Hellenistic Philosophy PHI 143
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Date Created: 09/09/15
Principles of Mathematics Chapter IV PROPER NAMES ADJECTIVES AND VERBS Bertrand Russell 1903 46 In the present chapter certain questions are to be discussed belonging to what may be called philosophical grammarl The study of grammar in my opinion is capable of throwing far more light on philosophical questions than is commonly supposed by philosophers Although a grammatical distinction cannot be uncritically assumed to correspond to a genuine philosophical differ ence yet the one is prima facie evidence of the other and may often be most usefully employed as a source of discovery Moreover it must be admitted I think that every word occurring in a sentence must have same meaning a per fectly meaningless sound could not be employed in the more or less xed way in which language employs words The correctness of our philosophical analysis of a proposition may therefore be usefully checked by the exercise of assigning the meaning of each word in the sentence expressing the proposition On the whole grammar seems to me to bring us much nearer to a correct logic than the current opinions of philosophers and in what follows grammar though not our master will yet be taken as our guide Note The excellence of grammar as a guide is proportional to the paucity of inflexions ie to the degree of analysis effected by the language considered Of the parts of speech three are specially important substantives adjec tives and verbs Among substantives some are derived from adjectives or verbs as humanity from human or sequence from follows I am not speaking of an etymological derivation but of a logical one Others such as proper names or space time and matter are not derivative but appear primarily as substan tivesl What we wish to obtain is a classi cation not of words but of ideas I shall therefore call adjectives or predicates all notions which are capable of being such even in a form in which grammar would call them substantivesl The fact is as we shall see that human and humanity denote precisely the same concept these words being employed respectively according to the kind of relation in which this concept stands to the other constituents of a proposition in which it occurs The distinction which we require pl 43 is not identical with the grammatical distinction between substantive and adjective since one single concept may according to circumstances be either substantive or adjec tive it is the distinction between proper and general names that we require or rather between the objects indicated by such names In every proposition as we saw in Chapter III we may make an analysis into something asserted and something about which the assertion is made A proper name when it occurs in a proposition is always at least according to one of the possible ways of analysis where there are several the subject that the proposition or some subordinate constituent proposition is about and not what is said about the subject Adjectives and verbs on the other hand are capable of occurring in propositions in which they cannot be regarded as subject but only as parts of the assertion Adjectives are distinguished by capacity for denotingia term which I intend to use in a technical sense to be discussed in Chapter V Verbs are distinguished by a special kind of connection exceedingly hard to de ne with truth and falsehood in virtue of which they distinguish an asserted propo sition from an unasserted one eg Caesar died77 from the death of Caesari77 These distinctions must now be ampli ed and I shall begin with the distinction between general and proper names 47 Philosophy is familiar with a certain set of distinctions all more or less equivalent 1 mean the distinctions of subject and predicate substance and attribute substantive and adjective this and what Note This last pair of terms is due to Mr Brad eyi I wish now to point out brie y what appears to me to be the truth concerning these cognate distinctionsi The subject is important since the issues between monism and monadism between idealism and empiricism and between those who maintain and those who deny that all truth is concerned with what exists all depend in whole or in part upon the theory we adopt in regard to the present question But the subject is treated here only because it is essential to any doctrine of number or of the nature of the variable lts bearings on general philosophy important as they are will be left wholly out of account Whatever may be an object of thought or may occur in any true or false proposition or can be counted as one I call a termi This then is the widest word in the philosophical vocabularyi I shall use as synonymous with it the words unit individual and entity The rst two emphasize the fact that every term is one while the third is derived from the fact that every term has being 239e is in some sense man a moment a number a class a relation a chimaera or anything else that can be mentioned is sure to be a term and to deny that such and such a thing is a term must always be false It might perhaps be thought that a word of such extreme generality could not be of any great user Such a view however owing to certain pl 44 widespread philosophical doctrines would be erroneousi A term is in fact possessed of all the properties commonly assigned to substances or substantivesi Every term to begin with is a logical subject it is for example the subject of the proposition that itself is one Again every term is immutable and indestructible W at a term is it is and no change can be conceived in it which would not destroy its identity and make it another termi Note The notion of a term here set forth is a modi cation of Mr G E Moorels notion of a concept in his article On the Nature of Judgmen Mind N S No 30 from which notion however it differs in some important respects Another mark which belongs to terms is numerical identity with themselves and numerical diversity from all other terms Note On identity see Mr G E Moorels article in the Proceedings of the Aristotelian Society 19001901 Numerical identity and diversity are the source of unity and plurality and thus the admission of many terms destroys monismi And it seems undeniable that every constituent of every proposition can be counted as one and that no proposition contains less than two constituentsi Term is therefore a useful word since it marks dissent from various philosophies as well as because in many statements we wish to speak of any term or some termi 48 Among terms it is possible to distinguish two kinds which I shall call respectively things and concepts The former are the terms indicated by proper names the latter those indicated by all other words Here proper names are to be understood in a somewhat wider sense than is usual and things also are to be understood as embracing all particular points and instants and many other entities not commonly called thingsi Among concepts again two kinds at least must be distinguished namely those indicated by adjectives and those indicated by verbsi The former kind will often be called predicates or classconcepts the latter are always or almost always relations In intransitive verbs the notion expressed by the verb is complex and usually asserts a de nite relation to an inde nite relatum as in Smith breathesi In a large class of propositions we agreed it is possible in one or more ways to distinguish a subject and an assertion about the subject The assertion must always contain a verb but except in this respect assertions appear to have no universal properties In a relational proposition say A is greater than B we may regard A as the subject and is greater than B as the assertion or B as the subject and A is greater than as the assertion There are thus in the case proposed two ways of analyzing the proposition into subject and assertioni Where a relation has more than two terms as in is here now Note This proposition means A is in this place at this time It will be shown in Part VII that the relation expressed is not reducible to a twoterm relationi there will be more than two ways of making the analysis But in some propositions there is only a single way These are the subject p45 predicate propositions such as Socrates is human The proposition humanity belongs to Socrates which is equivalent to Socrates is human is an assertion about humanity but it is a distinct propositioni ln Socrates is human the notion expressed by human occurs in a different way from that in which it occurs when it is called humanity the difference being that in the latter case but not in the former the proposition is about this notion This indicates that humanity is a concept not a thing I shall speak of the terms of a proposition as those terms however numerous which occur in a proposition and may be regarded as subjects about which the proposition is It is a characteristic of the terms of a proposition that any one of them may be replaced by any other entity without our ceasing to have a proposition Thus we shall say that Socrates is human is a proposition having only one term of the remaining components of the proposition one is the verb the other is a predicate With the sense which is has in this proposition we no longer have a proposition at all if we replace human by something other than a predicate Predicates then are concepts other than verbs which occur in propositions having only one term or subject Socrates is a thing because Socrates can never occur otherwise than as term in a proposition Socrates is not capable of that curious twofold use which is involved in human and humanity Points instants bits of matter particular states of mind and particular existents generally are things in the above sense and so are many terms which do not exist for example the points in a non Euclidean space and the pseudoexistents of a novel All classes it would seem as numbers men spaces etc when taken as single terms are things but this is a point for Chapter Vli Predicates are distinguished from other terms by a number of very interesting properties chief among which is their connection with what 1 shall call denotingi One predicate always gives rise to a host of cognate notions thus in addition to human and humanity which only differ grammatically we have man a man some man any man every man all men Note 1 use all men as collective ie as nearly synonymous with the human race but differing therefrom by being many and not one 1 shall always use all collectively con ning myself to every for the distributive sensei Thus 1 shall say every man is mortal77 not all men are mortali all of which appear to be genuinely distinct one from another The study of these various notions is absolutely vital to any philosophy of mathematics and it is on account of them that the theory of predicates is important 49 It might be thought that a distinction ought to be made between a concept as such and a concept used as a term between eg such pairs as is and being human and humanity one in such a proposition as this is one77 and 1 in 1 is a number77 But inextricable dif culties will envelop us if we allow such a viewi There is p46 of course a grammatical difference and this corresponds to a difference as regards relations In the rst case the concept in question is used as a concept that is it is actually predicated of a term or asserted to relate two or more terms while in the second case the concept is itself said to have a predicate or a relation There is therefore no dif culty in accounting for the grammatical difference But what 1 wish to urge is that the difference lies solely in external relations and not in the intrinsic nature of the terms For suppose that one as adjective differed from 1 as termi In this statement one as adjective has been made into a term hence either it has become 1 in which case the supposition is selfcontradictory or there is some other difference between one and 1 in addition to the fact that the rst denotes a concept not a term while the second denotes a concept which is a termi But in this latter hypothesis there must be propositions concerning one as term and we shall still ave to maintain propositions concerning one as adjective as opposed to one as term yet all such propositions must be false since a proposition about one as adjective makes one the subject and is therefore really about one as termi In short if there were any adjectives which could not be made into substantives without change of meaning all propositions concerning such adjectives since they would necessarily turn them into substantives would be false and so wou the proposition that all such propositions are false since this itself turns the adjectives into substantivesi But this state of things is selfcontradictoryi The above argument proves that we were right in saying that terms embrace everything that can occur in a proposition with the possible exception of com plexes of terms of the kind denoted by any and cognate words Note See the next chapter For if A occurs in a proposition then in this statement A is the subject and we have just seen that if A is ever not the subject it is exactly and numerically the same A which is not subject in one proposition and is sub ject in another Thus the theory that there are adjectives or attributes or ideal things or whatever they may be called which are in some way less substan tial less selfsubsistent less selfidentical than true substantives appears to be wholly erroneous and to be easily reduced to a contradiction Terms which are concepts differ from those which are not not in respect of selfsubsistence but in virtue of the fact that in certain true or false propositions they occur in a manner which is different in an inde nable way from the manner in which subjects or terms of relations occur 50 Two concepts have in addition to the numerical diversity which belongs to them as terms another special kind of diversity which may e called con ceptuali This may be characterized by the fact that two propositions in which the concepts occur otherwise than as terms even if in all other respects the two propositions are identical pl 47 yet differ in virtue of the fact that the concepts which occur in them are conceptually diversei Conceptual diversity implies numerical diversity but the converse implication does not hold since not all terms are conceptsi Numerical diversity as its name implies is the source of plurality and conceptual diversity is less important to mathematics But the whole possibility of making different assertions about a given term or set of terms depends upon conceptual diversity which is therefore fundamental in general logici 51 It is interesting and not unimportant to examine very brie y the con nection of the above doctrine of adjectives with certain traditional views on the nature of propositions It is customary to regard all propositions as having a subject and a predicate ie as having an immediate this and a general concept attached to it by way of description This is of course an account of the theory in question which will strike its adherents as extremely crude but it will serve for a general indication of the view to be discussed This doctrine develops by internal logical necessity into the theory of Mr Bradleyls Logic that all words stand for ideas having what he calls meaning and that in every judgment there is a something the true subject of the judgment which is not an idea and does not have meaning To have meaning it seems to me is a notion confusedly compounded of logical and psychological elementsi Words all have meaning in the simple sense that they are symbols which stand for something other than themselves But a proposition unless it happens to be linguistic does not itself contain words it contains the entities indicated by words Thus meaning in the sense in which words have meaning is irrelevant to logici But such concepts as a man have meaning in another sense they are so to speak symbolic in their own logical nature because they have the property which I call denoting That is to say when a man occurs in a proposition ag I met a man in the street the proposition is not about the concept a man but about something quite different some actual biped denoted by the concept Thus concepts of this kind have meaning in a nonpsychological sense And in this sense when we say this is a man we are making a proposition in which a concept is in some sense attached to what is not a concept But when meaning is thus understood the entity indicated by John does not have meaning as Mr Bradley contends Notez Logic Book 1 Chap ll secs 1 18 pp 5860 and even among concepts it is only those that denote that have meaning The confusion is largely due I believe to the notion that words occur in propositions which in turn is due to the notion that propositions are essentially mental and are to be identi ed with cognitionsi But these topics of general philosophy must be pursued no further in this wor i 52 It remains to discuss the verb and to nd marks by which it is distin guished from the adjective In regard to verbs also there is p 48 a twofold grammatical form corresponding to a difference in merely external relations There is the verb in the form which it has as verb the various in exions of this form may be left out of account and there is the verbal noun indicated by the in nitive or in English the present participle The distinction is that between Felton killed Buckingham and Killing no murderi By analyzing this difference the nature and function of the verb will appear It is plain to begin with that the concept which occurs in the verbal noun is the very same as that which occurs as verbl This results from the previous argument that every constituent of every proposition must on pain of self contradiction be capable of being made a logical subject If we say kills does not mean the same as to kill we have already made kills a subject and we cannot say that the concept expressed by the word kills cannot be made a subject Thus the very verb which occurs as verb can occur also as subject The question is What logical difference is expressed by the difference of grammatical form And it is plain that the difference must be one in external relations But in regard to verbs there is a further point By transforming the verb as it occurs in a proposition into a verbal noun the whole proposition can be turned into a single logical subject no longer asserted and no longer containing in itself truth or falsehoodl But here too there seems to be no possibility of maintaining that the logical subject which results is a different entity from the proposition Caesar died and the death of Caesar will illustrate this point If we ask What is asserted in the proposition Caesar died the answer must be the death of Caesar is asserted In that case it would seem it is the death of Caesar which is true or false and yet neither truth nor falsity belongs to a mere logical subject The answer here seems to be that the death of Caesar has an external relation to truth or falsehood as the case may be whereas Caesar died in some way or other contains its own truth or falsehood as an element But if this is the correct analysis it is dif cult to see how Caesar died differs from the truth of Caesar7s death in the case where it is true or the falsehood of Caesar7s death in the other case Yet it is quite plain that the latter at any rate is never equivalent to Caesar diedi There appears to be an ultimate notion of assertion given by the verb which is lost as soon as we substitute a verbal noun and is lost when the proposition in question is made the subject of some other propositioni This does not depend upon grammatical form for if I say Caesar died is a proposition 1 do not assert that Caesar did die and an element which is present in Caesar died has disappeared Thus the contradiction which was to have been avoided of an entity which cannot be made a logical subject appears to have here become inevitablei This dif culty which seems to be inherent in the very nature of truth and falsehood is one with which I do not know how to deal satisfactorily The most obvious course pl 49 would be to say that the difference between an asserted and an unasserted proposition is not logical but psychological In the sense in which false propositions may be asserted this is doubtless true But there is another sense of assertion very dif cult to bring clearly before the mind and yet quite undeniable in which only true propositions are assertedi True and false propositions alike are in some sense entities and are in some sense capable of being logical subjects but when a proposition happens to be true it has a further quality over and above that which it shares with false propositions and it is this further quality which is what I mean by assertion in a logical as opposed to a psychological sense The nature of truth however belongs no more to the principles of mathematics than to the principles of everything else I therefore leave this question to the logicians with the above brief indication of a dif cu ty 53 It may be asked whether everything that in the logical sense we are concerned with is a verb expresses a relation or not It seems plain that if we were right in holding that Socrates is human is a proposition having only one term the is in this proposition cannot express a relation in the ordinary sense In fact bj p d39 t A A T are quot 39 39 by just this non relational characteri Nevertheless a relation between Socrates and humanity is certainly implied and it is very dif cult to conceive the proposition as ex pressing no relation at all We may perhaps say that it is a relation although it is distinguished from other relations in that it does not permit itself to be regarded as an assertion concerning either of its terms indifferently but only as an assertion concerning the referenti A similar remark may apply to the proposition A is which holds of every term without exception The is here is quite different from the is in Socrates is human it may be regarded as complex and as really predicating Being of Al ln this way the true logical verb in a proposition may be always regarded as asserting a relation But it is so hard to know exactly what is meant by relation that the whole question is in danger of becoming purely verb 54 The twofold nature of the verb as actual verb and as verbal noun may be expressed if all verbs are held to be relations as the difference between a relation in itself and a relation actually relatingi Consider for example the proposition A differs from B The constituents of this proposition if we analyze it appear to be only A difference B Yet these constituents thus placed side by side do not reconstitute the proposition The difference which occurs in the proposition actually relates A and B whereas the difference after analysis is a notion which has no connection with A and B It may be said that we ought in the analysis to mention the relations which difference has to A and B relations which are expressed by is and from when we say A is different from B77 These relations consist in the pl 50 fact that A is referent and B relatum with respect to difference But A referent difference relatum B77 is still merely a list of terms not a proposition A proposition in fact is essentially a unity and when analysis has destroyed the unity no enumeration of constituents will restore the proposition The verb when used as a verb embo ies the unity of the proposition and is thus distinguishable from the verb considered as a term though I do not know how to give a clear account of the precise nature of the distinction 55 It may be doubted whether the general concept dz erence occurs at all in the proposition A differs from B77 or whether there is not rather a speci c difference of A and B and another speci c difference of C and D which are respectively af rmed in A differs from B77 and C differs from D77 In this way ifference becomes a class concept of which there are as many instances as there are pairs of different terms and the instances may be said in Platonic phrase to partake of the nature of difference As this point is quite vital in the theory of relations it may be well to dwell upon it And rst of all I must point out that in A differs from B77 I intend to consider the bare numerical difference in virtue of which they are two not difference in this or that respect Let us rst try the hypothesis that a difference is a complex notion com pounded of difference together with some special quality distinguishing a par ticular difference from every other particular difference So far as the relation of difference itself is concerned we are to suppose that no distinction can be made between different cases but there are to be different associated qualities in different cases But since cases are distinguished by their terms the quality must be primarily associated with the terms not with difference If the quality be not a relation it can have no special connection with the difference of A and B which it was to render distinguishable from bare difference and if it fails in this it becomes irrelevanti On the other hand if it be a new relation between A and B over and above difference we shall have to hold that any two terms have two relations difference and a speci c difference the latter not holding between any other pair of terms This view is a combination of two others of which the rst holds that the abstract general relation of difference itself holds between and B while the second holds that when two terms differ they have corre sponding to this fact a speci c relation of difference unique and unanalyzable and not shared by any other pair of terms Either of these views may be held with either the denial or the af rmation of the other Let us see what is to be said for and against themi Against the notion of speci c differences it may be urged that if differences differ their differences from each other must also differ and thus we are e into an endless processi Those who object to endless processes will see in this a proof that differences do not differ But in p51 the present work it will be maintained that there are no contradictions peculiar to the notion of in nity and that an endless process is not to be objected to unless it arises in the analysis of the actual meaning of a proposition In the present case the process is one of implications not one of analysis it must therefore be regarded as harmless Against the notion that the abstract relation of difference holds between A and B we have the argument derived from the analysis of A differs from B77 which gave rise to the present discussion It is to be observed that the hypothesis which combines the general and the speci c difference must suppose that there are two distinct propositions the one af rming the general the other the speci c difference Thus i there cannot be a general difference between A and B this mediating hypothesis is also impossiblei And we saw that the attempt to avoid the failure of analysis by including in the meaning of A differs B77 the relations of difference to A an E was vaini This attempt in fact leads to an endless process of the inadmissible kind for we shall have to include the relations of the said relations to A and B and difference and so on and in this continually increasing complexity we are supposed to be only analyzing the meaning of our original proposition This argument establishes a point of very great importance namely that when a relation holds between two terms the relations of the relation to the terms and of these relations to the relation and the terms and so on ad in nitum though all implied by the proposition af rming the original relation form no part of the meaning of this proposition But the above argument does not suf ce to prove that the relation of A to B cannot be abstract difference it remains tenable that as was suggested to begin with the true solution lies in regarding every proposition as having a kind of unity which analysis cannot preserve and which is lost even though it be mentioned by analysis as an element in the proposition This view has doubtless its own dif culties but the view that no two pairs of terms can have the same relation both contains dif culties of its own and fails to solve the dif culty for the sake of which it was invented For even if the difference of A and B be absolutely peculiar to A and B still the three terms A B difference of A from B do not reconstitute the proposition A differs from B77 any more than A and B and difference did And it seems plain that even if differences did differ they would still have to have something in common But the most general way in which two terms can have something in common is by both having a given relation to a given termi Hence if no two pairs of terms can have the same relation it follows that no two terms can have anything in common and hence different differences will not be in any de nable sense instances of difference Note The above argument appears to prove that Mr Moorels theory of universals with numerically diverse instances in his paper on ldentity Proceedings of the Aristotelian Society 19001901 must not be applied to all concepts The relation of an instance to its universal at any rate must be actually and numerically the same in all cases where it occurs I conclude then that p 52 the relation af rmed between A and B in the proposition differs from B77 is the general relation of difference and is precisely and numerically the same as the relation af rmed between C and D in C differs om D77 And this doctrine must be held for the same reasons to be true of all other relations relations do not have instances but are strictly the same in all propositions in which they occur e may now sum up the main points elicited in our discussion of the verb
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