W. E. Johnson, Logic: Part I (1921)
§ 1. A simple proposition 'S is P involves as subject a single uniquely determined substantive, and as predicate a single uncompounded adjective; a singular proposition must satisfy the first of these conditions, but its predicate may be simple or compound. Propositions of this nature give rise to the question how the reference in the subject can be uniquely determined. Speaking generally, singular names may be divided into two classes according as they contain or do not contain an explicit adjectival or relational component: to the first class belong such terms as 'the smallest planet,' 'the king of England who signed Magna Charta,' 'the cube root of 8'; to the second class 'Mercury,' 'John,' and '2'; and the former will, for convenience, be referred to as descriptive or significant, the latter as proper or non-significant.
CHAPTER V
THE PROPER NAME AND THE ARTICLESCompare now the proper name 'Poincare' with the descriptive name 'the President of France.' In order that this latter term may have unique application its component 'France' must have unique application: and hence here, as in almost every case, the uniqueness of a descriptive name is only secured through its reference to a proper name. On the other hand we shall find that many so-called proper names contain a descriptive factor: thus the term 'England' contains the termination 'land' which would be normally understood as bringing the term 'England ' within the general class expressed by the word 'land.' This, however, would not explicitly hold of the name 'France'; but, in point of fact, just as England might be taken to mean 'the land of the Angles,' so might France be taken to mean 'the land of the Franks.' In the same way the terms 'Mr Gladstone' and 'Lord Beaconsfield' have the partial significance expressed by the prefixes 'Mr' and 'Lord' respectively. As another example, the name 'Mont Blanc,' though etymologically equivalent to 'white mountain' and therefore apparently completely significant, must yet be called a proper name since its application is not to any white mountain, but to a specific one. We are here in the reverse position to that reached in discussing the term 'England'; for in 'England' we detected the concealed element of significance indicated by the termination 'land,' while in 'Mont Blanc' we have detected the concealed element of non-significance which prevents us from applying the name to any white mountain indiscriminately. Now, attributing to the term 'Mont Blanc' the maximum of significance that it can bear, and agreeing that there would be a species of incorrectness in using the term for any object which had not the characteristics 'white' and 'mountain,' yet this admitted significance is not the sufficient ground for applying the term as it is understood by those who use it with a common agreement as to its unique application. We may therefore say that any name which is commonly called a proper name has, so far as our analysis has proceeded, a residual element of non-significance over and above such significance as is naturally recognised in the verbal structure of the name.
§ 2. But if we allow of any name that it contains an element of non-significance, how is it possible that this name should be understood as applying to the same object when used at different times or by different persons or in different and varying connections? Where the name denotes a substantive, the possibility that it should mean the same substantive when used in different propositions, involves the possibility of substantival identification. A similar process, i.e. adjectival identification, is involved when the same adjective is used in different connections. Whether we ask how the substantive-name 'Snowdon,' for instance, can be understood to stand for a definite substantive, or how the adjective-name 'orange' can be understood to stand for a definite adjective, we are in fact confronted with precisely the same logical problem; and hence, if we regard the name 'Snowdon' as a proper substantive-name, we must regard 'orange' as a proper adjective-name. The analogy may be pressed a little further and applied to complex names; for just as an adjective name is exhibited as significant when it is expressed in the form of adjectives combined in certain relations, so a subtantive name is exhibited as significant when it is expressed in the form of substantives combined in certain relations. Note the analogy, for example, between the complex adjective-name 'the colour between red and yellow' and the complex substantive-name 'the highest mountain in Wales.' Here the former involves the proper adjective-names 'red' and 'yellow,' just as the latter involves the proper substantive-name 'Wales.' There is, then, in every explication of significance, a residual element in which we reach either a substantive-name or an adjective-name which can no longer be defined in this form of analysis. And further, the explication of the significance of this residual proper substantive or proper adjective-name involves the conception of identity: in the one case, substantival identity -- which is implied when we understand that the substantive denoted by the word 'Snowdon' in one proposition is identical with that denoted by 'Snowdon' in another proposition; and, in the other case, adjectival identity -- which is implied when we understand that the adjective denoted by 'orange' in one proposition is identical with the adjective denoted by 'orange' in another proposition. Our first approximate account of a proper name is then, that the intended application of the given name is to an object -- whether it be substantive or adjective -- which is identical with the object to which it may have been previously understood as applying in another proposition. For example, to explain what I mean by 'orange' I could say: 'You understand the word colour: and I shall mean by "orange" the colour which you can discern as characterising the object to which I am pointing. And when you identify the colour of any object with the colour of this, its colour is to be called "orange".' The possibility of such appeal presupposes that colour can be perceptually identified in different objects, apart from any other agreements or differences that the objects may manifest. In the same way the explication of a proper substantive-name requires a similar appeal, which assumes the possibility of identifying a concrete object when it may be presented or thought about in different contexts. Thus, if it was asked whom I meant when I talked of Mr Smith, I might say: 'I mean the man to whom you were introduced yesterday in my study.' The agreement, therefore, which can be maintained in the application of a proper name amongst those who continue to use it with mutual understanding, is secured by what in a quite general way we may call the method of introduction. An object is introduced, and in the introduction a name is given, and when further reference is intended to the same object, the name is repeated which was given in the act of introduction. In this way the nature of the residual element or undefinable factor in adjectives and relations as well as that in the case of proper names is further explained.
§ 3. It is worth pausing here to point out a confusion frequently made in discussing the nature of the proper name. The confusion is that between the cause which has led people to choose one name rather than another name for a given application, with the reason for applying the name -- once chosen -- to one object rather than to another object. This confusion again can be paralleled in ordinary adjectival names as well as in substantival names: thus, it is one thing to assign the etymological causes of the use of the name 'indigo' rather than some other name to denote a particular colour, and another thing to assign the reason for applying the name, when it has once come into common usage, to one of the colours rather than to some other: the reason for this latter is that the colour presented in a given instance is identical with that to which the name indigo was originally given. This is exactly parallel to the ground on which we should justify our applying the name 'Roger Tichborne' to the man presented in court, namely, the presumed identity of the man before us with the man to whom his godparents had given the name. Why they chose that name rather than some other name is a matter for historical enquiry. But, to repeat, the etymological or historical account of a name must not for a moment be confused with its significance, or with what, in the case of proper names (substantival or adjectival), takes the place of significance as the condition of mutual understanding.
§ 4. This discussion is closely bound up with the different ways in which the articles, indefinite and definite, are used. The indefinite article in its most general and completely indeterminate meaning is illustrated by such assertions as 'A man must have been in this room,' 'We need a sweep,' 'You ought to make a move with your bishop.' Now if we compare this use of the article with its meaning when it occurs at the beginning of a narrative as for instance: 'Once upon a time there was a boy who bought a beanstalk,' we note an important difference in its significance. In the first set of examples the full significance of the article is made explicit by substituting 'some or other': e.g. 'Some or other man must have been in this room'; in the case of a narrative, where the article prepares the way for future references to period, person or place, it means -- not 'some or other' -- but 'a certain.' Indeed our story might more logically have begun 'At a certain time a certain boy bought a beanstalk.' When the indefinite article is used in this way to introduce some period, person or place not otherwise indicated, it will henceforward be called the Introductory Indefinite, to distinguish it from the Alternative Indefinite.
Now suppose the narrative to continue: 'This boy was very lazy'; the phrase 'this boy' means 'the boy just mentioned,' the same boy as was introduced to us by means of the indefinite article. Here the article 'this,' or the analogous article 'the,' is used in what may be called its referential sense. The linguistic condition necessary to render such reference definite is that only one object of the class (whether person, period, or place) should have been immediately before mentioned. Other variations of the Referential Definite are such phrases as 'the former' and 'the latter,'which may be required to secure definite reference. The above analysis brings out the necessarily mutual association of the introductory use of the indefinite article with the referential use of the definite article. Again, instead of beginning the second sentence with the phrase 'this boy,' language permits us to use a pronoun: thus the word 'he,' in general, is sufficient to denote a specific individual understood by the verbal context; so that here the pronoun serves precisely the same logical function as the referential definite article 'the' or 'this.' A still more important further development of the referential 'the' comes up for consideration when, instead of depending upon immediacy of context -- as in the preceding cases of 'this' and 'he' -- we refer to an historical personage who has a wide circle of acquaintance as (e.g.) 'The well-known sceptical philosopher of the eighteenth century.' Here the phrase 'the well-known' functions as a referential definite, though there may have been no immediately previous mention of Hume, it being assumed that a certain philosopher will be unambiguously suggested to readers in general, in spite of the fact that there may have been more than one person answering to the description 'sceptical philosopher of the eighteenth century.' This extended use of the referential definite is quite interestingly illustrated in Greek, where a proper name is prefixed by the definite article 'ο'; a usage which appears very happily to bring out the precise function of the proper name, as referring back to an individual who was originally introduced in history or otherwise under that name. The same holds in English of geographical proper names, e.g. the Thames, the Hellespont, the Alps, the Isle of Wight, etc. Lastly, in a narrative, the juxtaposition of a proper name with the introductory indefinite supplies a substitute for the referential definite. Thus our story about the beanstalk which begins with the introductory indefinite 'a boy' may be continued either by using the phrase 'this boy' -- involving the referential article -- or by the pronoun 'he'; or thirdly by the proper name which prepares the way for repeated reference to the same boy: 'Once upon a time there was a boy named Jack who bought a beanstalk.' It will be noted therefore that the way in which the proper name occurs in a narrative where it secures continuity of reference, illustrates the same principle as its use in ordinary intercourse, where it ensures agreement amongst different persons as to its single definite application: in both cases, the understanding of the application of the name involves reference back to the act of introduction, when the name was originally imposed.
There is an important analogy between the singular descriptive name of the kind illustrated by 'the well-known sceptical philosopher of the eighteenth century' and the proper name, in that frequently it is only within a narrower or wider range of context that the proper name may be said to have a uniquely determined application. Tius, within a family, the name 'John' maybe understood to denote one brother of that name; whereas, in a certain period in English history, it will denote the king who signed Magna Charta. That uniqueness of reference to a particular context is similarly seen in such phrases as 'the table,' 'the garden,' 'the river,' which though applicable to different objects in different contexts are understood within a given circle or in a given situation to have a uniquely determined application. The article 'the' used in such cases may be called Indefinite Definite, to distinguish it from the most definite of all uses of the article, namely where the unique ipplication is understood without any limitation of context -- in cases, for example, like 'the sun,' 'the earth.'
We have thus divided articles (and what are logically equivalent to articles) into four classes:
- the Indefinite Indefinite, otherwise the Alternative Indefinite;
- the Definite Indefinite, otherwise the Instantial Indefinite, best expressed by the phrase 'a certain,' which includes the Introductory Indefinite;
- the Indefinite Definite, otherwise the Contextual Definite, which includes the Referential Definite; and
- the Definite Definite, for which the understood reference is independent of context.
§ 5. A special form of the contextual definite which is to be distinguished from the referential, is expressed by the term; 'this' and 'that' when used as demonstratives. Liteially, the demonstrative method is limited to the act of introducing an object within the scope of perception. But, when we point with the finger, for instance, to a particular person or mountain or star, our attempt to direct the attention of the hearer to the object intended may or may not succeed: if successful, it will be because there is no other conspicuous object belonging to the class indicated by the use of the general significant name (person, mountain, star, as the case may be) within the range of space to which we have directed attention. The condition for securing unambiguity is not that there should be only one object of the specified class within the range indicated, but that there should be only one such visible object; and here observe a parallel between the demonstrative definite, and the case illustrated by the example 'the well-known sceptical philosopher of the eighteenth century.'
§ 6. At this point in our discussion let us consider the special difficulty which attaches to the notion of a proper name. This problem presents a dilemma. If we maintain that the proper name is non-significant in some sense, then it would follow that any propositional phrase that might contain the proper name would be non-significant in the same sense. If, on the other hand, we attempt to assign some definite significance to the proper name, this will entail our substituting a uniquely descriptive name as equivalent in meaning to the proper name, in which case the distinction between the descriptive name and the proper name would vanish.
This problem raises a question relating to the wider problem of the definition of words or phrases. Taking the two words 'valour' and 'courage,' the brief formula 'valour means courage' is seen on reflection to be imperfectly expressed. Everybody would agree that what is intended here is that the two terms valour and courage have the same meaning; i.e. that the quality meant by the one term is the same as the quality meant by the other. Hence a more correct expression than 'valour means courage' would be 'the word valour means what is meant by the word courage.' Where a phrase instead of a single word is under consideration the same principle is involved. For example, 'p is a factor of q' means-what-is-meant-by 'q is divisible by p'; or again 'some benefactor of A' means-what-is-meant-by 'one or other person who has benefited A.' These illustrations bring out the distinction between (a) the relation which one word or phrase may bear to another word or phrase, and (b) the relation which a word or phrase may bear to what is called its 'meaning.'
Now the propositions which allow us to substitute one phrase for another may be called bi-verbal definitions1; and the relation that is to be affirmed as holding between two such phrases must be expressed in the complex form 'means what is meant by,' or even -- when we distinguish between the phrase which has not been understood and that which has been understood -- in the still more complicated form 'is to be understood to mean what has been understood to be meant by.' This last complication brings out the purpose that a definition has always to serve; namely the elucidation of a phrase assumed to require explanation in terms of a phrase presumed to be understood.
This formulation of the bi-verbal definition leads us to consider what, in contrast, we shall call the uni-verbal definition. When we speak of a phrase as being 'already understood,' it is equivalent to saying that the meaning of the phrase is known. The formula that 'phrase p means what is meant by phrase q,' in short, raises the question, What is it that phrase q means? Let us first consider the kind of entity that a phrase could mean. Phrases which would be grammatically or logically distinguished in regard to type or category would mean entities belonging to correspondingly different types or categories: thus one phrase would mean a certain proposition; another would mean a certain adjective, another a certain substantive, and so on. Thus 'courage' means a certain adjective or quality-of-conduct, 'horse' means a certain substantive or kind-of-animal. A phrase prefixed by an article such as a, the, some, every, any, requires special consideration. Thus, if we were to substitute for such phrase any phrase that means what is meant by the given phrase, the article or some equivalent would still remain. Thus 'the first novel of which Scott was the author' means what is meant by 'the romance that was written by Scott before any other of his romances.' In this bi-verbal substitution the word 'the' is retained. Now consider, in contrast to the proposition stating the equivalence in meaning of the above phrases, the proposition 'The first novel written by Scott was called Waver ley'; or, inasmuch as there is only one novel that is known bearing this name, we may put the statement in the form: 'The first novel written by Scott was the novel called Waverley.' Such a proposition is of nearly the same type as 'The author of Waverley was the author of Marmion.' In both of these propositions the relation of identity is asserted in regard to two uniquely descriptive terms. But neither of these propositions is verbal; in neither case could we substitute for the relation of identity the expression 'means what is meant by.' Hence we are not identifying the meaning of the two phrases: i.e. we are not identifying what is meant by one phrase with what is meant by the other. What then is it that we are identifying? In the language of Mill we should say we are identifying what is denoted -- and in the language of Frege what is indicated or (as we prefer to say) factually indicated -- by the one phrase with what is denoted or factually indicated by the other. Now, as our term suggests, an appeal to fact is required in order to understand what it is that is factually indicated in distinction from what is meant by a certain phrase. Hence, though a knowledge of the usage of language alone is sufficient to know what a phrase means, a knowledge of something more than mere linguistic usage is required to know what a phrase denotes or factually indicates, whenever we are dealing with a phrase that indicates something different from what it means. The word 'courage' or the phrase 'not flinching from danger' is of such a nature that there is no distinction between what it means and what it indicates or denotes; it is only phrases prefixed by an article or similar term for which the distinction between meaning and indication arises. Turn now to the peculiarities of the illustration given above: 'The first novel written by Scott was the novel called Waverley.' The interpretation of this statement is that the object indicated by the phrase that stands first is the same as that
indicated by the phrase 'the novel called Waverley' although the meanings of the two phrases differ. Take a parallel case: 'The colour of the object at which I am pointing is identical with the colour that is called red'; here again the identity of what is indicated by the two phrases does not carry with it identity in what is meant by the two phrases. In short, where we have an identification of what is indicated in spte of non-identity in what is meant, we recognise thajt the statement of identity is not merely verbal but factual.
In the above illustrations we have taken such names as Scott and Waverley to exemplify names universally recognised as proper; while the phrase 'the first novel written by Scott' -- or any phrase having the same meaning -- would be called descriptive in a sense primarily intended as antithetical to proper. Now one step was taken to bridge this antithesis when we used: the proper name in the extended phrase 'the novel called Waverley': i.e. the single name Waverley is a proper name and the compound phrase 'the novel called Waverley' is constructed in the form of a descriptive are thus leading up to the view that what is indicated by the descriptive phrase -- 'the novel called Waverley' -- is identical with what is meant by the proper name 'Waverley.' Thus, in interpreting the simple proposition 'Waverley was the first novel written by Scott,' which is recognised at once to be factual not verbal, we are identifying what is factually indicated by the subject and predicate terms respectively; and in the case of the proper name 'Waverley,' what it factually indicates is indistinguishable from what it means. Hence it seems legitimate or possible to define a proper name as a name which means the same as what it factually indicates.
§ 7. We may now introduce the technical term 'ostensive' which will suggest as its opposite the familiar term 'intensive.' A proper name may be said to be ostensively definable in contrast to those more ordinary terms which are said to be intensively definable. This ostensive definition will be only a special instance of a form of definition involving the complex relation 'means what is indicated by' -- a relation which is involved in any attempt to define a proper name by means of a descriptive name. The particular force of the notion of ostensive definition will now be explained, and it will be found to apply both to an adjectival and to a substantival name. The ordinary proper name applies to an object whose existence extends over some period of time and generally throughout some region of space. The appearance of such an object in perception (or rather of some spatially or temporally limited part of that object) provides the necessary condition for imposing a name in the act of indicating, presenting or introducing the object to which the name is to apply, and this it is that constitutes ostensive definition. In extending the notion of a proper name to certain adjectives our justification is that ultimately a simple adjective-name -- such as red -- cannot be defined analytically but only ostensively. Theoretically, we must suppose that any name, singular or general, proper or descriptive, substantival or adjectival, has originally been imposed on a particular occasion by a particular person or group of persons. In the case of ostensively defined names, the occasion on which definition is possible must be one on which the object is actually presented. When, however, the meaning or application of such a name has afterwards to be explained, or so-to-speak redefined, the only direct method is to secure for the enquirer another presentation of the object in question. Thus John Smith, having been presented to his family at birth -- which we may take to be the occasion on which the name was imposed -- must be presented again to the person ignorant of its application. Hence, in introducing a man under the name John Smith, we are using the same ostensive method as was required in the original definition, but such mention of the name does not, properly speaking, constitute definition. We are stating, in effect, the proposition -- which is not merely verbal -- that 'the person introduced is identical with the person upon whom the name was originally imposed.' This case of an ordinary substantival proper name is analogous to that of an adjectival name -- say cochineal -- which originally could only have been ostensively defined, and which must therefore be ostensively redefined for the person ignorant of its application, in the form 'the colour of this presented object is identical with that upon which the name cochineal was originally imposed -- a statement which again is not merely verbal. When a proper name is called arbitrary, this arbitrariness attaches only to the original act of imposition; but, when the application of the name is afterwards explained, such explanation is no longer arbitrary, since to be correct the real proposition that the substantive or adjective presented is identical with that upon which the name was originally imposed, must hold good, and this statement may be either true or false, apart from linguistic convention. Furthermore when ostensive definition is employed, it must be observed that we do not say that the proper name means what is meant by such a phrase as 'the object to which I am pointing' (which after all is only an instance of a descriptive phrase), but we say that the proper name means what is indicated 'by the descriptive phrase 'the object to which I am pointing.' For it is obvious in this case, as in the more general account of a descriptive phrase, that however we may further explicate the meaning of the phrase 'the object to which I am pointing,' the substituted phrase would not have the nature of a proper name but necessarily of a descriptive name.
When, then, finally we agree with the general position of the best logicians that the proper name (as Mill says) is non-connotative, this does not amount to saying that the proper name is non-significant or has no meaning; rather we find, negatively, that the proper name does not mean the same as anything that could be meant by a descriptive or connotative phrase; and positively, that it does precisely mean what could -- be indicated by some appropriate descriptive phrase. This exposition holds both for the names of objects which can be presented and thus ostensively defined; and also for the names of objects removed in time or place, for the definition of which a descriptive phrase (which is other than ostensive) must be employed.
Notes 1 It has been suggested that a more correct substitute for 'bi-verbal definition' would be 'translation.' But whichever terminology is employed, the distinction between the kind of definition called translation and some more ultimate definition remains.