. The distinction, it could be maintained, is sim­ ply a conventional one adopted in the English language for some reason that has long been forgotten. English might have had different distinctions, just as mod­ ern Engl ish need not have developed from Anglo-Saxon in the way that it has. We spell "cat" c-a-t, but the language could have developed in such a way that it could have been spelled k- a-t. Similarly, it might be argued, the commitment to a language of logical terms, predicates, and individual terms could have been otherwise than what it is. The language could have consisted only of logical and predicate terms or only of logical and individual terms or perhaps only of logical and some other kind of descriptive terms. Just as "cat" might have been spelled k-a-t and just as the inflectional endings of nouns and adjectives in the Anglo­ Saxon language might have persisted into the present, so also there could be pos­ sible alternatives to present-day Engl ish grammatical structure. But what could be the alternative to the distinction between individual naming terms and prop­ erty-referring terms? Could a language consist only of one kind of descriptive term? Could there be a language that, besides logical terms, has only what we would cal l predicate terms? If there is some argument that the very use of "predi­ cate" implies a contrast with "individual'' or "subject," the question could be put differently. Could there be a language that, besides logical terms, contains only designative expressions without any categorial divisions? Thus R would designate a 1 , and u and w would designate a 2 and a , , respectively. No distinction would be made among different kinds of entities. W hether such a language is possible might perhaps be answered by raising a somewhat similar question in relation to logical-connector terms. Is a language required to have logical connectors, or would it be sufficient to have a l ist of descriptive expressions? The answer here would seem to be that some logical connectors are required, even if they are not all those given in the usual interpretation. We might be able to eliminate one logical term in favor of another, or perhaps eliminate all but one. But that one is required. It is what permits a move from one formula to another formula that is not a mere substitution instance. And such a move is considered necessary in the Nevertheless, we construct B-S not arbitrarily but with regard to the facts about B" ( Foundations of Logic and Mathematics, International Encyclopedia of Unified Science [Chicago: Univ. of Chicago Pr. , 1 939], vol. l , no. 3, p. 7).

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construction of a language, since without it the language-if we can still call it a language-remains a mere listing of descriptive terms without any useful func­ tion. Every language must permit a move from one set of symbols to another set, since it is this inferential move that makes knowledge possible and thus justifies the existence of a language. Wittgenstein thought of language as having many functions. He speaks of lan­ guage as being used to give orders, to describe and to give the measurements of objects, to report events, to speculate, to form and to test hypotheses, and so forth. 1 2 But all these functions presuppose one primary function, namely, the possibility of drawing inferences. Without rules for making inferences, all of the functions listed by Wittgenstein become inapplicable. Orders, descriptions, re­ ports, speculations, and tests operate only in a context in which inferences can be drawn. Thus, for example, David Harrah has argued that questions are no more than a subclass of statements and, therefore, utilizable with the logic of statements. 1 3 Inference, however, is defined strictly by the syntactical part of the meta­ language. Rules for moving from one set of symbols or marks to another can be given without any commitment to an interpretation of these marks. On inter­ pretation these marks may be nonsensical, but the rules of inference would still hold. Thus logical rules and the logical constants to which these rules apply may be necessary for the construction of a language, but they are not sufficient . If we think of a language as having some function, then inference rules that gave us unintelligible combinations of letters as conclusions would not be enough to yield a language . Only as the logical constants are "appropriately filled out" does a language begin to appear. That is, only as the linguistic elements on both sides of ::> , for example, receive an appropriate interpretation do the logical terms be­ gin to function in a language. What is an "appropriate interpretation"? In other words, given the mark ::> , interpreted as "if . . . then ---," what linguistic expres­ sions can be substituted for . . . and --- in order to permit this connector to play a role in the resultant language? Could we simply introduce individual terms that designate individuals? If so, then "x::> y" and "a :> b" would be well-formed ex­ pressions. But this will not do. We cannot have an interpretation consisting of English words that contains as well formed such a structure as "If John Smith then Mary Jones." Why is this not permissible in the English language? Is it sim­ ply a convention that we do not permit this kind of linguistic structure? We might try comparing this structure with others that do seem to be permissible. Would a list of individual terms on each side of ::> be allowable? But this also would be as inadequate as the use of one individual term. 1 2. L. Wittgenstein, Philosophical Investigations, trans. G. E. M. Anscombe (New York: Mac­ millan, 1969), 3d ed. , pp. 1 1 - 12. 1 3. David Harrah, "A Logic of Questions and Answers," Philosophy of Science 28 ( l 96 1 ): 40-46.

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One linguistic structure that does seem to work with :::> consists of a combina­ tion of an individual term, variable or constant, with a predicate term, variable or constant. Thus "If John is strong then Mary is happy" is an allowable replace­ ment of ". . . :::>---.'; W hy is this allowable whereas the use of individual terms is not? The answer that is usually given is that a logical connector such as :::> can function only with that unique combination of linguistic expressions that we call a sen tence . It is this unit called a sentence that gives :::> its crucial role. W hat is a sentence and why should it have this kind of significance? The answer to these questions can come only if we have some awareness of why there are any languages at all. The origins of language are, of course, shrouded in the mysteries of antiquity. Still, we might ask what role a language plays for those who use it, for it is at least logically possible for human beings to have evolved-although, from a cultural viewpoint, not very far-even without language. Our answer has been that, although there are many functions of a lan­ guage, its most essential role seems to be one of inference . Mill has said, 'To draw inferences . . . [is] . . . the great business of life. Everyone has daily, hourly, and momentary need of ascertaining facts which he has not directly ob­ served: not from any general purpose of adding to his stock of knowledge, but because the facts themselves are of importance to his interests or to his occupa­ tions." 1 4 The introduction of language permits the beginning of the formaliza­ tion of the inference process and its investigation without the dangers of extra­ linguistic phenomena. Even the most primitive language of the most primitive man must include a sound or a mark by which a deduction can be made about some event prior to its actual appearance. To be able to say "There are lions com­ ing" before lions actually appear and then to deduce from this that lions may shortly arrive is to recognize the basic significance of a language. By allowing inference from one set of sounds to another, language makes possible a more rational response to danger and to problems. As Dewey once put it, " If it were not for the intervention of agencies (such as language) for representing absent and distant affairs, our experience would remain almost on the level of that of the brutes. Every step from savagery to civilization is dependent upon the invention of media which enlarge the range of purely immediate experience and give it deepened as well as wider meaning by connecting it with things which can only be signified or symbolized." 1 5 In other words, what is crucial in a language is the fact that with it we can draw inferences about things before they are upon us, that is, while they are still absent or distant either in space or in time. Thus even the most rudimentary languages have expressions relating to inference, and as lan­ guage evolves the logical constructions in the language are made more explicit and more sophisticated. 14 . J . S. Mill, System of Logic (London: Longmans, Green, 1879), 10th ed. , intro. , sec. 5. 15. John Dewey, Democracy and Education (New York: Macmillan, 1916), p. 272.

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The logical connectors that make inference possible, however, do not function alone. The l inguistic segments that complete the connectors cannot be mere l ists of words, even if they arc al l descriptive. If inference is to occur in a language, then the l inguistic segments must be able to incorporate a claim on what there is. The rules of inference are techniques that enable us to move from one claim­ making string of expressions to another claim-making string of expressions . It is for this reason that mere strings of words cannot function with the logical con­ nectors; they make no claims about what there is or what there wil l be or what there has been. "John Sm ith," taken by itself, tel ls us nothing about whether there is such a person whose name is "John Smith." I can say " If John Smith then Mary Jones," but it will be sensible to me only if I take the antecedent and the consequent to be abbreviations for claim-making constructions such as "John Smith is present" and " Mary Jones is present" or "John Smith comes" and "Mary Jones will come also." The names are supplanted by claims. Claim making, l ike table making or candle making, occurs only under certain conditions. One way of claiming is to say that there are certain entities in a spec­ ified domain. Another way is to say of an entity that it is a member of a given group or that it is related to other entities, including itself, in various ways. These are ways in which claims are made. In all these cases we ought to note that a claim asserts a relation among entities, even if the relation concerns a com­ monality of domain. For this reason linguistic segments that make claims must consist of parts that are related to one another in such a way that one part must be taken either as a predicate of another part that is a subject or as a member con­ tained in another part called a class term. Without these dichotomies of terms, a claim-making language would not be possible. Furthermore, claims can turn out to be mistaken or otherwise incorrect, for a claim is always set against a possible counterclaim. For this reason a claim-making l inguistic segment must be capa­ ble of having "true" or "false" appl icable to it, for claims either hold or do not hold. Such claim-making segments are called sentences, and the division of such sentences into units that are characterized as individual or predicate terms is due to the fact that claims could not be made without the introduction of such units. Every nonanalytic language, then, whatever its subject matter, has inference as its primary function. And, whatever this subject matter is, it must be charac­ terized in a certain way if inference is to occur. Something must be taken as hav­ ing a property or as being a member of a class or as being related in some fashion to something else. Sapir once said, " No language wholly fails to distinguish noun and verb, though in particular cases the nature of the distinction may be an elusive one." 16 The reason for the distinction now seems clear. Without it the claim-making devices in the language and, therefore, inference would not be possible. 1 6. Edward Sapir, Language (New York: Harcourt, 1 92 1 ), p. 1 1 9.

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The formalist philosopher, then, does not operate solely in a vacuum. His in­ terpretations are not so arbitrary as he would have us think they are. Prior to any interpretation of a calculus, a language is already in operation, and it is from this language-with its particular categorial structures-that the interpretation is de­ rived. This does not mean that a formal language takes all its terminology from the natural language used to construct it. In a natural language we can talk of elves and goblins as if they were existent entities, but in a formal language any commitment to existence is very carefully circumscribed. Thus, for example, in Russell and Whitehead's Principia Mathematica , language-vacuous names are changed into descriptions, whereas for Frege they all designate the same null entity. But we cannot eliminate all the characteristics of a natural language. The commitment to some basic set of sentences formed as subjects with predicates seems to be necessary, even though it is not always clear which expression is the subject and which the predicate. Prior to the forming of a formal language, the concepts of something or other having something or other as a property or as a member of a class seem to be necessary ingredients of any constructed language that is intended to be used to communicate empirical or scientific information. Thus, even prior to the introduction of the notion of values for the variable, there is already an ontological commitment in the language-formal or natural. Whatever entities make up the universe, they are describable in certain specific ways. Whatever domain is posited for a formal language, the entities must be propertied or classifiable. For this reason Quine is only partly right when he tells us that we discover what exists by referring to the values of the individual vari­ able. In what exists we ought to distinguish the content from the framework. The content of what exists is given to us by the values of the variable. But the inter­ pretation that calls one mark an individual variable and another class member­ ship gives us the existential framework. It is the squareness of the hole that pro­ hibits the use of other than square pegs. It is the need to have individual variables that requires a domain of individuals. In the light of the importance of natural language in the construction of for­ mal languages, it might be asked whether ontological commitment is justifiably sought in formal rather than in natural languages. If the commitment arises from natural language, then why should there be any interest in the construction of formal systems? Two answers can be given. First, formal languages are ways by which we make explicit all that is involved in the use of logical terminology. Just as the full implications of our use of mathematical terms are to be found in the mathematical systems we construct, so also our use of logical terms receives its full explication in the construction of logical systems. Second, formal languages give us the means for making clear where and what our commitments are (or are not) in a given sentence. Thus, without the use of a formal language, we could be misled, as Russell believed Meinong was, into thinking that "Pegasus" in

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"Pegasus was a winged horse" is the subject of the sentence requiring a n object for its denotation. We could mistakenly come to think that " Some metals are conductors" is a basic form of sentence with "some metals" as the subject and "are conductors" as the predicate. Only the translation of this sentence into for­ mal terms re\'eals how we are to treat it if we are to use it for making inferences and for understanding what if any particular entities the sentence commits us to if it is true. The natural language posits for us ways in which to categorize the \vorld. Thus analysis begins by positing objects, properties, and classes. It is the formalism that tells us what is acceptable and what is rejectable in a sentence if it is to be regarded as true. Carnap once described the way in which formal struc­ tures are connected to natural languages. 1 7 Such structures arise out of analysis of the language ordinarily used. What the analysis does is bring out in clear form all the logical and existential presuppositions. l 7 . Carnap, Foundations of Logic and Mathematics, International Encyclopedia o f Unified Sci­ l , no. 3, pp. 3 - 5 .

ence, vol .

4 Individual and Predicate Terms The commitment to a language of individual and predicate terms is sometimes said to be more than merely a convention in a given language. It seems to be more fundamental, in the sense that it does not seem that there could be a genu­ ine alternative to the predicate-individual term distinction. But this may be an unwarranted generalization, since some attempts have been made to show that this distinction is not as inviolate as we may think. Thus, for example, it is often pointed out that the combinatorial language of Schonfinkel and Curry show that individual variables can be eliminated from a language, and that individual terms are therefore not necessary. 1 But, as Quine has indicated, even in a com­ binatorial language the entities presupposed by such a language "must be reck­ oned as arguments or values of functions in order that the statements in question be true. " 2 In other words, the combinatorial language can be regarded as a lan­ guage in which "true" and "false" are applicable only insofar as it is translatable into terminology that contains predicate and individual terms. Quine, however, has also challenged the predicate and individual term com­ mitment. He has introduced his own way of demonstrating how individual vari­ ables and constants can be eliminated from a language. On Quine's analysis predicates as well as a certain select group of expressions called "operators" are 1. Moses Schonfinkel, "Uber die Bausteine der Mathematischen Logik," Mathematische An­ nalen 2 (1924): 305-16. H. B. Curry, R. Feys, and W Craig, Combinatory Logic (Amsterdam:

North Holland, 1958). 2 . W V Quine, From a Logical Poi n t of View (Cambridge, MA: Harvard Univ. 1961), 2d ed. rev . , p. 104.

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retained. Exactly what arc these operators? One of them is what Quine calls the derelativization operator, which is symbol ized as " Der. " � The use of " Der" sig­ nifies that the individual variable has been incorporated into the predicate. Thus the standard form " Something bites something" is symbolized as (3x)( 3 y)Bxy. But now, according to Quine's new method, we can el iminate the second quan­ tifier, and thus the y variable, by making it part of the predicate. We then obtain "(3x)(Der B)x. " " Der" tells us that a bound variable has been incorporated into B. The variable x is then el iminated by making it a part of the new predicate " Der B. " Thus we obtain " Der Der B," which means that something bites something. In this way, Quine maintains, it is possible to rid a language of individual variables . However, Quine's removal of the individual quantifier and variable is open to the same criticism he directed against Schonfinkel and Curry. In order for the sentence " Der Der B" to be regarded as true (or false), it must presuppose the same set of entities presupposed in the standard quantificational form. The sen­ tence-and it is assumed that " Der Der B" would be a sentence-would have to be understood as attributing a relation to some pair of objects. Otherwise it would be difficult to see how the truth or falsity of "Der Der B" is to be main­ tained. " Der Der B" is true because something, that is, some x, does indeed bite something else, that is, some y. It is this latter kind of understanding, with its commitment to some thing or some "it" or, more precisely, some individual vari­ able, that makes " Der Der B" an allowable form. The W ittgenstein of the Tractatus is also sometimes taken as denying the cate­ gorial commitment to individual and predicate terms. However, unl ike Quine, he seems to think that all predicate terms are reducible-in some not quite clear sense of reduction-to either individual variables or individual constants. 4 Thus for W ittgenstein atomic sentences consist solely of a concatenation or conjunc­ tion of names designating speci fic elementary objects. Predicate terms could ap­ pear in a language, but only as a convention. In the English language " is above" is used to say "a is above b. " But the language might have evolved in such a way that "a is above b" was stated as " � . " Here the very arrangement of the names would show, without actually expressing, that relationship that is stated in the Engl ish language as "is above. " Even monadic atomic sentences-if we assume 3. "Variables Explained Away," in Selected Logic Papers (New York: Random House, 1 966), p. 230. 4. See, for example, the article by Irving Copi in which he argues that, according to Wittgen­ stein, "no elementary proposition in a 'logical notation' can predicate a property of any object" ( Es­ says on W ittgenstein's 'Tractatus,' ed. I. Copi and R. W Beard [London: Routledge and Kegan Paul, 1 966], p. 1 85). Thus predicate terms are not necessary in an elementary proposition of logical notation.

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that there could be monadic atomic sentences for Wittgenstein 5 -could be con­ verted into forms that do not contain predicate terms. Thus, as Sellars points out, it is possible to imagine a language in which "monadic atomic facts would be represented by writing the name of the single object they contain in various col­ ours or in various styles of type. . . . Thus we could represent the sentential function, 'x is green,' by using the variable 'x' and writing it in bold face ." 6 Surely, Sellars argues, there is no reason to suppose that this idea of eliminating predicate terms ar.d showing them by means of names was not available to Witt­ genstein. But, if Wittgenstein did actually intend to limit his basic sentences solely to concatenations of names, then two criticisms can be directed against him. First, Wittgenstein's reductionism is similar to the attempt in mathematics to reduce properties and relations to groupings of individuals. In mathematics a re­ lation is defined in terms of classes of pairs (or triads, and so forth). Classes and pairs of individuals are retained in the definition, but no commitment is made to relations or to terms designating such relations. However, it is not merely pairs of individuals that are required in the mathematical definition, but rather ordered pairs of individuals. The pairs are ordered; otherwise Rab as a relational function could not be distinguished from R ba . But pairs are ordered by means of an order­ ing agent; and what is this ordering agent except the very relation itself? We pair a with b in that order because that order gives us "a is the father of b" rather than " b is the father of a." The ordering concept, if I may be permitted the use of this controversial term, is what makes a and b the kind of pair required to depict a relation. But this ordering concept is exhibited by the predicate term; a and b are ordered in such a way that a is the father of b. In other words, it is the use of the predicate term "is the father of" that gives a and b the ordering that is required . 7 Second, to say that the substitution of "� " for "a is above b" means that a predicate term has been eliminated is not true. It is perhaps possible to imagine a formal language in which all predicate constants are given solely in terms of dif­ ferent-size squares. Thus, instead of F and G as predicate constants, we should have D and □. Sizes could vary in accordance with the number of predicate con­ stants allowed. Here, of course, no one would maintain that a predicate term has been eliminated simply because the familiar predicate letter no longer appears. A 5. For a full discussion of whether Wittgenstein intended monadic predicate sentences to be taken as atomic, see James Griffin, Wittgenstein's Logical Atomism ( London: Oxford Univ. Pr., 1964), pp. 5 3-61. 6. Wilfred Sellars, "Naming and Say ing-," in Essays, ed. Copi and Beard, pp. 2 56- 57. 7. However, R. M. Martin, following a recommendation by Wiener and Kuratowski, does at­ tempt to give a definition of ordered pair that would at least be satisfactory for the purposes of set theory ; Truth and Denotation (Chicago: Univ. of Chicago Pr. , 1957) , p. 155. Sec also W V Qui ne, Set Theory and Its Logic, (Cambridge, MA: Harvard Univ. Pr. . 1 963). pp. 58-64.

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predicate term is not necessarily represented by a letter or by a word with a cer­ tain kind of suffix or prefix. An individual variable is not necessarily exhibited by letters of the alphabet. ( Some books exhibit it by means of three dots or dashes. ) Now. if such changes from the standard formal system are possible, then it is not difficult to imagine a nonstandard formal system in which space is used to repre­ sent predicate terms. Thus " a b " would represent something quite different from " a b" or " ab" or " a b." Similarly, the horizontal use of space in these instances would be quite different from the vertical use in such instances as "� " and ":," and so forth. The space itself would signify predicate terms. Thus to show that a language can be free of predicate terms- the way we know them in English-does not help to show that a language can indeed be free of such terms. What would be required to make Wittgenstein's point significant would be to show that, given any particular formal language, whatever in it can be said by means of a predicate term can be said as well by means of a concatenation of names. It is no great task to take a formula, ( 1) R uw,

and convert it into "� ," where this special arrangement is to be distinguished from " u , " since here the space between the letters serves the same function as the original predicate letter. W hat would be interesting and significant would be to show how ( I ) is translatable, without any loss of meaning, into a sentence that contains only names. But Wittgenstein never gives us a method for making such a translation. Thus neither Wittgenstein nor Quine is able to rid himself of the dual com­ mitment to predicate and individual terms. Still, even if Wittgenstein and Quine are wrong-even if there does not seem to be any general criterion for eliminat­ ing individual in favor of predicate terms, or the converse-certain sentences seem to be perfectly legitimate, and yet they use only individual or only predicate terms. It is difficult to argue that all sentences must consist of both predicate and individual terms. Thus the following are standard examples of sentences contain­ ing only individual or only predicate terms: (2) John Smith is (really) Fred Jones. ( 3 ) Black is more beautiful than white. Example (2) is apparently a sentence without predicates, and Kripke, for one, has argued that if (2) is true its surface form is its deep-structure form. We have two names, each rigidly designating the same entity. But Kripke's names might well require a notion of a sense in order to account for the fact that in each possible world the same name identifies the same individual. In each possible world the properties of objects change-Nixon might not have been president or have been in politics at all-but the name still identifies the same object. In brief,

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identification can occur only if we assume that at least one property-a unique essential one-will identify the individual named by the name, so that the no­ tion of a rigid designator seems to be directly related to the notion of an essential property. Predicates designating such properties would then be implicit in (2). Of course, if it turns out that Russell and Quine are correct, then "John Smith" and "Fred Jones" are really disguised definite descriptions, and this would make (2) a schema of individual and predicate terms. For Carnap (2) would simply be an ill­ formed sentence, since in his formal language (2) would be a violation of the principle of univocality, which disallows the formation of sentences in which two different names designate the same entity. Finally, there is some question about whether identity ought to be regarded as a primitive connector added to the usual truth-functional ones or whether it ought to be translated into material equiv­ alence. If the latter procedure is adopted, then a = b becomes defined as (F)(F a F b ), and the standard use of predicate and individual terms remains intact: Example (2), then, may turn out to be only apparently problematic. Example ( 3 ), however, is the really interesting case, since, on first analysis, it might be regarded as a legitimate interpretation for ( 1 ), where u stands for "black," w for "white," and R for "is more beautiful than." Here we have an example in which only predicates are employed, or, more specifically, only terms designating prop­ erties appear; u and w are replaceable by predicate rather than individual terms. Thus it would seem that there is neither a logical nor an ontological need to think of u and w as individual variables or constants taking proper names as their substituends. 8 But now let us consider ( 3 ) more carefully. If ( 3 ) is adequately symbolized by ( l ), then u and w are predicate constants referring to specific properties in the same way that they would refer to specific individuals if they were individual constants. Individual constants have the further characteristic that each one re­ fers to one and only one individual, not to a group or to some individual or other. It is for this reason that, except for oblique or modal contexts and in certain cases of natural deduction, 9 in the usual formal systems definite descriptions with indi­ vidual variables or expressions such as "this" or "that" are substitutable for proper names and individual constants. But, now, if we employ this analysis with u and

=

8. Languages whose variables can take either individuals, properties, or even properties of proper­ ties as values have been developed by Fraenkel, Von Neumann and others. But, as Carnap has pointed out, these languages are primarily directed toward the solution of certain problems in the formalization of arithmetic and set theory. They are not suitable for use with nonanaly tic languages _containing descriptive signs. See R. Carnap, Symbolic Logic (New York: Dover, 1958), p. 84. 9. The problem in natural deduction arises in inferences of universal instantiation and existential generalization. In these inferences, if the individual constant is replaced by a definite description, then a uniqueness sentence for the description must be added as an additional premise if the in­ ference is to be valid. See the discussion by R. Carnap, Meaning a nd Necessity (Chicago: Univ. of Chicago Pr. , 1964 ) , 2d. ed pp. 34-35.

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w as predicate constants. some major difficulties arise: u and w must be taken to refer to specific properties or, more techn ically, specific instances of determinate properties, and, as in the case of individual constants, arc all replaceable by defi­ nite descriptions with predicate variables. And just as definite descriptions with individual variables arc taken to be satisfiable by one and only one unique indi­ vidual that can be designated by "this" or "that," so also definite descriptions with predicate variables must be taken to be satisfiable by one and only one unique property that also can be designated by "this" or "that." In other words, if u and w are predicate constants, then (3) must be interpreted in C as saying ( 4) This and only this property of being black is more beautiful than that and only that property of being white.

But this distorts the obvious meaning of (3), which is that every instance of being black-not simply this specific one-is more beautiful than every instance of being white, not simply that specific one. By treating "black" and "white" as predicate constants analogous to individual constants, the universality of (3) is l ost. Thus ( 3) is not a simple substitution instance of a formula in C in which u and w are predicate constants designating specific instances of a determinate property. We shall shortly examine other difficulties in analyzing (3) , but, on the basis of the discussion in the preceding paragraph, it might be argued that (3) is not a very good paradigm example of a sentence containing only predicate terms, since "black" and "white" designate determinate properties. But we could have predi­ cates relating to instances of determinate properties, and this would give us a sentence consisting strictly of predicate terms. If instead of (3) we had a sentence such as "Midnight blue is darker than canary yellow," we could translate this into the ( undistorted) formalized version: "This and only this instance of blue (namely, midnight blue) is darker than that and only that i nstance of yellow (namely, canary yel low)." But even in this case, where we substitute instances of determinate properties for determinate properties, the formal ized sentence does not capture the sense of the original. It is not this particular blue, namely, mid­ night blue, that is darker than this particular yellow, namely, canary yellow. All the cases of midnight blue are to be regarded as darker than all the cases of canary yellow. So we ought not to think that formalizing sentences with predicate terms becomes an easy matter if the terms relate to instances of determinate properties. Returning then to ( 3), perhaps we can retain the total predicate status of ( 3) by treating it as a universally quantified statement:

(5) All black properties are more beautiful than all white properties.

Then ( 5 ) is symbolizable as

( 6 ) ( F)(BF :J (G)(W G :J MFG)),

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where B stands for "black," W for "white," and M for "more beautiful than." Here also, only predicate terms are designators. But is (6) an appropriate transla­ tion of ( 5)? Some philosophers have argued that, when a sentence has as its sub­ ject a term that is usually a predicate, then this sentence is really an elliptical way of stating a sentence in which an individual is said to have the property indicated by the predicate. Thus Ryle says, "Nor when we say 'unpunctuality is reprehensi­ ble' do we really suppose that unpunctuality ought to be ashamed of itself. What we do mean is what is also meant but better expressed by 'Whoever is unpunctual deserves that other people should reprove him for being unpunctual.' " 10 Thus Ryle is arguing here that, whenever we have a sentence that seems to avoid any commitment to individual terms, we "really suppose" that it does, implicitly, have this commitment. But the whole notion of what is "really supposed" by anything is vague. Nor does Ryle give us any good reason for accepting his view that a sentence employing individual terms is somehow "better expressed" than one that does not. Ryle takes the sentence "Colour involves extension" to mean "Whatever is coloured is extended." 1 1 But "Colour involves extension" can be formalized as "(F)(CF ::J EF)," and Ryle gives us no good reason for believing this formalization is not to be preferred to "(x)(Cx::J Ex)." Similarly, Quine seems to think that (3F) and (F) are not to be read in a way corresponding to (3 x) and (x), since general terms "do not purport to name at all." 1 2 That is, quantifying with general terms is not permitted, since they do not name any entities or take any names as their substituends. I cannot say 'There is a paleness" and expect to be understood as alluding to some entity. On the other hand, individual terms do name entities and do take names as their substituends. But this kind of argument begs the question, since it presumes that general terms, a priori, cannot name. It may well be true that, if a term does not name, then quantification is not applicable to it. If "F is G" is asserted and if F does not name an entity, then clearly one cannot go on to state that something is G. But who assumes that general terms are incapable of naming? Under other linguistic conditions, it could be perfectly appropriate to say "There is a paleness that some person has," just as under present linguistic conditions it is appropriate to say "There is a person who is pale." What Quine does is implicitly stipulate that general terms are not names and, therefore, not open to quantificational proce­ dures. However, stipulations are not arguments. Quine, like Ryle, has not shown why quantifying over predicate terms is not just as legitimate a logical activity as quantifying over individual terms, why sentences such as "Colour in1 0. Gilbert Ry le, "Systematically Misleading Expressions," in Logic and Language, ed. Anthony Flew (London: Basil Blackwell, Oxford, 1951), 1st ser. , p. 23. 1 1 . Ryle , ibid. 12 . W V Quine, Methods of Logic, (New York: Holt, 1 972), 3d ed. , p. 2 1 8.

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valves extension·· are more legitimately symbolized with individual rather than predicate variables. 1 ' Thus it is not quite clear why sentences that apparently contain only predicate designators are better expressed as sentences that have both predicate and individ­ ual designators. Why should a sentence that is easily formalizable without the introduction of individual variables be preferably formalized with the introduc­ tion of such variables? Specifically, what is required is some argument showing that between two given interpretations of a sentence-one that does and one that does not employ individual variables-the former is more correct than the latter. Can such an argument be given? Can it be shown that a sentence, S 1 , consisting solely of predicate terms as designators, is not merely alternatively expressible as a sentence, S:, consisting of both predicate and individual terms, but that S2 is in some logical sense "more correct" than S 1 ? I think that such an argument can be given, and it might be initiated by first indicating that the expression of ( 5) as (6) immediately involves paradox. For, if (6) is to be regarded as a correctly interpreted formula, then a distinction must be made between different types and levels of predicates. Otherwise B can itself be­ come a substituend for F and, thus, BB would become a well-formed formula of C. But, as is well known, unless some steps are taken to avoid self-referential predication, Russell's antinomy of impredicables appears. Thus there is a defect in (6). W hat must be done is to apply some theory of types-Russell's or perhaps Quine's more simplified NF system 1 4-to C so that (6) can occur only if its predi­ cates are stratified. Thus, technically, ( 5) must be symbolized as But, now, how is type theory to be understood here? There are two usual kinds of type theory that will avoid Russell's paradox. The first kind-which we shall call T0-has objects as its primary, that is, zero, level; properties that are predi­ cated of objects on its first level; properties that are predicated of properties of objects on its second level; and so forth. On this view all properties are intimately tied to the zero level of objects. In other words, the expression "a property of a property" is allowable only if it is taken to mean "a property of a property of an object." Whatever level of property is being used, it must entail, by the very fact 13. Actually Quine does permit predicate quantification. But this is done only to accommodate certain problems in set theory and also to give a more formal definition to identity and the ancestor relation. Ordinary descriptive sentences, however, are for the most part taken by Quine to be more appropriately formulated by means of individual variables. 14. From a Logical Point of View, ch. 5. Quine does not accept the theory of ty pes. But at least one formula, namely, that one such as BB, must be stratified, that is, formed in terms of levels, if Russell's paradox is to be avoided.

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that T has been stipulated as the type theory of the language, a reference to a property that modifies an object. This does not mean that every statement com­ mits us to the existence of an object. When we define a property F as a property of objects, we are defining and not predicating that property. We are indicating the kind of property that is being employed, and, of course, this does not entail that there exists an object to which the property is applicable. But when we predi­ cate this property of something, then type theory commits us to predication that must eventuaHy be of a property of an object. Thus (3) ought not to be stated in the manner of ( 5), but rather in the manner of 0

(8) A]] black properties of things are more beautiful than aH white properties of things. Then (8) is symbolizable as (9) (F n )(xJ( (B n+ I F n · F nx J ( CJ ( yJ( (W n + lc n - C n YJ ::> (M n + I F nCJ )). Formula (9) makes explicit what is implicit in (7), namely, that a predicate term is always to be used in relation to an (eventual) connection with individual terms-in this case the individual variable. This does not mean that we always unpack what is implicit in a sentence. Mathematicians do not constantly refer to Peano's axioms and to some theory of sets when they use numbers, even though the proper use of numbers commits them to Peano's axioms and sets. Formula (7) is correct as it stands as long as we are aware of what it means to unpack each of the predicates and to show all its commitments in terms of the type theory in­ volved . In other words, we assume that entities are stratified into types, where the lowest type is of individuals, the next of properties of individuals, the next of properties of properties of individuals, and so forth. All predicates attach to indi­ viduals or to other predicates that are definable in terms of predicates attachable to individuals. As to this first interpretation of type theory, both Ryle and Quine are correct. Formulas consisting solely of predicate terms are better expressed as formulas consisting of both predicate and individual terms. Even more impor­ tant is the fact that it is not a question of whether one sentence is a better for­ mulation than another. Since the zero level of type theory is made up of objects, all formulas with predicate terms must finaHy reduce to formulas consisting of predicate and individual terms. Even where we deal with nu]] entities or proper­ ties that are unpredicated, we first predicate a property of an object and then introduce negation, that is, - (3 x)F x. Is it necessary to interpret type theory in this way? Russell's paradox can be resolved even if there is no zero level of objects. All that is required to avoid the formulation BB is to attribute a level to every property and then to stipulate that no property of a given level can be predicated of a property of the same level. Thus B2 B 1 would be allowable, but not B 1 B 1 • The paradox would not occur, and,

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at the same time, no level of objects would be required. With this kind of type theory-which we shall call T,, - (7) would be a proper analysis of ( 5). A formula with only predicate terms would be just as well formed as one with both predicate and individual terms. However, T P is not satisfactory. First, the question arises as to whether or not a basic level of properties must be assumed here, just as in T,, a basic level of ob­ jects is required. Let us assume there is such a level. How are such properties to be distinguished from all others? In the case of T the distinction is clear; there is a built-in specification that two kinds of entities are in the domain, objects and properties . But in T P all levels are made up of properties. There is no unique distinction. How then are basic properties to be identified? It might be argued that a property can be said to be basic if it is definable of other properties but if no other property defines it. Thus some philosophers speak of the designata of "blue," "loud," "hot," "sweet," and other such predicates as elementary, in the sense that they designate that set of properties that is used to define all other prop­ erties. Let us assume that there are such basic properties. Then this means that all other properties are definable by reference to these basic ones. But, if basic properties are such that they define all other properties, then it can be easily shown that Russell's paradox cannot be avoided. For consider any formula B n + t B n . Since all predicates are definable by means of elementary predicates des­ ignating basic properties, B n + 1 must reduce to B11 • C 0 . . . N 0 • Similarly, B n must re­ duce to some set of basic properties, 00 • P 0 . . . Z0 . Both B n + 1 and B n would be ab­ breviations of or reducible to some set of elementary predicates, and this would result in Russell's paradox . For the significance of any type theory is that the function and the variable cannot be of the same level. Thus not only B0 B0 , but also B0C 0 , C 0 D0 , are not permissible. In other words, if both the function and the variable in B n + t B n consist of basic predicates, then they are both on the same type level, and the Russell antinomy is reinstated. We can avoid the paradox if we do not think of higher-level properties as de­ finable by basic ones. We can simply select one set of properties-perhaps those that are usually designated by the observation predicates "hot," "cold," "heavy," and so forth-and stipulate that they are properties out of which all other proper­ ties are constructed. Definition is not involved. Now we must ask whether it is sensible to speak of properties of which it cannot be the case that we can predi­ cate a property of them. Of course, of any property we can always predicate self­ identity. (But care must be taken to bar the statement of identity as simply FF, for example, " Red has the property of being red," since this would reinstate Russell's paradox . ) And, if analyticity is attributable to predicates, then any analytic predi­ cate, for example, F v F, can be predicated of a property. Furthermore, if we are to understand properties in the way we normally do, of any property we can al­ ways predicate another property. Being hot can be painful or stimulating or un0

,

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comfortable or red. We can ref u se to permit such predication, but only at the price of constructing a language that has no application to a major area of em­ pirical data. It would be as if we constructed a logic that could not accommodate set theory or did not include polyadic predicates. Finally, if we have learned any­ thing at all from Wittgenstein and from contemporary linguists, it is that words are not separate entities capable of being understood without regard to their con­ nection to other words and to various physical and behavioral conditions. No expression stands alone. Thus "predicate" and "property" are not simple words requiring no further explanation. We use these expressions with the sense of "being a predicate of ----" and "being a property of ----," where the blanks must eventually be fil led in by something other than another predicate or another property. We do not expect a property to occur without there being a thing of which the property is a property. In the same way, we do not expect the state of matrimony to occur without people. Thus, if the language we construct is not analytic and if it is to be used for human communication , then "predicate" and "property" must retain at least some of the basic connections that are normally attributed to them . Predicates must, so to speak, act like predicates . Thus it would seem that it is not sensible to speak of a basic property, one that is only predicable of other predicates and of which nothing else is predicable. But now consider that there are no basic properties. Then every property has some property and is also a property of some property. This then results in an infinite regress of properties. But infinite regresses have a philosophical history of nonrespectability. First, there is the intuitive objection that calling something a property ought to mean that it is predicable of some thing, that is, of something that is not itself a property. Or, if we insist, d la Gertrude Stein, upon speaking of properties of properties of properties, and so forth, then it is presupposed that such properties are meaningful if the series can end by being attributed to some­ thing that is not a property. Second, in terms of actual linguistic usage, it is not at all clear what it can mean to speak of a world consisting only of properties. We cannot pick up a property in the way we would pick up an object. We can not investigate blue, although we might very well investigate the blueness of an ob­ ject. We can speak of the blue sky, but here we attribute a property to something called "the sky," which designates an area or a region or an atmosphere that is not simply another property. Thus it seems difficult to believe that we can go on in­ definitely predicating properties of properties. Still , Quine has maintained that we can speak of classes and only classes. Individuals are simply identified as unit classes. Thus, if it is intelligible to speak of a domain of classes and since classes are translatable into properties, it is also intelligible to speak of a domain of properties. There are no individuals in this domain. But can such a language be other than a mathematical one? Can there be a language that is applica-

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ble to empirical data and that does not have a comm itment to individuals? Ex­ planation in terms of ind ividuals rather than abstract classes still leads the field in every physical and social science. We can begrudgingly admit abstract classes into scientific theory, but we do not thereby el iminate the need for admitting ind ividuals. Furthermore, a unit class is regarded as a special class. It is not a special class in the ordinary sense that it contains one and only one subset. If one says that all and only men are rational , then "rational beings" could be said to be the sole subset of the class of men . But the class of men is not, therefore, a unit class . To explain a unit class we must speak of a class that is identical to or has as a sole member an individual. The fact that a unit class replaces a unit, an i ndi­ vidual , identifies what a unit class is. There is no other way of explaining the function of a unit class in a formal system of classes. Thus the very explanation of a unit class requires the introduction of the notion of an individual . The purely formal istic system need only have a reference to classes. But, if it requires marking one class as a unit class, then the interpretation will require reference to individuals. Finally, if there are no basic properties or individuals, then a problem arises as to whether a truth val ue can be attached to any of our formulas. Given F"F"_ 1 , a necessary condition for the truth of this formula is that F n - , be predicable of some property. In other words, F n F n - 1 can be given a truth value only if F n - l F n - 2 can be given a truth val ue . But F n _ , F n -2 can be given a truth value only if F n - Z F n - 3 can be given a truth value. Similarly, the truth val ue that can be given to F"_ 2 F"_ 3 rests upon the truth val ue that can be attributed to F"_ 3 F"_ 4 , and so forth . But, since the series never ends, there is no way of ever determi ning the truth value of f

nf n - 1 '

Then TP i s not to be regarded as a n alternative way of interpreting a formal syste m . Perhaps a language that deals only with properties or classes, or with both , can be adequate to show the logical form of mathematical statements (al­ though even here a problem arises in the use of the truth predicate). But, if we expect the language to be used for the formalization of scientific and empirical statements, then it is unsatisfactory. Thus, even though a system permits predi­ cate quantification , it cannot eliminate the need for individual variables and constants . The appropriate translation of ( 3 ) is (9).

II If T with its commitment to objects and properties, is the kind of type theory required for an interpretation of C, we can now ask the following i mportant question: what kind of consequences of an ontological sort arise from the accep0

,

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tance of T/ Are there any philosophical problems in the acceptance of a domain consisting of objects having properties? Before these questions can be answered, one final problem in regard to T0 must be examined. Type theory, both T0 and Tp, has been considered in terms of objects and prop­ erties. Although this presumes that type theory is constructible primarily by refer­ ence to some existent domain of nonlinguistic entities, it is possible to think of type theory strictly in terms of linguistic entities. Thus the zero level consists of names, not of objects; the first level, of predicates, not of properties or classes; and so forth. Let us call such a type theory T". Both T" and T0 can be thought of as indicative of different uses of variables. T" states that only names can replace the individual variable. On the other hand, T0 states that nothing need replace the individual variable, since the variable represents a claim that there is an ele­ ment of a given domain. Thus, in T", (3 x)F x is true if and only if there is a name • in T" such that its replacement of x makes (3 x)F x true. On the other hand, in T 0 (3 x)F x is true if and only if there is an object in the domain of T0 such that F is applicable to or true of that object. Even without more formal arguments, it is easy to see why the obiectual inter­ pretation that T0 gives to a language has more crucial ontological consequences than the substitutional interpretation given by T". 1 5 T0 has a domain of entities that can be said to be independent of whether or not there are any linguistic terms that designate them. There are unspecifiable, that is, unnameable, real numbers, even if they are unspecifiable. On the other hand, the domain of T" is determined by the linguistic terms that can replace the variable. If there is no name for an object, then there is no such object. Thus T" would seem to make fewer ontological commitments than T0 would. T" could not countenance non­ denumerable unnamed real numbers or unnamed soldiers or Santayana's un­ enacted essences. T0 makes it at least logically possible to admit such entities. They are not a priori ruled out by the formal structure adopted. Thus for those who would like to deny that a formal language requires any commitment to some specific extralinguistic domain, T" is a much more acceptable theory than T0 Unfortunately-at least for those who like their formalized languages unclut­ tered by any serious existential claims-T" cannot replace T0 Quine's sentence ''There are unspecifiable real numbers" is either false or ill­ formed in a language that requires names for its individual variables. If there are no names, then there are no instances; and, if there are no instances, then the quantified sentence must be false. Thus in T" Quine's true sentence would be­ come false. But a more important consideration is that in such a language the theory of descriptions becomes inapplicable. For consider that, following Rus,

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sell's and Quine's proposals, names are el imi nated in favor of descriptions . Then all existential ly quantified sentences in the language must turn out to be false, since, if only names can replace the i ndividual variable and if there no longer are any names, then nothing can ever replace the individual variable. For similar reasons all universally quantified conditionals turn out true, since the antece­ dents of such sentences are always false. Thus, if names are no more than de­ scriptions, Tn is not satisfactory. These objections to T n , however, need not be formidable. The theory of de­ scriptions might be taken in its original primary sense, namely, that it is to be applicable not to all names, but only to those that are vacuous. "Sir Walter Scott" would then remain a name in the language, but "Pegasus" would be changed into "the winged horse of Bellerophon" or into some other uniquely identifying description. The sentences that would turn out to be false would presumably be those that we would want to turn out to be false. But this modification will still not do. Fi rst, we do make true statements with vacuous descriptions. I do not mean those controversial ones that involve fictitious entities such as "The round jolly man who flies through the air with his reindeer during Christmas lives at the North Pole rather than at the South Pole" or "The moody Dane in Shake­ speare's play Hamlet killed Polonius ." But we do say "The murderer of Jones is insane," even though we do not know whether the murderer will ever be found. And we do say "The man who can create cheap energy will be world famous," even though there may never be such a man. Nothing may ever satisfy the de­ scriptions in these sentences, but there are clearly good reasons for taking them to be true. Second, it is important to be aware that names do not create objects. We do not make statements with names in them and then presume that by fiat our names create a world of objects. Sometimes l inguistic philosophers, in their enthusiasm to show the import of language in describing a world, make it seem as if the language we use creates the world we are talking about. Only an extreme sol ipsist would maintain this. Normally, we say that our language describes a world that is at least in some sense there to be described, even if it is no more than a huge cluster of atoms . Our words can make us view the world with certain attitudes and with certain preconceived bel iefs . Perhaps we can even use lan­ guage to describe possible worlds. Our attitudes and bel iefs are about something already there, however, and our possible worlds are extrapolated from the one with which we normally deal . Thus a name, when it is used in other than l iterary and mythological contexts, refers to someone who was given the particular name at some time and place. The person was there to be named; the name was not there to create a person. For this reason the name that does refer does so because there is an object that at some time and at some place was given that name. Unlike the chicken and the egg, in this case it is sensible to maintain that the object comes before the name. T n is really definable by T0 Objects are elements •

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of the domain before they are named. In fact, this is Quine's point, namely, that the use of singular, that is, naming, terms "appeals implicitly to classical or ob­ jectual quantification. " 1 6 And even though Charles Parsons, in his response to Quine, argues that we ought to be able to find purely syntactical characteriza­ tions of singular terms, he is also forced to conclude that such characterizations "would not yield the distinction between singular terms that genuinely refer and those which do not. " 1 7 T11 gives way to T0 There are other reasons for rejecting T". Consider that only names are al!owed to replace the individual variable. Then the interpretation is allowable in a spe­ cific language, namely, the one to which the names belong. Thus, if we wish, for example, to employ universal generalization , we can do so only within a given language or a given set of languages with rules of synonymy that make names of one language synonymous with names of the others. Under these conditions T" produces the same kind of problem in relation to scientific statements that it would in relation to mathematical ones. If T" is used with a mathematical sys­ tem, there is no way of attributing properties to all numbers. We cannot say "every number has a successor," but rather "every number-name in this mathe­ matical system has a successor. " Similarly, scientific generalizations cannot be given in a language operating with T n , since only the names in that language are allowable as substituends for the individual variable. Statements such as "All men are rational" can be given in English, but it does not follow that this state­ ment will hold true in all languages, even though it is obvious that the intent of the statement is for it to hold in all languages. Then T" cannot replace T0 The individual variable must not be regarded as a place holder or as a replacement for some series of names. Its function is to play the role that "it" usually plays in ordinary language. When we say "It is a good chair," the "It" is not an abbreviation for a name. (What could it mean to say that the "It" here serves to replace a name?) The " It" indicates a claim being made on some element of a domain, namely, that the element has a property or set of properties applicable to it. For similar reasons the predicate constant (or variable) must be regarded as indicating a property that, it is being asserted, is applicable to an element of the domain. In brief, in every formal system there is a commit­ ment to some domain with which variables and constants of the system are to be employed. The system is not a mere extrapolation from a natural language. I t does not deal with the names and predicates of a language, but rather with the objects and properties designated by the language. With T0 as the final result of our analysis of types, a previous question can now be raised again: are there significant ontological consequences in the acceptance •

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1 6. Ibid . , p. 1 06. 1 7. Charles Parsons, "A Plea for Substitutional Quantification," The fou rnal of Philosophy 68 ( 1 97 1 ): 2 3 3 .

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of T] There obviously are such consequences, since many philosophers and log­ icians have sought to show that, even though T,, may not be acceptable, a T0 requiring a domain of both objects and properties is not the only alternative. Thus, as we have seen, Wittgenstein sought to show that only objects have exis­ tence; properties are mere arrangements of these objects. Quine also at one time argued that the only domain needed for the ordinary functional calculus is one consisting solely of individuals. Quine argues that the domain to be posited is that one that is required in order to permit values for the quantified variable. But since, ordinarily, only the individual variable is quantified, only the objects which become the values of the variable are the elements of the domain . What, then, becomes of predicate terms? Since these are to be regarded as general terms-at least whenever there is no need for classes-they are not predicate variables and, therefore, no quantification occurs with them, and neither proper­ ties nor classes are elements of the domain. For Quine only individuals are re­ garded as an ontological commitment . W hat is the status of the predicate term? What, if anything, does it designate? Quine tells us that there are individuals, since these are the values needed by existential quantification of the individual variable . Nothing else need be posited in the domain, however, since nothing else is quantified except individual vari­ ables. But it surely seems to be necessary to say something more about predicate terms . They are neither logical nor syntactical expressions, and, therefore, they would seem to be descriptive terms in some sense. We shall see in chapter 6 that Quine's notion of the function of a predicate is simply not satisfactory. It cannot account for the most important functions of a predicate, namely, to indicate the similarity of two individuals or to show the sameness of properties.

5 Linguistic and Traditional Ontology I n a language having as a framework a calculus in which quantifiers play a role, we can presumably quite clearly explicate what is intended by the view that there are ontological commitments. If we follow Quine we simply indicate the values that are allowable for various variables. Thus, if quantification is restricted to the individual variable, then we are committed ontologically only to individuals, that is, those entities of a given domain that are usually taken to be entities not predicable of anything else. This does not mean that they are nonpredicable in some absolute sense. They are neither Aristotelian substances nor Leibnizian monads nor Wittgensteinian simple objects that are the final eternal irreducible objects to which everything else is reducible. We select, by means of some ar­ bitrarily selected sortal universal, some given domain of entities and simply stip­ ulate that everything is predicable of them but that they are not predicable of anything else. We can say "Something is happy," where, because of our prior commitment to a domain of entities characterized as human beings, we mean "Some human being is happy," but we cannot say "Something is a human being," where "human being" operates as a predicate. Of course, in another in­ terpretation, in which another domain of entities is distinguished by some other sortal characteristic, "human being" could very well be a predicate. We might ask whether a domain must always be stipulated. It would seem that this is required; otherwise how are we to determine the truth or falsity of some existentially quantified sentence. It is only because we can say that, for example, (3 x)Fx is satisfiable by some identifiable entity, for example, a human being, that this sentence is true, whereas it would be false if no identifiable object could be supplied. Thus it is because we can identify a human being that we can then go on to ask whether F is applicable to him. And for a similar reason a free logic

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i s not really free from existential presuppositions. Its free constants require an existential premise-the positi ng of a domain of entities- in order to give a truth value of true to those sentences whose constants arc not vacuous. A further question might involve the need to posit some arbitrarily selected sortal un iversal in order to obtain a domain of entities. W hy do we introduce "human being" as a way of specifyi ng a domain of entities? Why not have "hu­ man bei ng" as a predicate applicable or inapplicable to any entity whatsoever? In this way a primary sortal universal expression need not be introduced at all, and ( 3 x)( x is a human bei ng) would be as legitimate a sentence as (3 x)Fx. However, this procedure would cause difficulties in obtaining a truth value for a truth func­ tion. W hen we want to say F is true of x, we mean F is true of this, that, or the other object denoted by this, that, or the other constant. In other words, we want to say that F is true of some object in a domain. Which domain is it? In a un i­ verse in which there can be an infin ite number of domains, "F is true of an ob­ ject" is false if the domain is one in which F is not applicable, for example, if F is "humorous" and if the domain is not one of human beings. Thus the domain is never one of objects. There is no solitary this or solitary that; there is always this human being or that rock. In the language of the tradition, bare particulars do not exist. If we quantify only over the individual variable and not over the predicate vari­ able, then it is often assumed that we make no commitments to another type of entity besides those of the individual variable . We can simply, in the manner of Quine, treat predicates as terms that may or may not be true of some entity, that is, that are or are not applicable to some entity. Of course, we might decide to quantify over the predicate; then we are committed ontologically to a type of en­ tity different from i ndividuals but of which individuals partake or become mem­ bers. In this way we begin to add to the components of the domain what are commonly known as properties or classes, that is, entities that are predicable of-although Platonists might wish to add that they need not actually be predi­ cable of-other entities. We might also quantify over propositional variables and thus find that the domain of the language now also includes propositions as well as classes, properties, and individuals. Those with a Quin ian love for bare, lonely landscapes might recoil at this sudden population explosion. But in any event, as far as the ontology of the language is concerned, it is quantification that does the trick. If we follow Carnap, ontology also receives a clear explication when it is re­ lated to a purely formal language. For him the ontology is to be defined not so much in terms of quantification, but in terms of the l inguistic categories that must be posited in the construction of the language . Every formal language con­ sists of a metalanguage that stipulates a given syntactic and semantic framework for an object language-that is, it gives an interpretation to an otherwise un-

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defined series of written (or spoken) marks. It stipulates that certain marks are to be regarded as individual variables and that these variables are to take physical, phenomenal, or other kinds of objects as values, whereas other marks are to be regarded as predicate variables that are to take physical, phenomenal, or other kinds of properties as values. This stipulation tells us what our ontology is, since it indicates that in every well-formed sentence there must be terms designating objects of a given sort and others designating properties of those objects, so that our minimum commitment will be at least to a universe of certain kinds of ob­ jects and properties. Carnap, however, does not believe that a commitment to properties is of great consequence. It does not, he believes, lead to a belief in universals or to controversy involving the traditional Platonic one of how there can be an identical item in more than one place. The claim is not important, according to Carnap, because he is not treating properties as metaphysical en­ tities, but simply as "something physical that things have, a side or aspect or component or character of the things. " 1 Still, whatever properties are for Car­ nap, it is difficult to see how he can avoid a commitment to universals. Properties can presumably be said to be the same or different. But how is one to speak of the same property in a formal language? We should probably translate "Some object has different properties" as (3 x)(Px. Gx). It is the quantifying of the individual variable that guarantees the identity of any value substituted for " x" in both in­ stances. Without the quantification there could be no assurance that we are speaking of the same object. Now, assuming that predicates designate properties, how are we to define identity of properties? Is "There are two objects that have the same property" to be translated as (3 x)(3 y)(Fx. F y. x :f:: y)? The translation is usually made in this way: we take "F" to be a predicate constant, so that "F" designates the same property or has the same extension in every (extensional) context. No quantification of "F" is required; no notion of a universal or of a class need be introduced. But consider two objects that have some property or other in common. We are not saying what properly it is, so that, if we use the letter "F" here, it must be as a predicate variable and not as a predicate constant. Hence 'There are two objects with some property or other in common" would be stated as (3 x)(3 y)(3 F)(F x. F y. x :,= y). If we wish to show that we are dealing with some property or other that "x" and " y " have in common, then we are required to introduce a new quantifier, (3 F), that binds both "F's," just as the quantifier with "x" and " y " binds any "x" or any " y " under its scope. But binding the prop­ erties in this way means that we have obligated ourselves to the existence of an entity that inhabits two places or that exists as identical in two separate entities. In brief, if we take predicates as designators and if we wish to speak of some prop­ erty that objects may have in common, then we cannot escape requiring prediI. R. Carnap, Meaning and Necessity (Chicago: Univ. of Chicago Pr., 1956), 2d ed., p. 20.

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cate quantification. But, because predicate quantification means positing a uni­ versal, it is a serious matter to accept the notion of a common property. It means that we have given formal justification for the existence of universals. It might be noted that, if we were to think of type theory conceptually in the way Quine once suggested or as excluding empty domains in the way William Kneale and others suggested, 2 then type theory can become a way of distinguish­ ing a Platonic from an Aristotelian position. Following Quine we can think of a language, L 0 that consists of concrete objects that are the values of the bound individual variable of the usual theory of quantification. Now, we can reify classes by simply limiting classes in such a way that membership in any of them is equivalent to some condition expressible in L,,. Thus any predicate term is ac­ ceptable only insofar as it can be shown to be a predicate relating to the concrete objects of L 0 The property of a property or the class of classes is expressible as (1 F i )F 2 F 1 , where F 1 is defined as the property of an object. The null class, that is, the class that has no members, is not expressible in L0 No membership-no class. If we regard type theory in this way, that is, not permitting a null class or a domain without entities, then the formula (3 F )( x ) - Fx, which is logically true in Russell's system, becomes simply ill-formed. A Platonist would accept Russell's formulation and reject L0 since it posits universals that need not have instances. An Aristotelian, on the other hand, would accept L0 and reject Russell's version, since the former does not permit universals that do not have instances. Carnap does attempt a final solution to the difficulties concerning properties by showing that they are eliminable in favor of what he calls "neutral entities," and we will examine this solution shortly. But the main point to keep in mind here is that, according to Carnap, our ontology is derivative from the way we interpret a formal system, and this in turn depends on how effectively the resul­ tant language can deal with the logical, mathematical, and scientific statements that we want it to incorporate. For example, a language that could not deal effec­ tively with Russell's paradox would be less adequate in delineating our ontologi­ cal commitments than one that could. We construct languages, Carnap argues, in terms of their fruitfulness, their simplicity, and their efficiency in accom­ modating scientific inference and logical coherence. Our ontology is a relative matter. We inherit the physical-thing- physical-property language, and while we use this language we are committed to a certain view of the universe. But its use is always dependent on its success. As Carnap puts it, "The acceptance or rejec­ tion of abstract linguistic forms, just as the acceptance or rejection of any other linguistic forms in any branch of science, will finally be decided by their effi,

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2. Cf. W V Quine, From a Logical Point of View (New York: Harper, 1963), 2d ed. rev. , pp. 123- 29; William and Martha Knealc, The Developmen t of Logic (Oxford: Clarendon Press, 1962), pp. 706-7; Alex Orenstein, Existence and the Particular Quan tifier (Philadelphia: Temple Univ. Pr. , 1978 ), pp. 64-66.

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ciency as instruments, the ratio of the results achieved to the amount and com­ plexity of the efforts required." 3 Furthermore, we need not really worry about any serious ontological commitment by our use of property language, since it is al­ ways possible to formulate a language that requires neither properties nor classes, so that whatever questions they have usually engendered can be completely avoided. Reference to properties and classes and to other nonindividual entities may be no more than mere "manners of speaking." 4 We can, for example, elimi­ nate all class and property references, so that the linguistic mark "H" is said to designate the neutral entity, Human, rather than the class or property Human. 5 Similarly, a linguistic mark "S" can be said simply to designate the neutral entity Sir Walter Scott. If we wish to distinguish the extension from the intension of a term, it is no longer necessary to introduce two kinds of objects, a class for the extension and a property for the intension; we rely on what Carnap calls "Desig­ nation" and "Logical designation." Thus " 'H' logically designates Human" is the translation of "The intension of 'H' is the property Human," and " 'H' designates Human" is the translation of "The extension of 'H' is the class Human." Since, for Carnap, logical designation, like logical equivalence, is due to the semantical rules of the language, no entity-neutral or otherwise-is required to be posited for such a designation. 'H' logically designates Human in the sense that "H" stands for "Human" is postulated by the rules of the language. On the other hand, " 'H' designates Human" is a statement relating to an extralinguistic entity, a neutral entity, as Carnap calls it. Thus Carnap thought that all reference to properties and classes could be eliminated. Unfortunately, Carnap's reductionism is not satisfactory. First, it is not clear how set theory, or the theory of classes, would fit into such a language. If sen­ tences are no longer to be analyzed in terms of class membership, then it is not clear how the logical techniques of class theory are to become applicable. More important, Carnap's reductionism apparently leads to a form of sentence ambi­ guity that cannot be eliminated. We want to be able to distinguish a well-formed sentence such as "Sir Walter Scott is human" from an ill-formed sentence such as "Human is Sir Walter Scott." It is Scott that is human, not the converse. But, since, according to Carnap, both "Human" and "Sir Walter Scott" designate neutral entities, neither expression has some priority by virtue of which it is the subject of the sentence. Being human is not a property of Sir Walter Scott, since human is simply another neutral entity no different in type or category from any other neutral entity. Nor could there be a difference, since a difference would rest on an assumption that entity A has some characteristic or property lacking in 3 . Carnap, Meaning and Necessity, p. 22 1 . 4. Ibid . , p. 1 4 5 . 5 . Ibid . , p. 1 59.

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entity B. In other words, if "property of" and "is a member of the class of " are not allowable phrases in defining what a sentence is, then we have no way of distin­ guishing a mere group of words from any but a select few of meaningful sen­ tences. Unless, in a domain, a distinction can be made between one entity and another that is not a mere spatial or temporal distinction, sentences about that domain will be restricted either to pure identity sentences or to sentences desig­ nating space-time coordinate relationships among entities. Carnap may have been aware of some of these problems, for apparently his last word on these mat­ ters equates neutral entities with intensions. 6 But on Carnap's own analysis inten­ sions of predicate terms are properties. The commitment to properties remains intact. How much can be effectively eliminated from a domain is an important issue, and, if Carnap's reductionism could be shown to be feasible, it would have se­ rious consequences for philosophic inquiry. In the remainder of this chapter and in the next, I should like to ask the more fundamental question: how satisfactory is a criterion for ontology that rests strictly on the variables of quantification and the linguistic framework? Has the linguistic criterion-as it is used by Quine and Carnap especially-really given us a way of erasing or perhaps finally solving some, if not all, the traditional issues of ontology? W hat is often taken to be one of the important consequences of the linguistic approach to ontology is the following: in tying ontology into a formal context, many of the more traditional systems of metaphysics are shown to be innocuous, since either their statements are not translatable into a formal language, and thus unable to withstand close and precise scrutiny, or their statements are translata­ ble, but then shown to be either ordinary empirical statements or statements about syntax. 7 Thus Carnap rejects as meaningless the important metaphysical statement of Heidegger, "The Nothing nothings." The sentence confuses logical with descriptive terminology. It mistakes quantifiers for subjects and verbs, and violates rules of language formation. 8 It treats "Nothing" as if it were a noun, 6. See the discussion by Donald Davidson, "The Method of Extension and Intension," in The Philosophy of Rudolph C arnap, ed. Paul Arthur Schilpp (LaSalle, IL: Open Court, 1 963), pp. 3 3 3-34. 7. For Carnap's attempt to show how metaphysical statements are very often no more than state­ ments about syntax, see his The Logical Syntax of Language (London: Routledge and Kegan Paul, 1937), pt. 5. Carnap later argued that not all metaphysical statements are syntactical; some are empirically testable statements. See Carnap's reply to Karl R. Popper in The Philosophy of Rudolph C arnap, ed. Schilpp, pp. 877-79. 8. R. Carnap, "The Elimination of Metaphysics Through Logical Analysis of Language," in Log­ ical Positivism, ed. A. J. Ayer (New York: Free Press, 1 959), pp. 69-73. Carnap would probably have directed the same charge against Sartre, who also treats "Nothing" and "Nothingness" as if they were proper names. See Jean-Paul Sartre, Being and Nothingness, trans. Hazel E. Barnes (New York: Phil­ osophical Library, 1956), p. 23.

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when an examination of the logic of the language would show that "Nothing" is a quantificational, not a descriptive, term. Carnap's point is reinforced by an ar­ gument given by Quine. If "Nothing" were a noun, then "Nothing is identical to everything" ought to be equivalent to "Everything is identical to Nothing," just as "Sir Walter Scott is identical to the author of Waverly" is equivalent to "The author of Waverly is identical to Sir Walter Scott." But, whereas "Nothing is identical to everything" is true and is formulated as - (3 x)( y)( x = y ) , on the other hand, "Everything is identical to nothing" is false (since everything is always at least identical to itself) and is formulated as (x) - (3 y)( x = y ) . 9 Thus a metaphysi­ cal concern with "Nothing" merely reflects an ignorance of the logic of the par­ ticular language. Undoubtedly, Carnap would also have found a great deal wrong with Heidegger's statement 'The Absoluteness of the Absolute-an absolution that being absolvent absolves itself-is the labour of unconditional self-certainty grasping itself." 1 0 In a similar vein Carnap asserts that a lack of awareness of the logical dif­ ferences among predicates leads us to attribute the same use to all of them. We think, for example, that, because most of the predicates we use can be taken to designate properties, therefore every expression that fits into the predicate space of a sentence must designate some property or other. This is incorrect. Consider the sentence "a is soluble." Since "soluble" is in the predicate position, we look for some property for it to designate. Since no overt property is to be found in the way that the property of being red or of having a certain size might be found, however, we posit an invisible property of some sort, a dispositional property sometimes regarded as a power or a potency or an essence or some other such metaphysical entity. Again, according to Carnap, the introduction of a meta­ physical entity arises because of ignorance of the logical function of so-called dispositional predicates. In many-perhaps in most-instances predicates are used to designate a specific overt property, and in such cases the meaning is. so to speak, closed or fixed insofar as the given context is concerned. At other times the predicate serves in an open-ended way so that its meaning is always under­ determined by any given set of data. Dispositional predicates are of this sort. They are introduced as a way of indicating that the most crucial designative terms of science are never immune to meaning revision. They permit meaning modification in the light of future evidence. It is for this reason that dispositional predicates are introduced by means of conditional rather than ostensive sen­ tences. When we say " a is soluble," we explain what we mean by stating what would occur if certain circumstances were to arise-if, for example, I were to place a in water. We do not pick up a and show it as we should if we wished to 9. W V Quine, Methods of Logic (New York: Holt, l 972 ), 3d ed., pp. l l 2- l 4, 1 4 1 -42. 1 0. Martin Heidegger, Hegel's C oncept of Experience (New York: Harper, 1 970), p. 44.

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explain what we meant by " a is a book. " The conditional sentence is basic to the explanation of dispositional predicates. But it is the counterfactual kind of condi­ tional that seems to be needed here, and this apparently leads to all the well­ known difficulties of this kind of conditional. 1 1 To avoid these difficulties Carnap introduces the method of reduction. Affinities, dispositions, and attractions are translatable into a series of special empirical statements that Carnap calls reduc­ tion statements, 1 2 statements that attribute a reaction or response of an object only under tested empirical conditions. To say "a is soluble," for example, is not to be attributing some special power or underlying affinity to a; it is to state a reaction of a under certain experimental conditions. We mean no more than "if a is placed in liquid H, then a is soluble if and only if a dissolves. " "Soluble" here is not being explicitly defined, since the term appears as a member of the biconditional. It is implicitly defined in that it appears only with the stated condi­ tions for its application. Thus those expressions that presumably lead to ontologi­ cal claims about essences, and so forth, are all dispositional terms that can be explicated without serious ontological commitment by the use of reduction sentences. Nor ought we to be led, in Carnap's view, to any issues involving substances, particulars, or things . Following W ittgenstein, Carnap rejects the reference to things as the introduction of a metaphysical problem. Talk about things is not talk about objects. "That is a coat and it is a thing" is not to be equated with the sentence of the same (outward) form "That is a coat and it is a mackintosh. " Something might be a coat and not be a mackintosh. But there would be some­ thing wrong in saying something is a coat and yet it is not a thing. Saying that the coat is a thing is not to make a descriptive statement about a coat, but rather to categorize the grammatical status of the term designating the coat. Only in a natural language do we constantly confuse syntax with semantics and thus mis­ take references to words as references to objects. "The coat is a thing" looks as if it ought to be equated with a sentence of the form "The coat is a mackintosh. " But, whereas the latter is a perfectly legitimate descriptive sentence, the former is a confused way of saying " 'The coat' is a thing-word" or " 'The coat' is a definite description. " In Carnap's terminology we have mistakenly taken a pseudo object sentence to be a genuine object sentence. In a similar way "There are universals" is a pseudo object sentence. We cannot say "There are universals" in the same 11. Perhaps the best summary of the various problems relating to the counterfactual conditional is to be found in Nelson Goodman, Fact, Fiction and Forecast (New York: Bobbs-Merrill, 1965). 12. R. Carnap, "Testability and Meaning," in Readings in the Philosophy of Science,- ed. H. Feig] and May Brodbeck (New York: Appleton, 1953), pp. 58-60. The view that dispositional predicates serve to incorporate continuing research is also expressed by C. G. Hempel, Fu nda men tals of Con­ cept Formation (Chicago: Univ. of Chicago Pr., 1952), pp. 23-29. See also the general discussion and criticism of the view in I. Scheffler, Anatom y of Inqu iry (New York: Knopf, 1963), pp. 174-76.

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way that we might say "There are dogs. " A reference to a universal is really a reference to the corresponding syntactical word "predicate. " Relations undergo similar analysis. "Some relations belong to the primitive data" ought, on Car­ nap's view, to be translated into "Some two- (or more) termed predicates belong to the undefined descriptive primitive symbols. " n Carnap bel ieved that most, if not all, metaphysical statements could be shown to be confusions of syntactical with semant ical matter� and that, once we disentangle these elements by show­ ing their roles in a formal language, we would be led to a disavowal of metaphys­ ics as a discipl ine deal ing with something in experience or in reality. We might make the same point differently by thinking of sentences in terms of W ittgenstein's analysis in the Tractatus. If the logical connectors are to be ex­ plained satisfactorily, then we must take them to be functioning with certain kinds of l inguistic structures that are formed in a certain way and to which true or false is applicable. For this reason W ittgenstein bel ieved that every sentence that purports to be uti lizable within a logical framework-within what W ittgenstein called logical space-must be translatable into a formal language, primarily a truth-functional language. But how would one state "There are things" or "There are properties" in a formal language, at least in the formal language en­ visaged by W ittgenstein? W ittgenstein held that "in order for a proposition to be capable of being true it must also be capable of being false. " I ➔ But what truth value can be attributed to "There are no things" or to 'There are no properties"? The first is self-contradictory and therefore incapable of being true, since its for­ mal ization would be "It is false there is something that is a thing, " and the sec­ ond leads to the absurd consequence of objects without properties or, i n W itt­ genstein's view, of nonarranged objects. Statements about objects or properties, therefore, cannot be formally stated. Formal ism, then, has important implications for traditional ontological issues. But, despite the clarification it has brought to the analysis of language and refer­ ence, it has not been altogether successful i n neutral izing these issues. Consider the notion of "Nothing" again. As we have seen, both Quine and Carnap argue that this expression is to be understood quantificationally. Thus, whereas "Noth­ ing is identical to everything" is formulated as -(3 x)( y)(x = y) and is true, "Every­ thing is identical to nothing" is formulated as (y)-(3x)(x = y) and is false. On the other hand, if "Nothing" and "Everything" were substantives, as Heidegger and other metaphysicians maintain, then both sentences of identity should have the same truth value. Geach, following Russell, 1 5 reinforces the argument for quan­ tification by asking how it is possible for a quantifier to have a referent. Thus, 13. Carnap, The Logical Syntax of Language, p. 300. 14. Notebooks 1 9 1 4 - 1 9 1 6, 4.6.15. 15. Bertrand Russell, In troduction to Mathematical Philosophy (London: George Allen, l 920), p. 173. Russell raises the question of how it is possible for "a man" to have a referent.

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Geach argues, "when 'nothing' or 'no man' stands as a grammatical subject, it is ridiculous to ask what it refers to. The phrases 'no men' and 'men alone' arc grammatically formed like 'wise man,' by attaching an adjective to 'men'; but whereas 'wise men' might be said to 'denote' certain men, who definitely form a part of the class of men, this is clearly not true of 'no men' or 'men alone.' " ,r, For contemporary logicians and formalists, Geach concludes, "all," "some," and "no" will be significant, not as prefixes to single terms, but as "parts of logical frameworks." But several questions can be raised here. First, not all logicians or mathemati­ cians have held that the quantifiers are purely syntactical and therefore without any designative quality. Keynes, for example, believed that "some men" did refer to some men, and both Boole and Schroeder took "nothing" to refer to the null class. 1 7 More recently Gustave Bergmann has argued that the universal quan­ tifier, "generality" as he calls it, is as much a part of the domain as the individual itself. In being presented with a single square, a, inside a circle, b, the transcrip­ tion of this occurrence should not be simply " a is inside b," but rather " a is inside b, and, if anything else is inside b then it is identical to a," that is, F( a , b ) . ( x)((x = a) v - F( x, b )). Bergmann concludes: ". . . generality is on th is oc­ casion presented to me in connection with the fact F( a , b) . . . . Generality and a chair . . . are two entities very different from each other. But there is no dif­ ference in the way either is presented to us, with an immediacy, as one says, which is not only the mark of ontological status but indeed the ground of all knowing:" 1 8 In other words, Bergmann is asserting that only our bias in favor of physical things makes us think a description of an occurrence must be only in terms of physical entities. If we are perfectly willing to describe an experience by using relational predicates, then we ought also to be willing to admit generality, since it is present with the same degree of immediacy that we attribute to rela­ tions. If "being inside" is an allowable expression for describing a feature of what is experienced, then why do we exclude "a and only a is inside"? Thus on Berg­ mann's account quantification is as much designative as predicate or individual constants. Second, the role of the quantifiers in a formal system has always been difficult to determine. The syntactical marks, such as the logical connectors interpreted 16. P. T Geach, Reference and Generality (Ithaca, NY: Cornell Univ. Pr. , 1962), p. 12. 17. See the discussion of the views of Keynes, Boole, and Schroeder in Geach, Reference, ch. 1. 18. G. Bergmann, Logic and Reality (Madison: Univ. of Wisconsin Pr. , 1964), p. 71. See the discussion of this point by Edwin B. Allaire, "Bergmann's Ontologies," in The On tological Tu rn , ed. M. S. Gram and E. D. Klemke (Iowa City: Univ. of Iowa Pr. , 1974), pp. 54-56. Max Black, who is not at all sy mpathetic to the viewpoint expressed by Bergmann, makes this interesting comment: "Perception of spatial relations, and the emergence of concepts . . . are at least as much to be found in 'experience' as immediate recognition of patches of color" (Caveats and Critiques [Ithaca, NY : Cornell Univ. Pr., 1975], p. 237).

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as "or," "and," and "if . . . then," can be given an explicit truth-functional analy­ sis. Their function as connectors of sentences can be clearly defined despite cer­ tain ambiguities that occasionally accrue to them in natural-language contexts. 1 9 On the other hand, the function of the quantifiers has never been clear. They are sometimes regarded as no more than abbreviations of conjunctions or disjunc­ tions of atomic sentences. They are also regarded as ways of indicating that we are dealing with nonempty domains. But none of these ways of explaining the function of the quantifiers has ever been entirely satisfactory. If the domain is infinite, which we expect of any language incorporating number theory and sen­ tences referring to atoms, then the quantifiers cannot be regarded as mere abbre­ viations of some specific set of conjunctions or disj unctions of atomic sentences. If the domain is finite, then the quantifiers are trivial, serving only as abbrevia­ tory devices. Nor can they be considered as ways of indicating that we are dealing with nonempty domains, since, in the "free logic" systems as well as in the sys­ tem of Lesniewski, the existential operator has no existential import. 2 ° Further­ more, as we have seen in a preceding chapter, calculi are not "born" with their own interpretations. We decide what the marks of the calculus will stand for. That is, (3 x) in the formal calculus is no more than what appears on paper-a set of parentheses with the symbols 3 and x on the inside. We then decide to go on to interpret these marks as an existential quantifier. But what does it mean to call these marks "existential"? Does it mean that the Fx of (3 x)Fx must have at least one true instance if the truth of some group characterized by F is to be true? But then we return to an old question: what is a true instance? Is it Fa, or is it F(tx)Gx? If it is the latter, then we have not succeeded in explaining the function of the quantifier, since the iota operator is itself reducible to a quantified schema. If it is the former, then we must determine what " a" is. Is it a logically proper name in Russell's sense? But then what is the referent of a logically proper name? Is it a sense datum, a physical think, a "this," a "that," a bare particular? If the referent must be an existent rather than a fictitious entity, then surely we must go 19. Thus Strawson argues against the identification of "or," "and," etc., with their alleged coun­ terparts in truth-functional logic; see Introduction to Logical Theory (London: Methuen, 1952), ch. 3. 20. Karel Lambert has been the prime proponent of a "free logic": see "Notes on E!" Philosophi­ cal Studies 9 ( l 958): 60-63; 12 ( l 961): l -15; 13 ( l 962): 51-59; 15 ( l 964): 85-88; "Existential Im­ port Revisited," Notre Dame Journal of Formal Logic 4 (1963): 288-92; idem, "On Logic and Exis­ tence," Notre Dame Journal of Formal Logic 6 (1965): 135-41; idem, with Bas C. van Fraassen, Derivation and C ounterexample (Encino, CA: Dickenson, 1972), chs. 9, 10. For Lcsniewski's view of quantifiers without existential import see his "Czy klasa, nie podporz�dkowany ch sobie, jest pod­ porz�dkowana sobie?" Przeglad Filozofzczny 17 ( 19 14): 63-75, and "Grundztige eines neuen Sy s­ tems der Grundlagen der Mathematik," Fundamenta Mathematicae 14 (1929): l -18. See also the discussion of Lesniewski's sy stem in Guido Kung, Ontology and the Logistic Analysis of Language (Dordrecht, Holland: D. Reidel, 1967), rev. ed., ch. 8.

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on to ask whether we understand what it means for a domain to consist of exis­ ten t entities, since it is then and only then that we can presumably use the exis­ tential quantifier. In other words, a sharp distinction must be drawn between the existential quantifier and an existent entity. The use of the former depends on an understanding of the latter. But then it would no longer be true to say that the meaning of "exists" has been absorbed into the meaning of the existential quantifier. Finally, if we deal with ordinary-language sentences, then the logical rules with which the quantifiers are used seem to be wrong or only partially expressed. Consider the example "No one is in the room." It is expressed in a formal lan­ guage as " I t is false that there is some person in the room." This sentence in turn reduces to " a is not in the room, b is not in the room, c is not in the room, etc. ," where a , b, and c are members of a stipulated domain of persons. But, whereas " No one is in the room" entails " a is not in the room, b is not in the room, c is not in the room, etc. ," the converse does not hold. Only if we can add to the conjunction of sentences "No one else is in the room," do we obtain the desired logical equivalence. If we add "No one else is in the room," then we are caught in an infinite regress, since this sentence also reduces to a conjunction of atomic sentences that must also eventually be conjoined to a quantified sentence assert­ ing that no one else is in the room. Thus, since an infinite conjunction of sen­ tences can never be given a truth value of true, whereas, on the other hand, "No one is in the room" is surely either true or false, it cannot be the case that " No one is in the room" is logically equivalent to " a is not in the room, b is not in the room, c is not in the room, etc." The same analysis would hold if we substituted "Nothing" for "No one." Thus it is by no means certain that the sole way of de­ fining " Nothing" is quantificationally. Carnap's translation of dispositional sentences is also not satisfactory. As we have seen, Carnap takes a predicate such as "solubility" to be defined by its inclu­ sion in a certain kind of sentential form that he calls a "reduction sentence." Thus "solubility" is defined as (x)(Fx:J(Sx = Ox)), that is, for all x, if x is dipped in water, then x is soluble if and only if x dissolves. Here, by making the disposi­ tional term part of the means for explaining it, Carnap avoids the possible sub­ junctive conditional definition of "solubility" with all the attendant problems that arise in the use of subjunctive conditionals. But the reduction sentence has its own difficulties. First, there is no way of attributing or denying solubility to an object unless the antecedent of the reduction sentence is true. If Fx is true, that is, if x is dipped in water, then x is soluble if Ox is true, that is, if x dissolves. If Fx is true, then x is not soluble if Ox is false. But if Fx is false, then, even though the reduction sentence turns out to be true, nothing follows concerning the truth or falsity of Sx. The reduction sentence then avoids the very problem that it was designed to meet. We wish to be able to say an object is soluble not only when it

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is being dipped in water and when it is dissolving, but before anything of this sort is happening, that is, even if F x is false. In fact, the use of the suffix in "solubility" indicates that we are taking the predicate to designate something quite' different from the designata of overt predicates, but what this difference is does not reveal itself in the reduction sentence. Second, as Scheffler has pointed out, the reduc­ tion sentence lends itself to the admission of any and all predicates, even those that are nonsense. 2 1 If instead of Sx we substituted Sx v Gx, then this latter predi­ cate would also be true if Fx and Ox are true. But Gx can be any predicate at all and thus becomes a legitimate predicate in the language no matter what linguis­ tic mark it may happen to be. It might be argued that meaningless predicates would not be allowed in a formal language, and thus Gx could not occur as an alternant if G is a meaningless predicate. But on Carnap's analysis the disposi­ tional predicate does not have a meaning in and of itself. It obtains its meaning through the observational predicates with which it is employed. Any word, then, can take the place of "soluble," since in the reduction sentence its extension and intension consists solely of the extensions and intensions of the observation pred­ icates. Hence, if Sx is allowable, then so also is Gx, whatever i!_represents. Scheffler also points out that, if for Sx we substitute OxF x v FxGx, then this is also true if Fx and Ox are true. But if OxFx v FxGx implies that, if x is not F, then x is G. In other words, it implies that, if x is not dipped in water, then any predicate is applicable to it. Thus the sense of a disposition or an affinity is not expressed by the use of Carnap's reduction sentences. Scheffler, who has examined not only Carnap's position but also alternatives to it, has concluded that all attempts fail if they try to define nonobservational expressions such as dispositional terms by means of observational ones. He concludes by stressing "the important place of theoretical constructions which are non-observational." 2 2 Before we leave the notion of dispositions, we might note that Quine has also sought to deal with dispositional terms. His technique is fairly simple. Given any dispositional term, it is attributable to an object if and only if that object is scien­ tifically similar to other objects to which the predicate has been attributed on the basis of actual observations. Thus, according to Quine, x is soluble if there is a y such that x is alike in molecular structure to y and that y dissolves. 2 3 In other words, if y with a given molecular structure, M, dissolves under certain condi­ tions, C, then if x also has M, it also will dissolve under C. "X is soluble" means that x has M and it will dissolve under C. But several questions arise here. Is Quine saying that, if there is at least one y with M that dissolves, then we can be assured that x with the same or similar M will dissolve? Clearly, we would not 2 1 . The A natomy o{ lnquiry, p. 1 72. 22. Ibid . , p. 3 2 5. 23. W V Quine, Word a n d Obiect (New York: Wiley, 1 960), p. 224.

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want to say that x is soluble on such flimsy evidence. To argue this way is to assert that there are inherent behavior patterns in atomic structure and that these pat­ terns determine the behavior of x under specified conditions. But this kind of determined behavior would be equivalent to the dispositional quality Quine seeks to avoid. Thus Quine must mean that it has been found scientifically that a great many-perhaps all-objects ever tested with M always dissolved under C. Therefore x that has the same M would also dissolve under the same C. We can say this even if x is not now, and perhaps will not be in the future, under C. But now we are caught in the subjunctive trap. If the antecedent is false, then why would one consequent be any more legitimate than another? We could reason­ ably argue for a given consequent if we could maintain that M is such that the very stru�ture entails certain reactions, for then if M entails that x dissolves, then M and C will still entail that x dissolves. But such entailment would mean that atoms have built into them certain necessary ways of reacting. In other words, dispositions would again become posited. Thus Quine does for dispositions what Wittgenstein did for objects. When Wittgenstein was asked how we are to dis­ cover his elementary objects, he simply replied that it was up to the scientist to find them for us. Quine also tells us to look to scientific theory in order to ground the subjunctive conditional. But scientific theory does nothing to solve the prob­ lem of dispositions, for eventually we must ask why atomic structure itself reacts in the way it does. Perhaps the answer is that it simply does and that it is the function of the scientist to describe what happens and nothing else. But even scientists are more apt to say it does because there is built into it a genetic or mathematical equation. Neither Carnap's nor Quine's analysis of dispositional predicates is adequate. Nor is either more successful in .translating a reference to things to a reference to thing-words. W hat distinguishes a thing-word from a predicate? How are the ob­ jects identified by thing-words distinguished from the objects identified by predi­ cate terms? In attempting to answer these questions, Carnap tries to define thing­ words (names) and predicates syntactically. The role that l inguistic expressions play in the language determines whether they are names or predicates. Quine makes the syntactic distinction even more explicit: "The mark of a name is its admissibility in positions of variables." 24 Elsewhere he says, "What distinguishes a name is that it can stand coherently in the place of a variable." 25 Then more specifically he maintains, "When we schematize a sentence in the predicative way ' Fa' or ' a is an F', our recognition of an ' a ' part and an 'F' part turns strictly on our use of variables of quantification; the 'a' represents a part of the sentence that stands where a quantifiable variable could stand, and the 'F' represents the 24. W V Quine, On tological Relativity a nd Other Essays (New York: Columbia Univ. Pr. , l 970), p. 62 . 2 5 . The Philosophy of Logic, pp. 27- 28.

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rest. " 26 Strawson summa rizes Quine's position in the following way: "There are two parts, then, to a complete, unquantified predication, a subject-part and a predicate-part. What distinguishes them is nothing other than the fact that the subject-part can coherently yield its place to a variable of quantification and the predicate part cannot. If quantification should lapse, or be dispensed with, the distinction of subject and predicate would lapse with it." 27 How satisfactory is this criterion of Quine's? There is a great deal of contro­ versy about whether quantification can apply to predicates. If it can, then, of course, quantification could not show us how to distinguish names from predi­ cates. Let us forego this controversial argument. Let us assume the kind of quan­ tification that Quine wants us to adopt. Could the distinction now be made suc­ cessfully? As Strawson points out, Quine accepts that a sentence has two parts. Which one is the name part and which one is the predicate part is determined by the quanti fication that is permitted. If it is permitted over the first part, then it is the name and the second is the predicate; if it is permitted over the second part, then it is the name and the first part is the predicate. Let us see whether this distinction can actually be made. Consider the ordinary sentence "John Smith is pale." Which part is the name? (We will assume that by some syntactical rule we can determine that "is" is not one of the relevant parts.) We could, in agreement with Quine, say the name is "John Smith," since it is replaceable by a quantified variable whereas "pale" is not. We might argue that we automatically assume a variable can replace "John Smith" because we already take it to be a name. It is familiar to us as a name, and for this reason we assume that the variable belongs here. But if this kind of familiarity is lacking, if "John Smith" is not constantly in use as a name, we would not know what to quantify. For example, what is the name and what is the predicate-in terms of Quine's criterion-of "Happy is Rich"? "Happy" could be the name if it is used as a name of someone and if we are stating that he (or she) is rich (with a capital R, meaning very rich). Or "Rich" could be the name if we take it to be an abbreviation for "Richard." Our quantification would depend on a prior understanding of whether or not the ex­ pression is being used as a name. But, perhaps even more important, if we return to our original example, "John is pale," there is no reason that quantification could not occur over "pale" to obtain (3 x)J x, that is, "There is something that John Smith has" or 'There is something had by John Smith" or "There is some­ thing belonging to John Smith" or even "There is something instantiated by John Smith," where "that John Smith has," "had by John Smith," "belonging to John Smith," and "instantiated by John Smith" are all predicates. Nor is it a count­ erargument to maintain that here we are really quantifying over predicates and 26. On tological Relativity, p. 9 5 . 27. P. F. Strawson, Su bject and Predicate in Logic a nd Grammar (London: Methuen, 1974),

p. 1 2 .

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that this has been disallowed. It is quantification, on Quine's analysis, that deter­ mints what is or is not a predicate or a name, not the other way around. In Quine's view, if a term can "coherently" be replaced by a variable , then that de­ termines whether it is a name; and, even though the move from "John Smith is pale" to "There is something had by John Smith" is awkward, it is surely co­ herent-unless Quine has some special way in which he wishes to define co­ herency. In fact, if \Ve were not dealing strictly with the English language, quan­ ti fication over verbs would be perfectly coherent. Thus, where in English we would say " Buddha has taught the doctrine," classical Tibetan would be "There has been teaching with respect to the doctrine of Buddha. " Or, where in English we would say "The scholars like science," the Tibetan would say "There is liking with respect to the scholars for science. " 2 8 Thus it turns out that, if coherency is the ultimate criterion for justifying quantification, then we really have no crite­ rion at all that will give us the thing-word - predicate-word distinction we are seeking. It might be added that, although Strawson does not find Quine's criterion for distinguishing names from predicates satisfactory, he proposes one of his own. 29 His fails as well. He argues that "it is true of," when attached to a sentence, will reveal which expression is the name and which the predicate. Thus, given any monadic predicate sentence such as "Socrates swims" or any polyadic predicate sentence such as "John beats Mary," we can employ special sentential forms that would tell us what the names are and what the predicate is. First, we would change "Socrates swims" into

( 1 ) It is true of Socrates that Socrates ( or he) swims.

Then we change "John beats Mary" into or

(2) It is true of John that John ( or he) beats Mary ( 3) It is true of Mary that John beats Mary ( o r her).

We then see how forms:

( 1 ),

( 2), and ( 3) fit into either one of the following sentential

(4) It is true of x that x y; ( 5) It is true of x that y x.

28. C. Regamey. "Text of contribu tion," in Proceedings of the 7 t h International Congress of Lin­ gu ists (September, l 9 5 2), pp. l 29- 30, and "A propos de la 'construction crgative' en indo-aryen moderne," in Sprachgesch ich te und Wortbedeutung: Festschrift fu r A. Debru n ner (Bern, l 9 54), pp. 363 - 8 l , q. in Kung, Ontology a nd the Logistic Analysis of Language, pp. 7 - 8 . 2 9 . Strawson, Subiect a n d Predicate in Logic a nd G rammar, pp. 9 - l l .

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( 1 ) fits di rectly into (4), with x standing for "Socrates" and y for "swims." (2) also fits directly into (4), with x standing for "John" and "beats Mary" for y. (3) fits directly into ( 5), and x standing for "Mary" and y for "John beats." On th is basis, we recognize " Socrates," "John," and "Mary" as names . On the other hand , if we try to fit "swimming" into the x slot, we obtain the incoherent sentences (6) It is true of swimming that swimming Socrates and (7) It is true of swimming that Socrates swi mming. Similarly, if we try to replace x by "beating" in (4) and ( 5), we obtain two inco­ herent sentences. (Perhaps we ought not even to call them sentences . ) Thus "John" and "Mary" are names, since they can replace the variable x, whereas "swimming" and "beating" are not, since they cannot replace the variable. Strawson's criterion , however, works as long as we know beforehand that we are dealing with an expression that is a name. Otherwise we could substitute "swims" in ( 5) and obtain "It is true of 'swims' that Socrates swims," and "swims" would then have to be labeled a name. Or, instead of "swimm ing," which does give us a genuinely incoherent sentence, we could substitute " is swimming"-a name need not necessarily consist of one and only one word-and ( 5) would again be satisfied . Strawson might want to argue that, in testing whether an expression is a name, both (4) and ( 5) must be satisfied . Then , even though "swims" and " is swimming" can be used with ( 5), these expressions cannot co­ herently be used with ( 4 ). Hence neither "swims" nor "is swimming" nor "swim­ ming" can be a candidate for the x slot in (4) and ( 5). A similar analysis can be made for "beating." But now consider a slightly unusual sentence that may be a bit archaic but is surely coherent: (8) Swiftly ran the horse. Applying (4) and ( 5 ) we obtain (9) It is true of "swiftly" that swiftly ran the horse and ( 1 0) It is true of "swiftly" that swiftly the horse ran . Here both (4) and ( 5 ) are satisfied, and "swiftly" must then b e taken a s a name. Strawson tells us that " it is true of" is required to be followed by a noun phrase, but this asserts what we wish to prove, namely, that the expression of the first x will be a noun phrase, that is, a name, if its assertion into the second x turns out to be coherent. It is for this reason that "beating" and "swimming" are rejected as

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noun phrases. They produce i ncoherent that-clauses i n (4) and ( 5 ) . Thus it turns out that, with a little shuffling of the normal sentence, Strawson's criterion­ although he does acknowledge that it is not the sole criterion-must rest on what is coherent, and this makes his criterion as ineffective as Quine's. This distinct ion between thing- and predicate-words, then, has not yet been made and, until it can be made, Carnap's and Quine's attempt to reduce "thing" to "thing-word" cannot be called successful . Can we say then that thing-words designate particulars and that predicate terms designate properties? But this of course defeats Carnap's desire to eliminate a sticky metaphysical problem, since it would then seem to be perfectly legitimate to ask what distinguishes particulars from properties and precisely how one is related to the other. In the same way, if I say "Cadillac" designates car A and that "Chevrolet" designates car B, it is per­ fectly legitimate to go on to ask how car A differs from car B. The troublesome ontological issue relating to what particulars are and how they relate to properties is not explained away by Carnap until he can show us that the explanation of a thing-word is itself devoid of any issues that relate to ontology. Carnap could answer that we have made a category error. Thing-words signify words in a given grammatical category of words; they do not signify anything extralinguistic. W ithin a language framework is a stipulation of a domain of space-time entities, and if a descriptive word is to occupy the place of a given variable (usually the individual variable), then that word must designate one or more of these space-time entities. 30 These entities are the so-called things. Using the expressions in the language, we might ask in some trivial sense "Are there things?" It is trivial in that it would be comparable to asking "Are there words?" when we know full well that to pose the very question is to answer it. Of course, there are things, since the very act of using the language assumes a domain of some sort and since in our language that domain consists of space-time entities . We can, therefore, ask during moments when we use the language idly whether there are things. But asking the question is, in this case, to be answering it as well. A similar kind of question cannot legitimately be asked at all . We cannot transform the trivial thing-question into the more subtle one, "Ah, yes, but are there really things? Exclusive of the language framework is there really a domain of things?" These questions are what Carnap calls "external" questions about the 30. For Carnap the name that replaces the individual variable designates, on the basis of the prin­ ciple of univocality, one and only one individual; Meaning and Necessity, p. 98. But for others, such as Woodger, Martin and Kotarbfnski names can refer to several objects, to exactly one, or to none; see J. H. Woodger, "Science without Properties," British Journal for the Philosophy of Science 2 ( 1952): 193-2 16; R. M. Martin, Truth and Denotation (Chicago: Univ. of Chicago Pr. , 1 958); T Ko­ tarbfnski, Elementy Teorii Poznania: Logiki Formalnej i Methodoligii Nauk (Wroclaw-Warsaw­ Krak6w, 196 1 ), 2d ed.

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language that cannot be raised. 31 We can ask whether in the domain of accepted things there is a red thing or a blue thing or a five-foot-ten-inch thing. W hat we cannot do is ask about things that are not part of the l inguistic domain. We can­ not ask about those things that are present without the language framework, since what is outside the framework is unknowable. In an important sense Carnap's language framework is analogous to Kant's forms and categories of human under­ standing. We cannot ask whether there are causes among things-in-themselves, that is, the realm of noumena. But we can ask-although the answer is synthetic a p riori-whether there are causes in the realm of phenomena. And there are causes for Kant, since the category of causal relation is imposed on al l sensory experience. In the same way, for Carnap there are things-although the category of things is not characterized by a Kantian necessity-but it does not make sense to ask whether there are really things, whether things are part of an objective real ity. W ithin our language commitment there are things, but outside of the commitment there is nothing to be said. This way of viewing thing-words, however, is also not satisfactory. First, Quine himself has disagreed with Carnap on the importance to be attributed to category words. 32 It is not trivial to ask categorial existence questions for the simple reason that it is always legitimate even in the austerest logical circles to ask whether we can avoid assuming certain sorts of entities or whether we can translate a sen­ tence committed to one kind of entity into a sentence committed to another. We may have the category of property, but it makes important sense to ask whether properties are el iminable in favor of classes; or we may have the category of points in a geometric system, but it makes sense, following W hitehead, to ask whether points can be replaced by abstractive sets. , -, Similarly, a language with a category of names may not be as satisfactory in presenting a view of the world as one in which the category has been replaced by descriptions. In fact, Carnap himself rejected his early attempt to construct a phenomenalistic language be­ cause the category of "phenomenal object," with its explicit dependence on sense-data predicates as the ultimate predicates, led to an inescapable sol ipsism. 34 In finally accepting a "thing" language, he showed the importance of being able to question the categorial commitments of any language. Second, it is not at all clear that, because "There are things" or "There are individuals" or "There are particulars" can be understood only within a language 3 1 . Carnap, Meaning and Necessity, p. 206. For further discussion of the differences between internal and external questions, see James W Cornman, Metaphysics, Reference, and Language (New Haven, CT: Yale Univ. Pr. , 1966), ch. 5. 32. W V Quine, "Existence and Quantification," in Fact a nd Existence, ed. Joseph Margolis (Toronto: Univ. of Toronto Pr., 1969), p. 2. 33. A. N. Whitehead, Process and Reality (New York: Macmillan, 1929), p. 454. 34. See Carnap's comments in The Philosophy of Rudolph Carnap, ed. Schilpp, p. 945.

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framework, it has very little ontological signi ficance, as Carnap would have us believe. Carnap tells us that "To recognize something as a real thing or event means to succeed in incorporating it into the system of things at a particular space-time position so that it fits together with the other things recognized as real, according to the rules of the framework. ' 5 W hat this means is that it is be­ cause we have the category of space-time things (or events) in the language that we can legitimately speak of there being things at a given place in time. We could have had another framework in which our commitments would have been dif­ ferent. We might have been committed to sense data rather than to things, or we could have replaced properties by classes. But why is it that our alternatives are so minimal? We can have a thing language or a phenomenalistic language, or we could, according to Carnap, "construct an alternative . . . with another struc­ ture. " 36 But what is this alternative with another structure? W hen we speak of what is extralinguistic we speak of things or properties or classes or events or rela­ tions . But very quickly we run out of alternatives. The conversion of the tradi­ tional Scholastic ontological categories into linguistic ones has not given us any way of changing them or replacing them by ones that do not employ traditional ontological terminology when they are interpreted. Things give way to thing­ words and not to some other kind of expression, apparently because we want to make sure that we do not confuse thing-words with predicate-words that refer to properties or classes. W hen W ittgenstein argued against relations, he tried to show that relational words can be explained by a reference to arrangements of objects. There was no need to explicate what relational words were by referring to relations . 37 Such a view would have enormous implications for ontological speculation. It would have eliminated as "merely linguistic" one crucial area that had been used by all metaphysicians, including even the antimetaphysician Rus­ sell, to prove that universals must exist. But changing thing and property into thing-word and predicate-word does not perform the same kind of function, since these categories must themselves be explicated by a reference to things, properties, and classes. In conclusion, we might observe only briefly that further developments in logic have led to more, rather than less, involvement in ontological issues. Thus, with the advent of modal logic and the recognition of its crucial role in the expla­ nation of certain statements in scientific, epistemological, and axiological in­ qui ry, 38 has come the belief that pure formal systems with modal operators can be 35. Carnap, Meaning and Necessity, p. 207. 36. Ibid. 37. See Tractatus 3. 1 432, 4.24( 1 ), and Notebooks, p. 99. 38. Thus, according to Dagfinn F0llesdal, modality problems as well as those involving indirect discourse must be resolved if we are to "built up adequate theories of causation, counterfactuals, probability, preference, knowledge, belief, action, duty, responsibility, rightness, goodness, etc . . . . "

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interpreted only with the introduction of such notions as essence and attribute. Quine's famous paradox that shows all modal contexts to be referentially opaque can be said to have started it all . 39 Chapter 7 examines this paradox in detail, but here we can simply note that Quine has shown that substitution in modal con­ texts does not hold unless the substitution is other than extensional. Otherwise, given that necessarily 9 is greater than 7 and that the number of planets is identi­ cal to 9, then necessarily the number of planets is greater than 7 . To avoid this false conclusion, we could modify the rule of substitution to state that in modal contexts the substitution must be in terms of intensional entities-that is, 9 can be replaced by 5 + 4, which is both extensionally and intensionally equivalent to 9, but it cannot be replaced by the number of planets, which is extensionally, but not intensionally, equivalent to 9. Intensional equivalence, however, is due to the meaning of the terms rather than to identity of denotation. Thus, whereas an essential relationship exists between 9 and 5 + 4, there is only a contingent relationship between 9 and the number of pla nets. In one fell swoop, then, the introduction of the logic of modality brings with it also the introduction of essen­ tial and contingent properties, those very concepts that formalism was designed to eliminate. 40 Nor has Kripke's semantics for a quantified modal logic been able to dispel the introduction of essences. 41 In fact, his semantics makes the commit­ ment crucial, since objects that exist and that are identifiable in every possible world are introduced. 4 2 There is, of course, an inherent vagueness in the whole allusion to a possible world and especially in the notion of identification of par­ ticular objects across possible worlds, a notion of which Quine admits he "can make little sense." 4 3 But more important than the vagueness is the fact that, if there is to be identification of the same object in an infinite number of possible worlds, then that object must be thought of as having at least one necessary prop­ erty. Otherwise, if no properties were necessary, then there logically could be a world in which the object could not be identified as the same object. But the need to posit such necessary properties and their counterpart, contingent proper("Quine on Modality," in Words and Objections: Essays on the Work of W V Quine, ed. Donald Davidson and Jaako Hintikka [Dordrecht, Holland: D. Reidel, 1 969], p. 1 79). 39. W V Quine, "Reference and Modality," in From a Logical Point of View (New York: Harper, 1 96 1 ), 2d ed., pp. 1 39-59. 40. Quine, however, does not countenance intensions or any form of essentialism. He concludes that if modal logic requires such commitments then "so much the worse for quantified modal logic" ( From a Logical Point of View, p. 1 56). 4 1 . See Saul Kripke, "Semantical Considerations in Modal Logic," Acta Philosophica Fennica 1 6 ( 1 963): 83-94. 42. For a discussion and criticism of Kripke's semantics, see L. Linsky, "Reference, Essentialism, and Modality," in Reference and Modality, ed. Leonard Linsky (London: Oxford Univ. Pr. , 1 97 1 ), pp. 97- 1 00, and idem, Names and Descriptions (Chicago: Univ. of Chicago Pr. , 1 977), ch. 3. 43. Words and Objections, ed. Davidson and Hintikka, p. 343.

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ties, reproduces the whole traditional metaphysical issue of what it means to speak of essences and contingencies, of individuals as distinct from mere mem­ bers of a class . The Aristotelian problem of what constitutes individuation re­ appears in Kripkc's interpretation of a quantified modal system. ·H As Linsky puts it, what comes out of modal logic is "not a logical problem but a metaphysi­ cal one . " -+, 44. Aristotle, Metaphysics bk. 5 , ch. 6; bk. 7, chs. 8, IO, 13; bk. I O, ch. 2; bk. 12, ch. 8, and On bk. 1, ch. 9. See also the discussion by W D. Ross, Aristotle (London: Methuen, 1923), pp. 169-73. 4 5. Reference and Modality, ed. Linsky, p. 99. the Heavens,

6 The Linguistic Criterion of Ontology As we have seen, Quine, Carnap, and others have been proclaiming a n ew way of studying what exists, or rather a new way of approaching the traditional problems of ontology. We no longer ask what the general essential characteristics of being qua being are. This kind of question is too amorphous and does not result in answers that can be included in rigorously formulated logical languages . It does not make clear how the term "being" i s to be utilized in a strict formal system-as a name, as a predicate, as a variable, or as something that is to un­ dergo transformation in the way that "exists" has been transformed from a predi­ cate into a quantifier and dispositional terms from predicates into counterfactual or reductive sentences. On Quine's analysis, if we wish to know what there is or what the characteristics of being qua being are, we approach the entire matter from the side of language. We ask ourselves what entities are required in order to make certain of our sentences true, and these entities turn out to be the compo­ nents that make up our ontological domain. Taken all together they make up the traditional realm of being without the traditional ambiguities of what such being is and how it is to be characterized. More specifically, we must think in terms of a formal rather than a natural language-one free of the contradictions� para­ doxes, and ambiguities inherent in natural languages-because only such a for­ mal language can give us a clear understanding of what entities are required. In this chapter I shall examine how a language becomes ontologically committed on this view and whether it is indeed the case that it is both sensible and true to say that a language in some way entails the admission of such a commitment. This chapter is a modification and revision of "Are There Any Ontological Commitments?" ( Pa­ per delivered at the International Philosophy Conference , New York, l 976).

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We might begin by starting in the middle of things, that is, by examining the fairly familiar contention that a language has as its ontological commitment, that is, its commitment to what exists, all those entities that can serve as values of the existentially quantified variable. Specifically, we shall examine the assertion that, if a language has as one of its sentential forms n-numbered existential quantifiers followed by n-numbered variables or has sentences that can be taken as synonyms for such forms, then all those entities that serve to confer truth on these sentences are ontological commitments of the language. Thus, if an object a can be taken as a value of the variable x in the formula ( 3 x)Fx, then a, accord­ ing to this view, is an ontological commitment of the language. 1 I should not want to maintain that this is exactly the criterion proposed by Quine, since, as Chihara has shown, Quine's criterion of ontology has been modified in various ways, and at times there are incongruities in Quine's formulations. 2 Thus for the most part Quine's position has been that "the objects whose existence is implied in our discourse are finally just the objects which must, for the truth of our asser­ tions, be acknowledged as 'values of variables' -i. e. be reckoned into the totality of objects over which our variables of quantification range. To be is to be the value of a variable. There are no ultimate philosophical problems concerning terms and their references, but only concerning variables and their values; and there are no ultimate philosophical problems concerning existence except insofar as existence is expressed by the quantifier '(3 x)' ." 3 But at least at one point Quine remarks that a theory is ontologically committed to an object "only if that object is common to all [interpretations of the range] ." 4 Thus on one analysis Quine is simply saying that a , in the above example, is part of the ontology of the lan­ guage, since it appears as a value of the variable. But on the other analysis a would be part of the ontology only if it appears as a value in all interpretations of the range, that is, only if no interpretation of (3 x)Fx excludes the use of a as a value. 5 In other words, a would be a required value in all interpretations. Quine does not pursue this modification of his usual criterion. The reason may be that it would entail the acceptance of some notion involving a necessary or required value, a notion Quine would reject, since it would mean the introduction of 1. I assume here the use of the existential quantifier as it appears in some formalized language. Quine often speaks of its use in "theories," "discourses," "doctrines," etc., and, at least according to C. S. Chihara, the context may affect our understanding of the quantifier. Sec C. S. Chihara, On­ tology a nd the Vicious Circle Principle (Ithaca, NY: Cornell Univ. Pr. , 1973), pp. 90- 95. 2. Chihara, ibid., p. 93. 3. W V Quine, Methods of Logic (New York: Holt, 1972), 3d ed. , p. 234. 4. Words a nd Objections: Essays on the Work of W V Quine, ed. Donald Davidson and Jaako Hintikka (Dordrecht, Holland: D. Reidel, 1969), p. 315. 5. Both the universal and the existential quantifier are conveyors of ontological import since one can be transformed into the other. Along with Quine 1 stress the existential quantifier because of its closer connection to the "exists" of ordinary language.

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intensions as values as well as possible domains of entities . In any event, our involvement here is with the criterion most frequently accepted by Quine, namely, that to be is to be the value of a variable. What exists are the entities that can become the values of the variable. Now, before we can begin to evaluate this position, before we can determine what it means and whether it is legitimate to speak of an ontological commitment that is derived from the relation of values to variables, an important ambiguity must be resolved . The ambiguity revolves around the move from values to vari­ ables, and vice versa. When a is taken as the value of a variable, exactly what has occurred? Do we mean that a is a specific linguistic element, for example, a proper name, and that it is the value of the variable and that it is to this linguistic element that we are ontologically committed? Or do we mean that a is a linguis­ tic element that replaces the variable but that it is the designatum of that element that is the value of the variable? Or do we mean that a is the very object itself that is the value of the variable regardless of whether there is or there is not a linguis­ tic element that is used to designate this object? Then we must finally ask what is meant by the phrase "be reckoned into the totality of objects over which our vari­ ables of quantification range." Are we speaking here of objects that are or that have been values of the variable, or do we also take into account possible values as well? Before we can fully appreciate and evaluate what we might well call the linguistic criterion of on tology, it is important to come to terms with these ques­ tions, since our understanding of what a is will affect what our ontological com­ mitment will be. Let us turn to the first question. When a is a value of the variable, can this be taken to mean that a is a linguistic expression and that it is the value of the vari­ able? C. I. Lewis believed so: "What is here called a value, for example, 'x' in ' x is a man' is the term or expression 'Socrates' or 'Apollo' or 'the speaker for tonight,' and not the thing named by such a term ." 6 More recently, according to Quine, Ruth Barcan Marcus seems also to have taken this position. " For Pro­ fessor Marcus," Quine claims, "the values are the expressions you can substitute . . . . Ryle objected somewhere to my dictum that to be is to be the value of a variable, arguing that the values of variables are expressions and hence that my dictum repudiates all things except expressions . . . . [Professor Marcus] simply speaks of values of variables in the Ryle sense ." 7 According to this view the re­ placements for the variable in (3 x)Fx are names and, therefore, no serious on­ tological commitment is involved. We are committed strictly to the name as a linguistic expression, not to its designatum. Thus, for example, if the name "John Smith" is an appropriate replacement for the variable in (3 x)F x, that is, if 6. C. I. Lewis, An Analysis of Knowledge and Valuation (LaSalle, IL: Open Court, l 946), p. 59. 7. W V Quine, "Reply to Professor Marcus," in C ontemporary Readings in Logical Theory, ed. I. Copi and J. A. Gould (New York: Macmillan, 1 967), p. 297.

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"John Smith is F" could be taken as a sentence to which "true" would be applica­ ble, then we are ontologically committed to the name "John Smith." We are not required to introduce the designatum of that name. In terms of this analysis our ontology turns out to be fairly trivial. We may require that there be linguistic elements, but not that there be anything extralinguistic, since, as Cornman has pointed out, from a linguistic element nothing can be inferred about its reference unless we stipulate some rule indicating what the reference is: "From a premise concerning commitments to the use of certain terms as substituends for variables to infer the conclusion that we are ontologically committed to certain entities as the values of those variables is surely not legitimate without an additional prem­ ise concerning the reference of the substituends ." � Since presumably names can be defined syntactically, 9 definition of names in terms of extensions and inten­ sions or of substances and attributes becomes irrelevant. Thus, for those who want to avoid any serious ontology, this interpretation of the linguistic criterion of ontology is pleasantly palatable. This interpretation, however, has problems. First, as Quine has indicated, there is a confusion here between the use of an expression and its being men­ tioned. When the variable is replaced by an expression, it is the expression in its role as being used to indicate its designatum that is serving as the replacement rather than the expression in its role as being mentioned. In other words, what we place x by is "John Smith" for which a suitable descriptive synonym might be " My next door neighbor"; we do not replace x by "John Smith" for which a suit­ able descriptive synonym might be "The expression with nine letters ." W hen we instantiate from "Someone is rational," we obtain "John Smith is rational," not " 'John Smith' is rational" or "The name 'John Smith' is rational." Expressions are never rational, but what they designate are (or are not). We might make the same point differently. It cannot be merely the linguistic expression that replaces the variable, for then our domain, with which quantification is functioning, turns out to be a domain of linguistic expressions . But, when we say "Someone is rational," we do not expect that an instance of this would be "The expression 'John Smith' is rational." It is a confusion of use and mention of expressions not to be aware that a replacement of a variable by "John Smith" as a pure linguistic element is quite distinct from the replacement of the variable by "John Smith" whose designatum is John Smith. Thus, if Marcus is right and if only linguistic expressions replace the variable, then she is indeed right in minimizing the on­ tological significance of such replacement. But replacement of this sort is not what is normally intended in the formal language . As Quine puts it, "Quan­ tification ordinarily so-called is purely and simply the logical idiom of objective 8. J. W Cornman, Metaphysics, Reference, and Language (New Haven, CT: Yale Univ. Pr. , 1966), p. 151. 9. See, for example, David Cry stal, Linguistics (Baltimore: Penguin, 1 971 ), p. 74.

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reference. When we reconstrue it in terms of substituted expressions rather than real values, we waive reference . " 1 0 Thus, if we want to expl icate ordinary and scientific discourse, which is one of the major reasons for constructing formal languages, then the domain must be primarily one that is extral inguistic. There is a second objection to the view that the values of the variable are sim­ ply the linguistic expressions themselves. If this view were correct, then whatever existential or un iversal sentences were used could be used only in the context of a given language . Linguistic expressions, for example, names, are by defin ition elements of a given language. "Jack Smith" is not a name in the German lan­ guage, " Hans Schmidt" is not a name in the English language, and c 1 may be a constant in one language but not in another. Only the names in a given language can be proper substitutions for the variable-if we accept the view that only the names or other expressions of a language can be substituted for the variable . Thus the quanti fied sentence "All men are rational" i s appl icable only t o the names in the Engl ish language, since only names in the English language are permitted as replacements for the individual variable . We cannot say "Al l men are rational" is true, but rather that "true" is applicable to all the substitution instances of this sentence in the English language. What we could not sensibly ask is whether the true sentences of Engl ish would also be true in all other lan­ guages, for what could it possibly mean to ask whether the Engl ish sentence "Al l men are rational'' i s also true in German . But i t i s apparent that the un iversal sentence "Al l men are rational ," if it is true at all, is intended to hold regardless of the particular language which is being used . If we say "All metals are conduc­ tors," we do not mean that this holds because of tests whose results have been formulated in the Engl ish language . We take it for granted that metals are con­ ductors not only here, but even in the Soviet Union . In the l ight of our analysis, we might now want to go on to say that l inguistic expressions cannot themselves be the values of the variable, but l inguistic expres­ sions only insofar as they are functioning as used expressions. I think, inciden­ tally, that this is the view that Marcus is really espousing. The language L that she constructs is not one that neglects a commitment to a domain of objects. She specifies a domain, D, of individuals which "are named by the constants of L. . . . To say . . . that the atomic sentence R(a 1 a 2 ) of L holds or is true in M, is to say that the ordered couple ( b 1 b 2 ) is a member of M, where a 1 and a2 are the names in L of b 1 and b 2 • • • • We say that a true sentence of L is defined relative to a model and a domain of individuals. " 1 1 Thus it is not the linguistic expres­ sion-in this case the name-that is the val ue of the variable for Marcus, but the name insofar as it is designating an individual in the postulated domain of 10. Quine, "Reply to Professor Marcus," p. 298. 1 1 . Ruth Barcan Marcus, "Modalities and Intensional Language," in Con temporary Readings in Logical Theory, ed. Copi and Gould, p. 292.

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individuals. Under these conditions ontological commitment would indeed be present. It would be the objects designated by the expressions permitted to be replacements for the variable. Thus, if "John Smith" is an allowable replacement for the variable, then there is an ontological commitment to the object desig­ nated by "John Smith. " But this interpretation of the linguistic criterion is not satisfactory either. An argument similar to that given against the previous interpretation is also applica­ ble here. In natural languages no one would argue that the rules governing the use of names in English are necessarily or even probably the same as the rules governing the use of names in Swahili. Similarly, a 1 and a 2 may be names in a formal language L, but this in no way entails that they will be names in all other languages. In Marcus's system only names designating the individuals of the do­ main specified for that system are permitted as substitutions for the variable. She does not undertake the difficult task of constructing rules of synonymy or transla­ tion that would make a name in one language identical to a name in another. All the Fregean problems of sense and reference as well as the Kripkian problems of rigid designators would here require investigation. But, even if rules could be given, our values for the variable would still always be restricted to named en­ tities regardless of what logically possible world they are members. W hat we could not do is speak of any unnamed entities, and, since we do not have or know of any names in any future language, we could not speak of the rationality of any men in the future. ''All men are rational" is not to be taken as applicable to tomorrow's children or to future men. But, of course, it is the need to have this kind of applicability that makes us replace the ordinary material by the counter­ factual conditional in all our important universal sentences. In any language it is important to be able to say what would be the case if something else were the case. But the counterfactual statement requires us to take a statement as either true or false on the basis of a false antecedent, that is, an antecedent whose indi­ vidual variable cannot or will not be instantiated. Thus we wish to be able to say " Even if at some time there were no men, if x were a man at that time, he would be rational." We wish to be able to speak of entities to which properties can be attributed even if they are not members of a domain at any given time and do not enjoy the special privilege of being named. But have we confused natural with formal languages? In a formal language we can simply, by recursive methods, obtain an infinite number of names and in this way obtain unrestricted universal sentences. The odd result of this infinite exten­ sion of the class of names is that every universal sentence turns out to be false. According to a theorem of Cantor, there are always more objects than there are names naming them. 1 2 Thus, in the instantiation of a universal sentence, there 1 2. For a discussion of Cantor's theorem, see W V Quine, The Ways of Pa radox (New York: Ran­ dom House, 1 966 ), pp. 1 6- 1 7.

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must eventually be a conjunct that has no name that can replace the variable, and this conjunct must be false if only named entities are permitted as values of the variable. Cantor's theorem also reinforces the view that there are clearly some quan­ tified sentences that we should wish to regard as true even though no linguistic expression is available for substitution of the variable. In classical theory the real numbers are indenumerable, but the expressions that designate these numbers are denumerable. Yet we still wish to make true statements about indenumerable real numbers. This means that ''There are real numbers that are unspecifiable" is to be regarded as true even if there are no appropriate expressions that specify such numbers. In other contexts we wish to be able to say that "There are un­ named prime numbers," "There are unknown soldiers," and "Bodies without forces operating on them will continue in a straight line" are all true even though the variables could not be instantiated by names. Finally, there is the by now familiar argument of Russell and Quine that names ought to be eliminated altogether from formal languages, since they not only lead to all the problems concerning nondenotable names, but they are also not necessary. 1 3 If a name does not denote, for example, "Pegasus," then the rules of natural deduction must be either suspended or carefully restricted. For exam­ ple, from " Pegasus was the winged horse of Bellerophon" we cannot, by existen­ tial generalization, move to "There exists a winged horse of Bellerophon." Or if we assert "Pegasus does not exist," and formalize it as - (3 x)(x = p), then from this true sentence we can derive by existential generalization the false sentence (3 y)(x)(x -:/= y)-that is, there is something that is not identical to anything­ which is false because something is always identical to itself. And, if a name does denote, then its inclusion in a language is not necessary, since the denotation can be given without the use of the name. Thus what is denoted by "John Smith" is that which is describable as "That man there" or "The man next door," and so forth. This thesis concerning the conversion of names to descriptions, however, has been strongly challenged by Strawson, Donnellen, and, especially, Kripke. 1 4 Kripke's main point is that we ought to distinguish the function of names from 1 3. Actually Russell argued only for the elimination of nondenotative names such as "Pegasus." Names learned by means of acquaintance with the objects denoted by them were legitimate. See Quine's discussion of singular terms in his Methods of Logic, pp. 230- 34. 1 4. See P. F. Strawson, "On Referring," reprinted in Philosophy and Ordinary Language, ed. Charles E. Caton ( Urbana: Univ. of Illinois Pr. , 1 963), pp. 1 62-93; Keith Donellan, "Reference and Definite Descriptions," The Philosophical Review 85 (July 1 966): 28 1 -304; Saul Kripke, "Identity and Necessity," in Identity and Individuation, ed. Milton K. Munitz (New York: New York Univ. Pr. , 1 97 1 ), pp. 1 35-64; Saul Kripke, "Naming and Necessity," in Semantics of Natural Language, ed. Donald Davidson and Gilbert Harman (Dordrecht, Holland: D. Reidel, 1 972), pp. 253355.

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the function of descriptions. Whatever satisfies a description fixes the referent of that description. 1 ' Thus, if we ask who the Peripatetic philosopher was, our an­ swer is that it is whoever satisfies the description. And to whatever satisfies the description we can give a name, namely, Aristotle. On this view a name is a result of one or more descriptions. But Kripke argues that names do not operate in this way, since it is always logically possible for descriptions to be false of an individual without this casting any doubt on the existence of that individual. Ar­ istotle vmuld surely not be said to cease to exist if we suddenly discovered that he had not been the teacher of Alexander. Nor would we deny his existence if we discovered that he had not really been a student of Plato. We should simply say that we were mistaken about what we had been attributing to Aristotle. Names are not merely the names that can satisfy the variable of some description. In Kripke's words, a name is a "rigid designator" in that it designates the same object in every possible world. And how could it be otherwise! If we say of Aristotle that there might be a possible world in which he was not the teacher of Alexander, we are saying that the "he" of that world and the "he" of this world are one and the same. And this same identity holds in all possible worlds in which Aristotle might be said to lack or to have one or more descriptions than we normally at­ tribute to him. In all these worlds, if we are speaking of Aristotle at all, it must be the same individual and not some clone or counterpart. Names, then, are here to stay and they ought not to be confused with descriptions . Several comments can be directed against Kripke. We might begin by ques­ tioning the whole notion of a possible world. It is not at all clear what it means to speak of a possible world as distinct from an actual one. Is a possible world an extrapolation from the actual one so that there are both legitimate and illegiti­ mate possible worlds? Are there possible humans in a possible world and are their notions of a possible world also to be taken as possible worlds? And in any pos­ sible world how do we distinguish what is true from what is false? Or are we to reject the use of "true" and "false" in such worlds? Still, to all these questions we might answer that, if we are to use modal logics at all, then just as we require an actual domain of objects if the usual first order quantifier is to be employed so also we need a possible domain of objects if the usual modal quantifier is to be employed. Of course, it is possible, in the manner of Quine, simply to reject modal logic. But let us assume the legitimacy of the notion of a possible world. How does transworld identity take place? How can we tell that the Aristotle we refer to here is the same as the Aristotle referred to there? Kripke argues against thinking of a possible world as one that is "out there" to be discovered and inves­ tigated as we do some alien planet. But, if we do not think of a possible world in this way, then how are we ever to claim that there is a man in this world who is 1 5. Kripke, "Naming and Necessity," p. 276.

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identical to a man in another possible world? How can we tell that the Aristotle we infer to be here is the same as the Aristotle we infer to be there if not by the use of descriptions? Aristotle here-in this world-was a disciple of Plato. Aristotle there may not have known Plato nor have been a teacher of Alexander. But, if we are talking about the same man, there must be some description that is attribut­ able to both. In other words, in identifying Aristotle we are required to compare descriptions and to check the degree of overlapping. Identification cannot occur without description. We ought also to ask ourselves whether Kripke is not forced to accept s0me notion of a bare particular once he has rejected descriptions as the means of identifying Aristotle. For consider what the referent of "Aristotle" would be. I t is not that which satisfies the variable of "The teacher of Alexander," since whatever satisfies the variable need not be Aristotle. Someone else besides Aris­ totle could have been the teacher of Alexander. The same reasoning would hold for any description. We are apparently left with thinking of "Aristotle" as having its own referent, as being a "logically proper" name in Russell's old sense. But this referent is one that no description entails and of which every description could be false. And is not this analogous to what we mean by a bare particular? It is that which is logically independent of all properties and of which the attribu­ tion of any property could be false. Thus "Aristotle" as a rigid designator name designates an "it" or a "this" or a "something we know not what." Kripke can, of course, escape these difficulties by introducing essential de­ scriptions, those that are necessarily associated with a name . But, first, this would void his main thesis that every name is logically independent of any de­ scription, and, second, it is highly questionable whether the notions of essence and essential property that would now reappear could withstand the traditional criticisms of both Hume and Wittgenstein. The main counterargument to Kripke, I believe, is (a) to retain names as con­ vertible into descriptions and (8) to define identity among different possible worlds (assuming "possible worlds" is an allowable expression) as alluding to overlapping values. More specifically, if we ask who Aristotle was we usually give some series of descriptions. He was the disciple of Plato, the teacher of Alex­ ander, the Peripatetic philosopher, and so forth. Now, if we go on to ask what Aristotle might have done or might have become, we are speculating about what Aristotle might have done or become if he had not been a disciple of Plato or if he had not been the teacher of Alexander, and so forth. In short, in such specula­ tion we eliminate one description or perhaps two or three and then ask how Aris­ totle would have fared under such limitations. Or sometimes we add a descrip­ tion: "How would Aristotle have been as the ruler of a country?" But in no case do we ask what Aristotle might have done or become if none of the descriptions we attribute to him hold. What can we possibly ask of an Aristotle to whom no description is ascribable? When we speak of Aristotle in a possible world, we are

The Linguistic Criterion of On tology

1 23

not denuding him; he is not a bare particular. What we are doing is l imiting or adding to the descriptions we normally use . What we arc saying is that descrip­ tions overlap and that Aristotle is the value of the variables of overlapping de­ scriptions. Sets of descriptions can have the same value satisfying most of their members and it is this value that we take to be Aristotle. It is the same Aristotle we are talking about when here-in th is world-we speak of the student of Plato , the teacher of Alexander, and the Peripatetic philosopher, and when there-in tha t world-we speak of the student of Plato , the Peripatetic philoso­ pher, and one who is not the teacher of Alexander. Both sets of descriptions have the same value satisfying most of the descriptions. That value we can name Aristotle. We reta i n , then , Russell 's theory of descriptions insofar as it relates to Kripke's attempt to make names rigid designators, and this leads to the third alternative for treating individual variables and their relation to values . We can think of the val ues of the variable as being the objects themselves-that is, as Quine puts it, under th is objectual, as d istinct from the substitutional, interpretation, the val ­ u e s are the "things which are thus a n d so. " 1 6 In other words, w e c a n think of ontological commitment in the following way: we are ontologically committed to all those objects that are requ ired by the use of the language in a particular theory to be among the values over which the bound variable ranges . There may not be a name for a given object, but, if it is a requirement that it be posited, that is, if in order to u nderstand the theory of real n umbers we m ust posit an unspeci fiable real n umber, then we are ontologically committed to that object. Although most objects may be nameable, it is not the name that determines our commitment, but the objects to wh ich names may or may not apply. This, then , seems to be the l i nguistic criterion of ontology, and , finally, we are ready to examine it. What ontology is being presupposed? Si nce in most of our examples we have been speaking of quanti fication over the individual variable and have been con­ sistently allud i ng to the individual objects of a domain, we are presumably ac­ cepting a nominalistic ontology. I n other words, the ontology of a formal lan­ guage with a fi rst-order functional calculus framework would seem to be nomi­ nalistic . Quantification is permitted only over the individual variable, and the i nd ividual variable takes only speci fic individuals as values. But there are two major arguments to be made against this rather clear and u ncomplicated acceptance of nominalism. First, this position assumes that the x of (3 x)Fx m ust be an individual variable. Why should a formal interpretation­ even where we are dealing with a first order calculus-requi re us to label the quantified variable as an individual one? What I mean is that given (3 x)Fx the x 1 6. W V Quine, Ontological Relativity and Other Essays (New York: Columbia Univ. Pr. , 1 970), p. 1 06.

1 24

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of F takes individuals as values only if we stipulate beforehand that this x is an individual variable. But why this stipulation? Why not a labeling of x as a predi­ cate variable taking properties or classes as values or as a neutral variable taking individuals, properties, classes, relations, or other entities as values? What I should like to do in the remainder of this chapter is to try to answer three ques­ tions: (a) Is it necessary to think of x as an individual variable? (b) Is there some fundamental reason for restricting quantification to individuals? And (c) I should like to conclude by raising a question about the use of quantification as a way of indicating ontological commitment. What is this ontology we are discussing? Is it really related to traditional views, or have we simply redefined ontology in some new but perhaps innocuous way? Now, is it necessary to think of x as an individual variable? Most logic books make this assumption. F, G, and H are predicate constants; x, y, and z are indi­ vidual variables. These stipulations are usually made within the very context of a pure, uninterpreted calculus, that is, in a formal logical structure that is sup­ posedly free of any application to any subject matter such as physics, chemistry, and so forth. They are made casually and without controversy as if the reason for calling a given letter an individual variable should be obvious and should call for no comment whatsoever about the interpretation that might eventually be given to the calculus. But is there no interpretation involved when we characterize a letter in a given way? Even in ordinary language, if we have a grammatical rule that a sentence must consist of a noun and a verb, this does not tell us which nouns and verbs will become elements of the language. But it does tell us that, if any word is to be admitted into the language and if it is not a logical connector, then it must be either a noun or a verb. And this basic categorial commitment determines to a large extent what kind of ontology will be acceptable in such a language. It already determines that, whatever else may be included in the do­ main, we can be assured that the domain will consist of the denotata of nouns and verbs, for example, of objects and n-numbered relations, since these are the usually accepted denotata. Similarly, the acceptance of an individual variable is not ontologically neutral; it already commits us to a domain of individuals as distinct from classes or universals or other nonindividual types of entities that may or may not be elements of the domain. We are saying that, no matter what else we shall say in the language, we shall accept only individuals as entities of the domain, since only individuals are values of the quantified variable. The world that will be described, then, will be one populated solely by individuals, not by any other kinds of entities. But all this assumes a way of viewing the world-a nominalistic way. I am not objecting to a nominalistic viewpoint, and for all I know it may be the right one. But it ought not to be stipulated as the right one; yet this is precisely what is being done when the variable of quantifica­ tion is taken to be an individual one. After all, it is not too difficult to imagine x

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as a variable taking individuals, properties, and classes as values so that ( 3 x)Fx would be made true not only by "The girl is beautiful ," but also by "Black is beautiful'' and "Being virtuous is beautiful"-that is, where the values of the \·ariable are properties or classes rather than objects. As we have seen in the pre­ ceding chapter, Gilbert Ryle has argued that any sentence that seems to commit us to the existence of properties ought to be replaced by a sentence that commits us to the existence of individuals. , - But Ryle never tells us why one kind of sen­ tence is a better expression than the other. Ryle never tells us why a formaliza­ tion, with proper type restrictions, over a predicate term is in some way not so adequate as the identical one expressing a synonymous sentence in which the formalization is over the individual variable. Until it can be shown why the indi­ vidual variable is preferable, the linguistic criterion is open for use not merely by the nominalist but by the Platonic realist as well, since all that the Platonist re­ quires is a system in which properties or classes are also permitted to undergo quantification. There is a second argument to be made against the nominalistic position that seems to be implicit in Quine's criterion. We can ask the following question about a given domain postulated for a language: when an object is not a value of a variable, can we talk about it? The question would seem to be nonsensical, since the question itself means that we can say something about such objects or since at least it seems to be one of Carnap's external questions that is not really proper. But we can ask the question differently. Consider a domain with an in­ finite number of objects. In a listing of disjuncts, we always simply list a finite number followed by "etc." Thus (3 x)Fx becomes Fa v F b v Fc v . . . etc. The val­ ues that are actually given are, therefore, finite. Can we refer to those objects that are not yet values of the variable and apply predicates or relations to them? It would seem that the substitutionalist will answer no to this question, whereas the objectualist will answer yes. The substitutionalist, like the intuitionist in mathe­ matics, will say that, until the object is an actually named value of the variable, there is no predication of properties that can be made about it. It is like a Kantian noumenon that becomes knowable only insofar as it becomes a phenomenon. On the other hand, the objectualist will reply that we must be able to speak of objects and predicate properties of them even though they are not yet and per­ haps never will be nameable values of the variable. First, in an infinite domain there must be objects that will never become actually named values for the vari­ able, for otherwise, if every object could be named, then the domain could no longer be considered infinite. Second, we can talk about objects that are not named values just as, in Kantian fashion, we can talk about noumena. In inter17. Gilbert Ry le, "Systematically Misleading Expressions," in Logic and Language, ed. Antony Flew (London: Basil Blackwell, Oxford, 195 1 ), 1st scri. , p. 23.

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preting Kant, S . Korner states, "The conception of a nou menon is self-consistent and formed in an entirely straightforward manner by means of the rules which govern negation of concepts . If we know the rules which govern a concept, say 'coloured ,' and the rules govern ing the auxil iary term 'not,' then we know ipso facto the rules which govern the negation of the concept, namely, 'not­ coloured . ' " 1 � Similarly, the concept of an object that is not a named value is also consistent. If we know the rules govern ing "value of a variable" and the rules govern ing "not," then we know what it is to speak of objects that are not named or are not even nameable values of the variable . Final ly, we know from Cantor's proof that the class of real numbers is nondenumerable. Th is means that there is at least one real number that cannot be correlated with any natural number and thus it cannot be designated by any integer. Of the class of real numbers, then , we can say that there are unspecifiable real numbers, that is, ( 3 x)U x, even though x here cannot have a name designating the real number. What the substitutional ist has done, according to the objectualist, is confuse "value of a variable" with "named value of a variable." We say "There are dogs," but no one imagines that this refers only to those dogs that have been named . By "There are dogs" we mean "Fido is a dog or Rover is a dog or Rin-tin-tin is a dog, etc. ," where "etc." is an abbreviation for " x 1 is a dog or x 2 is a dog or . . . x" is a dog." Here x 1 , x2 , and x" indicate that in these disjuncts the objects do not belong to the class of named objects although they are still members of the class. We do not restrict our quantified sentences simply to what is named in a language . We want them to go beyond the actual instances that have been verbal ized . I n the same way, when , in a scientific context, we say "All metals are conductors," we are not j ust talking about two or three or some specific number of experiments in which a metal actually turned out to be a conductor. We are also talking about cases that have not yet been tested . In the l ight of our analysis, the notion of a domain requires redefin ition . When we speak of the objects of a domain, we must include both actual ones as well as extrapolated, or what the formalist mathematician has sometimes called constructible, objects. 1 9 We can show by a process of recursive definition or by some similar techn ique that a given number is constructible, that is, demonstra­ ble, by some finite number of mathematically or logically val id moves. For ex­ ample, in the domain of prime numbers, by using the mathematical principle of induction, we can construct for any given prime number a larger prime number. Similarly, all numbers divisible by 4 are also divisible by 2, but this does not mean that at any given instance all numbers divisible by 4 and then shown to be

78.

18. S. Korner, Kant (Bristol: Penguin, 1 955), p. 94. 19. See the discussion by S. Korner, The Philosophy of Mathematics (New York: Harper, 1960), p.

The Linguistic Criterion of Ontology

1 27

divisible by 2 are actually available to us. What we mean is that, from the num­ bers divisible by 4 and 2, we can construct a new number divisible by 4 and then show that it also is divisible by 2 . � 0 Thus "There are unspecifiable real numbers" is true even without an object as a value of its variable because (a) there is a do­ main of specified real numbers and (b) we can construct, using Cantor's proof, a proof of a real number that cannot be designated. Similarly, "There are un­ named prime numbers" is true even without an object as a value of its variable because (a) there {s a domain of named prime numbers and (b) we can construct any unnamed prime number from those that are named. On the other hand, "There are unicorns" is false because there is neither a domain of unicorns nor a way of constructing the existence of a specific unicorn from prior elements. But, even though the notion of constructible objects may be satisfactory for a domain of mathematical objects, it is not so clear that it is a satisfactory notion when the domain consists of nonmathematical, for example, physical, objects. Mathematical entities are such that, given one entity, a method can be devised whereby the existence of other entities can be shown to be entailed. Simiarly, intensional entities are sometimes said to entail other intensional entities. For example, "being a man" might in the context of a given system containing mean­ ing postulates be said to entail "being mortal" or "being rational." 2 1 But physical objects, unlike mathematical and intensional ones, cannot be said to entail the existence of any other physical objects. Thus an objectual interpretation for 'There are unspecifiable real numbers" and "There are unnamed prime num­ bers" might be legitimate, but perhaps not for "There are unknown soldiers ." And, in fact, the latter sentence can be accommodated by a substitutional inter­ pretation. "There are unknown soldiers" does not mean "There are unnamed soldiers." It does mean "There is at least one soldier-that one buried there or that one that is buried here in Arlington Cemetery-whose American name is not known." It is naming in the logical, not the conventional, sense that is im­ portant here. The logical name, "that one buried here" or "that one that is buried here in Arlington Cemetery," is present even though the conventional American name is not. The logical name, even if it is merely "that one there," is the identifying expression in a sentence regardless of whether or not it coincides with any conventional name that may have been arbitrarily chosen in some con­ text . If I say "That man there is very tall," I am using an expression that identifies a particular object and is, therefore, a name even though I do not know the so­ cial or family name given to the man. However, when I say "All men are ra­ tional," I am not making a statement solely about men who can be named in one 20. Ibid . , p. 79. 2 1 . Thus, in Carnap's language, S 1 , "human being," and "rational animal" are stipulated to " mean the same" ; Meaning and Necessity ( Chicago: Univ. of Ch icago Pr. , 1 9 56 ) , 2d ed . , p. 4.

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language or another. I am also saying that of any extrapolated object, one that is unnamed but is of the same kind as those named, if it is a man then it is rational. W hat we do in the case of physical objects is to make actual physical objects members of a class and then extrapolate from the actual members to any member of that class. An unnamed object is simply a member of that class that has not actually been given. It is as if we were to speak of an apple at the bottom of a barrel once we have selected some apples from the top and have concluded that the barrel is made up of apples. We have not actually selected an apple on the bottom of the barrel. We cannot speak of it as "this apple," but we can character­ ize it and predicate properties of it in the same way we do of "this apple." The introduction of extrapolated or constructible entities in a domain means that it is not an object that is the value of the variable, but an object insofar as it is a member of a class. It is only because actual objects are members of a class that we can extrapolate to other members that have not actually been given . It is be­ cause of the implicit commitment to a class that, of all the possible names that could replace a variable, we select only a certain grouping. In "Everyone is happy" we use the predicate "is happy" to demarcate a certain class of objects, namely, those to whom the predicate is legitimately applicable, the class of hu­ man beings. It is of the members of this class that we ask whether "is happy" is applicable. And we determine what is legitimately applicable by a possible­ worlds test. If we can coherently describe a possible world in which a given predi­ cate may or may not be applicable to a given class of objects, then the predicate is legitimately applicable to that class. On the other hand, if no possible world in which the predicate is coherently applicable to that class is describable, then we say it is not legitimately applicable-for example, in no possible world can "red" be coherently said to be applicable to the number, not the numeral, four. Thus predicates pick out classes of objects to which they may apply. If a predicate could not pick out a class of objects, then determining the truth value of a quantified sentence might become an almost impossible task. In the example "Everyone is happy," we might decide to insert, for the variable, such names as " 5 ," "6," and so forth, as well as such descriptions as "the flowers on the shelf" and "the driven snow." With all these names and descriptions available-even if they are not in­ finite in number-we might never be able to decide the truth value of ( x)(x is happy). What we actually do is use the predicate "is happy" to determine what class of names is appropriate for replacement of the individual variable. Of all the possible names there are, we pick out "John Smith," "Robert Jones," "John Doe," and so forth, because these are the objects to which "is happy" may be applica­ ble. This does not mean that the selection of names determines truth values. What is determined are the truth conditions of "Everyone is happy." The sen­ tence "(x)( x is happy)," is true if and only if John Smith is happy and Robert Jones is happy and John Doe is happy, and so forth, for all the members of the selected

The Linguistic Criterion of Ontology

1 29

class of names. But the truth of each conjunct is determined by an appeal to experiential data or to scientific data, or to both. Is John Smith happy? Is Robert Jones happy? Is John Doc happy? Therefore, it is not the object itself that is the value of the variable. It is the classified object, and this could make an important difference in how we under­ stand Quine's criterion of ontological commitment. What determines our choice of names, what determines our move from the name in one conjunct to the name in another is not that we have simply postulated a domain of entities, some of which have been named. We select a specific class of entities for the domain and then specify that only names of these entities are allowable as replacements for the variable. There can be no objects or names of objects for the individual variable without classification. Classes, or their counterparts, properties, seem to be here to stay. It might now be argued that acceptance of a classified object in a domain means that we have accepted quantification over the predicate term, since a clas­ sified object is, redundantly, an object that is an element of a class, and the intro­ duction of classes means that we are permitting predicate quantification. But are we not then unable to avoid Russell's famous paradox of impredicables? In its simplest form the paradox arises when we take it to be meaningful to say of a property or of a class that it either applies to itself or it does not apply to itself. Thus we could call a property impredicable just in case it does not apply to itself, that is, "lmpredicable (F)= - F(F)." But, now, if we substitute "lmpredicable" itself for F, we obtain the logical contradiction "lmpredicable (Impredica­ ble)= - lmpredicable (lmpredicable)." But Russell solved this paradox by intro­ ducing the simple and later the ramified theory of types that, in essence, made it impossible for a property to have itself as a property. And Quine later showed that the problems arising out of the theory of types can themselves be overcome by less complicated procedures of term stratification. 22 Thus class or property quan­ tification is a tenable logical procedure if the appropriate restrictions are made. Nor can it be maintained, as Quine once seemed to maintain, that the intro­ duction of classes into the domain is really a kind of fiction and that quantifica­ tion over predicates does not really commit us to the introduction of any platonic entities such as classes or attributes. In his New Foundations system, Quine ar­ gues that, even though quantification over predicate letters is permitted, this ought not to be taken as entailing the existence of real classes in the old Platonic sense. The classes he posits are "conceptual in nature and created by man." His system "represents . . . a position of conceptualism as opposed to Platonic real22. W V Quine, Set Theory and its Logic (Cambridge, MA: Harvard Univ. Pr. , 1 963), pp. 24 l - 5 8; same section reprinted in Essays on Bertrand Russell, ed. E. D. Klemke (Urbana: Univ. of Illinois Pr. , 1 970), pp. 3 7 2 - 87.

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Essays in Linguistic Ontology

ism; it treats classes as constructions rather than discoveries. " 2 3 But even here Quine is hesitant. He does not wish to take a strict conventionalist position in which classes, like Russell's logical constructions or incomplete symbols, can be dispensed with by a formal reduction to concrete or zero-type entities. " It would be a mistake to suppose that this metaphor (of progressive creation of classes) really accounts for the classes, or explains them away; for there is no indication of how the conceptualist's quantification over classes can be rephrased into any more basic and ontologically more innocent notation. " 2-+ In the later 'Nork of Quine, the suggestion that classes are simply man-made conventions vanishes altogether, for Quine explicitly tells us that some statements simply cannot be formalized without the use of class variables. 2 5 Thus the following statements

(x)(a)[ rna . :)(3 y)( yea ) ]

and

(3 a)(3 b)(x)(n;a. = . rnb), which contain class variables, can be transformed and treated respectively as

Fx:)(3 y)Fy and

(x)(Fx= G x ),

where quantification occurs only over the individual variable. But this kind of transformation cannot occur with such statements as

( a)(3 b )(xea. = . xeb)

and

(x)(y)(3 a)(xea. = . yea), where the prenex quantifiers are mixedly universal and existential in that order. Nor are class variables eliminable in defining the ancestor relation for which all attempts at definition seem to require the use of classes. For, if being a Platonist means that quantification over predicates is a requirement for at least some sen­ tences, then Platonism apparently cannot be avoided. Still, one might argue that the grounds here for accepting Platonism are rather tenuous. Translation of one sentence into another is never that precise, and it is not logically impossible that a translation that requires classes will eventually be 2 3 . W V Quine, From a Logical Point of View (New York: Harper, 1 96 1 ), 2d ed . rev. , p. 1 2 5 . 24. Ibid . , pp. 1 27 - 28. 25. Quine, Methods of Logic, 3d ed . , pp. 236- 37.

The Linguistic Criterion of Ontology

I31

superseded by one that avoids them. As Goodman has shown, many statements that "look hopelessly Platonistic yield to nominal istic translation. " 26 The ances­ tor relation, for example, whose definition has seemingly been hopelessly com­ mitted to class quantification has been shown, under certain l imits, to be defin­ able within a strict language of individuals. 27 Thus what I should now like to do is to argue that the commitment to class or property quantification is not simply a way of formally accommodating certain kinds of sentences. The need for classes is already embedded in the logical framework itself of the first-order functional calculus. In other words, I should like to argue that predicate quantification is impl icit in the very process of constructing a formal system. We have been maintaining that something ontological arises in our use of the quantified variable. It is under these conditions that we can determine what can be said to exist when we use a given language. It follows that, where there is no quantification, there is no ontological commitment. But is it the case that nothing ontological arises when we are involved with unquantified expressions? Specifically, we have been talking about the variable x of (3 x)Fx. But what of the F of this formula? F is a predicate constant. But what does it do? W hat is its role in the formula? It would seem to indicate something in the domain of objects, but since it is unquantified are we to say that it commits us to nothing at all? For Quine some predicates are syncategorematic in that their meaning is totally de­ pendent on some other term, for example, as when we speak of a "mere child" or an "expectant mother. " Here the predicate terms "mere" and "expectant" are only imitations of genuine predicates such as "happy" in a "happy child" and "loving" in a "loving mother. " Syncategorematic expressions, Quine tells us, are "l ike prepositions, conjunctions, articles, commas, etc. " 28 But, of course, the vast majority of predicates are not of this kind at all . In most cases they are gen­ eral terms that can be said to be true of entities . 29 But what does it mean to say of a given term that it is "true of " some entity? Quine would have us bel ieve that here we are simply speaking of a given expression that has no designatum; it is an expression that either does or does not apply. But clearly the fact that a predicate is true of an entity depends on an acknowledgment of a feature by virtue of which the predicate can be said to be true of that entity. If I say "green" is true of or is applicable to this house, I am not merely using some arbitrarily selected expres­ sion. "Green" is true of this house because the house happens to have a certain quality rather than some other quality that would have allowed us to say that "red" is true of this house. In brief, Quine wants to tell us that there are indeed individuals, since these are the values needed by existential quanti fication of the 26. 27. 28. 29.

Nelson Goodman, The Structure of Appearance (New York: Bobbs-Merrill, 1 966), p. 4 5 . Ibid. , pp. 44- 4 5 . Quine, The Ways of Paradox, p . 64. Quine, Methods of Logic, 3d ed. , p. 80 .

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individual variable. But then he also seems to want to say that nothing else need be posited in the domain, since nothing else is quantified except individual vari­ ables. But this ]eaves the analysis of the predicate term in a completely un­ satisfactory situation. Surely something more must be said about predicate terms in a formal system. They wou]d certainly seem to be descriptive in the sense that, at least on first analysis, they are not the usua] run-of-the-mil1 ]ogica] or syntactical expressions with which we are familiar. "Red" as a predicate wou]d seem to be incapable of explication without some reference to something in the domain of the language. Even Searle, who strongly opposes the view that predicate terms refer to proper­ ties, must eventually say that a predicate "ascribes a property" to an object 30-as if, in some way, a term that ascribes a property to an object does not at the same time refer to that property. (Most dictionaries take ascribing a property to an ob­ ject as a way of referring to the property. ) Thus, if Quine does not permit predicate terms to have designata, then al1 predicate terms would seem to take on an amorphous and mysterious character. There is no way of accounting for the strong sense of descriptive signification most of us feel when we use predicate terms. There is no way of my saying "The house is white�' where I take myself to be reporting the two facts that there is a house and it is white. Now, why is it so difficult to say that, just as individual terms designate individ­ uals, so also predicate terms designate properties? Why is it such a serious matter to include properties in the domain of a language? One answer, given by Searle and, I think, easily disposed of, is that if a domain contains two kinds of entities, objects and properties, then al1 sentences describing such a domain must consist only of listings of names, names of objects and names of properties; 3 1 and surely this is not what we mean by sentences. But what is it that must be added or sub­ tracted from a list of names to make it a sentence? Searle makes it seem as if the elimination of predicate terms as names of properties would suddenly change lists into sentences. But this is clearly not the case. In "John is pale" the word "pale" may be taken to be true of an object or to ascribe a property to an object or to have any other nonreferring use, but we do not have a sentence here until we take the "is" to be a means of linking the predicate to the subject, not by con­ catenation, but by some notion such as class inclusion or property possession. Every sentence is open to Searle's criticism if we omit reference to the linking devices that connect designators. Even in a formal system, Fa is not appropri­ ately interpreted until we assume that we are dealing with more than simply a predicate fol1owed by a name. The name must be taken as designating an object having F, not merely preceded by F or being immediately to the right of F. Once 30. John R. Searle, Speech Acts (London: Cambridge Univ. Pr. , 1 969), p. l 02. 3 1 . Ibid . , p. 1 0 3 .

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the linkage is recognized, then "John is pale" can be analyzed as two terms refer­ ring to two different entities tied together by property possession-John has the property of being pale. The significant, controversial answer to the question of why there is so much resistance to the inclusion of properties in the domain of a language has, I be­ lieve, nothing to do with the positing of a domain of individuals and of properties had by these individuals. Even a strict nominalist might admit that there are things and that they have properties. But what troubles the nominalist is the be­ lief that, from the premise that there are things having properties, it might be possible to deduce that there are things having common properties . Attributing a common property to objects means that two or more of these objects share or exemplify or show the same property; and analysis of this sharing or exemplifying or showing leads directly into the whole problem of universals, that is, whether or not there are properties that are never known in and of them­ selves, but are simply revealed as instances in things . Quine himself tells us that he has no objection to the assertion that a given object is white, but what he wishes to deny is the whole notion of a common property such as "whiteness. " ' 2 Quine then might admit into the domain of a formal language things with spe­ cific properties, that is, particular properties of a given object. But, whereas indi­ vidual terms can occur as either individual variables or individual constants, predicate terms can occur only as predicate constants . (3 x)Fx, for example, is to be interpreted as "This object has the specific property F, or that object has the specific property F, or this other object has the specific property F etc. " In this way only specific properties are indicated, not the highly ontologically significant common properties. However, I do not think that this move of distinguishing specific- from com­ mon properties is really effective, because I do not think that the usual truth­ functional calculus can avoid a commitment to common properties . Or, to put it differently, I do not think that a commitment to common properties is avoided by simply restricting a calculus to individual variables, individual constants, and predicate constants . W hen existential quantification is applied to an individual variable, the predi­ cate term can be, presumably, regarded as a predicate constant designating a spe­ cific property. As I pointed out above, (3 x)Fx can be interpreted as "This object has the specific property F, or that object has the specific property F, or this other object has the specific property F etc. " F can be taken as designating no more than a specific property attributable to either this object, that object, or some other object. No notion of a common property arises . But now consider ( x)Fx. In this case ( x)Fx, paralleling (3 x)Fx, is taken to read "This object has the property 3 2 . Quine, From a Logical Point of View, p. 1 3 .

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F, and that object has the property F, and this other object has the property F etc." If F designates a specific property, then it can of course be a property of this object or that object or some other object. But what it ca nnot be is a property of all the obiects in the domain. This would be as if we believed that a hat could be worn by more than one person at a time. Thus, to make sense of "(x)Fx , " F cannot be a specific property. It must be the kind of property of which it is per­ missible to say that all the individuals in the domain have it. But what is such a property if not a common one? If universal quantification is to be permitted in a formal system, then, at least on the usual interpretation, predicates must refer to common properties. It is this problem of how predicates operate with universal quantification that is not answered by Lejewski, who has tried to show that all multiquantified for­ mulas are reducible to formulas that designate specific individuals that have spe­ cific properties. 3 3 Thus he shows how the expression "() : (3 x). cpx" can be ex­ panded into

(3 x). F 1 x : (3 x). 2 x : . . . (3x). Fn x : . . . , where F 1 , F 2 , • • • F 11 are all predicate constants. But here F 1 , F 2 , and F 11 can •

•

•

be treated as predicate constants designating specific properties, since F 1 , F 2 , and F 11 are not required to be the same predicate term . But now consider if Lejewski's example had been "(3) : (x). cpx." This expression expands into ( X) . F I X : V : ( X) . Fz X : V . . . : ( X) . Fnx : V . . . ,

where, following Lejewski, F 1 , F 2 , • • • F 11 are still to be regarded as predicate constants. This resultant disjunctive series is then further expanded into •

F l a . F i b. . . F l n : V : F z a. F z b. .

•

•

. F z n : V : . . . F na. F n b. . . F n n : V . . .

.

But now we are faced with the dilemma of how a specific property designated by any one of the predicate constants, F 1 or F 2 • • • or F n' can be a property of all the objects in the domain. Each disjunct requires a predicate that can designate such a property. But, whatever property is designated in this way, it must be one held in common by a , b, . . . and n . It must be a common property. The upshot of the preceding argument is that, if universal quantification is to be permitted, then, apparently, quantification over the predicate must also be allowed. For otherwise no guarantee could be given that the F of "(x)Fx" would be applicable to all the objects of the domain. The F of this object and the F of that object would not necessarily be the same F. To obtain the notion that the F is the same in all cases, we do what is done with the individual variable. If we 33. Czeslaw Lejewski, "Quantification and Ontological Commitment," in Physics, Logic and History, ed. Wolfgang Yourgrau and Allen D. Breck (New York: Plenum Press, l 970), p. l 75.

The Linguistic Criterion of Ontology

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wish to show that one object has two different properties, we bind it with a quan­ tifier. Thus "( x)(Fx. Cx)" tells us that, given any object, it will have the properties designated by F and C. Without the quantification it would not be clear whether the x attaching to F is to take the same object as the x attaching to C. Similarly, if we wish to show that one property is applicable to two different objects, we bind it with a quantifier. Thus "(F)(Fx. Fy)" tells us that, given any property, it is applica­ ble to any objects that are taken as the values of x and y. Without the quantifica­ tion it would not be clear whether the F attaching to x designates the same prop­ erty as the F attaching to y. But if quantification over predicate variables is permitted, then, as Quine has shown, we are now firmly committed to the exis­ tence of common properties, or, to use the more significant term, universals. I have stated in the preceding paragraph that, if universal quantification is per­ mitted, then apparen tly there must be quantification over the predicate. It might be possible to have universal quantification and yet not have quantification over the predicate. The sentence, "(x)Fx," could be taken to reduce to F 1 a . F 2 b . . . F "n, with the additional metalinguistic information that F 1 is similar to F 2 and F 2 is similar to . . . F n · The common property would then seem to be avoided. A metalinguistic rule could be incorporated that would make it clear that F 1 , F 2 , and F" are to be taken as similar and not identical. However, there are well-known difficulties relating to "similarity. " To say that F 1 is similar to F 2 must mean that there is some good reason for calling them similar rather than dissimilar. But this similarity must consist of at least one char­ acteristic that F 1 and F 2 have in common. Otherwise, if none of the characteris­ tics of F 1 and F 2 was held in common, then no good reason could be given for calling F 1 similar to F 2 • Assume, then, that F 1 and F 2 have at least one charac­ teristic in common. If it is held in common, then, of course, a common prop­ erty, a universal, has been conceded. If it is not held in common, then either the characteristics are similar and we are led into an infinite regress or there is no similarity. In any event, we must either admit an intolerable infinite regress or posit a common property, a universal. In concluding, I should like to make a brief comment about the broader ques­ tion of whether quantification is really such a crucial factor in defining ontologi­ cal commitment. It might be that the entire enterprise of looking for this com­ mitment by means of the quantified variable may be misguided. Let us consider again the nature of quantification. If we say that (3 x)Fx is true, then we mean that object a is F or object b is F or object c is F, and so forth. If any one of these is true, then (3 x)Fx is true. But not all of them need be true. In other words, no specific object is necessarily required in order for the quantified sentence to be true. But under these circumstances what can it mean to call an object an on­ tological commitment of a language? If we follow the traditional view of what ontology is and the definition given by Webster's Second In ternational Dictionary

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(although cruiously enough not in the Third) that ontology is a study of essential being, then clearly no object under the proposed linguistic definition of on­ tological commitment satisfies the definition. No specific object is needed as a value of the variable, and therefore no specific object can be part of the ontologi­ cal commitment of the language . When Aristotle and, more recently, F. H. Bradley and Santayana speak of an ontological commitment, they do not mean a reference to what simply exists, but rather to what exists essentially. If it is true that x is married to y, then there is a commitment here that there is an x and that there is a y in order for the marriage to occur. But the marriage need not have occurred, and then it is not essential for there to be an x or for there to be a y. In other words, there is a commitment here, but not an ontological one. In the domain of the language x and y are not necessary objects. It is existence in terms of essences, quiddities, or universals that involve ontological commitments and not merely the fact that there are things that come and go. For this reason, many philosophers and logicians find the crucial questions of ontology to be in modal logic, rather than in the ordinary quantificational logic with which we have been dealing here. It is in modal logic that there seems to be a need to speak of essen­ tial as distinct from accidental properties, of languages dealing with an identical object appearing in all possible worlds as distinct from languages dealing with objects of a given domain . Quine may be right when he calls essentialism meta­ physical nonsense. But it is not clear whether modality might not yet require the notion of essentialism in order to settle Quine's paradox about the number of planets. It is not the value of the variable that gives us our ontology, but the value that functions solely with essential properties. In any event, the real concern with ontology is perhaps here, with the question of whether it makes sense to distinguish essential from accidental properties, and not in the ordinary quan­ tificational language.

7 Is the Number of Planets 9? I f inqui ry into the nature of ontological commitments must involve modal con­ texts, then it becomes important to examine Quine's criticism of modal logic, for Quine has argued that all modal contexts are opaque and therefore unable to sustain any basic rules of identity. More specifically, Quine has asserted that modal contexts are plagued by major difficulties involving substitution and quan­ tification. 1 He has given a-by now-famous example that demonstrates these difficulties and that supports his general view that in modal contexts terms that are otherwise unambiguously referential and mutually substitutable become opaque-that is, they lose their clear reference and are no longer subject to the identity of substitutivity. Because of this kind of ambiguity, quantification into modal contexts leads either to the positing of certain unintelligible entities called "intensions" or to an equally unintelligible differentiation among different kinds of identity. Needless to say, neither alternative is accepted by Quine. In this chap­ ter I should like to examine the example that Quine has used to make these points about the defects of modal contexts and then to show that, at least so far as this one example is concerned, Quine's points are not substantial. Quine begins by positing the following true sentences: ( I) The number of planets is 9. ( 2) 9 is necessarily greater than 7.

Then, since the rule of substitution permits the replacement of "9" in ( 2) by "the number of planets," Quine derives the false conclusion ( 3) The number of planets is necessarily greater than 7.

l . W V Quine, "Reference and Modality," in From a Logical Point of View (New York: Harper, 1961), rev. ed. , pp. 139-57.

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Thus Quine constructs the paradox of modal logic. The premises are true; the conclusion is logically inferable; but the conclusion is false. 2 The paradox deep­ ens when existential quantification is applied to (2). For then we derive

(4) ( 3 x)(x is necessarily greater than 7). But what are the values of x? Surely 9 is one of its values, since the variable replaced 9 in the move to existential quantification. But, according to ( 1 ), 9 is replaceable by "the number of planets," which cannot be a legitimate value of the variable in (4). Thus ( 1 ) simultaneously permits and denies an inference to ( 4). Quine concludes that, if we wish to accept modal logic, then one way is to restrict the values of the variable to special select ones and thus pave the way for a return to Aristotelian essentialism. That is, we must be willing to maintain that "being greater than T' is an essential or intensional property of 9, in the sense that it would hold in every possible world while it is a contingent or extensional property of the number of planets, since there could be a possible world in which the number of planets is not greater than 7. With such reliance on essences and possible worlds, it could then be maintained that 9, but not the number of plan­ ets, is a legitimate value of the individual variable of ( 4). Quine, however, ar­ guing that intensions are "creatures of darkness" and cannot sustain either an identity or a synonymy relation, and that it does not make sense to speak of iden­ tification of particulars across possible worlds, prefers to reject modal logic rather than be led to the acceptance of an unintelligible metaphysics. · I am not sure whether a reversion to a belief in the existence of Aristotelian essences or Camapian intensions is required for an interpretation of modal logic. Certainly Terence Parsons and Leonard Linsky have asserted that modal logic requires only that essentialism be meaningful and not that it be true. -+ And I am not sure whether "possible worlds" is not a necessary concept for the understand­ ing of counterfactual sentences and proper names. But, no matter how these is­ sues are settled, I should now like to show that the paradoxical example that Quine uses does not suffice to prove his argument against modal logic. In fact, Quine's example can be made intelligible without involving paradox and without 2. Although it might be pointed out that the medieval astronomer, Francesco Sizi, claimed to prove that the number of planets was necessarily seven. Sec G. Holton and D. H. D. Roller, Foun­ dations of Modern Empirical Science (Reading, MA: Addison-Wesley, l 958), p. 160. 3. W V Quine, " Reference and Modality," pp. 152-54; Words and Objections: Essays on the Work of W V Quine, ed. Donald Davidson and Jaako Hintikka (Dordrecht, Holland: D. Reidel, l 969), p. 343. 4. Terence Parsons, "Essentialism and Quantified Modal Logic," in Reference and Modality, ed . Leonard Linsky (London: Oxford Univ. Pr., 1971), pp. 73-87; Leonard Linsky, Names and Descrip­ tions (Chicago: Univ. of Chicago Pr. , 1977), p. 145.

Is the Number of Planets 9?

1 39

a commitment to essences, intensions, or some strange set of Kripkian possible worlds. Quine accepts ( 1 ) and (2) on their face value . Both are, presumably, well­ formed sentences to which "true" or "false" are legitimately applicable. Quine nowhere does for ( 1) and ( 2) what he elsewhere does for other recognizable com­ plicated sentences. Elsewhere, in both his Wo rd and Object and his Methods of Logic, Quine is constantly showing how sentences that seem to be well con­ structed are really not well constructed at all. 5 Also, he is contantly indicating how a word wrongly placed or an expression mistaken to be a real name rather than a description leads to paradoxes and philosophical problems that ought not to arise. In face, in his Mathematical Logic Quine is very cautious about accept­ ing any description on its face value. He tells us that "ordinary usage gives us no clue as to the meaning of [many] descriptions.'' 6 But Quine does not ask whether there are any unusual complications in ( 1) and (2). 7 They are precisely what they are. Even the use of a modal term in (2) does not cause Quine any discomfort, presumably for the simple reason that the necessity of mathematical sentences can be given a fairly safe definition in terms of an axiomatic system, and the sense of (2), if here we may speak noncontroversially of a sense of a sentence, is normally taken to be quite clear and intelligible. Furthermore, Quine does not attempt to produce a formalized version of his paradoxical example. He does not attempt to formalize ( 1) and ( 2) or to ask whether a change of structure might result if such formalization were to take place. "All metals are conductors," as an English sentence, can be classified as a subject-predicate form with "all" as an adjective modifying the subject "metals. " But this would not be the appropriate form of the sentence when it is translated into formal terms. Yet such translation is required if we are to test the logic of any arguments in which such a sentence appears. However, it should be pointed out that Quine does not ignore any formal challenges to his argument. He is quite ready to answer those who attempt to fault his paradox on the grounds that a formal error is involved. Thus Smullyan has argued that if we formalize (3) we find that it contains a scope ambiguity that permits it also to be stated as (3 ') Necessarily the number of planets is greater than 7. 8

Once we are aware of this ambiguity, the paradox disappears. If the scope of

5 . Thus see Word and Obiect (New York: Wiley, 1 960), ch. 4, and Methods of Logic (New York: Holt, 1 972), 3d ed. , pp. 4 5 - 49. 6 . W V Quine, Mathematical Logic (New York: Harper, 195 l ), p. 1 46. 7. Thus R. B. Marcus criticizes Quine for taking ( l ) as a '"true identity' without hint of ambigu­ ity" ("Extensionality," in Reference and Modality, ed. Linsky, p. 50). 8. A. F. Smullyan, "Modality and Description," in Reference and Modality, ed. Linsky, pp. 3 5-43.

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the description is large, as in ( 3 ), then, according to Smullyan, the conclusion does follow, but it says no more than that, as a matter of brute fact, the number of planets satisfies the condition that it is necessary that that number is less than 1 0 and greater than 7 . If the scope is small, as in ( 3 ' ), then the conclusion is indeed false, but it does not follow from ( 1 ) and (2). Thus there is no paradox. Quine, however, responds by showing that Smullyan's criticism does not eliminate the paradox. We cannot accept ( 3 ) as an intelligible, since the existential quantifier extends to a variable thdt is past the modal operator and such quantification is for Quine always opaque. Furthermore, for Quine all modally quantified sen­ tences are opaque and, therefore, in both ( 3 ) and ( 3 ' ) substitutivity of terms is not legitimate . 9 Quine, then, is prepared to show that the paradox arises even if formalization occurs . But both he and Smullyan, as well as others who have sought to deal with Quine's paradox, 10 assume that, except for the ambiguity in the placing of the modal operator in (2) and ( 3), all three sentences are what they seem to be. They consist of modal operators, identity signs, relational predicates, singular signs, and definite descriptions . It is with these expressions that we must deal, and with no others . Our question then is whether ( 1 ), (2), and ( 3) are above reproach. More specif­ ically, are ( 1 ) and (2) above reproach, since whatever affects them will automat­ ically affect (3)? Are their component parts so clear and undeniable that the only issue in the paradox relates to the use of the modal operator? ( 1 ) seems to be unproblematical. Certainly in ordinary, nonformal contexts ( 1 ) would seem to be a clear identity statement. What is the number of planets? The number of planets is 9. The identity seems to be clear. But as soon as we begin to think of ( 1 ) in more formal terms, its structure and its obvious identity connective begin to lose their clarity. "The number of planets" is, of course, not a name. I t is not a name not only in the sense that the form is that of a description, but also in the sense that it is not to be regarded as a descriptional name in the way "The little Corporal," "The Prince of Denmark," 'The Sage of Concord," and "The Great Dissenter" might perhaps with some validity be taken as alternative proper names of Napoleon, Hamlet, Thoreau, and Oliver Wendell Holmes, respec­ tively. 1 1 "The number of planets" is an ordinary, or an apparently ordinary, phrase that no one would seriously think of capitalizing. But, now, is "the number of planets" a definite description? The fact that it 9. Words and Obiections, ed. Davidson and Hintikka, p. 338. 10. The most important papers on the paradox appear in Reference and Modality, ed. Linsky. 11. The examples are from R. B. Marcus, "Modalities and Intensional Language," in C ontem­ porary Readings in Logical Theory, ed. I . M. Copi and J. A. Gould (New York: Macmillan, 1967), p. 283.

Is the Number of Planets 9?

141

begins with "the" is not a primary consideration , since "the" often functions as a u n iversal rather than as a particular designator, for example, "The elephant is a huge animal . ·· But is it a defin ite description in the way "the author of Waverly" and "the king of France" would be considered defi nite descriptions? It would seem to be . 'The author of Waverly" appl ies to one and only one individual, namely, Sir Walter Scott, and "the king of France" would also apply to one and only one individual if there were a king of France. Similarly, "the number of planets" would seem to apply to one and only one i ndividual, namely, 9 . But there are certain striking differences. First, there is an obvious syntactic dif­ ference . " France" and "Waverly" are proper names; "planets" is a plural common nou n . What this means is that " France" and "Waverly" cannot function as predi­ cates i n the way "planets" can . We can say "Venus and Mars are planets" or "Earth is a planet," but we cannot say "This country is a France" or "Th is book is a Waverly. " Second, if we follow Russell , from "the author of Waverly" we can derive the conj unction "there is an x such that x is an author" and "x wrote Waverly. " A similar derivation can be made for "the king of France . " But con­ sider what occurs with the parallel move in "the number of planets . " We can derive "there is an x such that x is a number. " But what is the next conj unct? Is it "x n umbers planets" or "x numbers the planets" or "x is the sum of the planets"? The fi rst one is unintelligible; the latter two lead to an infinite regress of defin ite descriptions. Perhaps with sufficient manipulation we can eventually obtain a suitable derivation . But it is surely j ustifiable to say that "the n umber of planets" does not lend itself easily to conversion by Russell's theory of descriptions. Fi­ nally, it is exceedingly difficult to find a description that has a plural common noun replacing the proper name. Except for the case of "number," there are problems . We m ight have such expressions as "the lover of women" or "the friend of animals . " But it is interesting that these descriptions are not of a Rus­ sell ian sort, since their inclusion into sentences results in un iversal rather than existential quanti fiers with uniqueness clauses, for example, "The lover of wo­ men is happy," "The friend of animals is kind . " On the other hand , if we change these examples into ones containing genuine definite descriptions, then we would have "The lover of the women (in the harem) is happy," "The friend of the animals in the zoo is kind . " The common noun disappears in favor of another defin ite description . Thus "the number of planets" seems to be a legitimate de­ scription when we are dealing with n umbers, but, outside the context of num­ bers, the parallel expressions we obtain are not definite descriptions. If "the n umber of planets" has some strange characteristics, consider 9 as it appears in premise ( I ). S ince ( 1 ) is taken by Quine to be an identity statement, 9 m ust be either a description or a proper name. It is surely not a description i n any manner or form . Thus it must be a proper name . But it is an odd proper name.

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We need not get involved in the standard obvious question concerning how numbers can denote. Perhaps an argument can be made that somewhere in some world or in some conceptual realm there are certain Platonic entities that corre­ spond to our numerals. But let us step away from the hoary traditional issues that surround this argument and merely consider certain syntactical difficulties in­ volving 9. Proper names do not function as predicates except under very select and easily explainable conditions. In "He was a regular Don Juan," the name " Don Juan" seems to be functioning as a common noun. But this sentence is merely an ell iptical way of saying " He was l ike Don Juan" or " He was acting l ike Don Juan. " "Don Juan" itself still retains its proper-name status . In general , then, proper names do not lend themselves very easily to a sudden shift to predi­ cate status. But numbers, on the other hand, move back and forth easily from proper name to predicate. "The number of pennies in his pocket is 9" has 9 as a proper name. But "He has 9 pennies" has 9 as a predicate, or, at least, it is in the slot that is normally reserved for predicates. We speak of individuals as being 6 feet tall, and surely 6 here is a predicate or a part of the predicate verb modifying the individuals mentioned. Thus 9 is not a reliable proper name. However, with all the peculiarities that accrue to ( 1 ), there is one last odd fea­ ture that must be indicated . Consider the sentence "The brilliant author of Waverly is Sir Walter Scott. " If we formalized this sentence in the standard man­ ner, we should be able to infer from it " Sir Walter Scott is brilliant and is an author. " The latter sentence is well formed, involving no special syntactic or se­ mantic problems. (We assume here, of course, that proper names are allowable in the system. ) Similarly, from "The bald king of France is Louis XIV," we can derive "Louis XIV is a king and is bald. " Again, the latter sentence is well formed without any special difficulties . But now consider the following: "The terrible thing in the doorway was Frankenstein's monster." Following the previous proce­ dure we can obtain from this " Frankenstein's monster was a thing and terrible." But this sentence is not well formed, since we know that "thing" cannot be used as a common noun without involving paradox. "Frankenstein's monster was a thing and terrible," if it were a well-formed sentence, would be a contingent truth. But then "Frankenstein's monster was not a thing and terrible," which ought also to be a contingent truth, turns out to be, when existential quantification is ap­ plied, a contradiction, that is, "There is a thing that is terrible but not a thing. " Now, of course, the analyses of Wittgenstein, Carnap, and Ryle, who explored category errors in detail , have shown us what has gone wrong in such a sentence as "The terrible thing in the doorway was Frankenstein's monster." We cannot incorporate the category terms l isted in the metalanguage into the object lan­ guage. We cannot speak of things in the same way we speak of chairs, tables, and monsters. I cannot say "This is a thing" and then think I can perform the same logical operations that would be suitable for "This is a dog" and "This is a chair,"

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and so forth. As Wittgenstein and Carnap long ago pointed out, "thing," like "property" and "relation," is a syntactic category term that categorizes certain en­ tities without itself being one of the entities. A man can have a property of being an athlete; he does not also have a property of being a property. Thus, if we are not aware of the peculiar status of certain kinds of terms such as "thing," "prop­ erty," and so forth, we fall into paradox and become involved in issues that ought never really to have arisen. Now, the argument might be made that we can construct a formal language in which we introduce (a) a variable that ranges over entities and (b) a constant, T, representing the (categorial) property of being a thing, so that we can formalize "There are red things" as (3 e)(Te. Re). But then the following must also be well formed, (3 e)(Te. Re), that is, "There are red entities that are not things," and this seems to be a peculiar sentence. If e ranges over properties, then (3 e)(Te. Re) be­ comes "There is a property that is red and it is not a thing," which is also a peculiar sentence, but might seem plausible if it is plausible that there are red properties that are not properties of things. Furthermore, if e ranges over properties, then (3 e)Te is a well-formed formula, but this means that it can be correct to say that there is a property that is a thing or that has the property of being a thing . This may not be formally contradictory, but it is linguistically improper. Perhaps there can be a formal system in which a predicate constant represents the property of being a thing, but I think that such a system would be an example of one of Church's deviant systems that violate our most basic linguistic intuitions. W hen we turn to "The number of planets is 9," we find that the same kind of paradox arises here as in our "thing" example. From ( 1 ) I can derive "9 is a num­ ber." But this is not a well-formed sentence, just as "Frankenstein's monster is a thing" is not well formed. In the distinction he makes between sentences in the material mode and those in the formal mode, Carnap makes a special point about numbers. He warns explicitly that we ought not to say "5 is not a thing, but a number," but rather " 'Five' is not a thing-word, but a number-word ." 1 2 I am not sure that Carnap's translation is fully satisfactory, since there are undoubtedly problems involved in distinguishing thing-words from other categories of words. But the main point is that he is warning us about treating "number" as if it were an ordinary predicate or about treating "the number of planets" as if it were log­ ically comparable to such phrases as "the friend of animals" and "the lover of women." "Number," "thing," "object," "relation," and "property" are all what Carnap calls "universal words." These are very important in a language, but they are part of the syntax of the language. They must not be mistaken as material terms designating material entities. As Carnap tells us, "The habit of formulating in the material mode of speech causes us . . . to deceive ourselves about the 1 2. R. Carnap,

Logical Syntax of LAnguage (London:

Kegan Paul, 1 937), p, 286.

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objects of our own investigations: pseudo-object sentences (those such as 'Five is not a thing but a number' ) mislead us into thinking that we are dealing with extra-linguistic objects such as numbers, things, properties, experiences, states of affairs, space, time, and so on; and the fact that, in reality, it is a case of language and its connections (such as numerical expressions, thing-designations, spatial co-ordinates, etc. ) is disguised from us by the material mode of speech. This fact only becomes clear by translation into the formal mode of speech, or, in other words, into syntactical sentences about language and linguistic expressions:" 1 ' Is Carnap's analysis of the so-called universal words correct? Thing-words, for example, may require explication in terms of individuals, j ust as number-words, that is, numerals, may require explication in terms of numbers. But Carnap is surely correct when he warns us not to confuse different kinds of predicates. If a formal system permits me to say that something is colored and red, then it will also permit me to say that something is not colored and red. We already know that, if we are to avoid Russell's paradox, we must not permit predicates to be predicated of themselves. So it ought not to be so strange that certain categories of predicates ought not to be conjoined with certain other categories of predi­ cates. In other words, whatever the shortcomings of Carnap's analysis, the major point is valid. We cannot take expressions at face value. If now we return to Quine's paradox and examine it in the light of the sentence analysis given above, then the whole paradox is seen to hinge on the acceptance of ( 1 ) as an identity statement. As I have indicated earlier, the criticism concern­ ing the ambiguity of scope of the modal operator is correct, but, as Quine has pointed out, the paradox is not eliminated. Since quantification into and within a modal context is always referentially opaque, the conclusion (3), regarded in either its de re or its de dicto form, that is, with the description having either large or small scope, remains paradoxical. But if "the number of planets" is neither a name nor a description and if 9 is not a name, then the identity implied in ( 1 ) is not established and the paradox fails. W hat I suggest is that ( 1 ) should be treated as a linguistic deviant that, in ordinary language, seems to be an identity state­ ment but, formally, is something quite different. And, indeed, it is Quine him­ self who gives us the paradigm for dealing with ( 1 ). He tells us that "The Apostles are twelve" ought to be formalized as

( 5) (3x 1 2)Ax,

that is, "There are 1 2 Apostles," 1 4 where the number 1 2 can be eliminated by the expansion of ( 5 ) into a schemata of 1 3 variables. That is, if we take a simpler example such as "The Apostles are 2," then this sentence can be converted into "There are 2 Apostles" and then formalized into 1 3 . Carnap, Logical Syntax of Language, p. 298 . 1 4. Quine, Methods of Logic, p. 240.

Is the Number of Planets 9?

145

(6) (3 x)(3 y)(A x . A y . (z)(Az= : z� = x. v . z = y)),

where 2 does not appear. Similarly, we could expand ( 5 ) in such a way that only quantifiers, variables, general terms , and logical constants appear. The number 1 2 is d issolved . Now, "The Apostles are 1 2" is surely equivalent to "The n umber of Apostles is 1 2 ," and the same formalization would be given for both . Thus if we apply this reasoning to "The number of planets are 9," we obtain that is, "There are 9 planets," where the number 9 can be el imi nated by expan­ sion of (7) i nto a schemata of 1 0 variables. The obvious identity of ( I ) has lost its obviousness. But, more than that, the values of the variable are now planets and not n umbers . "Number" and "9" are no longer legitimate expressions in ( I ). What does the change of ( I ) to (7 ), that is, "There are n ine planets," mean for Quine's paradox? The immediate result is that, if we take (7) as a premise in con­ junction with (2), then the conclusion ( 3 ) no longer follows. We construct (7) by the use of quantification over individual variables and identity; the existence of classes is not required. On the other hand, if (2) is the pure mathematical sen­ tence we assume it is, then , as in the case of all pure mathematical sentences, it must be formulated in terms of classes. Thus, for example, we define I as the class of all those classes a which have exactly one member y apiece. But u nder these circumstances nothing in (7) can be replaced by anyth i ng in (2). I n other words, the rule of substitution is simply not applicable here. We might see this point more clearly if we examine a fairly simple example. Consider a premise 'There is only one chair," which we formal ize as

( 8) (3 x)(Cx. ( y)(C y= . y = x )).

Now we assume a second premise, " I is necessarily larger than O," which we formalize as

( 9) D ( L( a : (3 y )( x )( x e a . =. x = y)), d -(3 x)(xea)),

where " L" means "larger than . " Even if w e ignore the substitution difficulties that arise because o f the modal operator, we can ask whether any substitutions can be made between (8) and (9). The answer would turn out to be negative. Can we derive any paradoxical con­ clusions such as "There is necessarily at least one chair" and "There is neces­ sarily more than zero chairs"? None of these conclusions can be sustained . Nor ought any of this to be surprising, since what we have done here is made expl icit the old positivistic contention that the analyticity of pure mathematics ought not to be confused with the syntheticity of applied mathematics . Although "2 + 2" necessarily equals "4," it does not follow that " 2 apples put together with 2 ap­ ples" necessarily equals "4 apples . " We cannot connect our pure mathematics to

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observational statements in such a way that we derive necessarily true observa­ tional statements. But this is exactly what has happened in the formulation of Quine's paradox. A pure mathematical statement, (2), has been conjoined with an observational statemen't , ( 1 ). What has misled us is the quirk in natural lan­ guage that permits numerals in observation sentences to occupy slots that are normally reserved for proper names. Thus we can say "The number of planets is 9" even though the deep-structure form is "There are 9 planets." Two counterarguments might be made, and I should like to reply to them. First, it might be argued that we have not been fair in·our translations of ( 1 ) and (2). Although we have changed ( 1 ) into (7), the formal system employed for (7) is different from that employed for (2), and then, of course, it is understandable that no conclusion follows from ( 1 ) and (7) and that no rules of substitution are applicable. From "All men are mortal" and "Socrates is a man," nothing can be inferred unless both sentences are members of the same formal system. From (x)(Mx::JGx), in which M and C are general terms, conjoined with seM, in which M is a class term, no inference can be drawn unless a suitable translation rule converting general terms to class terms or class terms to general terms is included. Thus not only must we think of formalizing (2) and (7), but we must also formalize them under the same syntactic and semantic rules. The question then arises: would the paradox occur again if (7) were stated in class rather than general terms? Again, in order to simplify matters, let us deal with (8) and (9). If a paradox arises here once both (8) and (9) are stated in class terms, then it will also arise in (2) and (7). (9) is already in the appropriate form. (8) can easily be changed into

( 1 0) (3 x ) ( 3 C )( rnC. ( y )( y eC = . y = x )),

where "C" is "the class of chairs. '' What follows from ( 1 0) in conjunction with (9)? Again, if we overlook the problem of substitution in modal contexts and permit substitution of a by C in (9), we obtain the innocuous conclusion that necessarily the class of one chair is more than the class of zero chairs. No paradox arises. Therefore, no paradox would arise in (2) and (7). Second, it might be argued that there are surely some sentences that are not pure mathematical sentences and that do seem to commit us to the positing of a number as an existent entity. Thus 'The number of Apostles is equal to the num­ ber of Muses," if it were true, would commit us to the number 1 2 or to some other specific number. What else but a number would give a truth value to this sentence? If a domain of numbers must be posited, then "The number of planets is 9" ought to be a legitimate sentence. But, as Quine points out, there are no existent numbers, since numbers are always translatable into classes of classes in

Is the Number of Planets 9?

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which the variables do not take numbers as values. 1 ' Since we can translate 0, 1 , and + into class terms, the sentence "The number of Apostles i s equal to the number of Muses" can be stated as

( 1 1 ) (3 k)(N k. aek. bd), where a and b are the classes of Apostles and Muses, and their being members of k means that they belong to N, that is, every class to which O and 1 + each member belongs. And since O and 1 and + are definable solely by classes, no number object is designated by a numeral and no substitution occurs of 9 as a value of a variable in the formalization of "the number of planets ." Thus it would seem that Quine's paradox arises because of a fairly elementary error, namely, that of taking an apparen t identity as a genuine identity statement. There are indeed 9 planets, but this does not mean that the number of planets is identical to 9. 1 5 . Ibid. , p. 242 .

8 Individuals We have been arguing that ontological commitments are derived from a structure that is expressed by a language framework and from a set of values that can be fitted into the variables of that framework. But the values of the variable should not be confused with the substituends-the expressions-of the variable. The expression replacing the quantified variable ought not to be confused with the object designated by the expression. The commitment is to the object, even if it is unnamed, rather than to the name itself. But what kind of commitment is this? W hat kind of ontology are we committed to by Quine's criterion? Are we nominalists if we permit quantification to be used only with the individual vari­ able? Or are we realists if we speak of individuals as members of classes and, therefore, permit quantification over predicates? Or are d istinctions between in­ dividuals and classes a strictly arbitrary matter, so that an individual in one dis­ course can be a class in another? If we follow Quine's criterion, what are we­ nominalists, realists, idealists, conceptualists, or some variant of these? On first analysis it would seem as if the nominalist takes the palm. We consistently ask what the values of the variable in such a quantified form as ( 3 x)Fx would be. But (3 x)Fx in the normal first-order functional calculus takes individuals as values of the variable. We seem to be inclined toward a nominalistic position, since, if quantification is accepted as our criterion for ontological commitment, then it is the nominalist rather than the realist who insists that quantification must occur only over the variable that we characterize as individual. For the nominalist only ind ividuals exist, and therefore only quantification over the individual variable is permissible. But now a number of questions arise . Presumably quanti fication can occur over property, class, propositional, and perhaps conceptual variables without any violation of any fundamental rule of formation or of any semantical rule of interpretation. We might require the ad-

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mission of properties, classes, propositions, and concepts into our domain if we introduce such \'ariables and permit them to be quantified. And we might re­ quire some notion of type levels of expressions in order to avoid the standard paradoxes. But quantified systems of predicate and individual variables have been proved consistent and complete within the confines of Godel's restrictions. Thus if quantification of an individual variable has some prior claim over quan­ tification of some other kind of nonindividual variable, then this claim has still to be argued. The linguistic criterion simply states that, whatever variable is quantified, its values make up our ontological commitment The criterion does not tell us which variable is to undergo quantification. More important, even if quantification over individuals does have some claim to priority, it must still be determined what is or is not an individual. If the defini­ tion of an individual is too narrow, for example, if the definition only permits Wittgensteinian simple objects or Al lairean bare particulars, then all these nor­ mal , everyday entities we take to be individuals-John Smith, the boy next door, this chair, that man, and so forth-are excluded as values of the variable and make our formal language strangely removed from any connection with natural language. If the definition is too broad, then classes, numbers, anything can be­ come a value for the individual variable. In fact, Russell at one time believed that, with some lingual manipulation, predicates can be changed to names, and vice versa, so that an individual in one context can be a property in another. Thus he argued that "This is red," where "this" designates an individual , can just as easily be replaced by " Redness is compresent with centrality," where "redness" is a name. 1 The same translation can be made for such sentences as "This is hard," "This is pleasant," and so forth. Similarly, what we ordinarily think of as concrete individuals, for example, this house and that bal l , can be changed into universals. "This house is white and that ball is white" can be differently ex­ pressed as "The same phenomenal quale white is a member of two different classes, the house class and the ball class." The quale white, that is, the experi­ enced white, becomes an individual . (Of course, with the introduction of type theory, this interchange of predicates and names is not allowable.) More recently, Carnap makes the fol lowing claim: anything can be a value for the individual variable. It is all simply an arbitrary choice depending on what we take to be entities of the lowest level (the level zero, as Carnap calls it): " For one system the individuals may be physical things, for another space-time points, or numbers, or anything else." 2 This would seem to imply that there could be formal lan­ guages that take classes or properties or fictitious entities or propositions as their 1. Cf. Bertrand Russell, My Philosophical Development (New York: Simon and Schuster, 1959), pp. 161- 72. 2. R. Carnap, Meaning a nd Necessity (Chicago: Univ. of Chicago Pr. , 1956), 2d ed., p. 32.

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individuals, and, in their own way and in their own context, they could be just as genuine and perhaps even j ust as fruitful as languages that take what we normally regard as individuals, for example, that man, John Smith, and so forth. The up­ shot of this would be that ontological commitment would become trivial, since nothing could be legitimately disqualified from being an individual. Ontologies could be changed to fit the discourse. Literary contexts could be idealistic or phe­ nomenalistic if the basic individuals are taken as ideas or images in the minds of the authors and readers; mathematical contexts could be realistic if the individu­ als are sets or Platonic numbers; and physical contexts could be nominalistic if individuals are strictly atomic particles. But with this plethora of ontologies comes an interesting difficulty. Presumably each of these contexts would consist of a formal language in which existential quantification would be applicabie to some domain of entities. In a literary context, for example, we would be using the apparatus of quantification with a domain of literary entities rather than a domain of numbers or classes or properties or physical things. In a context of physics, we would be using quantification with a domain of atomic entities. Every context would have its own peculiar domain. But this has one very impor­ tant consequence: in every context there would be a need to show how the do­ main is distinguished from all other possible ones. We would be required to indi­ cate in what way this group of entities is uniquely differentiated from other possible groups of entities. Otherwise we might mistakenly come to believe that the domain of literary entities is different from the domain of physical entities only in the way chairs might be different from tables. Or we might come to be­ lieve, in the manner of Meinong or the early Russell, 3 that there is one all inclu­ sive domain-a domain that, according to Russell, attributed being to absolutely everything-whose species or subsets can be dogs, cats, Shakespeare's characters, numbers, the Homeric gods and chimeras, and anything at all. Meinong's do­ main is a bit more restrictive, since being is not attributable to everything, only to existent things such as horses and to subsistent possible things such as numbers, sets, and golden mountains. Impossible things, which Meinong labeled a us­ serzein, such as round squares and golden nongolden mountains, are beyond being and cannot be said to be in any sense. Russell's later theory of descrip­ tions is a criticism of his earlier view about the all-inclusiveness of being. That all objects of thought have being seems to imply a totally unacceptable popu­ lation explosion. Vacuous names do not refer to nonexistent objects; they are merely disguised descriptions that are unsatisfiable. Nor is Meinong's analysis satisfactory. It seems to assume that existence, subsistence, and nonbeing are le3. Cf. the discussion of Meinong's theory of objects by R. M. Chisholm, "Beyond Being and Nonbeing," in New Readings in Philosophical Analysis, ed. H. Feig!, W Sellars, K. Lehrer (New York: Appleton, 1972), pp. 15- 22. See also Bertrand Russell, The Principles of Mathematics (New York: Norton, 1937), 2d ed., p. 449.

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gitimate predicates, and this assumption has been fairly well repudiated by Kant, Russell, and other philosophers . Also, the problem of making objects beyond being and nonbeing intelligible seems to be an awesome task. But most impor­ tant, as Russell points out, if we can speak of such objects as round squares, then this would seem to entail a violation of the law of noncontradiction. For if the round square is round and if the round square is also square, then the round square is both round and square, a contradiction if what is round is not square. Meinong might argue that round squares are neither existent nor subsistent en­ tities so that, whereas "being round" and "being square" are not attributable to the same actual entity, they can be attributed to the same impossible entity. (After all, why should it matter what is attributable to impossible entities?) But if con­ tradictory predicates can be applied to an object, it seems difficult to understand what the object is . It is not because there are actual things that we say that objects cannot be both red and green. Even of ethereal objects we would make the same claim, so that the very status of an object being an object-existent, subsistent, or otherwise-would be suspect if contradictory predicates could be applied to it. The upshot of al l this is that there is something suspicious about the assertion that we can blithely refer to various levels of abstractness going from concrete actual things to subsistent possible things and then on to impossible things. Dif­ ferent levels of colors are intel ligible . I can say that this green is darker than that green. But there is not a parallel discourse in which we can move from existence to subsistence and then to nonbeing. No one takes seriously the view that, like the Cheshire cat, an object can become less real until only its smile remains. Still, domains must be distinguished; otherwise we could mistakenly come to believe, as I think Bergmann and some of his school do, that there can be one domain consisting of physical things, numbers, and even logical connectors. Reinhardt Grossmann argues that the empirical world, the world we experi­ ence, does not consist solely of material or perceptual objects. Agreeing with Bergmann, he asserts that we perceive such negative states-of-affairs as this is not green and such universal states-of-affairs as all the things in this room a re green . We perceive "not only individuals, properties, and relations but also negation, connectives and quantifiers (including numbers)," 4 so that presumably, if in a formal system we are dealing with an empirical subject matter, even quantifiers can become values of the variable! Grossmann is right in indicating the diffi­ culties of explicating quantification, negation, and even th� ordinary logical connectors. Truth-table definition of "p or q," for example, as the disjunction " pq v{Jq v pq" produces only circularity, since " v " is still interpreted as "or." 4. Cf. G. Bergmann, "Ineffability, Ontology, and Method ," and "Generality and Existence," in Logic and Reality (Madison: Univ. of Wisconsin Pr. , 1 964). Sec also Reinhardt Grossmann, "Bergmann's Ontology and the Principle of Acquaintance," in The Ontological Tum, ed . M . S . Gram a n d E. D. Klemke (Iowa City: Univ. o f Iowa Pr. , 1 974), p. I 09.

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But such difficulties ought not to mean that logical expressions are designators. It seems hard to believe that "if and only if" refers to an entity. Can we then just permit numbers and physical objects to be members of the same domain? Those who think numbers are merely numerals or similar inscriptions would want to argue in this way. After all, "being round" may not be applicable to this or that object, but this surely should not be taken to mean that we reject these objects from the domain. "Being greater than five" is not applicable to this house; yet the nonapplication of a predicate does not cause loss of membership of this house in the domain of physical things. Similarly, while "being red" is not applicable to 7, this fact in itself does not preclude 7 from being a member of the domain of physical things. The counterargument to this, of course, is that things are not simply lumped together in the same domain. All objects must be groups or sets of the same genus. This does not mean that "genus" must be hypostatized into some essence or some other Platonic entity. We can simply say that we only put together in the same domain things that have some predicate that is applicable to them. Chairs and tables belong to the same genus because there is a predicate that is applicable to both, namely, "being physical." On the other hand, "being physical" is not applicable to numbers, and therefore they are excluded from the domain. But it is well known that if we look hard enough we can always find some predicate that would bring excluded objects into the same domain. In fact, there is no need to look that hard at all, for, if we are allowed disjunctive predi­ cates, we can say that "being either a number or a physical object" is applicable to the domain of physical objects and numbers, and, therefore, numbers are part of the same domain as physical objects. But, if disjunctive predicates of this sort seem to be a kind of sleight of hand and if we do not permit molecular predicates, we can still discover an atomic predicate that would permit the most disparate entities into a domain. Indeed, it might be argued that "being physical" is itself a complex predicate that can be defined by means of terms designating elementary Wittgensteinian objects. And, if we follow one important interpretation of Witt­ genstein, these objects are not material particles; they are " bare particulars . . . possessing formal but not material properties." 5 I am not sure that I understand what it means to speak of formal properties of nonmaterial objects. But presum­ ably a "formal property" of an object refers to its potentiality as distinct from a "material property" that refers to its actuality. "Being red" designates a material property. "Being capable of being red" designates a formal property. A domain could be characterized by "having formal properties" and then both material en­ tities and numbers would be part of the domain, since numbers surely have for5. Irving M. Copi, "Objects, Properties, and Relations in the Tractatus,"' in Essays on Wittgen­ stein's 'Tractatus,' ed. Irving M. Copi and R. W Beard (London: Routledge and Kegan Paul, 1966), p. 184.

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mal properties . The n umber 5 has the capacity of being added to 2 to make 7; ergo, chai rs , tables , and n umbers belong to the same doma i n . Aga in we might counter this by si mply denying the kind of reduction ism practiced by Wittgen­ stein and later rej ected by him . We m ight argue that a nonmaterial object can be equated with a nonexistent object, si nce the two surely cannot be d istinguished from one another. And , if we are dealing with nonexistent objects , it is difficult to see not only how we can actually be deal ing with them , but also how it is at all possible to be attributing properties to them . Of cou rse , we are always charac­ terizing fictitious entities , for example, Pegasus was winged and Hamlet was moody, but we never incl ude Hamlet and Pegasus in the same doma in as our physical objects . And , as far as numbers are concerned , if they are nonmaterial obj ects, yet i n some way still existent objects , it is surely a m istake to say that they have formal properties in the sense of having certain capacities . The number 5 does not have a capacity of being added to 2 to make 7 . Capacities enta i l the possibil ity of failure or lack of real ization. My having a capacity to be a musician means that I m ight fail to become a musician or j ust si mply decide not to. Other­ wise I would actually be a musician or be in some way ordained to become a musician . It would no longer be a capacity. On the other hand , 5 is necessarily connected to 2 to make 7. It is not a question of 5 's trying to de,c ide whether it should actually join with 2 to make 7. For this reason we speak of mathematics as analytic rather than synthetic. There are no formal (potential) properties of mathematics. The formal properties of the Wittgensteinian nonmaterial object cannot be used to bring numbers i nto the same domain as physical objects . Sti l l , I m ight write down a mark and then say " Here is a number" and then write down a nother mark and say " Here is another number. " I observe these writ­ ten man-made marks j ust as I observe those man-made chairs in th is classroom a nd then stipulate certain rules about these marks and these chai rs . Every chai r w i l l b e l i ned up i n such-and-such a way; every mark w i l l b e combined a nd a r­ ranged i n accordance with such-and-such a rule. The physical man ipulation of the marks is obviously more complex than that of the chai rs . The chairs have to be picked up and carried here and there; marks cannot very wel l be picked up and carried . But stil l , if we were dealing with stars and comets, physical man ipula­ tion wou ld not be very sign ificant here either. In fact, the games we play with n umbers m ight not be that far different from the games we play with chess pieces. The king, the rook, the pawn are entities that must fulfill certai n rules of the game. Chess is a physical game involving physical entities, but no piece is requi red to look like a king or a queen or a rook or a pawn . We could replace them all by rocks and pieces of unca rved wood and still be playing chess. The main point is that some physical pieces are sti l l required; we could not go very fa r playing chess by simply verbalizing the moves . Similarly, mathematics requires some physical marks, and to this extent it m ight be called a game i nvolving phys-

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ical objects and, therefore, like chess, belongs in the domain of physical objects. And if we can speak of numbers and chess and atoms as belonging to the same domain, we might want to take the final step and include literary entities as well. For just as I can set down rules stipulating how a certain set of marks is to be manipulated, so also I might set down rules on how marks that I label proper names can be used. I might say, "This mark, 'Hamlet,' is always to appear in conjunction with such predicate expressions as 'is a moody Dane,' 'killed Po­ lonius,' 'drove Ophelia to suicide,' and all the others that can be extracted from a certain play called Ha mlet written by William Shakespeare." Whatever has these predicates applied to it in the context of a Shakespearean play called Hamlet is to be called "Hamlet." Thus David Garrick, Laurence Olivier, John Gielgud, Richard Burton, Derek Jacobi, and Richard Chamberlain could all legitimately be called "Hamlet," just as anything will be called "rook" so long as it functions in accordance with the predicates assigned to the word "rook" in chess. Still, these attempts to place physical things, numbers, and fictitious entities into the same domain will not do. In the case of mathematics, it is surely a com­ plete misunderstanding of mathematics to identify numbers with their inscrip­ tions or with any other set of physical marks. We may use some physical means in order to express some mathematical principle more adequately just as we use building blocks in order to interest a child in spelling. But no one confuses the particular heuristic device with the reason for its employment. The inscription of a number is surely not that number. The inscription can be said to be in red or italicized. But what would such descriptive predicates have to do with the num­ ber itself? A mark, 7, may be placed on a piece of paper and through the years that mark may fade. But this does not mean that the number 7 fades. As one mathematician has remarked, "Let it be said, to prevent misunderstanding, that the subject of these investigations is not the individual realizations of the figures. Thus if, say, the figures 1 , 1 1 , 1 1 1 . . . which are composed only of 1 , are called 'numbers,' this does not imply that when the realizations now seen by the reader have perhaps rotted away there will be no numbers. Anybody who has the capac­ ity of producing such figures can at any time speak of numbers." 6 Furthermore, if we think of mathematics as dealing with objects, no less physical objects, then something odd occurs to our analysis describing such objects. We think of pure mathematical sentences as analytically true. Even Kant, who attributed a syn­ thetic character to mathematical statements, did not deny that they were neces­ sarily true. But if there is a domain of mathematical objects that numerals, as they are written or uttered, are said to designate and that Russell at one time believed could all be found "sitting in a row somewhere," � then mathematical 6. P. Lorenzen, Einfiihrung in Die Logik und Mathematik (Berlin, l 955), ch. l , q. in S. Korner, The Philosophy of Mathematics (New York: Harper, 1 960), p. 102. 7. Russell, My Philosophical Development, p. 62.

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statements must be strictly synthetic, since both Hume's and Wittgenstein's anal­ ysis of any plurality of objects-whatever they arc-is applicable here as well. Objects can be configured; they can be heaped; they can be aligned. But it can be shown that no object is necessarily connected to any other object, and the proof is simple to sec. If two objects were necessarily connected, then the two state­ ments describing them, p and q, would be given as ( p. q) . But D(p. q) is true if and only if Op and Dq are both true. But for Op and Dq to be true, both p and q must be logical truths. But a logical truth, an L-truth, is one that, according to Carnap, "can be established on the basis of the semantical rules of the system . . . without any reference to (extralinguistic) facts. " b Thus if a sentence did re­ quire an appeal to facts, that is, to some set of physical objects, then it could not be an L-truth. But D(p. q) is an L-truth. Therefore, it cannot have a11y reference to some set of physical objects. And, since in a customary interpretation of a mathematical calculus every sign in it is interpreted as a logical sign, every math­ ematical sentence "consists only of logical signs and is therefore L-determi­ nate. " 9 Mathematics cannot have a referent. Similar reasoning is applicable to fictitious entities. If we can speak of fic­ titious entities in literature, if "Hamlet," for example, is taken as referring to some special kind of object, then certain descriptive sentences that are taken to be analytically true of Hamlet in Hamlet would become synthetically true. Thus, if there is an object that "Hamlet" designates, then it is clearly syn­ thetically true that he is a prince of Denmark. It is logically possible that the object we name does not have the characteristic we attribute to it. Names may, by stipulation or convention, be connected to a set of predicates. " Uncle Sam" does not designate anyone, but by convention it has become attached to a set of predi­ cates such as "being just," "being fair," "being strong," "being tolerant," and so forth. The name functions solely as an abbreviation for these predicates. But this is not at all the case with names that name objects. "Caesar" names Caesar, but as Kripke has pointed out, it does not entail by convention or otherwise any set of predicates. Every predicate might be incorrectly associated with Caesar. Caesar might not have crossed the Rubicon; he might not have been killed by Brutus. Similarly, if we take "Shakespeare" as naming some person, then he might not have written Hamlet. And, in the same way, if "Hamlet" were required to refer to some special unique entity, then it is logically possible that he was not a prince of Denmark. When we are dealing with a named entity, no predicates are guaran­ teed. But " Hamlet was a prince of Denmark" is surely analytically true in Ham­ let . We would not ask whether it might be incorrect to assert that Hamlet was a prince of Denmark. And if we did ask, one would think that we were making

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8. Carnap, Meaning and Necessity, p. I 0 . 9 . R. Carnap, Foundations of Logic and Mathematics, International Encyclopedia of Unified Sci­ ence, vol . I, no. 3, p. 43.

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some important mistake about the play. One would think that we were confusing a possible historical Hamlet with the Hamlet of the play. To find the historical Hamlet we can legitimately look into the third book of the Historia Danica of Saxo Grammaticus (c. 1 200; printed 1 5 1 4) to see whether there real ly was some­ one called "Hamlet" and whether he was indeed a prince of Denmark. And even if Saxo Grammaticus affirms that Hamlet was a prince of Denmark, it is always logically possible that he could have been mistaken. But we could not be mis­ taken about the Hamlet in the play. In other words, if the name is taken to refer to some entity, then any statement describing it can be a misdescription. Histor­ ical investigations are based on this premise. But in analyzing Shakespeare's Richard III, no one asks whether Richard III was deformed. Of course, Richard was deformed. It says so in the play. Could Shakespeare have been mistaken? Of course not, since it makes no sense to ask whether Shakespeare might have been mistaken about Richard Ill's deformity. We can question motives and ethical be­ havior, for these are never expl icitly given in the play, but we cannot question what is explicitly given. On the other hand, the expl icit informative sentences of history can all be questioned. W ith al l the data that we have about Jul ius Caesar, an historian could legitimately ask, "Was there really such a person as Jul ius Caesar?" But no one could ask legitimately, "In the play Julius Caesar by Shake­ speare is there really such a person as Julius Caesar?" Of course, we might not know the play at all and ask whether there really is a character called "Julius Caesar" in the play. After all, Godot never appears in Samuel Beckett's Waiting for Godot, nor does Rebecca in Daphne DuMaurier's Rebecca. But once we read the plays, the question can not be raised. In fact, if Kripke's notion of a rigid designator has any application, it is surely in relation to plays. For the Hamlet of Hamlet is precisely who he is for all time and all places. In every possible world that contains the Shakespearean play, Hamlet could not be otherwise than he is in the play we know; if he were we would be deal ing with a different play. To speak blithely of domains of objects that include numbers as wel l as fictitious entities is to turn analytical sentences into synthetic ones. It is to confuse science and history with mathematics and fiction. Hence those who reduce ontology simply to a difference in domains, that is, who assert that our ontological commitment is relative to the domain of a given language or context, must tell us how one domain is differentiated from another, how the domain of numbers is to be distinguished from that of physical objects and l iterary entities. And the first step in making this differentiation is to deter­ mine what it is to be an individual . Until this is clarified it is always possible that we are attributing individual ity to what ought not be given such a status, and in this way introducing unnecessary problems. If numerals, for example, do not designate entities of some domain, but are really no more than abbreviations of certain advanced logical operations, then the question of what numerals do des-

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ignate would be an idle one. We would be pursuing an issue because of a lack of knowledge of certain logical systems. It would be like looking for an ethereal sub­ stance, even though the Michelson-Morley experiments and Einstein's theory of relativity have demonstrated that no such substance exists. The major question for us, then, must be this: what is it for something to be an individual? We have seen that quantifying over the individual variable is meaningless as a criterion for ontology unless there is clarification of what counts as an individual. Furthermore, even if this clarification be given, the nominalist position can stand secure only if it can also be shown that no other quantification besides individual quantification is legitimate. Otherwise, if quantification can occur over propositional or predicate variables as well as over individual ones or if it can be shown that in many cases predicate is a legitimate alternative to individ­ ual quantification, then the realist position-the one acknowledging that there exists at least one abstract entity such as a universal or a proposition-becomes compatible with nominalism. The realist does not deny that individuals exist. He only denies that nothing else but individuals exist. Therefore, it must be shown, if the nominalist position is to succeed at all, how individuals are to be explicated. What are individuals? We might approach the question in a traditional way by thinking of what names and predicates are usually said to designate and then ask­ ing how the designatum of one is related to that of the other. How are the desig­ nata of names, namely, individuals (or objects or things or particulars) related to the designata of predicates, namely, properties (or classes or qualia or characteris­ tics)? But, if we analyze individuals in this way, then we ought to be aware that we shall be led into one of those standard cul-de-sacs that philosophers are for­ ever finding. We will eventually be led to conclude that individuals are either Locke's something "we know not what" or Wittgenstein's simple objects that could never be found, no less named, or Bergmann and Allaire's "bare particu­ lars," which, being absolutely devoid of properties, are indescribable and uni­ dentifiable . 10 Bergmann might counter by saying that bare particulars are not de­ void of properties, and hence they are both describable and identifiable. The bare particular contained in this table before me has the property of being a table, of being brown, and so forth, and these properties distinguish it from the bare particular contained in the pen or chair. But what can it mean to speak of a I O. An Essay C oncerning Human Understanding, bk. 2, ch. 23, sec. 3. Sec Norman Malcolm's discussion of Wittgenstein's own perplexities about what would be an example of a "simple object" in Ludwig Wittgenstein: a Memoir (London: Oxford Univ. Pr., 1 958), p. 86. Cf. G. Bcrgmann's de­ fense of bare particulars in "The Revolt against Logical Atom ism," in Meaning and Existence (Madi­ son: Univ. of Wisconsin Pr. , I959), p. 47; idem, "Inclusion, Exemplification and lnherence in G. E. Moore," in Logic and Reality (Madison: Univ. of Wisconsin Pr. , 1 964), p. 1 66; idem, "Sy n­ thetic a Priori," in Logic and Reality, p. 24. Sec also Edwin B. Allaire, "Bare Particulars," Philosoph-

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bare particular contained in the table? We do not encounter bare particulars as we do the color of this table or its size or its material. We cannot count up al l or most of the properties of this table and then finally add, "Oh yes, and then there is the bare particular." 1 1 Grossmann tries to avoid the difficulties inherent in the notion of a bare particular by simply saying that it is not contained in any set of properties, as Bergmann sometimes seems to think; nor do properties inhere in it. It is the very individual itself . There is no bare particular in this square; the bare particular is the square itself! As Grossmann puts it, " . . . there can be no question of one's attention being directed to the particular 'in' the individual thing A. There is nothing 'in' this square at all, ontologically speaking. In order to pay attention to an individual rather than a property, one merely has to pay attention to the square A rather than to any of its properties." 1 2 But now we ought to ask what the square itself is. Can we pay attention to the square withou t paying attention to any of its properties? Perhaps someone can. But I am not sure how the experience would be described. Can we speak of seeing the square as a square without seeing its properties such as its outline or its shape or its area? Further, "being a square" is a property of the square. But then must we say that the bare particular is this square itself regardless of its property of being a square? And if "being a square" is not a property, then we ought to ask why it is not. W hy is "being a square" not as much a property as "being red" or "being a rectangle"? So it turns out that Grossmann's modification of Bergmann's problems has its own problems. All attempts to think of individuals in this way, as certain entities distinct from their properties, seem to lead to a kind of mysticism or, as Wittgenstein himself seemed to realize at one point, to an infinite regress since the definition of any term designating an individual could be infinite in length. 1 3 If we take this ap­ proach to understanding individuals, we become involved in all the traditional problems concerning the relationship between objects and their properties. Are ical S tudies 1 4 ( 1 963): 1 - 8; idem, "Another Look at Bare Particulars," Ph ilosophical S tudies 1 6 ( 1 965): 1 6- 2 1 . Criticisms of the notion of bare particulars arc given by J . W Mciland, D. C. Long, Vere Chappell, and others in Un iversals and Pa rticulars, ed. M. J. Loux (New York: Doubleday, 1 970). See also detailed discussion, defense, and criticism of Bergmann's bare particulars by Rein­

hardt Grossmann, "Bergmann's Ontology and the Principle of Acquaintance," in The On tological

97- 1 0 1 . 1 1 . Thus D. C . Long argues, ". . . the pencil need not have this colour or shape or size or other

Tu rn , ed. Cram and Klemke, pp.

particular value of its various determinables. But this does not entail that the pencil could exist with­ out having any qualities or that the concept of something remaining when all of its qualities are 'stripped away ' is intelligible" ("Particulars and their Qualities," in Universals and Pa rticula rs, ed. Loux, p. 28 1 ). 12. Grossmann, "Bergmann's Ontology," p. 100. 1 3 . Cf. Wittgenstein's Notebooks, 1 9 1 4 - 1 9 1 6, ed. C. H . von Wright and C. E. M. Anscombe (London: Basil Blackwell, 1 96 1 ) , p. 62.

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objects conceivable as distinct from their properties? Or are objects no more than the sum of all their properties? If we peel away all the properties of a thing, will we finally be left with the thing itself? Can there be things that are no more than clusters of properties? If so, what holds these properties together and how are we able to speak of two different objects having the same properties? These are the questions that led Allaire into the odd dilemma of speaking of a something that is not a something at all: if it is logically possible to speak of two objects having the same properties, then to account for their numerical difference, for the fact that we take one not to be identical to the other, we must posit this strange ding-an­ sich, a "bare particular," which is probably as metaphysically embarrassing as one critic's reference to that "particular, naked and nude." 14 These questions lead to more enigmas that are apparently inherently incapable of being solved. For how can one ever prove the existence of something that is apparently identical to nothing? It is for this reason that the attempt to translate the language of things and properties into the language of names and predicates has seemed to be more fruitful. A linguistic problem has a concreteness about it; one can at least give examples of a name and a predicate, whereas no one can ever give an example of a bare particular. But the linguistic turn has by no means settled the issue of how to determine what an individual is. The emphasis on the categories of name and predicate has not eliminated the need to be able to identify whether a term be­ longs to one category or another. It is still necessary to ask, "W hat is it that makes this expression a predicate and this other a name?" And even though there have been various attempts to define names and predicates syntactically by indicating their positions in classes of sentences or by noting their inflections (as in Latin), we still ask why a term at a given position or with a given inflection is a name rather than a predicate or an adverb or even a logical connector. The answer often given is that the term at a given position or with a given inflection denotes an individual rather than a property or a class. But this answer presupposes pre­ cisely what we are trying to understand. W hat is it that a term is referring to when it is taken to refer to an individual rather than, say, to a class or a property? W hat makes the designatum of a name or of the substituend of an individual variable an individual? It is not the name per se that tells us it can replace an individual variable in a formal system , but the name insofar as it denotes an individual. Even if we agree that ontology is to be found by looking to the values of the variable, we must first know what it means for a value to be an individual rather than to be something else. We m ight think of individuals in terms of the role such entities are required to play in strict formal systems. Once we have made this determination, we can go on to see whether individuals are introduced into a natural language for the same l 4. Robert Baker, "Particulars: Bare, Naked and Nude," Nous 1 ( 1967), 2 1 1- 12.

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reason. But, as we shall shortly see, it is no easy matter to determine how individ­ uals function in a formal language. It seems clear that, except for certain specialized combinatorial languages, 1 5 most formal systems require some expressions that will serve as either individual constants or individual variables. (Usually both constants and variables are in­ cluded, but some systems substitute names for constants. ) For Carnap expres­ sions for individuals become essential for formalizing set theory, arithmetic, geometry, topological physics, and biology. 16 All these subject matters have dif­ ferent individuals in their domains-points are the individuals of geometry whereas slices of particles are the individuals of topological physics-but they all require the positing of a category of individuals. Thus it could be argued that individuals are needed to satisfy the formulas of formal systems. But if we think of individuals in this way, then nothing has been accomplished in the way of explicating what an individual is. The introduchon of individuals here is, if we may borrow the expression from Searle, done regulatively rather than con­ stitutively. 1 7 The identity of individuals has already been established rather than defined within the system itself. We are required to know beforehand what an individual is before its admission as a value of a variable. It is as if we see a sign that says: " If anyone is a graduate student, then he or she will be admitted to the Campus Club." To know who can be admitted, we would be required to know who is a graduate student . The rules for determining who is and who is not a graduate student would not necessarily be given in the rules governing the Cam­ pus Club, since the sign could assume that on other grounds one could establish who is or is not a graduate student. Similarly, to be told that if anything is an individual then it can satisfy a particular variable tells us nothing about what determines something to be an individual. It might be more fruitful if we thought of an individual in terms of the con­ stitutive rules of the system. Thus we might, in the case of the student example, have the Campus Club introduce new rules that specify exactly what conditions have to be met before someone can be called a graduate student. It might be specifically stated that, as far as the club is concerned, a graduate student is one who goes to college at the graduate level or who is able to read James Joyce or who drinks beer all night, and so forth. Membership in the club, then, will be determined by its own rules. Similarly, we might assert that there are no individ15. Although even in combinatorial languages Quine has pointed out that the truth of the for­ mulas in such sy stems must depend on just the entities "that must be reckoned as arguments or values of functions," i. e. , individuals (From a Logical Point of View [New York: Harper, 1961], 2d ed. rev., p. 104). 16. R. Carnap, I n troduction to Symbolic Logic ( New York: Dover, 1958), pp. 157-225. 17. John Searle, Speech Acts (London: Cambridge Univ. Pr. , 1970), pp. 33-34.

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uals that are, so to speak, looking for admission into a formal system. There arc no individuals "out there" to which every system-at least every system that is not purely analytic-must accommodate itself. Rather, if anything satisfies a cer­ tain variable or a certain formula in the system , then it is an individual. There are no prior conditions attached. We are not required to know beforehand what an individual is. If something can function in a certain role in the system , then it is an individual; otherwise it is not. But all this is still too abstract, and we ought to ask how, according to this analysis, something becomes an individual in a for­ mal system. We might begin by first thinking in terms of a pure uninterpreted system containing well-formed formulas such as (3 x)Fx, (x)(Fx. Cx), (3 x)(y)Fxy, and so forth. Being "uninterpreted" signifies that meaning has not yet been given to any of the letters or other components. Thus no letters are variables or con­ stants; nor can we even speak of any other marks such as v or :) as logical con­ nectors. At this stage we can say only that the recursive rules of formation permit combinations of symbols such as (3 x)Fx and (3 x)(y)Fxy, but not such combina­ tions as ()xxF or ( ())x3 yxyF. But now we can begin to label, that is, "interpret, " some of the symbols. This group of symbols, say, x, y, and z, w i l l be individual variables; this other group, a, b, and c, will be individual constants; this third group, F, C, and H, will be predicates; another group, v , . , -, and :) will be logical connectors; and finally the combinations (3 x)Fx and (x)Fx, and so forth, will be existentially and universally quantified formulas abbreviating a series of disjunctive or conjunctive formulas consisting of a predicate immediately fol­ lowed by an individual constant. We can now go on to say something about how a formula is satisfied and how such satisfaction is related to the introduction of individuals. A formula, say, (3 x)Fx, is satisfied if its instantiation, that is, its con­ version into a series of disjunctive formulas, results in at least one true disjunct, for example, Fa. We then simply stipulate that the value replacing the x in an instantiated true sentence is to be taken as an individual . In this way individuals are defined within the system . However, an interesting question arises here. How does "true" function? Given a true instantiation, Fa, then a is an individual. But how is the truth of Fa determined? We must be able to say, "Since Fa is true, then a is an individ­ ual . " But how does "true" become applicable to Fa? Following Tarski we can say " Fa" is true if and only if Fa. But, as Carnap points out, this definition presup­ poses ( 1) Rules of Designation by which the individual constants and predicates are given Engl ish translations-for example, Hx is a symbol ic translation of " x is human (a human being)" and s is a symbolic translation of "Walter Scott"; (2) Rule o{Truth for the simplest atomic sentence: "An atomic sentence in S 1 consis­ ting of a predicate followed by an individual constant is true if and only if the individual to which the individual constant refers possesses the property to which

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the predicate refers." 1 � W hat al l this means is that we can attribute truth to the sentence "Fa" if the entity denoted by a has the property F. But the entity de­ noted by a is an individual as distinct from F, which is a property. In other words, we cannot define an individual constitutively by simply asking what satisfies a given formula, since the notion of satisfaction involves truth, and the notion of truth depends on our being able to distinguish individuals from properties. The circularity is quite clear. We might object to Carnap's statement of Tarski's criterion, since Tarski makes it quite clear that his semantic definition of truth has no implications for any special ontological position. As Tarski puts it, ". . . we may accept the semantic conception of truth without giving up any epistemological attitude we may have had; we may remain naive realists, critical realists or idealists, empiricists or metaphysicians-whatever we were before. The semantic conception is neutral towards all these issues. 19 Thus to say that the sentence "Fa" is true if and only if Fa is simply to say that Fa is true if whatever is referred to by a-whether it is an individual or otherwise-has F. There is no specific commitment to individuals. But this returns us to our original difficulty: if satisfaction of a formula can be accomplished by entities other than individuals or if there is no commitment about what replaces the variable x, then we are stil l involved in determining what an individual is. Now, we might approach the problem of individuals in a negative manner. Anything is an individual so long as it is a member of a class or is a possessor of properties and is itself never a class or a property in the system. This is equivalent to Aristotle's definition that an individual is that of which properties are predi­ cated, but is itself never predicated of anything else. 20 In more formal terms we can say that, if an expression in a given system serves only as a substituend of an individual variable, but never as a predicate, then the designatum of that expres­ sion is an individual. This view assumes that individuals would be relative to a system. But this could not legitimately be cal led an Aristotelian view, since Aris­ totle would probably want to argue the much stronger claim that there are some expressions that can only serve as the subsituends for the individual variable. They would be names in every system. So we should raise this question: can there be names that function solely as names in every context? Are there sen­ tences whose names could not be translated, without loss of meaning, into some other form? If we follow Russell and Quine, every name can be changed into a description and, since descriptions do not name, we ought not to count on names as indicators of individuals. Or we could, following Quine, simply 18. 19. ed. H. 20.

Carnap, Meaning and Necessity, p. 5. Alfred Tarski, 'The Semantic Conception of Truth," in Readings in Philosophical Analysis, Feig! and W Sellars (New York: Appleton, 1949), p. 71. Aristotle, Metaphysics, bk. 8, ch. 13.

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change names into predicates by "adjectiving" them, that is, by giving them predicate suffixes. � 1 Thus "Pegasus exists" would become ( 3 x)(pegasizes x), where "pegasizes' ' abbreviates some unique set of predicates. We might try to counter this form of relativism by arguing that, once we have translated all names into logical expressions and predicates, then we can indicate what expressions must refer to individuals. Whatever substituend satisfies the individual variable is an individual. Now we return to an earlier objection. What does sentential satisfaction mean? We have taken it to mean that a basic atomic sentence is true. That is, (3 x)Fx is satisfied if and only if one of its disjuncts, say Fa, turns out to be true. But F a is true if and only if the a refers to an individual that has the property F, and this implies that we already know how to identify an individual. Thus the attempt to define individuals by simply saying what they are not is not very helpful. And, in fact, there is one feature of many set-theory systems that makes the entire attempt futile. In some set-theory systems, any individual can be taken as a class of one unit, or a unit class, as it is sometimes called. 2 2 W hatever individuals are, they apparently do not bar us from a commitment to classes, since individuals are identical to classes, albeit unit classes. In fact, each individual a)so entails an infinite number of classes, since from every unit class we can derive another unit class and then a unit class of this unit class, and so forth. Classes become inescapable, so that even if quantification turned out to be permissible only over individuals and if the category of predicates turned out to be no more than linguistic elements that had no ontological counterpart, the nominalist would still not have won the battle. The nominalist would still have to explain how unit classes can be equated with individuals. At one time Quine thought that "the fusion of every individual with its unit class . . . is harmless." 2 3 I t is not harmless to the nominalist. It should be pointed out, however, that this fusion of individual and unit class is not universally acceptable. n There are intuitive and logical problems. The in­ tuitive problem is quite simple. If individuals can be regarded as classes, then what is the distinction between a member of a class and the class itself? If every member of a class is a unit class, then every unit class is a member of itself, that is, aea, which leads directly into Russell's paradox. Furthermore, since each 2 1 . W V Quine, Word a nd Obiect (New York: Wiley, l 960), p. l79; idem , From a Logical Poi nt

o f View, pp. 7-8.

22. Cf. W V Quine, Mathematical Logic (Cambridge, MA: Harvard Univ. Pr. , l96 l ), rev. ed. , p. l35, and Set Theory a nd its Logic (Cambridge, MA: Harvard Univ. Pr. , l 963 ), pp. 47- 52. 23. Quine, From a Logical Poi n t of View, p. 82 n. 24. Thus C. I. Lewis wrote: " Even if a term correctly applies to one existent only, as is the �ase for all singular terms, it is stil l doubtful to identify this one object denoted with the class of v.·hieh it is the only member" ( An Analysis of K nowledge and Valuation [LaSalle, IL: Open Court, 1 946] , pp. 39 - 40 ).

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member is its own class, a class always has classes as its members. Individuals in the ordinary sense disappear. But then how do we distinguish classes of non­ empty classes from classes of null classes, since both contain only classes and neither contains individuals? The logical problem occurs if we try to avoid Rus­ sell's paradox. For Russell aeb is a formula only if the values of b are of the next higher type than those of a. Thus b cannot take ind ividuals as values. But if individuals are equivalent to unit classes, then they can be values of b, and this would be a violation of type theory. As Quine concludes, the need for typ� theory sweeps away the equivalence of unit class and individual. 2 5 Another possible way of analyzing individuals is to consider characteristics that we would be willing to attribute to whatever we call individuals but that we would be unwilling to attribute to properties or classes. One such characteristic might be that of having parts. Individuals can be said to have parts, but properties and classes do not. Classes have members, and properties have instances, surely they do not have parts. But even here there is disagreement, Goodman has ar­ gued that it is possible to think of a class as an individual with discontinuous parts. 26 For example, we can speak of the class of dogs as a "certain discontinuous [whole] composed of dogs," 27 so that "A, B, and C are members of the class of dogs" would become "A, B, and C are parts of the (discontinuous) individual dog." For Goodman, then, there would be no difference between classes and what we usually think of as an individual. The former would simply be more discontinuous than the latter, just as a heap of stones would still be an individual heap even though it is more discontinuous than an individual stone. Goodman himself points out some difficulties in this nominalistic elimination of classes­ for example, "is an ancestor of' can still not be completely defined without the use of bound class variables. 28 But the general position is clear: everything con­ sists of individuals. Classes are no more than individuals taken on a larger scale. In Goodman's system there is no need to distinguish individua1s from anything else. "Is an individual" is a "universal predicate and so of little use." 29 But the question still persists: can we regard classes and properties as no more than indi­ viduals "writ large"? Is the color red no more than a very large object with a large number of discontinuous parts? Our normal use of "individual" is considerably different. Even if we intuitively accepted the notion of a red whole consisting of red parts, still each part would not be something added to an object that is al25. classes 26. 40. 27. 28. 29.

From a Logical Point o{View, p. 90 n . But Quine returns to the view that individuals are unit i n Set Theory, p. 47. Nelson Goodman , The Structure of Appearance (New York: Bobbs-Merrill, 1 966), 2d ed . , p. Ibid . Ibid. , pp. 48- 49. Ibid . , p. 48.

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ready present. I cannot say "This part of red has been added to this house just as I added an extra room last year. " Parts can be extracted, but I cannot extract colors in the way I can extract parts of a broken glass embedded in mud. Of a broken glass it makes sense to speak of each part and to examine each part separately and individually. Can I do this with a color? Can I pick up a red part and examine it in detail, or must I always pick up a red object, that is, an object that has red as a property and not as one of its parts. Furthermore, we tend to think that individu­ als have boundaries. There is a limiting shape or form of which we can say "This is the entire individual. " Can we ever say this about colors? No matter how much time passes, will we ever reach the boundary of red? In regard to an individual, a rule can always be found by which we can divide the individual into a finite number of parts. Can there ever be such a rule if we are dealing with colors? It would seem odd for us to say that we have counted all the parts of red and there are no more. It would seem odder for us to say that the color red, like the author of Waverly, has ceased to exist. Finally, consider several colors that consist of parts. We say that red, green, and blue all consist of their specific parts. Which part belongs to which color? How do we determine that this particular part be­ longs to the color red rather than to the color blue or the color green? We can say that this particular part exemplifies or is an instance of red rather than of blue or green. But this would again make color a property that parts have rather than a part itself. Or we can say that this part is similar to that part, and for this reason they are both called by the same color name. But similarity involves the claim that there is at least one element that both parts have in common by virtue of which both are held to be similar. What is this common element? If it is another part, then we are involved in the traditional third-man infinite regress argument. If it is not another part, then the only plausible alternative would seem to be the positing of a property. Clearly the attempt to change properties and classes into individuals is not successful. In fact, once we make the part-whole distinction, it is quite easy to be led back into the traditional positing of indefinable individuals. For consider whether parts have parts. If parts do have parts, then we are either led back into an infinite regress again or we must fina1ly reach a part that is not divisible. To avoid this regress we must posit a part that is itself partless. This would now give us a way of speaking of an individual. It is that final part that is partless. But again we would have been drawn into accepting the notion of a tota1ly alien kind of individual that, like Wittgenstein's and Bergmann's basic objects, is not at a1l comprehensi­ ble or at a1l the way we normally employ the notion of an individual. It is inter­ esting also that there is a slippery quality about parts. The parts of a whole can be thought of in many different ways. There can be four large parts or eight sma1ler parts or sixteen still sma1ler parts. But how can a whole of four parts be identical to a whole of eight or sixteen parts? Rolf A. Eberle raises the same difficulty in

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attempting to clarify the distinction between individuals and classes: "With re­ gard to a given heap of stones, the following two classes can be distinguished: ( 1 ) the class of stones in a heap, and (2) the class of molecules of stones in the heap. Since there are more molecules than stones in the heap, the two classes are cer­ tainly distinct. On the other hand, a nominalist's intuition regarding individuals is such that he would not wish to distinguish the following corresponding indi­ viduals: ( 1 ) the concrete whole composed of all stones in the heap, and (2) the concrete whole composed of all molecules of stones in the heap (in the given spatial arrangement of molecules. )" '0 The nominalist's intuition is such that the nominalist would not wish to distinguish between the whole made up of four parts and the same whole made up of eight parts. The identification is usually made by reference to the smallest parts, the "ultimate constituents," into which a whole can be decomposed. Then we can say that A and B are identical if the smallest parts into which they can be divided are identical and arranged in the same way. If molecules are the ultimate constituents, then A and B are required to have the identical molecules arranged in the same way. But again these con­ siderations presuppose that there are ultimate constituents. Molecules are, of course, not the ultimate constituents of physical objects; nor are electrons; nor are neutrons or even quarks, since the latter are said to have a certain characteristic called "charm," and nothing with a characteristic can be called an ultimate parti­ cle. Only partless parts seem to be appropriate candidates for ultimate constitu­ ents, but these entail all the difficulties previously indicated. Two possible counterarguments might be made here. It might be argued that an individual can be divided into a different number or parts without requiring a commitment to ultimate constituents. Goodman, M. G. Yoes, and Eberle have constructed formal systems or suggested principles of individuation that would apply to individuals that either do not have or do not require subdivisions that must eventually reach ultimate constituents. 3 1 Goodman's suggestion is that we adopt some predicate that we take to be basic or primitive to the system we are constructing and then call anything an individual that satisfies that particular predicate. Goodman takes as his primitive predicate "overlaps" and then asserts that any entities to which this predicate is applicable, regardless of whether or not it is an ultimate constituent, is to be called an individual. 3 2 Therefore, we need not be concerned about partless parts. If a overlaps b, then a and b are individu­ als. The complexity of a and b does not matter. Another way of accounting for the different numbers of parts into which wholes can be subdivided is to adopt a procedure analogous to one often used by 30. R. A. Eberle, Nominalistic Systems (New York: Humanities Press, 1970), p. 2 5. 31. Goodman, The Structure of Appearance, pp. 190-91; M. G. Yoes, Jr. , "Nominalism and Non-Atomic Sy stems," Nous 1, 2 (1964): 193-200; Eberle, Nominalistic Systems, pp. 73- 77. 32. Goodman, The Structure of Appearance, p. 117.

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Carnap. Carnap at one time thought that any term is definable either by the thing-terminology. that is, the terminology that we use "in everyday speaking about the perceptible thi ngs surrounding us" or by the language of physics. These are two different languages , but they are related to one another in that a term in one can be defined by some set of terms in the other. In brief, Carnap took it for granted that there were what he cal led "correspondence rules" that correlated terms of one language with terms of another. 3 3 Sometimes such cor­ relation was definitional , at other times reductive, that is, employing reductive sentences. Now, if we accept such correlations, then certain distinctions become apparent rather than real. We can derive "all heaps of stones are heaps of mole­ cules" if "molecules of stones" in the language of science is connected by corre­ spondence rules to "stones" in the thing-language of ordinary discourse, and our scientific theory makes such a correspondence easy to accept. Even those with very l ittle scientific knowledge take for granted the fact that every physical object is made up of molecules. On this basis there is nothing strange about speaking of different organized wholes as identical so long as an appropriate correspondence rule is available . The individual A is identical to the individual B because all statements about parts of A are intertranslatable with statements about parts of B. Given four parts of a whole, the rules of arithmetic, and the rules governing "is smaller than," it is not difficult to demonstrate that "a group of four parts" can be taken as identical to "a group of eight parts of a group of four parts." Goodman asks how a whole consisting of Caesar's nose and the state of Utah can be identi­ cal to a whole consisting of Caesar's nose and the counties of Utah. 3 4 The answer is not so difficult. Legal documents define a state in terms of its counties , and thus we obtain the required correspondence rule. For Goodman, then, individual ity does not require the introduction of ulti­ mate constituents. He tells us specifically that "an individual may be divisible into any number of parts; for individuality does not depend upon indivisibil ity. . . . Indeed nothing has intrinsic or absolute status as an individual or a class." 3 5 And, at first, this could lead us to bel ieve that Goodman is leaving the choice of individuals open in Carnap's and W ittgenstein's sense that it is the scientist, not the philosopher, who must supply the elements that will be called individuals in any given system. But Goodman, as a phenomenalist seeking to reconstruct Car­ nap's Aufba u , posits his own individuals . They turn out to be "qualia" that can become the values of the variable of his particular formal system, the calculus of individuals . 36 Qualia, like Locke's secondary qualities, are colors, sounds, per33. Cf. R. Carnap, Philosophical Foundations of Physics (New York: Basic Books, 1 966), ch. 24. 34. Goodman, Structure, p. 51. 3 5. Ibid., p. 47. 36. Cf. Henry S. Leonard and Nelson Goodman, "The Calculus of Individuals and Its Uses," /ournal of Symbolic Logic 5 (1940): 45-55. See also Goodman's discussion in The Structure of Ap­ pearance, pp. 46-56.

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haps tastes, with spatial and temporal features as wel l. 3 7 They are the elements that make up the concrete entities that we find in experience. They and their combinations-"concreta," as Goodman calls them-make up the concrete en­ tities, the basic individuals, that overlap and that we find in the "stream of expe­ rience." Thus Goodman himself seems to return to the search for some ultimate individuals that make up whatever we experience. These qual ia are perceptual in nature and as final and primitive as Carnap's elementarerlebnisse 38 and Russell's sense data. By the same token they are open to similar criticisms. If all individu­ als consist of qual ia and if qual ia are the fondamental units in the stream of expe­ rience, then we are committed here to a phenomenalism that makes it extemely difficult to deal with the physical world. As Goodman is aware, this is Carnap's own criticism against the elemen ta rerlebnisse of his Aufba u system. 39 Are the statements of physics to be regarded as statements of psychology? Are atoms and neutrons no more than combinations of qual ia? It is because of this basic psy­ chologism that Carnap eventually rejected the Aufbau system. 40 Goodman's qualia seem to involve the same problem. Nor is this all. Qualia, l ike sense data, are curiously elusive. They are individuals on Goodman's analysis. But now con­ sider the color red. Is each individual color red a qual ia, or is the qualia that which all these individual experiences of color reds have in common? .If what they have in common is the qualia, then it is an individual, and this would seem to lead directly into the third-man argument. W hat does this individual have in common with the individual color reds that are experienced? And if there is nothing in common among the particular color reds, then why is it that we call them all by the same name? W hy should this be red and that be red if there is nothing they share in common? Furthermore, if "red" is a name of an individ­ ual, then, by the principle of univocal ity in a formal language, a name names one and only one individual. 4 1 So that if we encounter a name that is used with many different individuals, then we ought to ask how this is possibl e without pos­ tulating someth ing-a property-that all these individuals have in common. The problems begin to multiply rapidly. After this lengthy and involved discussion, we still seem to be plagued by our original question: what is an individual? I should now l ike to suggest a possibility of explicating what an individual is that I believe would avoid most if not all the issues that have been examined in preceding paragraphs. I would l ike to begin by 37. Goodn.an, The Structure of Appearance, pp. 132-34. 38. Der Logische Aufbau Der Welt, sec. 67; see also the translation by Rolf A. George, The Logi­ cal Structure of the World (Berkeley and Los Angeles: Univ. of California Pr. , 1967 ), p. 107. 39. Goodman, The Structure of Appearance, p. l 52. 40. See Carnap's own remarks about why he finally rejected the phenomenalistic sy stem of the Aufbau in The Philosophy of Rudolph Carnap, ed. Paul Arthur Schilpp (LaSalle, IL: Open Court, 1963), pp. 50-53. 4 l . Carnap, Meaning and Necessity, p. 98.

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asking why anything ought to be regarded as an individual. We construct calculi, and then we take it for granted that at least some of the va riables will be individ­ ual ones taking individuals as values. And for some reason this is an important categorization. With all the efforts expended in trying to discover what an indi­ vidual is, few logicians or philosophers generally would omit the inclusion of a category of individuals in any description of natural phenomena. Now, A. N. W hitehead argues against this supremacy of the category of individuals, and at least one of the reasons he gives is especially interesting. -+ 2 Whitehead believes that we could eliminate individuals in favor of processes. Names and descriptions would designate processes rather than individuals. W hitehead's reason for believ­ ing that this change is necessary gives us an interesting insight into why the cate­ gory of individuals plays an important role in any language. W hitehead states that, if we had a language in which there were process rather than individual variables, then we could better explicate physical theory. The paradoxes involv­ ing the corpuscular and wave theories of light could finally be settled. W hether W hitehead is right or wrong on this point is not so important as what he is saying about the category of individuals. The commitment to individuals may or may not be satisfactory in terms of physical theory as a commitment to processes. But note how W hitehead regards both processes and individuals. They are not ele­ ments in their own right. They are categories that are used to explain natural phenomena. Let us expand W hitehead's position a little further and say that we wish our theories not only to explain physical phenomena but also to give us some way of controlling them or changing them or remaking them. As Dewey long ago pointed out, scientific theory is not the result of a passive bystander's observing a never-ending Aow of events. Scientific theory is a result of human beings' involvement in remodeling and revamping an often recalcitrant nature. -+ 3 Taken in this context, individuals then have to be regarded as entities that be­ come individuals because they have performed a certain service. Let us try then to consider what this service might be. If there is anything we want from natural phenomena, it is that they be em­ ployable by us. But, for something to be employable, we must be able to shape it, to measure it, to weigh it, to state where it is and what time it will be there. These are the properties we wish to find in nature, and it is precisely for this reason that the category of individuals makes its appearance. If individuals were meant to designate or to refer to some special set of entities, then we would constantly have an impossible situation, since every individual entails an infinite number of individuals or some set of now discredited ultimate individuals. The reason for calling something an individual would be so trivial that it would be difficult to 42. A. N. Whitehead, Science and the Modern World (New York: Macmillan, 1925), pp. 101-5. 43. Cf. John Dewey, Experience and Nature (London: George Allen and Unwin, 1929), pp. 160-62.

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understand why any language-formal or otherwise-would be continually re­ quired to posit a category of individuals. But this commitment to individuals is surely one of the most persistent commitments that has ever appeared in any lan­ guage . W ith all the variant kinds of formal languages that have been constructed, the need for a category of individuals never disappears. Produce a formal lan­ guage without individual variables, then a metalanguage or a meta-meta­ language must show how the sentences of such a language are translatable i nto forms containing individual constants and variables. Then and only then do we begin to understand what is being talked about in the variant language. The cate­ gory of individuals, then, is not a relativistic notion easily disposable by some W hiteheadian or logical technique. It is a major ontological commitment, and I think the reason for its necessity is clear. We need it in order to make inferences about this world and other possible worlds. Individualhood-if we can introduce the term-is the necessary category whereby we can construct systems that per­ mit inferences from what is actual to what is possible . It is the means by which we can speak of something now and of how the same thing might be tomorrow. And this should give us a hint about what it is that makes something into an individual. W hatever permits identification and reidentification in this world and other possible worlds creates individuals. But what does permit such identi­ fication? The question of transworld identity is a difficult one, but at least cer­ tain necessary conditions must be present. Whatever attains individualhood is bounded, measurable, weighable, and capable of being described by space-time predicates. W hen this set of predicates is appl icable to an entity, then and only then does that entity become an individual . The entity becomes knighted, so to speak, and then becomes uti l izable in both physical and logical systems. lndivid­ ualhood is a requirement by human beings making demands on an often hostile environment. It gives us the guarantee that in its fundamental structures the fu­ ture will be l ike the past; possible worlds will be l ike the actual one. If we had been born into a world in which everything was in much more rapid Aux than it is, if as in a speeded-up movie everything continually changed from moment to moment, we should still have been forced to look for what we could call individ­ uals. Logicians did indeed think up individual variables. But they did not think up individual values for those variables. They assumed, as do all of us, that there must be something that can become a value of the variable, something to which a predicate was applicable. The values of the individual variable are not entities divorced from the predicates used with them. If an entity has certain predicates appl icable to it, then we call it an individual so that it can become a value of a variable. If these predicates are not applicable, then we have no need to regard it as an individual . The search for basic individuals is a misguided search, for it is as if one went searching for a basic hammer. There is no such tool. There are

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only entities that, with the proper shape and the proper material , can serve pa r­ ticular functions . No sooner do we concl ude that individuals must be bounded , measurable, and weighable, then counterexamples come immed iately to mind . Surely there are particular thoughts occurring at a particular moment, and yet it seems to be ludicrous to say that such thoughts are measurable or weighable or are even in space (even though people normally say that thoughts take place in their heads). We could deal with this criticism in short order by indicating that for many phi­ losophers and psychologists mental events are either reducible to some set of be­ havioral properties or unanalyzable since, as Wittgenstein pointed out, such events are only describable by a private language and there can be no private language. But these ways of treating mental events have flaws . It has become more and more unl ikely that anyone wi ll ever succeed in showing that mental even ts are really no more than certain material events . No logical transforma­ tions of psychological predicates by means of bilateral reduction sentences have ever been successfu l . And , of course, treating sentences with psychological verbs as translatable into counterfactuals simply moves the problem from the frying pan into the fi re. Who has as yet been able to give an adequate account of the logical form of a counterfactual ? And of Wittgenstein's charge that there are no private languages, no one denies that public languages meaningfully use psycho­ logical term inology. So we will assume that there is something going on in hu­ man beings that is called mental and ask why we cannot speak of specific individ­ ual thoughts occurring at a given place and time. I n other words, why should thoughts not be ind ividuals? We ought to recogn ize that there is something odd about call ing a thought an i ndividual . We might call it an event or an occurrence, but it is not an individual in the sense of an entity or an object. Thoughts, unlike individuals, take place. Objects do not take place although , unl ike thoughts, they can be put in a certain place. Second , statements about thoughts , unlike those about individuals, seem to be easily translatable into statements in which thoughts are no longer treated as entities . Thus, if I say " I had an apple yesterday," it is difficult to translate this into another fairly familiar form in wh ich we are no longer referring directly to an apple. (I m ight say " I appled yesterday," but this is surely not a standard form . ) O n the other hand , " I had a particular thought yesterday" i s easily translatable into a form where reference to a particular thought no longer appears, for exam­ ple, "I was thinking about something yesterday." (Notice that the quanti fication word "somethi ng" does not unpack into a reference to a thought, but to a part of the content of a thought. ) Finally, the fact that we use such expressions as "a thought" or "the thought" is no guarantee that there are thoughts that can be treated as individuals. If I say "I have a headache," it would be a m istake to think

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that there is some entity called "headache" running around loose in my body. Similarly, I may have a cold in my body, but I doubt whether any doctor would spend time trying to find it. People claim to have thoughts, headaches, and colds but before individualhood can be bestowed on them, we have to be able to locate them, that is, place them as here and not there. In brief, there may not be any thoughts at all-only thinking, which, like making, hoping, believing and other such verbs do not lend themselves to analysis into discrete elements. If I make a table there does not exist a table that I am making. The table comes to exist after I have made it. If I hope to make a table there does not exist a table I hope to make. Similarly, no one assumes that whatever I think or whatever I believe must exist. Still I must surely be able to speak of my hopes, beliefs, and thoughts. Perhaps not. Hopes are always hopes for something or other. Beliefs and thoughts are always of something or other. The descriptive part is a necessary ingredient of all beliefs, hopes, and thoughts. But if the necessary ingredient cannot be exis­ tentially quantified then it makes no sense to speak of this or that thought. Thinking occurs, perhaps as a dispositional process among certain brain states, but this does not entail that there exist particular thoughts. Before I conclude this discussion of individuals, we ought to return to one question that haunts every analysis of individuals: how do we account for fic­ titious entities? If an individual is a space-time entity and if names obtain their significance by referring to such entities, what occurs when we speak of Hamlet and Santa Claus? It is usually argued that, if we permit these names to remain names, then we shall eventually be led to the admission of at least two worlds with at least two modes of being; we shall return to posit certain Meinongian subsistent entities that are open to all of Russell's objections and that would lead to an unending and uncontrollable population explosion. (Think of all the names in fiction that would now become designators of subsistent entities!) On the other hand, if we follow Russell's advice and change these names into defi­ nite descriptions, then many important sentences that we take to be true, for ex­ ample, "Hamlet killed Polonius,'' will turn out to be false. How then are we to account for all those names in fiction and mythology that do not seem to be nonsensical, do not have a referent, and seem to be perfectly legitimate subjects of true sentences? It will not do to argue that talk of Hamlet cannot really be stated in such sentences as "Hamlet is indecisive" and "Hamlet killed Polonius" since these sentences do not take into consideration the fact that Hamlet is a creation of Shakespeare. Even if we restated these sentences as "Hamlet is de­ scribed by Shakespeare as indecisive" and "Hamlet is pictured (by Shakespeare) as killing Polonius," they would still turn out false if we were permitted to sub­ stitute a Russellian definite description for "Hamlet." There certainly does not exist someone described by Shakespeare as indecisive or pictured by Shakespeare as killing Polonius. Shakespeare is not naming actual people, even though he

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relies on actual people and events in fashioning his plays. Nor will it do simply to say that names have meaning and that for this reason sentences that contain them can be meaningful. No one asks whether "Richard Nixon" has a meaning (although one could ask whether his presidency had some special meaning in American or in world history), and many logicians regard names as having de­ notation but no connotation. Even if names were said to have a meaning of some sort, we are not merely saying that it is meaningful to say "Hamlet killed Polonius''; we are also saying that it is true. We are saying that, if someone denied that Hamlet killed Polonius, he would be wrong. But truth or falsity, presumably, have to do with the reference of expressions and not only their meanings. In more formal terms, we are concerned with how we can manage to say that the predicates "indecisive" and "killed Polonius" can be applied to an object if there is no such object. In other words, if there is a way of showing that the form (3 x)Fx can be true, even if there are no actual instances of Fa , then we shall be on our way to settling the problem of vacuous names. So we return again to the problem of accounting for these odd-nonreferential names. I should like first to propose the beginning of a solution and then to go on to a fuller solution. A number of the problems relating to nonreferential names arise because of an insidious error in the way we think of domains of individuals. When asked for examples of individuals, we might very normally say trees, chairs, apples, houses, human beings, and so forth. All of these are indeed correctly regarded as individuals. But there is a marked distinction that we tend to overlook or to mini­ mize. Some of these entities are natural, but others are made. Trees, apples, and human beings are natural individuals; they are not our technological or artistic constructions. Chairs and houses are man-made constructions. We add individ­ uals to the natural population of the world, and we do this by constructing things that were not present before. Thus we build houses, automobiles, skyscrapers, refrigerators, and mousetraps. We also construct sculptures, paintings, musical compositions, plays and literature, and other works of art. Musical compositions and plays may be created out of marks and lines on paper, but they are still as much man-made constructions as are sculpture and painting. All of these are individuals-the composition, the play, the sculpture, the skyscraper. All are man-made rather than natural. Now, if we are not aware of this distinction, then the use of quantification with names becomes problematic. How can we make the move to "Someone killed Polonius" from "Hamlet killed Polonius" if there is neither a Hamlet nor a Polonius? But, once we recognize that there are both man-made and natural individuals, the problem evaporates. Of course, there is no Hamlet or Polonius in the real, natural world, but there is certainly a verbally created figure called Hamlet in the world. Polonius does not exist in the way this tree exists, but he does exist in the way any work of art exists. As a verbally cre­ ated figure he is as much an existent individual as the sculptured figure in Flor-

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ence called David. David is an individual, but a man-made one. Hamlet and Polonius are individuals, but they are both man-made. What I should like to suggest, therefore, is that, when we are dealing with nonreferential names such as Pegasus and Hamlet, we are not referring to either null or subsistent entities but to created ones. As a sculpture or a painting uses marble and paint, the con­ structions of Pegasus and Hamlet use words. We can make verbal constructions just as we can make marble and painted constructions. And the figures in such constructions exist. They are man-made creations that are added to the number of objects in the world. Consider how we think of a painting of a man-a man who may or may not represent an actual man. What we see are lines and colors so combined that the figure on canvas looks like an actual man or at least makes us think of an actual man. We can speak of this figure, perhaps even give it a name-"Mr. X"-and Mr. X exists, not as a man or as some other natural ob­ ject, but as something created by a painter. Thus when we ask what "Mr. X" denotes, we point to the figure in the painting. That is what the name denotes, just as "Mona Lisa" would, in most circumstances, be taken to refer to the figure in that famous painting. Can we make true and false statements about M r. X? Yes. The color is flesh tone or it is not. He is painted as smiling or he is not. All our statements can be put into quantificational form. But what we are required to remember is that our values are not natural objects, but created ones. We are not referring to null entities or to subsistent ones. Nor are we dealing with ab­ stract concepts or with possible objects. There is Mr. X about whom we are talk­ ing. There is that strange enigmatic woman-Mona Lisa-whom we have just mentioned. They both exist. It is merely a matter of being careful that we do not confuse created objects with natural ones. Verbal constructions would then seem to be the answer to those questions that relate to the referents of nonreferring names. But are we sure that we understand what a verbal construction is? Sculptures, buildings, and paintings are there to be seen and touched, but a verbal construction surely does not have this kind of solidity. Hamlet is not a statue or a figure in a painting. Nor is he to be taken as a series of written words pasted together to form a certain kind of shape. We require a more detailed explication of what a verbal construction is before it can be taken to be philosophically respectable. My main argument is derived from Russell's theory of descriptions and Kripke's criticism of that theory. I shall argue that Kripke's point against Russell is essentially correct, even though his own attempt to explicate rigid designators is not satisfactory. Finally, I shall claim that Kripke's distinction between fixing the reference and fixing the meaning of a name gives us a crucial way of understand­ ing what a verbal construction is and how names operate in such a construction. I should like to begin by turning to the contention by Russell and by many of his later followers, such as Quine, that all names-even those logically proper ones

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that denote objects with which we are directly acquainted-are elim inable in favor of descriptions and that these in turn are eliminable in favor of Russell's schema involving only quantifiers, logical connectors, predicates and variables. Two major reasons have been given for the rejection of Russell's translation of names into descriptions. The first reason comes from Kripke, who has argued that, since no description is ever entailed by any name, therefore names cannot be synonyms of descriptions. 44 Or, to put it differently, the fact that a description may turn out false, that is, unsatisfiable, does not mean that the name it is meant to replace no longer has a designatum. If historians suddenly discovered from newly found documents that Aristotle had not been a teacher of Alexander, this would not be taken to mean that there never had been someone who was Aris­ totle. Historians would simply say that they had been mistaken about what they had believed about Aristotle. For Kripke descriptions fix the reference of a name, but not its meaning. They indicate the changing properties Aristotle might have had in different worlds. They do not fix the meaning of the name. If descriptions did fix the meaning of a name, there would be no way of accounting for those counterfactual possibilities we attribute to objects. There could be no such thing as possibility. This is the basis for Kripke's major contention that names are rigid designators. From possible world to possible world, descriptions might be true or false of an individual. But the name used to designate that individual continues to designate him, regardless of what descriptions are true or false of him. A second criticism of Russell, one that will be of major concern to us, has been that his translation of names to descriptions very often reverses the truth values we expect of certain kinds of sentences. We take "Hamlet killed Polonius" to be true; according to Russell's analysis, since both "Hamlet" and " Polonius" are nonreferring terms whose descriptions cannot be satisfied , the sentence turns out false. "Odysseus was set ashore at Ithaca while sound asleep" is regarded as true. But for Russell, since "Odysseus" has no reference, it is a disguised descrip­ tion that also cannot be satisfied, and therefore the sentence is false. Even where the terms are not vacuous, unwanted truth-value changes seem to occur. "Aris­ totle is necessarily Aristotle" is surely true. But if "Aristotle" is replaced by a defi­ nite description, say, "The teacher of Alexander," then the statement "The teacher of Alexander is necessarily the teacher of Alexander" turns out false. The teacher of Alexander certainly did not necessarily have to be the teacher of Alexander. He could have decided to refuse to teach Alexander. (Placing the modal expression after the description, as we have done, that is, making the scope of the descrip­ tion large, presents us with a de re interpretation of modality. On the other hand, in a de dicta interpretation of the modal operator, that is, where the scope of the 44. Cf. Saul Kripke, "Identity and Necessity," in Naming, Necessity, and Natural Kinds, ed . Ste­ phen P. Schwartz (Ithaca, NY: Cornell Univ. Pr. , 1 977), pp. 66- 1 0 1 .

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description is small, the sentence becomes "Necessarily the teacher of Alexander is the teacher of Alexander" and is true. ) Thus not all names and contexts are amenable to Russell's proposal that names be changed to descriptions . Of the first criticism , as I have indicated earl ier, it would seem to me that Kripke's position leads him to an eventual commitment either to Locke's some­ thing- I-know-not-what or to Kant's noumenon or to Bergmann's bare particuiars . For consider what i t means t o assert that Aristotle would sti ll b e Aristotle even if the descriptions that normally identify him turned out to be false. Who would Aristotle then be? How would we identify Aristotle if no description were avail­ able? What we would be looking for is that Kantian noumenon , that " it" that remains the same even if all the properties change. But, like the "it" of Kant and the thing-I-know-not-what of Locke, Kripke's something that remains the same in all possible worlds so that a name can name it has the same enigmatic and unknowable quality. For if Aristotle were not identified in terms of one descrip­ tion , we would look for another, and if that one failed we would look for still another. From possible world to possible world, Aristotle is identified by the fact that clusters of overlapping descriptions constantly occur, and whatever saiisfies that cluster is Aristotle. We might think of the situation in the following way. Even though Kripke warns us that his possible worlds are not to be regarded as in some way "out there," 4 5 available to us, once we have constructed the proper spaceship, we can assume that there is some way in which we can say this is possible world A and that is possible world B. Let us assume further that we imagine four such worlds, A, B, C, and D. We picture A and there we find Aris­ totle described by three descriptions a, b, and c. We then picture B and find Aristotle described by a and b. In C Aristotle is described by a . Can we then extrapolate and say that Aristotle is also in D, even though there is no description describing him? I t seems difficult to bel ieve that "Aristotle" would still be a rigid designator in D. The moral of the story is clear. If Kripke insists that "Aristotle" is a rigid designator and not to be equated with any set of descriptions, then he must explain to us what it would be like to use the name in a possible world in which there are no suitable descriptions. I shall now turn to the second criticism directed against Russell , namely, that his translation of names into descriptions very often reverses the truth values we expect from certain sentences. It seem quite clear that, if we substitute an exis­ tential description for "Santa Claus" or "Hamlet" or "Polon ius," then we shall make only false statements, since none of these descriptions is satisfiable . But perhaps there is a way that vacuous names can yield true sentences even if they are replaced by descriptions. We know that some existential sentences are true even if no values can replace the individual variables, for example, "There are 4 5 . Ibid . , p . 8 1 .

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unspecifiable real numbers" or "There arc unknown soldiers." And even if we never know the murderer of some person, such as Jones, it could still be true to say "The murderer of Jones was insane. " In all these instances existentially quan­ tified sentences are true, but no values need replace the variable. So it need not automatically be the case that replacing a vacuous name by a description results in a false sentence. The murderer of Jones might, in a note to the police, use a fictitious name, "Robert Smith." "Robert Smith is insane" might then be false, but this would not make "The murderer of Jones is insane" false. Can there, then, be descriptions that can replace vacuous names and yet result in true sentences? We might begin our analysis by first clarifying how we perceive the relations between descriptions and names. We should recall Kripke's argument. Descrip­ tions fix the reference of names but not their meanings. Otherwise, if meanings were fixed by descriptions, no counterfactual statements could be made. But surely there could be situations in which counterfactual statements would be ei­ ther irrelevant or illegitimate. For example, if "triangle" were a name, then "the having of three sides" could be said to fix the meaning of "triangle" and not merely its reference. There could not, in the context of Euclidean geometry, be a counterfactual statement such as "if this triangle were to have more than three sides, then such and such would be the case." Kripke might be right if he argues that descriptions do not normally fix the meanings of names. We usually assert that there is no necessary connection between a name and a given description. But there could be some names in which the description does fix the meaning, that is, in which there is a necessary connection between the name and the de­ scription. We shal l maintain that, when we are dealing with verbal construc­ tions, a description does have this unique relationship to a name. A description is necessarily connected to a name so that whatever satisfies the description must be named by the name. Now, we ought to be clear about what we take to be verbal constructions. Any play or novel or poem is a verbal construction. In these cases the writing is pri­ marily concerned with creating rather than with describing or reporting. I t may also describe or report, but, in cases of verbal construction, the primary function is to produce an aesthetic effect rather than to give actual descriptions of natural states of affairs. Truth is not so important as the presentation of consistent pos­ sibilities that may or may not ever be acted out. Ha mlet, then, is a paradigm example of a verbal construction written by Shakespeare. And our concern now will be with how it is possible, if it is possible, to make true statements about the famous indecisive Dane, Hamlet, without committing ourselves to some cate­ gory of fictitious or subsistent individuals. We should, first, note that the name " Hamlet" functions in a particular verbal construction, that is, the play Hamlet written by William Shakespeare. I t might

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take a great deal of time, but eventually we could obtain one description stating what Hamlet does in the play, how he conducts himself, what his moods are, and so forth, so that "Hamlet" would be associated with the description "The man (in the play Ha mlet) who was indecisive, who killed Polonius, who was convinced that his stepfather killed his father, and so forth." But this association of a name with a description is not a mere contingent one. Hamlet could not be Hamlet if there were any fundamental change in the description. We cannot ask whether there could have been a possible situation in which Hamlet did not kill Polonius or was not indecisive or did not believe that his stepfather killed his father. Only in a different verbal construction-in a different play-could Hamlet have done otherwise. But, of course, in a different play Hamlet would not be the great Shakespearean Hamlet. In brief, the description associated with "Hamlet" fixes the meaning of the name. Whatever satisfies that description in that particular verbal construction is named "Hamlet." But who can satisfy this description? The answer is Laurence Olivier, John Gielgud, Richard Chamberlain, Richard Burton, Derek Jacobi, and anyone else who can participate in the verbal con­ struction Hamlet and take upon himself the predicates of the description of Hamlet. All of them are Hamlets insofar as they are participants in the play, just as one is a salesman when he becomes a salesman. This does not mean that we must have actual values for the variable in the description. Not all plays are per­ formed; not all novels become movies or television scripts. What we require is that someone be able to play the role of Hamlet. That is, the variable must be satisfiable, not satisfied. For this reason ordinary existential statements are usu­ ally trivially true. They are easily satisfiable, even though they may not be satis­ fied at any given time or place. If I say "There are chairs," I do not require that a chair be before me in order for the sentence to be true. All that is required is that I be able to produce a chair if need be; and since there is normally no question about my being able to present a chair or even to build one, we accept the truth of "There are chairs" without ever really asking for instances. It is too simple to obtain or to make an instance for us to demand one. Similarly, the variable in the description associated with "Hamlet" is easily satisfiable. There is always some­ one who can be used to play the role of Hamlet. He or she might not be an Olivier or a Burton or a Gielgud, but anyone can participate in the play and take on the descriptive predicates that fix the meaning of ''Hamlet." Each reader, by the very fact that he or she can read, can satisfy the variable of the Hamlet de­ scription. So who is Hamlet? He is all the professional actors who performed in the play and also all of us who could perform in the play. Hamlet exists. He is us. So long as there are human beings reading Hamlet, the description of Hamlet is always satisfiable. The difficulties involving vacuous names, however, are not settled. No sooner do we propose a possible way of dealing with characters in plays than other issues

Individuals

1 79

immediately arise relating to characters in novels and short stories, especial ly those who are elements of fantasy and science fiction. W ho can satisfy the de­ scriptions that fix the mean ing of Buck Rogers or of any of the other science­ fiction heroes who fight Martians and who ride in incredible spaceships that go from star to star at the speed of l ight? W hat existent being can satisfy the variable of such descriptions? No one. I might be able to take on myself the properties attributable to Hamlet, but can I take on the properties attributable to Buck Rogers? We might be able to answer th is question affirmatively if quantification over the modal operator were permissible. In other words, if ( 3 x)DFx is a per­ missible formula and if Fx is the set of descriptions attributable to Buck Rogers, then the formula would fix the meaning of the name "Buck Rogers." Just as in the Hamlet example, here we would be dealing with a variable that is satisfia­ ble-for example, some existent object can replace the variable. The only dif­ ference would be that the predicates are logical ly possible ones and not those that we normally attribute to objects. And objects with logically possible, but not physically possible, predicates would seem to produce logical ly possible, but not physically possible, objects. Quine's objections to modal ity would now come into force. We know that (3 x)DFx results in Quine's paradox in which it is charged that the variable is opaque. "There exists an x such that necessarily x is greater than 7" is true if x is replaced by 9, but false if x is replaced by "The number of planets." Similarly, "There exists an x such that x is possibly greater than 7" is true if x is replaced by "The number of planets," but false if x is re­ placed by 9. In a previous chapter I have questioned the validity of this paradox. But I am still not sure that quantification into modal contexts is all that sound. I questioned the identity premise in Quine's argument. But this did not entail per­ mission for a quantifier outside a modal context to extend its scope to a variable within that context. If logically possible predicates produce logically possible ob­ jects, then the ordinary domain of physical objects now becomes tremendously expanded. Quine's sparse landscape becomes dotted not only with existent ob­ jects but also with all logically possible objects. Thus we must conclude that a fu l l expl ication of verbal constructions must wait for further analysis of modality and quanti fication. For, if it turns out that there can be logically possible objects in a domain, then Quine's mythical philosophers, McX and W yman, as well as Meinong might have the last word.

Bibliography Index

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Index Acceptability, 14 , 1 5, 29 Addis, Laird, 50n Adverb-preposing rule, 32, 33 Albert, Ethel M. , 3n Allaire, Edwin B. , 10n, 101n, 149, 157, 159 Allen, J. P. B. , 31 Alston, W P., 15, 52, 52n American Heritage Dictionary, 37 Analy ticity, 35, 36, 38 Analy tic universals, 36, 37 Anscombe, C. E. M., 5n, 158n Apparent subject, 21 Aquinas, Thomas, 47, 59 Aristotle, 41, 42, 47, 92, 113, 113n, 121, 122, 123, 138, 162, 175 Ausserzein, 150 Austin, J. L., 52 Ayer, A. J . , 97n Baker, Robert, 159n Bambrough, Renford, 52 Barcan formula, 63 Bare particular, xi, 1, 7, 93, 102, 122, 123, 152, 157, 158, 158n, 176 Barnes, Hazel F. , 97n Basic form, 11, 22 Beard, R. W , 4n, 77n, 78n, 152n Beckett, Samuel, 156 Belnap, Nuel D. , Jr., 58n Bergmann, C., xi, 7, 10, 10n, 50n, 101, 101n, 151, 151n, 157, 158, 158n, 165, 176. See also Bare particular Bishop, Morris, 37 Black, Max, xi, 7, 101n

Bradley, F. H . , 136 Bradley, R., 34n Brentano, Franz, 55n Brodbeck, May, 99n Brouwer, L. E. J., 48 Buck Rogers, 179 Burton, Richard, 154, 178 Calculus, 63, 64, 66, 68, 69 Cantor's theorem, 119, 119n, 120, 126 Carnap, R., 3, 34n, 48, 50, 56n, 69n, 114, 127n, 142; on correspondence rules, 167, 167n; on dispositional statements, 98, 103, 104, 105; on "external questions," 109; on formalism, 93, 94, 94n; on intensions, 138; on logical truth, 155, 155n; on metaphy sical statements, 97, 97n, 98, 99, 99n, 109; on names, 55; on natural language, 75, 75n; on null entities, 24; on number and universal words, 143, 143n, 144, 144n; on oblique sentences, 33, 40; on observation predicates, 10, 28; on phenomenalistic language, 110, 11On, 111, 111n, 168, 168n; on predicates, 8, 56, 98; on principle of univocality, 80, 80n; on reductionism, 96, 96n, 99; on truth, 161, 162, 162n; on values of variables, 149, 149n, 160, 160n Caton, Charles E., 120 Chamberlain, Richard, 154, 178 Chappell, Vere, 158n Chihara, C. S., 115, 115n Chisholm, R. M. , 150n Chomsky, Noam, 3, 3n, 12n, 20, 21, 26, 30, 58; on acceptability, 19; on deep structure,

1 94 Chomsky ( continued) 11, 14, 2 2, 23; on innate ideas, 17, 21n, 32, 49; on knowing, 16, 16n, 27; on logical sub­ jects and predicates, 21, 22, 25, 28; on men­ talism, 18; on phrase structure grammar, 1 8; rejection of Grice, Searle, and Alston, 15; on tree diagrams, 20; on universal grammar, 32, 43 Church, Alonzo, 27, 33, 69, 69n, 143 Claim-making, 73 Classes, ix, 39, 41, 48, 57, 65, 67, 70, 78, 86, 87, 93, 95, 96, 128, 129, 149, 164 Cohen, Jonathan, 21 n Combinatorial language, 76, 160 Common properties, 133, 134, 135 Concreta, 168. See also Goodman, Nelson Constructible objects, 126, 128 Cook, John W , 13n Copi, Irving, 4n, 7n, 69n, 77n, 78n, 116n, 118n, 140n, 152, 152n Cornman, James, 110n, 117n Correspondence rules, 167. See also Carnap, R. Counterfactuals, 32, 34, 35, 99, 103, 105, 171, 175, 177 Craig, W , 76n Cresswell, M. J . , 46n, 63n Cry stal, David, 117n Curry, H. B., 76n, 77 David, 174 Davidson, Donald, 12n, 17n, 40n, 54, 54n, 57n, 97n, 113n, 115n, 120n, 140n De Dicta-De Re, 42, 175 Deep structure, 11, 14, 22, 23, 24, 25, 79, 146 Derelativization operator, 77 Der Logische Aufbau Der Welt, 167, 168, 168n Descartes, Rene, 59 Dewey, John, 5, 5n, 49n, 72, 72n, 169, 169n Dispositional predicates, 3 2, 61, 68, 98, 99, 99n, 103, 104, 105. See also Carnap, R. Donellan, Keith, 120, 120n Du Maurier, Daphne, 156 Eberle, Rolf A., 11, l ln, 165, 166, 166n Einstein's theory of relativity, 157 Elementarerlebnisse, 168. See also Goodman, Nelson Elgin, Suzette H. , 3n Enumerative universals, 36, 37

Essays in Linguistic Ontology Essences, 43, 47, 51, 53, 88, 99, 1 36, 138, 139; Wittgenstein's criticism of, 57, 60; Kripke on, 80, 112, 112n, 122. See also Kripke, S., on essential properties Exists, x External questions, 109. See also Carnap, R. Etrapolated objects, 126, 128 Faris, J. A., 55n Feigl, Herbert, 44n, 99, 150n, 162n Fey s, R., 76n Fictitious entities, xi, 149, 153, 154, 155, 172 Fillmore, Charles, 24, 24n, 25, 43, 43n Fodor, Jerry A. , 28, 28n, 29, 29n, 30, 31 F0llesdale, Dagfinn, 111n Formal languages, x Formal mode of speech, 143, 144 Formal property, 15 2 Fraassen, Bas C. Van, 102n Free logic, x, 24, 31, 92, 102 Frege, G. , 24, 33, 34, 34n, 39, 40, 41, 45, 46, 48, 55, 56, 74, 119 Garrick, David, 154 Geach, P. T , 100, 101, I0l n Generative grammar, 15 George, Rolf A., 168n Gielgud, John, 154, 178 Godel's theorem, 59, 149 Goodman, Nelson, 4, 4n, 99n, 131, 131n, 164, 164n, 166, 166n, 167, 167n, 168, 168n Gould, J. A. , 69n, 116n, 118n, 140n Gram, M. S. , l0n, l O l n, 151n, 158n Grammatical form, 6, 13, 23, 38 Greene, Judith, 19 Grice, H. P. , 15 Griffin, James, 78n Grossmann, Reinhardt, 151, 151n, 158, 158n Gumperz, John J., 3n Hallett, Garth, 7n, 13n, 52n Hamlet, 155, 156, 172, 173, 174, 175, 176, 177 Hamlet, 89, 155, 156, 177, 178 Harman, Gilbert, 12n, 40n, 120n Harrah, David, 71, 71n Harre, Rom, xi Hegel, G. W F. , 59 Heidegger, Martin, 97, 98, 98n, 100

Index Hempel, C . C . . 99n H ilbert, D . . 48 H ill. Archibald A . . 3 Hintikka, Jaako. l 7n, 57n. l l 3n, l l 5 n . l 40n Historia Danica, l 56 Hughes. C. E . . 46n , 6 3n H uman nouns. 20 Hume, David. 4. 4n. l 22, l 5 5 Hymes, Dell, 3n lndi\·iduals, ix, x, xi, 5 n . 7. l 8, 39, 4 l , 65, 66, 68, 84, 9 1 , 93, l 3 3 Innate rules, 1 7, 1 8, 32 lntensions, 26, 34, 38, 54, 96, 97 , l l 2, l l 2n, 1 1 6. 1 27 , l 37, l 38, 1 39. See also Sense Internalized rules, l 7 Interpretation, 63, 6 5 , 66, 67, 68, 9 3 , l l 5 , Ch . 3 lseminger, Cary, 5 5n Jacobi, Derek, l 54, 1 78 Julius Caesar, 1 56 1ulius C aesar, l 56 Kant, Immanuel , x, 1 7, 3 1 , 3 5 , 36, 59, 1 1 0, 1 2 5 , 1 26, 1 5 1 , 1 54, 1 76 Katz, Jerrold, 1 8, 28, 28n, 29, 29n , 30, 3 1 , 3 l n , 3 2, 3 5 , 3 5 n , 36, 37, 4 1 , 4 1 n Keynes, J . M . , 1 0 1 , I O l n Khatchadourian, Haig, 52n Klemke, E . D. , ! On , l O l n , l 29n, 1 5 1 n , 1 58n Kneale, Martha, 9 5 n Kneale, William, 9 5 , 9 5 n Komer, S . , 48n , 1 26, 1 26n, 1 54n Kotarbinski, T , 1 09n Kripke, S . , 2, 7, 26, 3 1 , 6 3 , 1 1 3 , 1 39; on es­ sential properties, 4 1 , 1 22; on rigid designa­ tors, x, 7, 7n, 34, 4 1 , 42, 42n, 5 5n , 62, 79, 80, 1 1 9, 1 2 1 , 1 22, 1 76; on Russell's theory of descriptions, ix, 1 20, 1 20n, 1 2 l , l 2 l n , l 2 2 , 1 5 5 , 1 74, 1 7 5 , l 7 5n . See also Essences Kung, Guido, 1 02n, 1 07n Lakoff, George, 26, 3 2 , 3 2n , 3 3, 34, 34n , 40, 40n, 4 1 Lambert, Karel , 1 02n Language games, 57 Lehrer, Keith, 44n, 1 50n Leibniz, C. W , I 0, 92

195 Lejewski , Czeslaw, 1 34, 1 3411 Lemmon, E. J . , 5 3 , 5 3n Leonard , Henry, 1 6711 Lesniewski, S . , l 02, l 02n Lewis, C . I . , 63, l 1 6, 1 1 6n , l 6 3n Lewis, David , 26 Linguistic C riterion of Ontology, 1 1 6 Linsky, Leonard , 26, 34, 34n , 5 5 n , l 1 3 , 1 1 3n , I 38, 1 38n, l 40n Lob, M . H . , 46n Locke, John , 1 57, 1 76 Logical form , 6, 1 1 , 1 8, 22, 2 3 , 2 5 , 27, 28, 3 9, 40, 4 l , 4 3, 4 7, 5 0, 5 1 , 5 3 , 5 5 , 5 6, 5 7, 5 8 , 59 Logical predicate, 2 1 , 22, 2 5 , 28 Logical property, 28 Logical subject, 2 1 , 22, 2 5 , 28 Long, D. C. , 1 5 8n Loux, M ichael J. , ! On , 1 58n Lyons, John , 3n, 40n Malcolm, Norman, ! On , 1 7n, 2 5 , 47, 47n , 52, 5 2n , 1 57n Man-made constructions, 1 7 3 Marcus, Ruth Barcan, 1 1 6, 1 1 7, 1 1 8, 1 1 8n , 1 1 9, 1 39n , 1 40n Margolis, Joseph, 1 1 On Martin, R. M . , 64, 64n , 6 5 , 69, 69n , 78, 1 09n Material mode of speech , 1 4 3 , 1 44 Material property, l 5 2 Meiland, J . W , 1 58n Meinong, A. , xi, 2 5 , 4 1 , 74, 1 50, 1 50n , 1 5 1 , 1 72, 1 79 Metalanguage, 64, 6 5 , 67, 68, 69, 9 3 , 1 70 Michelson-Morley experiments, 1 57 Mill , John Stuart, 5 5 , 72, 72n Modal expressions, 26, 3 1 , 34, 46, 1 37 Montague, Richards, 26 Montifiore, A. , 5 3n Moore, C. E. , l 5 7n Munitz, Milton , 1 20n Names, xi, 2, 6, 7, 27, 42, 5 1 , 5 5 , 68, 89, 1 1 0, 1 20, 1 2 1 , 1 2 3 , 1 42, 1 59, 1 69 Natural language, x Natural logic, 40 Neumann, von , J. , 66 Neutral entities, 9 5 , 96, 97 Nixon , Richard, 1 7 3

1 96 Noumena, 1 1 0, 1 2 5 , 1 26, 1 76 NP-preposing, 2 1 Objectual interpretation, 88, 1 1 6, 1 1 7, 1 1 8, 1 2 3 , 1 2 5 , 1 26, 1 27 Oblique sentence, 26, 27, 3 3 , 39, 40 Occurrent predicates, 43, 68 O'Connor, John, 44n Olivier, Laurence, 1 54, 1 78 Ontological commitment, 2, 3 , 4, 6, 14, 22, 30, 35, 42, 48, 57, 59, 60, 66, 88, 92, 96, 1 1 4, 1 1 5 , 1 1 6, 1 1 9, 1 2 3, 1 29, l 3 1 , I 3 5 . 1 36, 1 48 , 1 50, 1 70 Ordering relation , 78 Orenstein, Alex, 9 5 Parsons, Charles, 90, 90n Parsons, Terence, 1 38, 1 38n Peano's axioms, 84 Phenomenal object, 1 1 0 Phrase structure grammar, 1 8, 1 9, 3 1 Pitcher, George, 7n, 1 3n, 52n Plato, 5 , 1 2 1 , 1 22, 1 2 3 Platonism, 47, 49, 54, 57, 93, 94, 9 5 , 1 2 5 , 1 29, 1 30, 1 3 1 , 1 42, 1 50, 1 5 2 Platts, Mark, 5 1 n , 54, 5 5n Polonius, 89, 1 72, 1 7 3 , 1 7 5 , 1 76, l 78 Popper, Karl R. , 97n Pragmatic commitment, 48 Predicates, x, 2, 6, 8, 1 8, 2 1 , 22, 26, 3 1 , 32, 5 l , 64, 66, 67, 68, 69, 74, Ch. 4, 77, 78, 80, 82, 84, 86, 94, 1 0 1 , 1 09, 1 3 2, 1 59, 1 62 Principia Mathematica, x, 4 1 , 4 7, 48, 50, 5 1 , 5 5 , 74 Private language, 1 7 1 Properties, ix, x , xi, 6 , 7 , 9 , 1 0, 39, 4 1 , 48, 6 5 , 67, 7 0 , 74, 86, 90, 93, 94, 9 5 , 96, 97, 1 3 2, 1 3 3 , 1 49, 1 62, 1 64; formal, 1 52; material, 1 52 Proposition, 27, 5 3 , 54, 1 49 Pseudo object sentence, 99, 1 44. See also Car­ nap, R. , on metaphysical statements Qualia, 4n, 1 0, 1 49, 1 67, 1 68 Quine, W V , ix, 14, 1 5 , 1 5n, l 7n, 2 3 , 36, 36n, 48, 5 5 , 79, 97, 1 09, 1 1 0, 1 1 0n, 1 1 8n; on Cantor's theorem, l l 9n, 1 20, l 20n; on common properties, 1 3 3, 1 3 3n, 1 3 5; on con­ ceptual ism, 1 30, 1 30n; on the derelativiza-

Essays in Linguistic Ontology tion operator, 77, 77n; on dispositional terms, 1 04, 1 04n, 1 0 5 , 1 0 5n; on essential­ ism , l 36; on general terms, 6, 7, 7n, 66, 82, 82n, 93, l 32; on identity, 98, 98n; on inten­ sions, 34, 44, 44n; on modal operators, 34, 1 79; on names and predicates, 1 06, 1 06n , 1 07; on objectual quantification, 90, 1 2 3 , 1 2 3n; o n oblique contexts, 26, 3 3 , 40; on ontological commitment, l , 56, 56n, 67, 67n, 1 1 4, l 1 5 , 1 2 5 , 1 29, 1 48; on the para­ dox of modality, Ch. 7; on the principle of indeterminacy, 57, 5 7n; on reducing names to descriptions, 68, 80, 89, 1 62, l 74; on ref­ erential opacity, 1 1 2 , 1 1 2n; on syncategore­ matic expressions, 1 3 1 , l 3 1 n; on time, 50, 50n; on type theory, 8 3 , 83n, 84, 1 64; on unit classes, 4, 5n, 86, 163, 1 63n, 1 64; on unnamed values, 69, 69n, 88, 88n; on use and mention, l 1 7; on values of the variable, 74, 76, 76n, 9 1 , 92, 9 5 , 9 5n, l 1 5 , l 1 6, l l 6n, l 60; on "virtual classes," l , l n Reduction sentence, 32, 99, 1 0 3 , 1 04, 1 67 Regamey, C. , 1 07n Rebecca, l 56 Rebecca, l 56 Recursive function system, l 8 Richard III, 1 56 Richard 111, l 56 Rorty, Richard, 44, 44n Rosenberg, Jay F. , l 5n, 52n Ross, W D. , l l 3 n Rule of Truth , 1 6 1 Rules of Designation, l 6 l Russell, Bertrand, ix, 5 , 5n, 7, 2 l , 22, 2 3 , 2 5 , 27, 3 3 , 40, 4 1 , 42, 47, 68, 74, 80, 8 3 , 88, 1 00, 1 00n , 1 02 , l l l , 1 20, 1 20n, 1 22, 1 49, 1 49n, 1 50, 1 50n, 1 5 1 , 1 54, 1 54n, 1 62, 1 64, 1 68, 1 72 , 1 74, 1 7 5 , 1 76; Russell's paradox, 66, 84, 8 5 , 9 5 , 1 29, 1 44, 1 63; theory of de­ scriptions, ix, 2, 22, 24, 32, 42, 5 5n, 88, 1 23, 141 Ryle, Gilbert, 49, 49n , 5 5 , 5 5 n, 8 2 , 82n, 84 , 1 1 6, 1 2 5 , 1 2 5n , 1 42 Santa Claus, l 72, 1 76 Santayana, George, 1 36 Sapir, Edward, 73 Sartre, Jean-Paul, 97n

1 97

I ndex Saxo Grammaticus. 1 56 Scheffler, I . , 99n , 1 04 Schilpp. P. A. , 5 5 n , 97n . 1 68n Schonfinkel . Moses, 76. 76n. 77 Schroeder, E. , 1 0 1 , 1 0 1 n Schwartz, Stephen P. . 7n, 1 7 5n Searle. John , 1 5 , 1 3 2, 1 3 2n, 1 60 Sellars, Wilfrid , 44n , 78, 78n, 1 50n, 1 62n Sense, 29, 30, 3 1 , H, 3 5, 36, 37, 1 1 9, 1 39. See also lntensions Sentences, 72, 73 Shakespeare, William, 1 50, 1 54, 1 56, 1 72, 1 77, 1 78 Shorter Oxford English Dictionary, 3 1 Similarity, 1 3 5 Smullyan, A. F. , 1 39, 1 40 Specific properties, 1 3 3 Steel, Thomas B. , Jr. , 58n Stenius, E. , 7 Strawson , P. F. , 1 5 , 24, 4 5 , 5 5 , 5 5n, 60, 60n , 1 02n, 1 06, 1 06n , 1 07, 1 07n, 1 08, 1 09, 1 20, 1 20n Stroud, Barry, 57n Sturtevant, E. H . , 3n Substitutional interpretation, 88, 1 1 7, 1 1 8, 1 2 3 , 1 2 5 , 1 26 Surface structure, 1 1 , 1 2, 1 3 , 2 5 , 38, 79 Swartz, N . , 34n Syncategorematic predicates, 1 3 1 Tarski , Alfred, 3 , 1 6 1 , 1 62, 1 62n Theory of force, 54 Thing-words, x, 1 0 5 , 1 09, 14 3 , 1 44 Transformational rules, 20 Travis, Charles, 1 5n, 52n Tree diagram, 20, 29, 30, 3 1 , 32, 3 5, 36 Type Theory, 83, 84, 87, 88, 95, 1 49, 1 64

Ultimate constituents, 1 66, 1 69 Unit class, 5n, 86, 87, 163 Universal words, 1 4 3 , 1 44 U rlanguage, 59 Vacuous names, 1 72, 1 7 3 Yan Buren, P. , 3 1 Variables, ix, 6 5 , 94, 1 2 3 , 1 4 5 ; i ndividual, ix, 65, 66, 67, 68, 94, 1 2 3 , 1 4 5 , 1 5 7; predicate, ix, 65, 66, 67, 93, 94 Verbal construction, 1 74, 1 77 Waiting for Godot, 1 56 Wallace, John, 26 Webster's Second International Dictionary, 2 Whitehead, A. N . , 47, 74, 1 1 0, l l 0n, 1 69, 1 69n , 1 70 Whitfield, Francis, 3n Wharf, B . , 1 8 Williams, B . , 5 3n Wittgenstein, L. , x, 5 , 5n, 1 3 , 27, 62, 99, 1 00, 1 42, 1 4 3 , 1 5 5 , 1 67, 1 7 l ; on basic sentences, 22, 2 3 , 40; on essences, 5 3 , 60, 1 22; on lan­ guage games, 57, 60; on logical form , 6, 2 3 , 43; o n objects in configuration, 4, 4n; on predicates, 6, 6n, 8, 9, 77, 77n, 78, 78n, 79, 9 1 , 1 1 1 ; on resemblances, 52, 52n; on sensa­ tions, 1 2, 1 2n; on simple objects, xi, 7, l 0, 1 0n, 92, 1 0 5 , 1 49, 1 5 2, 1 5 3 , 1 57, 1 58, 1 58n, 1 6 5 ; on word use, 57, 7 1 , 7 1 n, 86 Woodger, J. H. , 1 09n Wright, G. H. von , 1 58n

Yoes, M. G. , 1 66, 1 66n Ziff, Paul, 1 5 , 1 5n