$OME RECENT 1145031225 OF EXl‘SfiNCi AND THE 1.06137“: APPROACM TO ONTOLQGY. Thesis (er the: Mgr-ea a? M. A MéCHlGAN sm‘a COLLEGE Gamma in Palvifié 1:932 we 0-169 This is to certify that the thesis entitled ISOME RECENT THEORIES OF EXISTENCE AND THE LOGISTIC APPROACH TO ONTOLOGY presented by George J. Pelviste has been accepted towards fulfillment of the requirements for _M.._A.._ degree in .Ehflnaaphy flaw/M C/ Major professor mew .' .+_‘.__. “r -unrn-oua lg,- “ I "- u...” i“ SOLE ECE’I’JT 'l‘hEORIES OF EDES'I‘EIICE AND THE LOGISTIC APPROACH TO OKTOLOGY SCXZE £8021th TFEORIES 011' 33113 EJCL EQ‘J'D THE LOGIS‘i'IC MPROACH 'l'O OIQTOLOGY' by GEORGE J . PALVIS‘i'E A TEESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of " ‘xSTER OF ARTS Department of Philosophy 1952 THESle PREEACE This paper reports, in some cases with critical remarks, on a few relatively recent ideas and theories concerning ontology. The first chapter is devoted to a brief examination of the ontological aspects of Bertrand Russell's theory of descriptions and other singular terms. In chapter two a comiarison is drawn between *.ssell's and U. V. Quine's theories of singu- lar terms which is then followed by an exposition and examination of Quine's theory of the "ontological com- mitments" implicit in constructional systems. In the final chapter a few problems are discussed connected with the type of nominalism.uhich has been proposed in recent years by helson Goodman. To bring together these three authors is not an accident. They all have contributed to the clarifica- tion of the problem of existence by using.methods sini- lar in spirit. Due to this similarity in method one can clearly observe an important difference as to the basis of their investigations. In gussell's case the basis for ontology is largely epistemology. For Quins and Goodman, on the other hand, epistemology is onto— logically irrelevant. This abandonment of epistemological $371353: ’2 U i considerations by these two authors results in what may be called the logistic approach to ontology. The author is greatly indebted to Professor Henry S. Leonard, under whose constant instruction and supervision this work was undertaken and accomplished. he also wishes to express his sincere thanks to Professor Lewis K. Zerby, whose discussions of related topics proved immensely valu— able. PM? ACE TABLE OF CON‘ 'E-?’TS TABLE OF CONTENTS INTRODUCTION 1. Ontology and Abstraction 2. The Three Phases of Ontology 3. Ontology and Universals I. EISSELL'S THLORY OF EXISTEHCE l. 2. 5. 4. 5. 6. 7. Kenning and Entities Names and Descriptions flames, Descriptions, and Designation Are Descriptions Constituents of Propositions? Existence and Descriptions The Formalistic Interpretation of Descriptions as Constituents of Propositions Summary of Criticisms II. QUINE'S TEEORX OF "ONTOLOGICAL COLKIIMERTS" l. 2. 5. 4. 5. "Singular" and "General" Existence Statements Language and Existence The Epistemological and Semantical Theory of Names Existence and Variables The Theory of "Ontological Commitments" iii 10 15 19 23 33 36 40 45 51 II LI I. fl [T1 .Lu 8. iv res ONTOLOGICAL Assn "rs or cocmrmvs its S'l'RUC'l'URE or AerliAlhhéC’“ Preliminary Discussion of Terms Individual lioriinali sm Two Examples Two Possible‘lisconceptions of Hominalism Particularistic and Realistic Systems Individuals and Qualification The Problem.of Universals RATUiE CITED 62 64 69 75 78 81 85 89 "The explanatory purpose of philosophy is often misunderstood. Its business is to explain the emergence of the more abstract things from the more concrete. It is a complete mistake to ask how concrete particular fact can be built out of universals. . . In other words, philo- sophy is explanatory of abstraction and not of concreteness."--A. N.‘Whitehead IHTRODUCTION l. Ontology and Abstraction The language of science, and perhaps, to a certain extent, also our ordinary language, interpret concrete experience toward generality and abstractness. Language usually abstracts, generalizes, systematizes. But lan- guage itself can become the object of analysis and inter- pretation. In such a case the process is oftentimes the reverse. In using language to interpret systematically concrete experience we advance toward the more abstract, but in interpreting language itself we search for the more concrete. To interpret language systems in the di- rection of concreteness is to try to discover their basis, i.e., the most concrete and ultimately given elements of experience. The scientist, and, in some sense, the.man in the street, are preoccupied with abstractive systemati- zation of concrete experience. The interpretation of lan- guage itself is left for the philosopher. The scientist and the common man use language to talk about experience, -1- the philosopher, in many cases, talks about language itself. Bach science develops an abstractive scheme to explai concrete facts. These concrete facts constitute the subject matter of a given science and they are, for the scientist, simply given, i.e., the character of their givenness and their status in the total framework of experience are hardly ever recognized byw the scientist as problems. Philosophy, on the other hand, makes it its business to inquire into the character and scope of this givenness of concrete facts which the scientist presupposes but neglects. Questions like "That does it mean to be given?" and "what is ultimate- ly given in experience?" are philosophical questions pg; excellence. In the course of such investigations it.might very well turn out that what is presupposed as given by the scientist or by common sense, can not be said to be given philosophically. .neside systematizing experience, the phil- osopher's job involves, therefore, interpretation and cri- tique of systematization itself. By the ultimately given in experience I do not mean the immediately given or the datum. The ultimately given makes no claim to epistemological priority. The ultimately given in experience is the actual and might perhaps be better de- scribed as that which is relevant for experience. In that sense it is simply everything that there is. The search for the ultimately given elements of experience as the basis for abstraction and for scientific system building is '[llll' l III-ll. In"! -3- therefore not epistemological but ontological. 2. The Three Phases of Ontology In this endeavor to criticize abstraction by finding its basis as the ultimately given, we can distinguish between three phases. Some philOSOphers confine their reasoning to devising methods of exact discovery of the scope of the subject matter of given abstractive schemes.l It is by no means obvious what exactly a given system.as- sumes as given or as existing. The ordinary notion of "naming", for example, will prove inadequate as a criterion for judging what a given system.or language pattern presup- poses as existing. "Cerberus" is a name but it names no- thing, i.e., it names a nonexisting entity. Similarly "meaning" will not constitute such a criterion, as we can easily have two meanings but only one corresponding entity, as, for example, in the case of "morningstar" and "Evening- star". Again, it is not at all clear what is presupposed as existing by even so simple a statement as "Tiger is big- ger than cat." Is it only individual tigers and cats or also the abstract things "tigerhood" and"cathood"? Is it only tigers and cats or all animals? Is it only the ani- mals but no other physical objects? Is it also the relation "bigger than"? Is it all dyadic relations? Is it relations in general? To investigate what and how linguistic forms do, 1In recent years guine,.more than others, has been engaged in ontological investigations of this type. in fact, Operate as unambiguous indications of e: {isting entities is therefore not a trivial matter. Such investig' ations attemit then, to establi oh rules in terms of which we can determine what exactly a given system or languare pattern does presuppose by way of entities. ."e have to notice that such ontological enquiries are gpggp existing abstractive schemes and not themselves systematic treatments of the ontological problem. ”When we enquire into the ontological presuppositions or cor I‘mitments of a system we only ask what exists in terms of that system, we do not ask what exists in general. To discover the exact ontologi- cal assumptions of a given system, in other words, leaves us in complete darkness as to how to evaluate the results of our discoveries. The next phase is the direct treatment of the ontologi- cal problem.within a "constructional system".1 Such systema- tic treatments can utilize the rules and devices developed in the first phase as the criteria through which the range of the universe of the system in question is discovered. If a "constructional system" is general enough it will Operate as asnhema for other systems with more limited subject matter. Once the ontology of the wider system.is accepted, the onto- logical problem is thereby also solved for such more limited lCarnap'a Der Logische hufbau der .Ielt, Berlin, 1928 and Goodman's I'he Structure of appearance, Cambridge: Harvard University Press, 1951 can be listed as exa.ples of such con- structional syste-s systems as the wider system accommodates as a schema. The advantage of this more direct treatment of the ontological problem within a "constructional system" is that the accepta- bility of the range of the universe of such a system is not left to be judged solely by appeal to instinct and common sense but is judged in terms of the coherence and adequacy of the system itself. The third phase is the treatment of the ontological problem in terms of systems which claim to be not merely coherent and adequate but also necessary. This claim to necessity gives to such systems their (in the traditional sense) metaphysical character. A "constructional system" is usually looked upon as only one among several equally possible systems. A.metaphysical system of the more traditional kind claims to be the only true explication of the structure of the universe. Furthermore, the range of the subject matter of a "constructional system", al- though being very wide, still has its recognized limits: a "constructional system" purports to explicate only a segment, however large, of the total universe. A "meta- physical system", on the other hand, claims to cover the universe in its totality. Accordingly the ontological doctrine contained in such systems is held to be compel- ling not only to a variety but to all possible more limited systems and theories. The range of all possible systems is determined by the universal character and scepe of experience itself, The ontological question becomes, therefore, for the proponent of a necessary metaphysical system, the ques- tion of what does experience as such disclose as the ulti- mately given or the actual. A "metaphysical system", in other words, purports to exhaust the scope of ultimate reality. 3. Ontology and Universals That which is ultimately given in experience, we said, is that which is. Traditionally, that which is has been conceived to be most generally either concrete particulars or abstract universals, and the ontological disputes have centered largely around the question whether only concrete particulars can be said to be or exist, or whether the abstract universals should also be included in the cate- gory of existence or being. I shall argue that the problem of universals, as traditionally conceived, really involves two problems which should be kept separate from.each other. The first of these problems I shall conceive as the problem of universal or repeatable and of particular or unrepeatable elements of experience. The second problem I shall conceive as the problem of individual and nonindividual (e.g., clas- sial) entities. Traditionally one has treated the distinction: of particular from.universal and of individual from.nonindivid— ual by and large as parallel distinctions so that "particular" and "individual", as also "universal" and "nonindividual", have become almost pairs of synonyms. Following Goodman, I shall argue that these distinctions do not run parallel but cut across each other. These questions shall be dis- cussed mainly in the third chapter of the present paper. In the previous two chapters I shall be concerned with the ontological aSpects of hussell's and @uine's theories about singular terms. It is hOped that from this discussion clarifications of the notion of existence will gradually emerge which can then with some gain be applied to the problem of the existence of universals. Cry-‘LE'i'h‘n 0M; RUSSELL'S Tamonx OE EXISTENCE 1. meaning and Entities Ihe can formulate meaningful sentences about things which we say do not exist. we can thus say "Unicorns are- white," or "The round square is a triangle" and know what . we.mean. It may be asked: How is it possible to under- stand these statements if their grammatical subjects do not exist? To many philosophers the difficulty has ap- peared so grave that they have felt compelled to argue that therefore the unicorns and the round square must be allowed to exist in some sense. "Unicorns" or ~ "round square", they have held, do not denote in the . ordinary sense but in a special "logical" sense. Thus: the unicorns and the round square, although not having actual existence have been said to have a "logical" existence of some sort. However, by following this line of reasoning there will be no limit for multiplying exis- tence in our universe. According to an argument in Plato's Sophist even not-being itself would have to be accommodated in our universe. The Eleatic Stranger argues that to deny the existence of not-being is a self-contradiction because that which plainly is not is unutterable, unspeakable, un- thinkable. hot-being cannot be said or thought not to be, otherwise, what is it that we say or think that there is not? -8- To take mere.meaningfulness of words in sentences to be the sign of the existence of corresponding entities would therefore not do. If meaning would grant existence entities could be multiplied at will, as every figment of our imagination would then have to be included in our uni- verse. hnother way of dealing with the difficulty of inter- preting sentences like "Unicorns are white," or "The round square is a triangle" has been to admit meanings as entities. In our examples the predicates "is white" and "is a triangle" could be thought of as being sustained by the meanings "uni- corn" and "round square" respectively. In this view, mean- ings would become metaphysical entities of some sort and constitute a separate category or realm of being. The sen- tences "Unicorns are white" and "The round square is a triangle" would be conceived not any more as being about . any "logically" existing objects but as being about the . metaphysical entities-emeanings. Aside from the vagueness of "meanings" as a category or realm of entities there are, in general, two objections to this view. first, meanings are extremely multifarious. Once admitted, they would make us end up with the same un- pleasantly numerous and complex universe as when unicorns and round squares were admitted as "logically" existing objects. rrom the standpoint of economy and simplicity it makes little or no difference whether we say that for -10- each meaning there is a corresponding entity or we conceive of meanings themselves as entities. Secondly, to view sentences as being about meanings, rather than about things, persons, or events, seems far fetched. Sentences like "Horses are white" or "The square is a triangle" are, it would seem, about horses and the square and not about the meanings "horse" or "square". however, there is nothing in the form of these sentences that would distinguish them from our examples about unicorns and the round square. If, on the other hand, we say, e.g., that "Horses are white" is about horses but "Unicorns are white" is merely about a meaning because horses exist as physical objects but unicorns do not, our argument would comp rat an ignoratio elenchi. "Horses are white" purports to be about physical objects because the word "horse" has Spacio- temporal connotations and not because there are horses. Clearly "unicorn" has similar connotations. The fact that there are physical objects which are horses but there are none which are unicorns is irrelevant as to the question of what "Horses are white" and "Unicorns are vhite" purport to be about. To say that "Unicorns are white" or "The round square is a triangle" are about meanings and not about any objects, would thus have the curious consequence that we would have to claim the same for all sentences. 2. Names and Descriptions Russell's theory of descriptions arose as a criticismv -11- of ontological arguments such as I have characterized above as resulting from certain apparently puzzling features- of our ordinary language. Broadly Speaking, the two claims ' of Russell's criticism are (I) that descriptions of the form» "the so-and-so" are radically different from.names and (2)' that the.meanings of certain phrases occuéing in preposi- tions do not enter those propositions as their constituents.- Russell.makes the first claim by arguing that descrip- ‘ tive phrases of the form."the so-and-so" are not names be- ~ cause they do not, as names do, directly refer to objects.~ Furthermore, descriptions, for Russell, never designate ‘ objects, whereas names always do. Even if a description- describes the same entity as a name names, Russell clhims that the description does not designate that entity. Russell.makes his second claim.by treating phrases of the form "the so-and-so" as incomplete symbols, i.e., as symbols void of meaning in isolation. The meanings of such phrases, Russell claims, can be analysed and defined only within and together with more complex expressions in which they occur. The meanings of such phrases, Russell argues, are therefore not constituents or parts of preposi- tions in which they occur. I shall first examine Russell's distinction between . names and descriptions, the discussion of descriptions as"incomplete symbols" will be taken up in a later sec- tion. A name, for Russell, "is a simple symbol directly . -12... designating an individual which is its meaning."1 The meaning of a name is given by pointing to its designatum.- If the designatum is a thing, person, etc., the name is only a "relative" name, if it is a particular sense datum or a certain universal, it is an "absolute name". The meaning of a name is given as an item in direct experience, and no meaning adheres to the symbol prior to the direct - cognition of its designatum. Descriptions, on the other hand, describe matters of fact because they possess fixed meanings prior to and independent of the matters of fact which they describe. Let us take the following example: (1) homer is the author of the Iliad, and let us assume that "homer" functions in that sentence as a "logical name," i.e., hat it designates an actual entity, the man who lived so and so many years ago. we have to notice then that the name "Homer" applies only because we, so to speak, make it apply, i.e., its appli- cation is fully dependent on volunary acts and persistency of habit among human beings. In other words, its applica- tion is quite arbitrary and conventional. Furthermore, the whole meaning of the word "Homer" derives from.the accep- tance of this convention as establishing "Homer" as a demon- strative symbol pointing to the actual individual. The mean- lBertrand Russell, Introduction to Mathematical Philo- sophy. London: George Allen a Unwin, Ltd., 1919, p. 174. -13- ing of the word "homer" as a name is the individual Homer and the symbol "Homer" is meaningless when detached from its referent. The description "the author of the Iliad," on the other hand, applies to or is true of the actual man (waatever his name) because he, that man, actually sat down and composed the Iliad. The description "the author of the Iliad" describes a prOperty which we, correctly or incorrectly, attribute to the actual man Iomer in sentences like "Homer is the author of the Iliad," "Homer was blind," etc. Descriptions describe physical and other facts and are not, like names, merely conventional symbols.1 "The author of the Iliad" describes and does not name a prOperty; it describes that property by virtue of being a complex symbol with a meaning fixed pre- viously to its application. Its fixed meaning derives from the composite meanings of its parts "author," "Iliad,” etc. The.meanings of these parts fix the meaning of the entire descriptive phrase by virtue of which the phrase is then c pable of describing a fact. The point that names are different from descriptions is also argued by Russell as follows:2 Let us interpret the lItmay be argued, of course, that also descriptions depend on conventions, although more indirectly than names. All words (symbols) are "conventional." This, however, seems irrelevant to the point in question. 2Bertrand Russell,"The Philosophy of Logical htomism." Hind, 1918-1919, reprinted by the Department of Philosophy, University of‘Minnesota, pp.43-44. -14- prOposition (1) homer is the author of the Iliad as identifying the actual man homer with a description. The fact "the author of the Ilgag"is not a name can then be_shown, Russell claims, by substituting in (l) e.g., the expression "Iomerus" for the expression "the author of the Iliad:" (2) homer is homerus If we then interpret in (2) both "Homer" and "Homerus" as names, (2), Russell claims, will be tautologous and not any different from "Homer is homer." (l), on the other hand, is an empirical statement and therefore (1) and (2) are not instances of the same prOpositional func- tion at all. If, however, we interpret (2) as including two descriptions, (2) would.mean that the person called homer is also called Eomerus, or (3) (1x)(x is called Homer)-(7x)(x is called Homer- us) which would be analogous to the proposition (4) The blind poet of Greece is the author of the Iliad. Again, (5) and (4) are not tautologous but empirical. After the initiation of the meaning of a name through cognitive acquaintance with its designatum has been conven- tionalized, names might often function as descriptions. By using the word "Homer," for example, we usually describe rather than name an object. By "Homer" we might mean "the author of the Iliad," "the blind poet of Greece," or the -15- like. In this.manner words like "Homer," "Caesar," "Bill" function not as names but as abbreviated descriptions and identify entities by describing one or more of their prop- erties. Usually we identify objects by describing their properties and not, in Russell's sense, by naming theme In naming, i.e., in fixing the meaning of a symbol through direct reference to some elements in our knowledge by ac- quaintance, the identity of that element is presupposed, it is the element in experience under consideration. 5. hames, Description, and Designation Even if a description describes the same object as a name names, a description does not name and therefore does not designate that object. A name for Russell, as we said, "is a simple symbol directly designating an individual which is its meaning."1 A description, on the other hand, never directly designates an entity. ‘While names are the sort of thing which always have designate, descriptions are the sort of thing which never do. Descriptive symbols such as "the blind poet of Greece," "the author of‘fiaverly," "the British foreign secretary" merely describe character- istics or prOperties and they do not designate the objects the prOperties of which they describe. However, in many cases descriptions do have designate in the sense simply 1Bertrand Russell, Introduction to Kathematical Phi- losthy. London: George Allen & Unwin, Ltd., 1919, p. 107. -l6- that the objects described exist. Thus the description "the blind poet of Greece" has Homer for its designatum in the sense that according to historians there probably was a man whose name was Homer and who fits our description. It seems, therefore, that "designates," for Russell, is not the semantical relation between a symbol and its referent. In Russell's writings the supposedly logical distinction between names and descriptions is tied up with its episte- mological counterpart, i.e., with the distinction between knowledge by acquaintance and knowledge by description. Names, for Russell, are symbols which directly designate all and only those objects with which we are cognitively acquainted. Descriptions, on the other hand, are logical constructs which lack such direct reference to such objects. For Russell a symbol has a designatum if and only if it is a name, i.e., a demonstrative symbol pointing to an object with which we are cognitively acquainted, and a symbol does not have a designatum.merely because it is taken to have a referent. The epistemological distinction between knowledge by acquaintance and knowledge by description determines thus, for Russell, by way of analogy, the supposedly logical dis- tinction between names and description. All and only those things with which we are cognitively acquainted can be named. Things known merely by description we cannot name. It seems, however, that epistemological considerations can -17- hardly serve as arguments for the tenability of logical distinctions. The question whether analogies between epistemological and logical distinctions are thorough- going is a question w.ich neither epistemology nor logic is able to decide alone. The epistemological distinction between knowledge by acquaintance and knowledge by description serves for Russell furthermore as an ontological criterion. For Russell, not only the logic of names but also ontology is tied up with epistemology. These and only those entities exist which we know exist (1) through direct acquaintance or (2) through inference. Thus, for example, I.might directly know that a patch of carmine in the center of my visual field exists simply because I directly perceive it. But I might use inference and also claim to know that there are tigers in India, although I have never been there and seen them. Acquaintance with objects gives us direct knowledge about their existence and therefore their existence is no problem. ”he existence of entities not known by direct acquaintance, i.e., known merely by description, on the other hand, constitutes a problem” we can know whether a so-and-so exists only through inference. All entities known by acquaint- ance must exist; whereas entities known only by description might or might not exist. But only objects known by acquaint- ance can be named. Consequently, only existing entities can be named, but both existing and nonexisting entities can be -18- described. According to Russell, if sentences "Did homer exist?" be meaningful, ordinary preper names like "Homer," "Caesar," "bill" should not be treated logically as proper names at all but as truncated descriptions. Thus the sentence "Did homer exist?" when written out more fully would become, for example: "Did the blind poet of Greece exist?" Similarly, "Homer exists" becomes "The blind poet of Greece exists," or the like. Russell argues that if "homer" were a "logical name," the sentence "Homer exists" would be analytic and tautologous as the negation of "Homer exists," "Homer does not exist," would be self contradictory. To use ”Homer" as a "logical name" is to presuppose the fact that homer does exist and therefore "Homer does not exist," where "Homer" is a preper name, asserts both that homer exists and does not exist. we must notice, however, that “homer exists" becomes analytic only if we accept Russell's interpretation of names. Furthermore, "Homer exists" becomes then analytic only in the sense that we cannot say that homer does not exist, and not of course, in the sense that the fact of Homer's existence is a necessary fact. Clearly, Homer's existence is an empirical fact which might have happened (as it probably did) or.might not have happened. "Homer exists" is analytic only if we choose to use words in a certain (viz., Russell's) way. In ordinary English, "Homer -19- exists" is clearly not analytic and disregarding other con- siderations which.might speak for Russell's usage, at this point, i.e., choosing between the analytic or empirical Psynthetic") character of "homer exists," it seems that ordinary English should be preferred. To be able to say both that Homer exists and that Homer does not exist is clearly an advantage as it enables us to talk more directly about the empirical fact of Homer's existence. In Russell's language, however, in order to talk about homer's existence we must first translate "Homer"into a description. 4. Are Descriptions Constituents of Proppsitions? The second claim of Russell's theory of descriptions, we said, is that descriptions are void of meaning in isola- tion and therefore not constituents of prepositions in which they occur. Russell claims that the phrases of the form "the so-and-so" can not be analysed as they stand; we can analyse only sentences in which they occur. The true analy— sis of a phrase such as "the author of the Iliad" is there- fore the analysis of sentences, "The author of the Iligd'was blind," "The author of the Iliad was Greek," and the like. Russell claims that in the course of this analysis the des- cription "the author of the Iliad" is broken up and disap- pears. Let us choose "The author of the Iliad.was blind" as our example. The analysis proceeds then as follows: the proposition "The author of the Iliad_was blind" is divided into three component assertions such that the proposition -20- "The author of the Iliad was blind" is logically equivalent to their conjunction. (1) At least one person composed the Iliad, (2) At.most one person composed the Iliad, (5) There never was a person who composed the Iliad but was not blind.1 From this analysis it appears, Russell claims, that the proposition "The author of the Ilia d was blind" does not have "the author of the Iliad" for its logical subject. The propo- sition is not of the form "x was blind." It is not about the actual individual who composed the Iliad'but rather about the property "blind." It says that the preperty belongs to only one object which at the same time has also a certain other property, viz., the property of having composed the Iliad, Consequently in the proposition "The author of the Iliad was blind" the description "the author of the Iliad" does not occur as a constituent of that proposition. According to Russell the only constituents of a proposition are those things with which we are directly acquainted.2 Or, and this is only to put the same thing differently, the constituents of a proposition are only those things for which we have names For Russell the description "the author of the Iliad" is 192'. cit., p. 177, also G. E. Loore, "Russell's Theory of Descriptions," in Paul Arthur Schilpp, ed., The Philosophy of Bertrand Russell. Evanston, Ill.: The Library of Living Philos0phers, Inc., 1946, p. 180. 2Bertrand Russell, "Knowledge by ncquaintance and by De? scription." Precedings of the Aristotelian Society, 1910- ll, pp 0 118-120 0 -21- only a constituent of the sentence "The author of the Iliad was blind" and not a part of the prOposition which that sentence eXpresses. The description "the author of the Iliad} is a part of the sentence only as a concrete shape or sound and it does not designate the actual individual Homer as a part of the proposition which the sentence ex- presses. The prOposition expressed by "Homer was blind," on the other hand (where "homer" is a logical name) does have Homer for one of its constituents, but it is not the same proposition as the one empressed by "The author of the Iliad was blind." Descriptions, for Russell, occur in propositions only in the sense that they are parts of the verbal expressions of those propositions. Descriptions do not occur in propositions in the sense that they directly designate objects which are parts or constituents of those propositions. Only names directly designate or denote such objects. Russell's theory of descriptions and names is thus based on the fundamental distinction between sentences and prOpositions. A sentence is a mere string of marks but the proposition is the denotation of the sentence. The whole queStion of pr0positions as entities is, however, confused. What sort of entities are propositions? In An Inquiry into 1 Leaning_and Truth Russell claims that the meaningfulness of 1Bertrand Russell, An Inquiry into Meaning_and Truth. New York: U. W. Norton & Company, Inc., 1940. sentences involves two things. A sentence "signifies" a "subjective state" and it "indicates" a fact. The fact that a given sentence "indicates" can be hardly the proposi- tion, as in that case there would be no false propositions. i \— The pro.osition as the "subjective state" or "belief" which i a given sentence "signifies," on the other hand, has its own objections. The "subjective state" as an entity must be the state of a metaphysical "soul" or "mind" as no behevioristic conception of Russell's "subjective states" or "beliefs" would justify the existence of such entities. Furthermore, as Wittgenstein has argued, such "subjective states" would be merely another symbolism, perhaps only of a more intimate kind, and therefore on a par with sentences as mere verbal expressions. Several other possibilities for interpreting preposi- tions as entities remain: they can be conceived as Pla- tonic ideas, as "possibilities" or, with Frege, as truth- values. It is outside the scope of this paper to discuss '1 any of these interpretations. nor our purposes we shall only remark that nowhere in Russell's writings does one find an unambiguous and direct treatment of the ontological aspect of propositions. Consequently, the parallelism be- tween the two distinctions, names versus descriptions, and propositions versus sentences, appears to be a mere assump- tion. -23- 5. Existence and Descriptions According to Russell, then, descriptions occur in prOpositions only in the sense that they are constituents of sentences which express those propositions and there are no constituents in such propositions which directly correspond to the descriptions in them. In the occurrence of descriptions in prOpositions Russell distinguishes between two cases. Descriptions have either "primary" or "secondary" occurrences. A des- cription has a "secondary" occurrence when it occurs within a proposition which is only a part of some larger prOposi- tion. When this is not the case, the description has a "primary" occurrence. Thus, in the proposition: (1) The unicorn by the lake is white, the description "the unicorn by the lake" has a "primary" occurrence. In the prOposition (2) I believe the unicorn by the lake is white, however, the description has only a "secondary" occur- rence. Again, in (3) The unicorn by the lake is not white, the occurrence of the description is either "primary" or x” "secondary." Its occurrence in (5) is "primary" if we conceive (3) as an instance of the propos'tional func- tion "x is not white;" its occurrence is "secondary" if we conceive (3) as an instance of "x is white" and -24- then negate the proposition. Russell contends that in the event of a "primary" occurrence of a descriptive phrase in a proposition, the existence of the entity described is presupposed and a part of that proposition. In respect to our example, "The unicorn by the lake exists," is thus a part of the proposition, "The unicorn by the lake is white," and that proposition is therefore false if no unicorns in fact exist. The fact that we agree that unicorns do not exist does not, however, make the proposition "The unicorn by the lake is not white" false, if the description in that proposition has a "secondary" occurrence; on the contrary, our proposi- tion would then be true. These last considerations evoke the question of what is Russell's meaning when, in connec- tion with descriptions, he uses the word "exist." In respect to names, we saW'that to say that an entity exists is, for Russell, to say that the entity in question is an item in our direct cognitive experience. But in what sense does an entity exist which we know only by description? The problem.of existence is, for Russell, bound together 1Bertrand Russell, Introduction to‘Mathematical Philoso- §a%. London: George Allen & UnWin, Ltd., 1919, pp. 179- . Bertrand Russell, "The PhilOSOphy of Logical Atomism." Mind, 1918-1919, reprinted by the Department of Philosophy, University of'Linnesota, pp. 46-47. A. N. Whitehead and Bertrand Russell, Principia‘mathematica. Vol. I, 2nd ed. Cambridge: The University Press, 1925, pp. 68—69. -25- with the notion of a propositional function. The most important thing to be said about prepositional functions is that they are either "true in all cases," "true in . "1 some cases," or "false in all cases. To say that a propositional function is always true or true in all cases 0 q o o 2 18 to say that it IS "necessary." To say that it is only sometimes true or true in some cases is to say that it is possible."3 And finally, to say that a prepositional func- tion is never true, or that it is false in all cases, is to say that it is "impossible."4 These properties of preposi- tional functions, Russell xplains further, involve the words, "everything," "something," "nothing," "all," and "some." Russell calls such words "denotative phrases" or "incomplete symbols."5 They are "incomplete symbols" be- cause they, xactly like phrases of the form "the so-and- so," have no "meaning in isolation." The meaning which they do have, Russell claims, depends on the context in 1Bertrand Russell, Introduction to'Mathcmatical Phi- losophy. London: George Allen & Unwin, Ltd., 1919, Chapter XV . 2Loc. cit. 3Loc. cit. 4Loc. cit. 5"Incomplete symbols" is a more inclusive category than "denotative phrases." Incomplete symbols include descrip- tions, classes, and relations whereas denotative phrases are only descriptions. We have been using the term "descrip- tion" in the sense of "definite description." Descriptions can also be ambiguous descriptions. "Everything," "something? "nothing," "a man," "some man," "every man," "a royal person," "some twentieth century statesman," "all revolutionary move- ments," etc., are all ambiguous descriptions. which they occur. Thus, ('1) quverything.) or (x)(¢x) means "dx is true for all values of x, (2) ¢(nothing) or (23(0x1 means " x is false for all values of x, (3) ¢(something) or’(ixj(¢x0 means "¢x is true for some values of x. Here (3) expresses the fundamental meaning of existence. To say that for ¢x something is the value of x, or that there is a value of x, or that¢x is true for some values of x, or that (bx is possible, is to express the fundamental meaning of existence. Existence, in other words, is for Russell essentially a property of propositional functions. To say that "Unicorns exist" or "Tables exist" is not to say anything about unicorns or tables but is rather to assign a certain property, namely "possibility," to the propositional function "x is a unicorn" or "x is a table." In accordance with the above interpretation of existence Russell's contention that propositions containing a primary occurrence of a description have the existence of the described object for one of its parts can be proved as follows. The proposition "The author of the Iliad was blind" we analysed, according to Russell, into the conjoint assertion of (1) At least one person composed the Iliad, or 1Bertrand Russell, "0n Denoting." 'Mind, 1905, reprinted in Herbert Feigl and Wilfrid Sellers, Readings in Philosophi- cal nnalysiS. New fork: Appleton-Century-Crofts, Inc., 1949, p. 104. -27- K (32:) «pm. (2) At.most one person composed the Iliad,or ¢x.fy.3.i,& xay, (5) There never was a person who composed the lliad but never was blind, or ~(3x) (0x.~?x) . The proposition "The author of the Iliad_exists," on the other hand, is equivalent to the conjoint assertion of (4) At least one person composed the Iliad, or (3x)(fx), and (5) At most one person composed the Iliad, or *x.¢y.3x,y.x-y. Here (1) and (2) are identical with (4) and (5) and therefore "The author of the IliadDexists" is a part of the proposition "The author of the Iliadlwas blind." ‘We have to notice that (4) and (5) together, and not (4) alone, make up the meaning of the existence of the des- cription in question. If (4) alone were involved, the propo- sition "The author of the Iliad was blind" would be true also if there weretwo or more persons who composed the Iliad, This, however, our proposition does not allow. Phrases of the form, "the so-and-so"imply the uniqueness of the object in question and consequently the meaning of existence ex- pressed by "a" in "(3x0¢x" would, in respect to "definite" descriptions, not do. An adequate description of the.mean- ing of the existence of a description must express what is asserted by both (4) and (5) above. This is accomplished -28— by the following definition: (6) E!(1x)(4>x).=: (3b):¢x.2X1x-b,l to say that a description exists is to say that there is exactly one object which satisfies a given condition. A description has a "primary" occurrence in proposi- tions of the form Y( rx)(¢x). lf {)xJFXsb, then to say that Y(2x)(4>x) is to say thatf’b. hence we have (7) In 1x) (fx) .3: (3b) :éx.§x.x=b :Yb.2 rrom.(7) by distribution of quantifiers we get (8) 1”(7x)(¢x).3:.(3b):Qx.2x.x-b:.(3b).f’b. Replacement in (8) according to (6) gives us (9) 1r(7x)(+x).3:E:(7x)(¢x).(3b).rb from which we can easily deduce (10) Y(7x)(¢x).D:El(7x)(fx)3 Any prOposition which contains a "primary" occurrence of a description implies the existence of the described entity and contains, thus, the existence of that entity as one of its parts. 6. The Formalistic Interpretation of Descriptions as Cbnstituents of Propositions. Russell's claim.that descriptions are not parts of propositions is, as we saw, tied up with the notion of 1A. N. Whitehead and Bertrand Russell, Principia'Lathe- matica, Vol. I, 2nd ed. Cambridge: The University Press, I§§§T‘*14.02. 2Ibid. *14.101. 5Ibld. *14.2. -29- propositions as metaphysical entities. If the notion of propositions as entities were abandoned it is possible to offer a different interpretation of description as "incom- plete" symbols. In that case, to say that (7xfl(¢xfl in \f(1x)(¢x) is an "incomplete" symbol, i.e., that it disappears in the analysis (1) Y(7x) (éx) .=: (3b) :¢x.5x.x=b :‘fb, is to say simply that the definition of (7xfl(¢xfl is contex- tual. The only thing we would be concerned with is the expression (7xj(¢xj and to say that its definition is con- textual is to say that we do not ascribe meaning to (7x)(4>x) as it stands but only to more complex expressions such as Y(7x)(¢x). The expression (7x)(¢x) is clearly a part of the expressiazi Y(7x)(¢x) and the fact that (7x)(¢x) has disappeared in the definiens of (1) would merely mean that we can write other expressions which are logically equiva- lent but need not contain all the parts of our initial expression. The same can be said about other expressions that Russell lists as "incomplete" symbols, i.e., classes and relations. Furthermore, there are obviously many more expressions than these three, descriptions, classes and relations, that have the characteristic of being defined contextually. For example, we do not define "if, then," and the logical "and" as they stand, but we define only more complex expressions in which they occur: (2) p3q.a.~pvq -50- (3) P-Q-=-"(~PV”C1)- If by saying that an expression has no meaning in isolation or is an "incomplete" symbol we simply mean that the expression is defined contextually, i.e., we define only certain uses of it, then there are many more expressions than Russell lists which are incomplete symbols and have no meaning in isolation. But to claim, in addition, that by calling a symbol an "incomplete" symbol we mean that the meaning of that symbol does not enter into propositions in which they occur or that the symbol is not a part of propo- sitions in which it occurs, is, if we adopt the formalistic interpretation of propositions, simply false. 7. Summary of Criticisms In Russell's logic the existence of entities cannot be talked about directly in terms of names. All questions about existence of entities has to proceed via descrip- tions. This, it seems, is an unnecessary complication. It is extra-linguistic considerations, as we saw, that.moti- vated Russell to make the sharp distinction between names and descriptions. The distinction between names and descrip- tions was determined by the epistemological distinction between knowledge by acquaintance and knowledge by descrip- tion. Linguistically it seems clear that no distinction need be made between names and description. In ordinary language the sentence "Did Homer exist?" is as meaningful as "Did the blind poet of Greece exist?" If one considers logic as much as possible a neutral tool, free from epistemological and metaphysical biases, one should drop the distinction between names and descriptions. It can be argued whether our approach to logic should be epistemological or whether we should take a more purely linguistic attitude, but Russell himself favors the linguis- tic approach. Russell has argued that the shortcomings of the Aristotelian logic were mainly due to the too close connection between metaphysical beliefs and linguistic ex- pressions. The problem of substance could not be fruit- fully discussed, Russell points out, simply because the notion of substance was, so to speak, a built-in feature of the language of Aristotelian logic. One might ask whether the same sort of criticism can not be made of Russell himself. we can claim that the problem of existence cannot be dealt withhn terms of Russell's logic because "existence" is a built-in feature of that language. Thus in the formula (x).¢x.:>.¢z the existence of the object designated by z is presupposed although no record of this presupposition appears in this symbolism. The existence of z cannot be explicitly stated as we cannot, according to Russell, write: (x) #x.E!z.3.¢z. Similarly in 42.3. (HXNPX the existence of z is presupposed but cannot be explicitly stated, i.e., we cannot write 4’2 .312”). (wax. Existence, as substance for Aristotle, is therefore, so to Speak, a built-in feature of Russell's logic. Furthermore, we pointed out, the epistemological distinc- tion between knowledge by acquaintance and knowledge by description has also more directly an ontological signifi- cance. Things known by acquaintance are directly known to exist, whereas the existence of things known by description lust be inferred. Tor Russell, in other words, ontology is largely determined by epistemology as from our ways of knowing he infers to the ontological structure of the world. ChflPTER ”U qDlRE'S TRRORY OR "ORTOLOGICIL COLLITLRRTS" l. "Singular" and "General" Existence Statements Quine, in his article "Designation and Existence,"l commences his discussion of existence by making a distinc- tion between what he calls "singular" and "general" exist- ence statements. The distinction is important and as fol- lows. x "singular" existence statement is of the form "There is such a thing as so-and-so." A"general"ex‘stence statement, on the other hand, has the form "There is such a thing as a so-and-so," or more briefly "There is a so- and-so" or "There are so-and-sos." Examples of Singular A. existence statements would be: "There is such a thing as 1 t1 'ros," "There isbuch a thing as Harry Truman," "There is such a thing as Burgundy," "There is such a thing as tiger," "There is such a thing as triangularity," "There is such a thing as piety." Examples of general existence statements are statements such as "There is such a thing as a tiger," "There are tigers," "There are pious people," "There is a wine called Burgundy," "There are gods," "There is such a thing as a god." lWillard Van Orman guine, "Designation and Existence." The Journal of Philosophy, 1939, pp. 701-709. The whole of this section is based mainly on this article. .453- -34- General existence statements say that there is at least one entity which satisfies a certain condition or fits a certain description. In logic general existence statements are expressed in terms of existential quantification. we could thus rewrite all our examples of general existence statements by using existentially bound variables: (3x)(x is a tiger), (3x)( x is a person. x is pious), (3x)(x is a wine. x is called Burgundy), (3x)(x is a god). In logical symbols, general existence statements thus refer to entities always through a bound variable. In ordinary speech the place of the bound variable can be filled by a pronoun such as "which" or "something which." If we rewrite our examples of general existence statements by.making use of such pronouns they become: There is something which is a tiger. There is something which is a person and which is pious. There is something which is a wine and which is called Burgundy. There is something which is a god. In singular existence statements, on the other hand, one refers to entities not through a bound variable or an undeter- mined pronoun but through grammatical names. In our examples of singular existence statements, for instance, we refer to entities through "Eros," "Harry Truman," "Burgundy," "tiger," "triangularity," and "piety." It is clear that these words are not "logical names" in Russell's sense. These words only intend to name entities and the question whether they do name entities in the semantical sense is left open completely. “We have to notice also that our examples include, as grammatical names, what are usually called concrete and abstract words, and that consequently the entities the existence of which one asserts in singular existence statements can be both concrete and abstract. Thus, "There is such a thing as Harry Truman" asserts the existence of something concrete; whereas, "where is such a thing as piety" asserts the existence of something abstract. Fur- thermore, even if a word is concrete it can, in a singular existence statement, purport to designate something abstract. A concrete word which turns up in a singular existence state- ment purports to designate something abstract if it is a general and not a singular term.l Thus although the word "tiger" is concrete, "There is such a thing as tiger" as- serts the existence of something abstract, 1i§., the property "tigerhood." In a similar manner also general existence statements can affirm the existence of both concrete and abstract entities, as can be shown by examples lSingular terms are terms which refer, sometimes am» biguously, only to one object, e.g., "Harry Truman," "bros," "this man," "I," "you." General terms are terms which can be significantly prefixed by such words as "all," "any," "some," etc. such as "There are numbers," "There are functions," "There is such a thing as a good performance." The distinction between singular and general existence statements is there- fore not the distinction between statements which assert the existence or concrete objects and statements which assert the existence of abstract properties or things. The distinction is rather the distinction between state- ments which assert the existence of certain entities, either concrete or abstract, by referring to those entities through the use of a variable or a pronoun and statements which assert the existence of certain entities by referring to these entities through grammatical names. 2. Language and Existence Singular existence statements, then, are of the general form "There is such a thing as so-and-so." In a specific instance of statements of this general form the phrase "so- and-so" gives place to an expression which purports to desig- nate an object, property or thing and the statement is true just in case there is, in fact, such an entity. The state- ment is false if there is no such entity. Therefore, nouns which occur in singular existence statements and purport to designate or name might or might not designate or name in the semantical sense. We cannot assume that the mere occur- rence of a noun in a sentence means that that noun desig- nates an ex’sting object or entity. Such an assumption was, as we saw, involved in the type of fallacious reasoning that Russell's theory of descriptions was intended to refute. we recall that in our discussion of hussell's theory of existence a curious problem was said to arise vhenever we wanted to deny the existence of some entity. Sentences like "Eros does not exist," or "There is no such thing as Eros," so it seemed, were paradoxical. If such a statement were true, i.e., if there were in fact nothing that "Eros" designated, the statement would seem.to be void of subject matter and therefore meaningless. One argued, therefore, that in order to rescue the meaningfulness of the statement "There is no such thing as hros," Eros must exist if not in spacio-temporal, then at least in some "logical" sense. This assumption, however, as we saw, Russell has pointed out, rests on the failure to realize that meanings are really of two sorts. ‘Uords have.meaning either by virtue of the fact that we are directly acquainted with their referents or the meanings of words are merely descriptive. The latter is the case with "Erosz" its meaning is any descriptive phrase that we agree is sufficient to identify it. Any appropriate dictionary would give us the meaning of the word "Eros" and it would give the meaning apart from any question of existence. Existence is not a matter of lexicography or grammar. It is other considerations than those of mere meaning that could settle the question of whether bros in fact exists. We saw that nussell's approach to the question of existence was at least in part epistemological. Some meanings, Russell contends, are derived from direct cognitive acquaintance with certain things in the world. Words with such meanings are, for Russell, "logical names" always designating and the problem of existence can be solved therefore, at least partly, through epistemology. A certain shade of blue, for example, exists because it is the sort of thing which we directly perceive. On the other hand, wheth- er such a thing as E mer exists Russell cannot tell by rely- ing merely on epistemology. homer is the sort of thing which he knows only by description. In order to decide whether things known descriptively exist, one has to look outside of epistemology. If one abandons Russell's epistemological approach to ontology, as Quins seems to do, one might find oneself in the same position in respect to all things as Russell finds himself in respect to Homer and unicorns. The problem of universals and the controversy between nominalists and platonistsl is largely the question of what is required by way of entities in order that our language be meaningful. According to Russell, among singular termslonly names require the existence of some entities in order to be meaningful. The meanings of names are the existing entities which names designate. Descriptions, on the other hand, being "incomplete" 1To use "platonism" in place of "realism" is a practice introduced by guine in order to avoid the ambiguity of "realism." -59- symbols, are meaningful only in certain linguistic con- texts in which they occur and they do not presuppose the existence of any entities as a condition of their meaning- fulness. Consequently, if one abandons Russell‘s notion of "logical" names and treats all singular terms as des- criptions, the meaningfulness of language would not involve any question of existence at all, and the question whether some words designate existing objects would become meaning— less. ‘Without an epistemological criterion of meaning, it would seem, all words become descriptions in Russell's sense and will have meaning only on a.merely linguistic plane. But from a purely linguistic standpoint there is no more reason to say that "blue," "horse," and "table" designate or stand for entities than there is to say that "unicorn" and "Eros," or even such words as "up," "and," "if" designate or stand for entities. All words, "blue" as much as "Bios" or "up," have meaning in the sense that th y are capable of determining the meaning of statements in which they occur, but they need not have any meaning apart from such statements. Their meaning will be determined contextually and not through direct reference to existing objects. A radical nominalist might interpret all terms in ordinary speech as syncategorematic expressions, useful for construction of sentences and for communication, but in no way reflecting matters of fact or other extralinguistic realities. Kany things, no doubt, will continue to exist but language will say nothing about their existence as the connection between language and the existence of entities would thus have disappeared completely. Consequently the distinction between nominalism.and platonism.would become a pseudo-distinction. Therefore, once the epistemological approach to ontology, such as Russell's, has been abandoned, we.must, in order to avoid ontological anarchy, devise other methods through which the connection between language and the extralinauistic realities can be re-established. U 5. The Epistemological and Semantical Theory of Kames Quine contends that language does reflect extralinguis- tic realities and that the issue between nominalism and platon- ism as an issue between different ontological doctrines is by no means meaningless. To use Quine's own terms, our use of language often involves us in "ontological commitments." Before we return to the direct examination of Quine's theory of ontological commitments of language we shall extend our preliminary discussion of guine's ontological theory through a further comparison with Russell. For Russell, we saw, existence was not a predicate and to write "x exists" where x can be replaced by a "logical" name was nonsense. To assert or deny existence is to assert or to deny that a propositional function is possible. In other words, the assertion or denial of existence involves always a variable. Such assertions of existence which in- volve exvariable and in Russell’s sense say that a proposi- tional function is possible are, for Quine, the general existence statement. Singular existence statements, on the other hand, would be, for Russell, meaningless if the phrase "There is such a thing as" were followed by a "logical" name. Thus for example "There is such a thing as carmine" would be meaningless if, on epistemological grounds, we decide that "carmine" stands for a shade of color with which we are directly acquainted. Such epistemological considerations are, for Quine, irrelevant. Quine holds that we can treat of existence on a purely semantical level. The logic of names, we saw,'was for Russell essentially an epistemological study. Names for Quine, on the other hand, can be treated apart from epistemology. Such a treatment of names can be called the semantical theory of names as opposed to Russell's epis- temological theory. To treat of names on the semantical plane is to conceive of them as inessential and eliminable features of language, i.e., they can always be eliminated by descriptions. ‘We.might say that Russell's "logical" names are epis- temologically primitive terms and not only abbreviations of logical abstractions, gig., of descriptions. In. §27 of his Mathematical Logic:L Quins has shown how such epistemologically l"i’fillard Van Orman Quine,‘fiathematical Logic. New York: 'U. W. Norton a Company, Inc., 1940. For further discussion of names see also Quine's Kethods of Logic, New York: Henry Holt 8c Company, 1950, §36, "On Universals." Journal of gymbolic Logic, 1947, pp. 74-84, and "On What There Is." Review of Hetaphysics, 1948. pp. 21-38. or otherwise primitive terms or names can be easily elimi- nated in favor of abstractions in terms of primitive predi- cates. Thus, instead of adopting, e.g., "Europe" as a primitive term of geography we can conceive of "Europe"as a descriptive abstraction built out of the matrix "eur x" which we can write "(7x)(eur x)." In such an abstraction the primitive concept of geography does not appear at all as a singular term or name but as a predicate. Through this device the "primitiveness" of names that we want to employ in a given discourse can be always raised to the level of predicates and the logic of names can be thus separated from extra-logical considerations such as those of geography or epistemology. for any name we can always find a predicate, trivially, as we did in the case of "Europer or otherwise, as Russell has done in the case of "Scott" and "Iomer," and by means of such a predicate we can then expand the name into a description. Let us for example take the term "carmine" and suppose that it is, in Russell's epistemology, a logical name for a particular shade of color. He might then insist that what we learned by direct acquaintance should not appear as a name but only as a predicate and to properly symbolize we must write "(1x)(x is colored carmine)" or "(7x)(car x)," and not just "carmine." ‘What is then epistemologically primitive or ostensively defined is the predicate and not a name. This should make no difference to epistemology -43... as we are not refuting the claim that there is the experience in question. The difference that it makes to ontology is that we have eliminated the source of confusion between epistemology and ontology by isolating epistemological assumptions from our logic. Quine's semantical theory of names differs from Russell's epistemological theory of names by the fact that when for Russell "logical" names have some causal connection with experience and cannot be eliminated from language, then for Quine the alleged connection that singular terms have with experience can be made explicit through a predicate and grammatical names can always be replaced by descriptions. If such replacement of a grammatical name is, in fact, not made, the singular term in question is treated as a’Seman- tical" name and claimed to designate an object. Such a claim, h waver, need not be made on epistemological grounds. All singular terms are, for Quine, logically equivalent to descriptions and therefore the meaningfulness of names in sentences in which they occur does not in any way pre- suppose that there actually are entities which those terms purport to name. A singular existence statement such as "There is such a thing as carmine" is therefore not meaning- less but asserts the existence of carmine, or the fact that "carmine" designates, or that "carmine" is a "semantical" name, and the question whether carmine exists on epistemo- logical grounds is in no way presupposed in that statement. -44- The statement is true or false on any grounds that we find appropriate for our ontological criteria. The statement affirms the existence of carmine because it explicitly says so but the fact which it affirms it does not presuppose. If we assert the statement "where is such a thing as carmine," then we do so because we want to recognize "carmine" in our ontology as designating an entity, and that not necessarily on epistemological grounds. To say that names can always be replaced by descriptions is to say that names and descriptions are logically equivalent. However, if we do not replace them.by descriptions, we commit ourselves to the belief that the entities in question exist. In that case we are treating singular terms not merely as grammatical names but as "semantical" names. To treat a singular term as a semantical name is to treat it as an ontological prim'tive. What is ontologically primitive, however, need not be epistemologically primitive. For Quine, then, it is not through names that the onto- logically important connection is established between language and extra-linguistic matters of fact. Any ostensive use of names in a language can be replaced through the use of osten- sively defined predicates. No ontological commitments are made through the use of names. Names are ontologically irrelevant. however, one question might be raised at this point. Granted that no ontological commitments are made through names, because all names can be easily expanded into descriptions a la (nine, and thus lose their "epistemologi- cal primitiveness," one might still argue that these des- criptions will still make direct reference to experience because they are built up by means of ostensively defined predicates. One might remark, in other words, that although through Quine's method we escape from ontological commit- ments in respect to names, we will make the same ontological commitments through the use of primitive predicates which we employ to translate names into descriptions. ‘We'will not attempt an answer to this criticism at this point: the tOpic will be discussed again in later sections. At the present we shall be content with the assertion that names, as names, are ontologically insignificant. 4. fixistence and Variables What then, if not names, does establish the connection between language and the extra-linguistic realities? For Quine it is variables and their grammatical equivalents, pronouns such as "something," "something which," through which this connection is made. The truth value of a singular existence statement does not affect the truth value of other ordinary statements in which the word which follows the phrase "there is such a thing as" in the singular existence statement appears in the position of the grammatical subject. For example, the truth value of "There is such a thing as Eros" does not af- fect the truth or falsehood of statements such as "Eros was -45- for the Greeks the god of love" or "Eros was worshipped by the Greeks."1 However, the truth value of "There is such a thing as Eros" has other effects. If our singular xist- ence statement is true, any statement having "arcs" for its subsject will be about the entity hros. If "There is such a thing as Eros" is true, "Eros was worshipped by the Greeks" will be about Bros and will imply the consequence that something_was worshipped by the Greeks, or (3x)(x was worshipped by the Greeks). If, however, "There is such a thing as nros" is false, and "Eros" designates nothing, no such consequence will follow. Singular existence statements, therefore, 333 connected with other statements of our language. If a singular existence statement is true, any sentential expression which has the word following the phrase "There is such a thing as" in the position of its subject will be about the entity whose existence is affirmed by that singular existence statement. Such sentential expressions, in their turn, will imply a general existence statement to the effect that there‘gs something_or that there is an §_which satisfies the condition specified by that sentential expression. If we affirm a sin- gular existence statement, e.g., "There is such a thing as xros" we must consider the existential generalization 1Notice that, strictly speaking, according to Russell, the two propositions expressed by these two sentences should be considered false, as they have the existence of "Eros" as a description for one of their parts. -47- (3x)(. . . x . . .) to follow from any statement of the form.". . . hros . . ." that we want to affirm. If, on the other hand, we deny a singular existence statement no such inference can be drawn. Let us take a few more examples. If we want to affirm the singular existence statement (1) There is such a thing as Burgundy, a sentential expression such as Burgundy is a wine will have the consequence that there is something which is a wine, or (3x)(x is a wine). If we affirm (2) There is such a thing as harry Truman, . . . Harry Truman . . . will have the consequence (3x)(. . . x . . .). The entity affirmed by the singular existence statement does not have to be concrete. Thus, if we affirm (3) There is such a thing as piety Piety is good, will have the consequence (533(x is good) and . . . piety . . . will have the consequence (3x)(. . . x . . .). -48- To say, then, that a singular existence statement is true we can describe as saying that existential generali- zation in respect to corresponding sentential expressions is a valid form of inference. Such an inference is valid if and only if from true sentences, such as "burgundy is a wine," and "Ea ry fruman is the president of the United States," only true general existence statements, such as (3x)(x is a wine) and (3x)(x is the President of the Uni— ted States), will follow. How, according to this criterion can we distinguish between singular existence statements such as "where is such a thing as Eros," and "rhere is such a thing as Harry Truman?" fhe latter, one will ordinarily say, is true, whereas the former is false. A false singular existence statement will make the corresponding operation of existen- tially generalizing invalid. whus, for xample, although a, (l) (3x)(x was wor31ipped by the Greeks) may be considered as a true consequence of a true statement "Eros was worshipped by the creeks," we can find other true statements in respect to which the Operation of existentially generalizing will not yield true statements. we are inclined to say that (2) Hothing is identical with Eros is true, i.e., that there is no entity which is gros. fhe result of existential generalization in respect to "zros," however, (3) (3xJ(Hothing is identical with x , is false. On the basis of the foregoing discussion Quine can now define a "semantical" name (an expression which designates an object) as an expression in respect to which the operation of existentially generalizing is valid. A word W designates, or is a "sem itical" name, if and only if existential generali- zation in respect to W'leads from true sentences only to other true sentences. In the case of existential generalization we drop the name by replacing it with an existentially bound variable. There is another basic form of inference or logical opera- tion where names can be interchanged with variables. In the case of specificatiop_we drop the universally bound variable and replace it by a name. Thus, for example, (4) (x)(x was created by God) will lead to (5) Harry Truman was created by God. f existential generalization is valid in respect to a given term, specification is also valid in respect to that term. Let us assume that existential generalization in respect to "Harry Tr nan" is valid. a false statement such as (6) Harry Truman is the first president of the United States will give us then (7) (3x1~(x is the first president of the United States) which is the same as (8) ‘v(x)(x is the first president of the United States. The falsehood of . . . Harry Truman . . . thus entails the falsehood of (x)(. .f. x . . .) and therefore the truth of (x)(. . . x . . .) entails' the truth of . . . Harry Tru- man . . . Quine claims further that the use of variables in ex- pressions (3x)(. . . x . . .) and (x)(. . . x . . .) is basic in the sense that all expressions containing free variables can be translated into eXpressions containing only existentially or universally bound variables. Ex- pressions containing free variables are, for Quine,.merely .abbreviations for expressions containing only bound variables. flames can be therefore defined.more generally as those expres- sions which, according to the usual logical laws, can replace or can be replaced by variables. Names, in other'words, are substituends of variables. The substituends of variables, however, are not their values. The substituends are merely terms, whereas values are entities. Thus the range of values of a variable is not constituted by its substituends but by the entities named or designated by its substituends. To summarize the above discussion Quine cites four al- ternative ways to claim the same thing as is claimed by a l Willard Van Orman Qnine, "Designation and Existence." The Journal of Philosophy, 1939, p. 708. -51.. singular existence statement. "There is such a thing as Eros" is the same as to say (1) the word "Eros" designates, (2) the word "Eros" is a (semantical) name, (3) the word "Eros" is a substituend for a variable, (4) the entity Eros is a value of a variable. Names, however, as we saw, are inessential to language and can be easily eliminated in favor of descriptions. we are left, therefore, in essence, with the fourth alternative. It is the variables of a language thro gh which direct reference is made to extra-linguistic realities. "The uni- verse of entities is the range of values of variables. To be is to be the value of a variable."2 5. The Theory of "Cntological Commitments" Quine summarizes his ontological theory as follows: The ontology to which an (interpreted) theory is committed comprises all and only the objects over which the bound variables of the theory have to be construed as ranging in order that n the statements affirmed in the theory be true. 0 Quine is not interested in the "ontological truth" about the world but only in the "ontological commitments" of a given constructional theory or system. According to Quine's lLoc. cit. 2Loc. cit. OUillard van Orman Quine, "Ontology and Ideology." Philosophical Studies, 1951, n. ll. .1- theory we cannot decide which entities in fact exist in the total universe, we can only decide what a discourse (most widely a linguistic behavior) presupposes as exist- ing. guine's ontological standard is therefore only a preamble to ontological doctrines which interpretative systematizations of experience contain and is not direct- ly an ontological doctrine itself. ‘Kany other philosophers have attacked the problem of ontology more directly, i.e., within an epistemological or metaphysical system. Thus, for ex ;ple, we discovered that Russell's ontology was determined by his epistemological distinction between knowledge by acquaintance and by description. For a dif- ferent type of example, Whitehead has develOped, mainly in his Process_and Reality,l a.metaphysical system.and has tried to solve the ontological problem of scientific ab- straction within the framework of that system. For‘flhitehead that which is given in experience is all that there is, it is the full universe. Something is given in eXperience by entering into a relationship with the "immediate occasion," i.e., with the "individual act of judgment." If anything does not enter into a relation- ship with the immediate occasion there is no possible knowledge of it, in fact it would not exist, it would be a mere nothingness. Whitehead's ontological doctrine is n‘ 1A. N.'fihitehead, Process and Reality. Kew York: The hacmillan Company, 1929. -53- further elucidated within his wider theory of prehensions. ‘Within Whitehead's system there are a number of ways ("modes of prehension") in which an occasion can enter into a relationship vith or prehend other entities. From the standpoint of ontology it is necessary only that an interrelatedness of some sort exist between occasions in order that these occasions would form a togetherness which can be termed the universe. These interrelationships between occasions are, however, determined by what White- head calls "eternal objects." Occasions as such are mere inarticulated togetherness and enter into intelligible relationships with each other only by being determined by eternal objects. It is the eternal objects (roughly speaking the universals) that make scientific abstraction possible. The universe is thus, for Whitehead, constituted by the two ultimate realities: actual occasions and eternal objects (or their eight subdivisions or the categories of existence: "actual occasions or entities," "prehensions," "nexus," "subjective forms," "eternal objects or forms of definiteness," "propositions,"'multiplicities," and "con- 3‘ trasts"). These realities form the ultimate basis for all scientific theorizing and system building. In contrast with'Whitehead, Quine's contribution to ontology is indirect, and in a sense,‘incomplete. Quine, unlike thitehead, does not offer a systematic interpreta- tion of the realities of the world but is concerned only with questions which come prior to any such interpretative system building. To be engaged in such prior investigations by inquiring into the ontological commitments of given sys- tems in Quine's terms, is, so to speak, to try to solve the ontological problem by not committing oneself ontologically. Whitehead, on the other hand, endeavors to solve the ontologi- cal problems of scientific abstraction by making ontological commitments of universal consequence. Qnine's ontological theory raises the question of exist- ence on a linguistic plane. Quine's theory makes no direct reference to experience as such but only to interpretative language systems which, in their turn, do make direct refer- ence to experience. A different ontological standard of linguistic or logistic character has been preposed by uustav Sergmann.l In order to formulate his standard, bergmann first adopts the rather speculative fiction of an "ideal language." Nothing is really said about the total range of entities in the world when we limit our discourse to one among several theories or systems with limited subject matter. The theory under consideration would have to have the scope of an "ideal language" and to exhibit the ulti- mate categoreal features of the world before we can make any claim to universality. For Bergmann an "ideal language" is a "formally constructed linguistic schema that is complete lGustav Bergmann, "A hote on Ontology." Philosophical Studies, 1950, pp. 89-92. -55- and adequate." It is complete if "everything" can be said in it and it is adequate "if by informally discoursing about it in ordinary.3nglish we can dissolve all philo- sophical puzzles."l By appealing to such "ideal language" bergmann reformulates guine's ontological standard to the effect that not variables but "descriptive constants" are said to be the channel through which reference is made to existing entities. my limiting himself to predicates of the first type he says ". . . properties of the first type exist in a world if in speaking about an ideal language of this world I find it to contain undefined descriptive con- stants that are substitution instances for its predicate variables of the first type."2 Such descriptive constants, however, Quine points out, are always eliminable.3 The .method of elimination is the same as the one described in section one for the elimination of names. after such elimi- nation of descriptive constants we would be left only with predicates as the only constants. Constant predicates, how- ever, Quine claims, in no way presuppose the existence of corresponding universal entities. According to guine the lIbid., p. 89. 21bid., p. 91. 3Willard Van Orman Quine, "Ontology and Ideology." Philosophical Studies, 1951, p. 13. 'hathematigal Logic. Cambridge, Mass.: Harvard'University Press, 1947. 27. ‘Kethods of Logic. Eew'York: Henry Holt & Company, 950, _§37. question of constant predicates belongs to that part of metaphysics which he calls "ideology." The questions about constant predicates are those about ideas or meanings and not questions about the existence of entities. Ontology is the inquiry into the real constituents of the world, whereas ideology is the part of metaphysics which inquires into what ideas constitute the basis for our thinking. In semantics we should make a similar distinction. The ques- tion of the ontology of a system.is a question which belongs to what Quine calls the "theory of reference," whereas the question of meanings or ideas employed in a system belongs to what Quine calls the "theory of meaning." The theory of reference comp ises the study of such concepts as naming, denotation, extension, coextensiveness, values of variables, and truth. The theory of meaning, on the hand, would treat of such concepts as synonymy, analyticity, syntheticity, en- tailment, intension. For the sake of clarity in ontological investigations these two theories should be kept apart al— though, Quine remarks, they are mutually complementary. A further disagreement with Quine's treatment of ontology has been expressed by Carnap.l Although he seems to accept Quine's standard for judging what entities a given theory presupposes, Carnap makes a further distinction. In reapect to investigations into the ontological commitments of given lRudolf Carnap, "Empiricism, Semantics, and Ontology." Revue Internationale de Philosophie,l950. -57- theories or systems we should, carnap contends, distin- guish between two kinds of questions. whenever we wish to talk about a new kind of entities, we have to introduce a new way of speaking. This new way of speaking Carnap calls the framework of the new entities in question. The intro- duction of such fram work involves first a new general term, a predicate of higher logical type than the terms designating the entities in question. Such a predicate enables us to say that a particular entity belongs among the entities in question. Thus if the entities that we want to consider are simple qualities of physical objects such as "red," "carmine," "blue," the general predicate that we need.might be, e.g., "property." In terms of this predi- cate we can then formulate statements like "Red is a proper- ty," "Carmine is a property," etc. The second step in the introduction of a framework of entities is the creating of variables of the new type such that the entities in ques- tion will be the values of those variables. In terms of such variables general statements about the new {ind of entities can then be formulated. In reSpect to such frameworks two kinds of existence questions can be raised. The "internal" questions are raised within the framework. Thus if our framework is that of physical objects, we can ask, e.g., "Is there an ashtray on my desk?" "Is Eros real or merely imaginary?" "Do physical atoms exist?" Such internal ques- tions are all empirical questions and should be answered through empirical investigations. from these questions we must distinguish the "external" questions of existence. The external questions of existence are not asked within a given framework but are questions about the reality of a given framework itself. Such questions, however, Carnap holds, are not theoretical questions at all. To accept the framework of physical objects, for example, does not amount to a theoretical belief which is capable of being either true or false. To accept the existence of the world of physical objects, is nothing more than to accept a certain form of language. But the acceptance or rejec- tion of a form of language, Carnap holds, is not a theoreti— cal but rather a practical.matter. Traditional ontology, as far as it is concerned with external existence questions, Carnap therefore declares to be meaningless. Quine, on the other hand, holds that a nucleus of signifi- cance inherent in traditional ontology has to be preserved. This nucleus of significance is exactly the part of tradi- tional metaphysics which guine's theory of ontological com- mitments purports to define. Carnap's distinction between external and internal exist- ence questions, Quins points out, is essentially the distinc- tion between what Quins calls "category questions" and "sub- 1 class questions." The category questions Quine defines as lWillard van Orman Quine, "On Carnap's Views on Ontology." PhiIOSOphical Studies, 1951. pp. 65-72. -59.. the existence questions which purport to exhaust the entire range of a particular kind of variables or the entire range of a particular existence category. The subclass questions, on the other hand, do not purport to exhaust the entire range of a particular kind of variables. Where to draw the line between category questions and subclass questions depends, however, solely on how the range of different kinds of variables is determined. If, for example, in our language there is only one kind of variable to refer to all classes, the questions of existence in respect to all entities that we construe as classes will be subclass ques- tions. If both qualities and numbers, for example, are construed as classes, i.e., as values of class variables, the questions of existence of both qualities and numbers will all be subclass questions. If, however, a particular kind of variables is appropriated for the exclusive use of referring to numbers, the question concerning the existence of all numbers will be a category question. Furthermore, Quine argues, the distinction between the external (or category) questions and the internal (or sub- class) questions deponds on the acceptance of the theory of types. Only in a language where styles of variables are separated from.one another through syntactical rules, will the distinction be of any consequence. However, such strict compartmentalization of variables as well as the underlying dichotomization of the analytic and synthetic, Quine rejects. -go- It would be outside the scope of the present paper to dis- cuss Quine's reasons for these rejections. For the purposes of the present study it is more relevant to observe the con- nections between Carnap's distinction between the two types of existence questions and the type of constructional nominal- ism developed by Goodman and which we shall discuss in Chap- ter III. The distinction between external and internal existence questions, we said, presupposes a tight division of variables into logical types. Goodman's nominalism, however, proposes to use variables of only one logical type. The only variables that a nominalist will recognize will be ones that take only individuals for their values. The only other logical type involved in nominalistic constructions is the type of predi- cates of individuals. On the predicate type level, however, the nominalist will recognize only constants. But such con- stants we remarked, are without ontological significance. In a nominalistic system the range of individual variables is universal: everything in the universe can be considered as their values. Questions about the existence of particu- lar entities as well as about the existence of broad types or categories of being will therefore, all of them, be inter- nal questions as they must be asked within the framework of individuals. The only external question would be that con- cerning the framework of individuals itself. But the indivi- duals, are, for the nominalists, all that we can legitimately -51- say that there is. Therefore, for the nominalist if there are no individuals, there will be nothing; a negative answer to the question about the reality of individuals will imply, at least for the nominalist, nihilism. Char-ran .thfilb * Tan Obi-'l'OLOGIGAL ASPECTS or soommws ran s-muc'ruma or APPEAMWE 1. Preliminary Discussion of her: is for Quins, so also for Goodman, the question of ontology is that of quantification over variables and the difference between nominalism and platonism is ontological in that sense. Both of these authors agree that in order to be able to decide whether a system is nominalistic or platonistic we have to detect and consider the "ontologi- cal commitments" implicit in that systems If the "onto- logical commitments" of a system involve certain entities not admissible to nominalism.the system is called platon- istic, and a system is nominalistic only if it is free of any such commitments. In their joint article "Steps Toward a Constructive Nominalism"l both Quins and Goodman have stated that nominalism is the doctrine of renouncing ab- stract entities, in other words, the entities to be excluded from a nominalistic universe are those of the abstract kind. In that article "concrete object or entity" is treated syn- omously with "concrete individual" and it seems that the lNelson Goodman and'W. V. Quins, "Steps Toward a Con- structive Nominalisn." The Journal of Symbolic Logic, 1947, -62... concrete individuals are taken to be all the individuals that there are. In The Structure of Appearance,l however, Goodman recognizes abstract individuals,and the kind of entities the recognition of which, for Goodman, makes a system platonistic are not the abstract objects but rather the nonindividuals--classes, predicates, relations, prOposi- tions.. But one has to notice that "abstract," for Goodman, has a rather Special sense. For him "abstract" means "qualitative" and is therefore not contrasted with "concrete" in the same way as "concrete" meaning "particular" is con- trasted with "universal." In that sense the distinctions concrete-abstract and individual-nonindividual do not co- incide. Some abstract or qualitative entities, such as qualia for example, are treated by Goodman as individuals. Furthermore, he points out, it is possible to construe even the most concrete object as a class of other objects, and therefore as a nonindividual.2 Instead of making "abstract object" synonymous with "nonindividual" and "concrete ob- ject" synonymous with "individual," Goodman treats "ab- stract" and "concrete" as predicates of individuals. Such treatment of these terms is, of course, appropriate only within a nominalistic system.as, for the nominalist, the meaning of "predicate of individuals" is stretched to cover M lNelson Goodman, rhe Structure_pf Appearance. Cambridge, mass.: harvard Univer81ty Press, 1951. 2 lbid., p. 150. meanings and serve purposes which are in platonistic systems dealt with through the use of nonindividual terms such as classes, relations, etc. So for example a s'uple sense quality or quale is for the platonist not an abstract individ- ual_but rather a class of concrete objects. The terms "universal" and "particular" are treated by Goodman much in parallel with "abstract" and "concrete" although, here again, we discover that these traditionally synonymous distinctions do not coincide. The rather special treatment of these terms "particular," "universal," "concrete," and "abstract," is effected by Goodman through the introduc— tion of a division of constructional systems into realistic and particularistic systems. We shall come to a closer 8L- amination of realism and particularism in a later section. The immediately following section we shall devote to the more pressing task of clarifying the term "individual." 2. Individual Kost generally there are two choices in answer to the question: what determines an individual? “fie can say (1) the individuality of something is determined by its"thisness," or "haecceity," i.e., by a quality not expressible in general terms, (2) the individual is constituted by the totality of Specifiable and general qualities which it has or wants. In Opposition to both of these views we might say that the defi- niteness of an individual is revealed to us empirically and consider "individual" as a simple term not explainable in -55- other more simple or basic terms. If we take individuality to be a uniqueness of form or of essence inexplicable in general terms we would have to admit the possibility of there beingtwo exactly similar and yet distinct individuals. What a given individual precisely is, we would be unable to describe. Uonsequent- ly we would be forced to deny the basic intelligibility of the world or to abandon the belief that the world is constituted of individuals. The second proposal proves equally defective because it rests on the doctrine of substance. If the individual is determined by the totality of its qualities, in what sense can it be said to be separate from this totality? duali- ties can be said to inhere in the individual as attributes inhere in the substance. But.this "inhering" of qualities and attributes is fatally obscure. In this view the meta- physical notion of individual or of substance is claimed to be prior to that of attribute or quality but it cannot be made logically prior as the existence of a substance can be defined only derivatively from the existence of its quali— ties.l It seems, then, that "individual" cannot be defined at all: either we define it as "thisness" or "haecceity" or we define it by its predicates, in both cases the definition lSee,‘e.g., Bertrand Russell, Philosophypof Leibniz. London: Allen & Unwin Ltd., 1900, -66- would be of no explanatory value. The third proposal for solving the problem of what constitutes an individual, we said, was not to attempt a reduction of "individual" to a: more fundamental notion at all and to treat "individual" as a simple term. The reasons in favor of this procedure can be summarized roughly as follows. Hot to attempt a definition of individual which will go beyond stipulating or explaining the role of "individual" in formalistic systems frees one from the necessity of belief in some definite metaphysical structure of the universe at this point. To say that an individual is revealed through experience is to treat it as a brute fact. ‘When‘we discover an individual through experience we discover it as reacting against or being in some relationship with some other things, but experience does not reveal the metaphysical essence or character of these relationships or reactions. An individ— ual is simply something which is found to have its place in the world of experience. What constitutes an individual is conceptually obscure but experience itself is obscure in the sare sense. Experience does not come in ready made packages and its content, in other words, the content of individuals, is to be eXplored and not judged at‘a prior . Once we abandon the metaphysical question two directions of study concerning the individual still remain. There is first the task of establishing a formal calculus of in— dividuals similar in purpose to the propositional and class -67.. calculi.l Secondly, we might develOp a comprehensive con- structional system where certain entities are construed as individuals.2 After the establishment of such calculi and systems of individuals the question of what constitutes an individual can be answered by reference to the most general features of these calculi and systems. So, for example, we can say that in reference to the calculus of individuals developed by Leonard and Goodman an individual is what can be an argument for the primitive predicate "discreteness" ("1'"). Furthermore, we shall find that "individual" is construed in sharp contrast to "class." An individual differs from a class by being capable of being subdivided into parts which themselves are individuals whereas to say that a portion of the world is a class is to superimpose upon that portion a definite scheme of subdivision.into members and sub-classes. If three elements a, b, c are said to constitute the class a, a, b, c will be the members oft: and the couples (a,b), (b,c), (a,c) will be examples of sub-classes of!!! but ac- cording to the type theory (a,b), (b,c), (a,c) cannot be aembers ofu . On the other hand if the elements a,b, c are said to form an individual A, the sums a+b, béc, a+c A V 13.55., H. S. Leonard and Nelson Goodman, "The Calculus of Individuals and Its Uses." The Journal of Symbolic ngic, 1940, pp. 45-55. 23.g., Nelson Goodman, The Structure of Appearance. Cambridge,‘Kass.: Harvard University Press, 1951. -68- are parts of n in the same sense as a, b, e are parts of n .110 Further information as to what constitutes an individ- ual can be discovered in interpretative or constructional systems which make use of the calculus of individuals as a part of their "general apparatus."l If in uninterpreted calculi "individual" is treated in respect to its formal features, comprehensive interpreted systems endeavor to shOW'what individuals there are in experience. for a nominalistic philosopher, i.e., for a philoSOpher who treats elements of experience exclusively as individuals, however, "is an individual" is a universal predicate and does not involve any Specification as to what elements of experience can be taken as individuals. for further specification we have to consider which individuals in a system are chosen for the "basic units" and which individuals are construed as the "atomic individuals" in that system. Basic units are those ind‘viduals which satisfy at least one of the "special primitive predicates" of a system, and the atomic individuals are those individuals which do not have any other individuals as systematic parts.2 however, the basic units and the atomic individuals are more fundamental only in relation to the various systems, and it might very well be that the basic 1A term used by Goodman. ghor further discussion of basic units, atomic individ- uals and special primitives, see below. ..69.. individuals of one system.undergo a completely different treatment in some other system.or are not recognized at all. 5. Nominalism In order to discover of which entities a given theory treats we have to look at the bound variables of that theory. A theory treats or affirms as existing exactly these entities over which the bound variables of quantifi- cation of that theory range. According to Quine, we re- marked, if a theory assumes as existing or treats of uni- versals or of abstract entities or of non-individuals the theory is platonistic and is Opposed to nominalistic theories which admit only particulars, concrete objects and individuals as their legitimate subject matter. Goodman's interpretation of nominalismrplatonism controversy, we re- marked also, is noticeably different: it is at the same time lore Specialized and less resthictive. Goodman's approach is more specialized in the sense that although he adOpts guine's doctrine of the "ontological com- mitments," his primary interest does not seem to lie in ontology but rather in ways and means of theory construction. For Goodman, it seems, nominalism is primarily a question of restricted means for system building and only secondarily a question of restricted ontology although he fully recognizes the inter-connectedness of these two questions. -70- Due to this more specialized interest Goodman draws a number of distinctions which allow him a less restrictive reformulation of the dictum of nominalism. In Quine's discussion the terms "abstract," "universal," and "non- individual" are lumped together: they are all said to signify entities inadmissible in nominalistic constructions. Goodman provides systematic definitions of each of these terms and points out the inadequacy of treating them as synonyms. For Goodman, nominalism does not have to avoid abstract entities and universals. If an abstract entity, such as a quale or a sun of qualia, is systematically con- strued as an individual, it can be included in a nominalis— tic universe.l All non-individuals, however, Goodman claims, have to be excluded. Individuals can be conceived as the elements represented by the variables of the lowest logical type of a system. Non-individuals, such as classes, rela- tions, predicates, are represented by variables of higher types than those of individuals. The dictum of nominalimm, according to Goodman, thus rules out quantification over variables other than those ranging over individuals. This requirement of nominalism pertains to what Goodman calls the "general apparatus" of a system and not to its 2 "special basis." The general apparatus of a system consists For discussion of "abstract" and "universal" see below. zFor discussion of "special" or "extralogical" bases of systems see belov. -71- of the "basic logic" or the truth-functional algebra together with the calculi of higher logic of which the system makes use. The basic logic comprises logical terms and ideas, primitive or defined, such as the stroke func— tion of the truth-functional incompatibility, the notion of logical negation, disjunction, conjunction, implication, and assertion. It further comprises the general theory of real and apparent variables, the idea of propositional functions and the concept of formal eguivalence. In other words the basic logic of a system.may be said to consist only of the material covered by sections A and B of the first part of the first volume of Principia‘mathematica called respectively "The Theory of Deduction" and the "Theory of Apparent Variables."l In addition to these two theories a system.might adopt the calculus of classes and relations or the calculus of individuals or both as parts of its general apparatus. The requirements of nominalism are concerned with those parts of the general apparatus of a system.which are not its basic logic, i.e., they are concerned with the admissibility or inadmissibility of these parts of logic which treat of classes, relations, and predicates. Considered as uninterpreted calculi, neither the calculus of classes nor the calculus of individuals l"ifith a few items, such as the axiom of reducibility, definition of "being of the same type," definition of iden- tity excluded. -72- presupposes that there are classes or individuals. They can be looked upon as neutral tools of analysis which do not involve any presupposed ontology. If, however, these calculi are incorporated in an interpreted or construction- al system, which claims to treat not of terms but of real elements of the world, their ontological neutrality can not be retained. To make free use of the calculus of clas- ses in a constructional system.is to commit oneself to the "belief that there exist elements of the world which are classes. The use of the calculus of individuals, of course, has for its consequence the admittance of individual entié ties. But practically all systems assume the existence of individuals and to escape this assumption seems pointless. The.more important fact resulting from.the use of the cal- culus of individuals in systems is that it can effect a reduction of the more populous ontologies of platonistic systems. Similarly as to classes the platonistically minded philosopher, in his endeavor to interpret experience, can make free use of predicates of individuals (i.e., predicates which take individuals for arguments, or predicates on the first type level) and of predicates of predicates of individ- uals (i.e., predicates which take predicates on the first type level for arguments, or predicates on the second type level) etc. The nominalist, on the other hand, must confine himself to predicates of individuals, i.e., to predicates on -73- the first type level. ‘Moreover, the predicates of individ- uals cannot, for the nominalist, be treated as variables but only as constants. To admit predicates of individuals as values for variables is to commit oneself to the exist- ence of these predicates or functions. The use of constant predicates, however, as we shall see, involves no such com- mitment. To confine oneself to the use of constant predicates of individuals curtails drastically the means of theory con- struction. If the platonist can talk about the predicates of individuals and the classes which they define, the nom- inalist can talk only about individuals. All that the platon- ist can say about predicates, functions, relations, and the classes which they define, the nominalist must say only by l speaking of the individuals involved. The only constant predicates of individuals of which the traditional logic treats are the two—place predicates of dyadic relations "identity" and "diversity." The task of the nominalist is therefore to find an economical set of constant predicates of individuals which is capable of expressing what is more commonly expressed in terms of constructions based on a more extensive logical type hierarchy. A large part of the nomin- alist's labors, in other words, must consist of the utiliza- tion and refinement of the calculus of individuals in which lhowthese restrictions exactly affect the practice of system building can be seen from the two examples in section 4. -74- the logic of constant predicates of individuals is treated. however, the nominalist is allowed to utilize the plato- nistic portions of logic in a restricted sense. He can do so if he consistently refuses to interpret the language of nonindividuals and treats it as an abacus. This treatment can be effected through the establishment of a formal syn— tax which exhibits the formal rules according to which the platonistic machinery of deduction and computation is run. rhe aim of such a syntax is to make it unnecessary to assume that nonindividual terms which occur in the platonistic language have an ontological foundation. The platonistic language will be considered as not referring to any elements in our actual experience and as free from ontological com- mitments. The only meaning that would be left to nonindivid- ual terms would be one similar to the "meaning" that we at- tribute to the beads of a computation table. The formal syntax itself, however, which makes it possible to look at the language of nonindividuals solely as a piece of convenient machinery has to be formulated according to the requirements of nominalism.l Goodman points out that the formulation of such rules will provide often great difficulties and to over- come these difficulties would enable us often to dispense :ith large parts of this auxiliary machinery of platonistic lAn attempttn develop rules which would enable us to look at mathematics as such an abacus can be found in Lelson Goodman and w. v. Quins, "Steps Toward a Constructive €0minal- ism." Journal of Symbolic Logic, 1947, pp. 105-122. logic altogether. The problems which motivated us to seek the aid of some platonistic language would then be solvable, to a large extent, directly in our nominalistic language itself. 4. Two Examples Nominalism then, is a proposal to restrict the means of theory construction. the main restriction is that quantifi- cation is not permissible over variables other than those representing individuals. Let us take an example. Suppose that we want to define the predicate "is an ancestor of" when the predicate "is a parent of" is already available in our system. For the platonistic philosopher, who can make free use of classes, a familiar method, devel- oped by Frege, is readily available.1 Let us for "x is a parent of y" write "ny" and for "x is an ancestor of y? "*ny." "*ny" can then be defined in terms of "Pry" as follows: (1) any: )[yum (z) (w) hm .rzw.:.zsa) .3.x;d], which can be read: x is an ancestor of y if and only if x belongs to every'class,u3 to which y belongs and to which also every parent of every member of 0! belongs. This definition is clearly platonistic as it includes a quantified class variable, and it is therefore inadmissible let. the exemplification of this method in Willard Van Crman guine,‘Kethods of Logic. New York: Henry Eolt & Company, 1950, p. 239. ~76- for the nominalist. fhe nominalist has to find other means for constructing the same definition. First, the nominalist has to replace the class variable "a" by a variable which represents only individuals. Secondly, the membership re- lation of the class calculus must be replaced by some two- place predicate which takes only individuals as its argu- ments. One such predicate is the predicate "is a part of" of the calculus of individuals. Through these replacements and in close analogy with Frege's method the nominalist will then arrive at the following definition: (2) *Pry‘(a)[y