Bertrand Russell Proper Names, Adjectives and Verbs 1 Analysis 46 Philosophical grammar can shed light on philosophical questions. Grammatical differences can be used as a source of discovery and a guide to philosophical differences. Every word must have some meaning since meaningless sounds couldn t be employed in the more or less fixed way language employs words. We can check our analysis of a proposition by assigning meanings to each word in the sentence that expresses it. There are three important parts of speech substantives, adjectives and verbs. Russell discusses the interrelationships between these parts of speech and notes that we want a classification not of words, but ideas. Eg. human and humanity denote precisely the same concept, the different words being employed according to the kind of relation this concept stands to the other constituents of the proposition in which it occurs. The distinction we require, therefore, isn t between substantive and adjective but between proper and general names. Propositions can be analysed into something asserted and something about which the assertion is made. A proper name is the subject that the proposition, or a subordinate proposition, is about and not what is said about the subject. Adjectives and verbs can occur in propositions where they can only be parts of the assertion. Adjectives are distinguished by their capacity for denoting. Verbs distinguish an asserted proposition from an unasserted one Caesar died from The death of Caesar 2. 47 Russell begins his analysis of these distinctions by looking at the distinction between general and proper names. Philosophy makes several equivalent distinctions: between subject and predicate, substance and attribute, substantive and adjective, and this and what. Russell thinks that the issues between monism and monadism, idealism and empiricism, and whether or not truth is concerned with what exists all depend on the theory we adopt for these distinctions. Russell will only account here for the bearing of the problem on that of number or the variable. Russell defines a term maybe the widest word in the philosophical vocabulary as what can be an object of thought, occur in a proposition or be counted as one 3 synonymous with unit, individual and entity. The first two emphasise that a term is one, the last that every term has being is in some sense. Russell allows anything that can be mentioned the status of a term a man, a moment, a number, a class, a relation, a chimera. It s always false to deny that a thing is a term. It is a mistake to think such a wide-ranging word is useless, since it possesses all the properties assigned to substances or substantives. So, every term (a) is a logical subject, eg. of the proposition that the term itself is one; (b) is immutable and indestructible; (c) can undergo no change that would not destroy its identity 1 Chapter IV of The Principles of Mathematics. 2 This doesn t even seem to be a proposition. What is an unasserted proposition? 3 What does this mean? Theotodman@lineone.net Page 1 of 7
and make it another term; (d) numerically identical to itself and diverse from all others. This notion of a term is a modified version of Moore s notion of concept in On the Nature of Judgement. Numerical identity and diversity are the sources of unity and plurality, so the existence of many terms destroys monism. Every constituent of every proposition counts as a term, and every proposition must contain at least two terms. Term marks dissent from many philosophies and is useful because, in many statements we wish to speak of any or some term. 48 Russell distinguishes between two types of term things and concepts, the former for terms indicated by proper names, the latter for those indicated by all other words. Both things and proper names are to be considered in a wider sense than normal, with points and instants being counted as things. Russell distinguishes two types of concept; those indicated by adjectives always predicates or class concepts and verbs almost always relations respectively. In a large class of propositions, it s possible to distinguish a subject from an assertion about it, the latter having no universal properties other than containing a verb. There are two ways of analysing relational propositions: 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. Where a relation has more than two terms, as in A is here now, there are more than two ways of making the analysis; but in subject-predicate propositions there is only one way. Humanity belongs to Socrates is a different proposition from Socrates is human, in being an assertion about humanity rather than Socrates. Hence, humanity is a concept rather than a thing. According to Russell, the terms of a proposition are those terms occurring in the proposition that can be regarded as the subjects the proposition is about. Any of these terms may be replaced by another entity without the proposition ceasing to be a proposition. So, Socrates is human contains only one term, the remaining components being a verb and a predicate. Replacing human by a non-predicate destroys the proposition. So, predicates are concepts other than verbs that occur in propositions having only one term or subject. Socrates is a thing, because Socrates can never occur other than as a term in a proposition, and cannot have the twofold use noted of human and Humanity. Particular existents generally are things, as are many terms that don t exist, such as points in non-euclidean 4 space and the pseudo-existents of a novel. Russell thinks that classes, when taken as single terms, are things. Predicates are distinguished from other terms chiefly by their connection with denoting. Russell claims that any predicate gives rise to a host of cognate notions that are genuinely distinct. So, from human and humanity, which only differ grammatically, we have man, and man prefixed by a, some, any, every, all 5. Russell notes that the study of such notions is vital to the philosophy of mathematics and is what gives the study of predicates its importance. Russell uses all collectively and every distributively, so that every man is mortal rather than all men are mortal. 4 This paper presumably hails from the time Russell held a Kantian view of geometry. 5 Russell doesn t refer to these as quantifiers. Theotodman@lineone.net Page 2 of 7
49 Russell thinks we run into inextricable difficulties if we allow a distinction between a concept as such and its use as a term: his examples is and being, human and humanity, and one in this is one and 1 in 1 is a number. There is a grammatical difference corresponding to differences as regards relations. In the first case, the concept is used as a concept, either actually predicated of a term or asserted to relate two or more terms. In the second case the concept is itself said to have a predicate or relation. Russell insists this explains the difference, which lies solely in external relations and not in the intrinsic nature of the terms 6. By way of proof a reductio he imagines that one as adjective differed from 1 as term. In this very statement, one as adjective has been made into a term 7, in which case either one has become 1, in contradiction to the supposition, or else there is some other distinction between the two other than their being concepts that are not and are, respectively, terms. However, in this latter hypothesis, there must be propositions to be affirmed concerning one as term in addition to, and as opposed to, those concerning one as adjective. Yet, all such propositions about one as adjective must be false 8 since they make one the subject and so a term. In summary, we end up with a contradiction, for, if there were any adjectives that couldn t be changed into substantives without change of meaning, then (a) all propositions concerning such adjectives would be false, since they would perforce change them into substantives, and (b) the proposition that all such propositions are false would also be false, since it also turns the adjective into a substantive. Russell concludes that the above argument demonstrates the correctness of the supposition that cover everything that can occur in a proposition, with the possible exception of complexes of terms of the kind denoted by any and its cognates (which Russell will address in the next chapter). His reason is that if A occurs in a proposition, then in this very statement A is the subject, and we ve just seen that even where A isn t the subject, it is numerically the same A that is the subject in another proposition. Consequently, Russell concludes that it s contradictory to think that there are adjectives, attributes or ideal things that are less substantial, self-subsistent or self-identical than true substances. He concludes, rather feebly, that terms which are concepts differ from those that aren t by their occurrence in propositions in a manner which differs in an indefinable way 9. 50 Two concepts differ conceptually as well as in virtue of their being different terms. So, two otherwise identical propositions in which the concepts occur other than as terms differ because the concepts are conceptually diverse 10. Conceptual diversity implies numerical diversity, but not vice versa, since not all terms are concepts. Only numerical diversity is important to mathematics, though 6 I m a bit confused as to whether or not Russell uses terms in this sentence in its technical sense, though concepts are a type of term. 7 It seems to me that it is one as adjective that is the term, and not one. 8 Are they false, or simply not about one the adjective. 9 Re-read the end of this section later in the hope of enlightenment! 10 Is this telling us anything useful? Theotodman@lineone.net Page 3 of 7
51 conceptual diversity is important to general logic since it enables the making of different assertions about terms. It s customary to regard all propositions as having a subject and a predicate as having an immediate this and a general concept attached by way of description. This doctrine develops by internal logical necessity into Bradley s Logic, the theory that all words stand for ideas having meaning and that in every judgement there is the true subject of the judgement which isn t an idea and doesn t have meaning. Russell thinks that Bradley s meaning confuses logical and psychological elements. Words all have meaning simply because they are symbols which stand for something other than themselves. However, a proposition, unless it happens to be linguistic, doesn t itself contain words but rather the entities indicated by words 11. Hence, Russell thinks, meaning in the sense that words have meaning is irrelevant to logic. However, he thinks that concepts such as a man have meaning in another sense, being symbolic in their own logical nature because having the property of denoting. So, the proposition I met a man in the street isn t about the concept a man but about some actual biped denoted by the concept. Consequently, such concepts have meaning in a non-psychological sense. When we say This is a man, we re making a proposition in which a concept is attached to a non-concept. But, when meaning is understood in this sense, the entity indicated by John doesn t have meaning contra Bradley and even amongst concepts, only those that denote have meaning. Russell thinks the confusion arises from supposing words occur in propositions which is itself due to thinking that propositions are essentially mental and are to be identified with thoughts. 52 Russell now turns to the verb, and how it is distinguished from the adjective. It has two grammatical forms corresponding to different external relations the verb per se and the verbal noun (infinitive and present participle). The nature and function of the verb will appear in the distinction between Felton killed Buckingham and Killing no murder. We can show that the verb and the verbal noun contain the very same concept by the same argument as previously that every constituent of a proposition can be made a logical subject on pain of contradiction. We make kills a logical subject by saying kills doesn t mean the same as to kill. The logical difference that lies behind these differences of grammatical form must be one of external relations. There s a further point in the case of verbs, because in transforming the verb as it occurs in a proposition into a verbal noun, we can turn the whole proposition into a logical subject that is neither asserted nor contains truth or falsity within itself. Even so, Russell doesn t think the resulting logical subject a different entity from the proposition. 11 NB. This is what was alluded to in lectures; that Russell s early view of the proposition was that it contained physical entities - but doesn t this misconstrue Russell? Propositions contain ideas that various verbal forms can summon up (all that stuff about snow being white in various languages but only one proposition), but they don t contain material snow. Theotodman@lineone.net Page 4 of 7
He illustrates this contention with Caesar died and the death of Caesar. In asserting the former, we assert the latter. Consequently, it would seem that it s the death of Caesar that s true or false, yet neither truth nor falsity belongs to a mere logical subject. Russell thinks the solution to lie in the death of Caesar 12 having an external relation to truth or falsehood, whereas Caesar died contains its own truth or falsehood. However, in this case Caesar died wouldn t differ from the truth (or falsehood) of Caesar s death though it s plain that the falsehood of Caesar s death is never equivalent to Caesar died. Russell thinks the verb contains within it an assertiveness that s lost once a verbal noun is substituted or the proposition is made the subject of another proposition. That this doesn t depend on grammatical form is evident from the fact that saying Caesar died is a proposition doesn t assert that Caesar died, so an element in Caesar died has disappeared. Consequently, the contradiction to be avoided that an entity cannot be made into a logical subject appears inevitable. Russell has no satisfactory answer to this problem, which appears to be inherent in the very nature of truth and falsehood. He thinks the obvious approach is to say the difference between asserted and unasserted propositions is psychological rather than logical, and that this is definitely the case in the assertion of false propositions. However, he thinks that there is a sense of assertion in which only true propositions are asserted. Both true and false propositions are in some sense entities which are capable of being logical subjects, but a true proposition has another quality assertion in a logical rather than psychological sense not shared with false propositions. 53 Russell now asks whether every logical verb expresses a relation. If we were right to say that the proposition Socrates is human has only one term 13, the is cannot express an ordinary relation, subject-predicate propositions being distinguished by this non-relational character. Even so, there is the implication of a relation between Socrates and humanity, distinguished from other relations in that it isn t an assertion about either 14 term indifferently, but only an assertion concerning the referent 15. A is holds of every term, the is predicating Being of A. Thus, we may regard the true logical verb in any proposition as asserting a relation, though Russell thinks it so hard to know exactly what s meant by relation that the question becomes merely verbal. 54 The difference between actual verbs and verbal nouns is thus that between a relation in itself and a relation actually relating. Eg. in A differs from B, the constituents seem to be A, difference and B, yet the juxtaposition of these constituents doesn t reconstitute the proposition, which was a relation between A and B, which are unrelated in the analysis which ought to include the relations 12 Russell seems careless of when to put expressions in scare quotes, and I suspect this has something to do with his problems in analysing this issue. 13 Which is the term? Socrates human is a predicate according to 48. 14 The implied relation to humanity is to another term rather than to a predicate. 15 Ie. Socrates. Theotodman@lineone.net Page 5 of 7
55 expressed by is and from in A is different from B, where A is referent and B relatum. Even so, A, referent, difference, relatum, B still isn t a proposition, but only a list of terms. Russell thinks a proposition is essentially a unity, which is destroyed by analysis 16, and concludes that the verb as such embodies the unity of a proposition, in contrast to the verb as term. Russell closes this chapter with an extensive analysis of difference. He doubts whether there is a general concept of difference, but merely a class-concept of which there as many instances which partake of the nature of difference as there are pairs of different terms. In what follows, by A differs from B, Russell is concerned only with bare numerical difference and not with the respect in which there is difference. Russell first tries the hypothesis that a particular difference is a compound of universal difference and some special quality distinguishing it from all other particular differences. Since cases are distinguished by their terms, the special quality must depend on the terms rather than on difference itself. The question now arises whether this quality is a relation or not. (1) If it isn t, it can have no special connection to the difference of A and B, and so becomes irrelevant. (2) If it is a new relation over and above bare difference, we have to suppose that any two terms have two relations difference and a specific difference the latter not holding between any other pair of terms. The second of the above views is equivalent to a combination of two others which can be held independently. The first of these is that there is an abstract general relation of difference, the second being that where two terms differ there is a second unique and unanalysable relation of difference not shared by any other pair of terms. Russell now considers the points pro and con the above views. Contra the specific differences hypothesis, we might argue that we and up with infinite regress in that if differences differ, then their differences from each other must also differ. Russell thinks this is a benign regress, and that regress is only vicious if it arises in the analysis of the meaning of a proposition. Contra the abstract relation of difference hypothesis, Russell notes that the joint hypothesis that combines a general and a specific difference must maintain that there are two distinct propositions the one maintaining the general and the other the specific difference and that without the general difference this hypothesis is also impossible. We saw the futility of the attempt to avoid the failure of the analysis of A differs from B by including the relations of difference to A and B in the meaning of this proposition. In fact, this attempted analysis leads to vicious regress, for in analysing the meaning of our original proposition we d need to include the continually increasing complexity of the relations of such relations to A and B and difference, and so on. Russell thinks the analysis immediately above establishes an important point: that when a relation holds between two terms, the relations of the relation to the terms, and the relations of these relations to the relation and the terms, and so on ad 16 There seems to be confusion in early Russell between propositions and the words in which they are expressed. Theotodman@lineone.net Page 6 of 7
infinitum, form no part of the meaning of the proposition affirming the relation, in spite of being implied by it. Even so, this isn t sufficient to disprove abstract differences, since it s tenable that the true solution is to regard every proposition as a unity that is destroyed by analysis, even if this unity is mentioned in the analysis itself. Whatever the difficulties of this view, the view that no two pairs of terms can have the same relation fails even to solve the difficulty for the sake of which it was invented. Even if the difference of 17 A and B be absolutely peculiar to A and B, the three terms A, B and difference of A from B don t reconstitute A differs from B any more than A, B and difference did. Even if differences 18 did differ, it seems plain to Russell that they would still have something in common. Since the most general way for two terms to have something in common is for them both to have a given relation to a third term, it follows that if no two pairs of terms can have the same relation then no two terms can have anything in common with one another. Since this means that different differences couldn t then be instances of difference, Russell concludes that when we say A differs from B the relation affirmed is the general relation of difference, and that this relation is numerically the same as that between any other two terms. For similar reasons, there are no instances of any other relation, which are strictly the same in all propositions in which they occur. Russell now sums up the main points related to the verb: a) It is a concept that can (like the adjective) occur in a proposition without being one of its terms, though it can be made into a logical subject. b) Precisely one verb must occur as such in any proposition. c) Any proposition can be changed into a single logical subject (a propositional concept) by turning its verb into a verbal noun. d) Every logical verb may be regarded as a relation which actually relates when the logical verb occurs as verb, but when it occurs as verbal noun it is as bare relation considered independently of the terms related 19. e) Verbs, unlike adjectives, don t have instances 20, but are universally identical. f) The unity of the proposition arises from the way the verb actually unites its terms, which renders it more than the sum of its parts. Russell will deal further with adjectives in the next two Chapters (V VI) and further with verbs in Chapter VII. Roughly, classes are connected with adjectives and propositional functions with verbs. 17 This implies that we can form the difference of two terms. In what does this difference consist in the case of incommensurables? 18 If the difference of A from B was something like A B, then there seems no reason why there should be anything in common amongst the class of differences any more than there is amongst the class of things. 19 Look up the example of this on a second reading. 20 This is because Russell thinks of them as bare relations. What are the instances of adjectives? Different shades of blue, perhaps? Theotodman@lineone.net Page 7 of 7