12*. On Russell’s Theory of Descriptions

I shall argue

1. that Russell’s Theory of Descriptions, definite and indefinite, is correct in the sense that the analysis he offers of propositions containing denoting phrases in subject-positions is right and useful at least outside the foundations of mathematics;

2. that he is wrong in that conception of ‘logically proper names’ which demands the existence of a logically guaranteed bearer for every real proper name;

3. that he is wrong in his belief that propositions cannot change their truth-value.

I shall argue for these positions in the reverse order to that in which I have given them.

I

In The Principles of Mathematics Russell explains ‘Change is the difference, in respect of truth or falsehood, between a proposition concerning an entity and a time T and a proposition concerning an entity and another time T , provided that the two propositions differ only by the fact that T occurs in the one where T occurs in the other.’ It is clear what he means: if and only if, given a proposition ‘φ (a) at t’ and another ‘φ (a) at t ‘, one true and the other false, there is no other difference between them, then a change has taken place or is taking place or will take place. We ought to concede that certain differences between propositions would be irrelevant—e.g. that one was to be found (stated) at one place in a book and another at another; for these differences most often do not express anything and we may suppose that they do not here.

I do not unreservedly accept Russell’s account; it seems to suggest that there can only be change where there is a nameable individual which persists through the change, the change consisting in something’s holding of that individual at one time which does not hold at another time; and this seems doubtful. But let us accept it for the moment.

A time specification such as is needed for Russell’s explanation must give a stage in a process which is used as a clock; most usually it would give a stage in the nth period from some point of origin. The point of origin would be so many periods ago; thus all time specifications will depend in some way on ‘now’.

Disregarding this, however, let the clock we actually use be the ‘entity’ of which Russell speaks in his account of change. Let our clock be e.g. the sun, and the sentence ‘The sun is in the middle of the sky’ be a specification of time, like ‘It’s two o’clock’. If we consider the proposition ‘The sun is in the middle of the sky’ we must say that it is sometimes true and sometimes false. We could find another clock to give a time at which it was true and at which it was false, but certainly do not need to do so in order to state the change that takes place. Russell would say that ‘The sun is in the middle of the sky’, if it is a complete proposition, means ‘The sun is in the middle of the sky now’; and that this is a different proposition at each time it is said; or again, he would say that ‘now’ means ‘the time of this’, ‘this’ being used as a name of something different every time it is used; for its only constant feature is its relation to its user.

Now it is possible that someone may want to attack Russell, on the ground that ‘now’ and ‘this’ are not names. But the following formulation of Russell’s point might be accepted by such a critic: ‘the word “now” is used to refer to a different time every (relevantly) different time it is used’; and ‘the word “this” is constantly used to refer to different objects’.

This formulation is not to my mind importantly different from Russell’s. I should contend that in such statements the word ‘reference’ is being used in a way that wavers between an argumentative (and incorrect) application of its ordinary sense, and a technical sense in which it ought to be restricted to proper names. Russell’s formulation is more clear cut.

‘Refer’, like ‘mention’, in ordinary language is a thoroughly vague word. This can be seen from the following example. In a conversation it might be said ‘He turned very red’; and someone who was checking reports of the conversation might ask ‘Was any reference made to the colour of his face?’ and get the answer ‘Yes’, because of that remark.

Similarly, it might be asked ‘Was there any mention of the time at which he was in England?’ and answered ‘Yes, Mr. N. made some reference to that—I think he said something about its having been in the first week of July’.

On the strength of this vague use of ‘refer’ it might be said that a date could be used to refer to a time; and if we speak of a proper name as being used to refer to, say, a place or person, and also of a demonstrative pronoun as being used to refer to a person etc., then by an easy transition of thought, we may speak of ‘now’ as being used to refer to a time; for ‘now’ is rather to a date as ‘this’ is to a proper name or definite description of an object. But in ordinary usage it would not be said that a time had been referred to because someone had said ‘I think I had better be going now’.

I do not think the ordinary usage of ‘refer’ is of interest, except for the part it is apt to play in aiding the movement of thought I have just described.

What is of the greatest interest is a technical sense of ‘refer’ in which we may say that a proper name refers to its bearer. That is to say, the term ‘refer’ has been used for the relation between a proper name and its bearer. But the relation in question has been variously taken not to be restricted to ordinary proper names and their bearers. For Frege, a predicate—i.e. what is left of a sentence if you remove at least one proper name from it—also has reference: the reference of a predicate is a concept, not an object. He also held that a non-vacuous definite description referred to the object it described, and that whole sentences containing non-vacuous proper names and definite descriptions referred to the objects true and false. He held that definite descriptions and sentences of the kind described were proper names; so this part of his theory is not an extension of the notion of ‘reference’ beyond proper names but only of that of proper names beyond what are ordinarily so called; but he did not hold that predicates were proper names, so in this part of the theory there is an extension of the notion of reference itself. So far as I know, he does not discuss demonstratives, ‘now’, or personal pronouns. Russell holds that designating or naming is done by what he calls ‘real’ proper names and words for ego-centric particulars but not by definite descriptions or sentences or predicates; others, that ‘referring’ is done by means of all the candidates except predicates and sentences. Exactly what it is that is done when referring is done is also a disputed matter; as also, what does the referring—a word, or only a person using a word. I.e. is referring in the soul alone, or also in the grammar of sentences?

It seems fairly clear that proper names are at the centre of this topic; for there is a relation between proper names and their bearers, which is variously conceived by various philosophers and is also variously conceived to hold between other expressions and various kinds of thing. For Russell, it is not the relation between what are usually called proper names and their bearers, but that is a rather coarse, macroscopic indication of it. This is because the main feature of a proper name is that it refers to a single thing of some sort or other; but for Russell a thing like an individual man or city falls short of really being a single object.

The most common view is that the technical sense of ‘referring’ or ‘designating’ in which we are interested is one in which only individuals are referred to or designated. But ‘individual’ and ‘particular’ are rather problematic terms. Hence one wants to speak of ‘an individual person’ or ‘a particular place’ or ‘a single object’ or ‘a particular event’ (I am using Mr Strawson’s list) and so on, in order to explain what one is driving at. But don’t we need a specification of what sort of general term can come after the word ‘a single …’ or ‘a particular …’ or ‘an individual …’? A particular constellation, such as Orion, would seem to qualify; ‘a particular colour’ perhaps not— but why not?; and how about ‘a particular time’, e.g. ‘the eighth year of the French Revolution’? If ‘a particular time’ qualifies, then is ‘now’ just like ‘this’, a word used to ‘refer uniquely’? If so, then since it can hardly fail to have reference, it presents us with a real example of a ‘logically proper name’ in Russell’s sense. But perhaps a particular time is not something that expressions can be used to ‘refer to uniquely’; in that case we need an account of the restrictions on the kinds, particular ones of which can be made the objects of unique reference.

I want to argue that neither Russell, nor anyone—if there is anyone—who would reformulate Russell’s point by saying that different times are referred to by different uses of ‘now’, is right. The appearance that ‘now’ refers to a time is produced as follows: the question ‘When is “now”?’ has a good sense when asked in connection with an old letter, say, containing the sentence ‘Such and such is happening now’. We find the date when the letter was written in order to know when the things it describes happened if what it says is true. Hence, in a quite non-technical way, we can say that the letter, the sentences and the words in it, refer to or relate to a particular time; the nature of the ‘relating to’ is not indicated in such a remark. It is quite another thing to say that the word ‘now’ in the letter refers to a particular time in a sharp, technical sense of ‘refer’.

There are two possible views to this effect: according to both ‘now’ means ‘the time of this’; according to one ‘this’ is to be explained as a token reflexive, and according to the other it is to be considered as naming anything the speaker likes to make his object of attention.

The token reflexive substitutions for ‘now’ are not wrong, and yet the associated explanation of the word ‘now’ cannot be correct; its persuasiveness derives from the fact that vocal utterances of the kind brought forward are of very short duration; they last no longer than the time required to take them in. On the token reflexive view, an ancient inscription running ‘Say, O stranger, if you can, the date of my inscribing’ raises a similar question for the traveller who is looking at it to the question of someone who approaches him and says ‘What’s the time, please?’.

The other explanation—that ‘now’ means ‘the time of this’ and ‘this’ is to be considered as naming anything the speaker is attending to—is faulty because he may be thinking of something in the distant past or future. However, someone who held this view would probably deny that, say, Aristotle can be an object of attention for me; he would say that only such things as an image of Aristotle or a page of Aristotle can be so. Leaving the difficult problems involved in such a dispute, let us reformulate the position by saying that ‘now’ means ‘the time of this’ when ‘this’ is used to name some object of sense-perception. Even if it is an antique temple, still it has to be admitted that its time includes the present if I can see it now.

This consideration brings out how much nearer to the truth the token reflexive view of ‘now’ is than this one; indeed on this view we cannot understand the word ‘now’ at all except when we are saying or hearing it used in relation to the time at which we are saying or hearing it; or else we have to bring in token reflexiveness to explain our general understanding of it, or our understanding of it in an old letter.

On the token reflexive view, ‘What time is it now?’ means ‘What is the time at which these words are uttered?’; this question, however, is like the inscription’s challenge—but seems not to be, because of the short duration of the utterance, which is simultaneous with its being taken in; this enables the hearer to accept the present tense of ‘these words are uttered’ as true. But on the token-reflexive view the ‘are’ here is not really a tense: it is a purely logical word.

The hearer of a speech containing ‘as I utter these words’ could tell himself ‘he says he is uttering them—and so he is!’ But that is accidental; if I get a letter saying ‘Even as I write these words the children are starting another fight’, I can’t say to myself ‘She says she’s writing the words—and so she is’; and yet there is nothing misleading about the letter. The sentence in the letter has indeed just the same meaning as if it had run ‘The children are now starting a fight’; and that is what is correct about the token reflexive view. But since ‘now’ could be replaced by ‘the time of this’, ‘this’ being understood token reflexively wherever it occurs in the relevant sense, I need the additional information that the time of the token’s production is now if I am to understand a sentence containing ‘now’ to relate to now. The sentence itself cannot include this information in what it says. The procedures adopted by the traveller to answer the question posed by the inscription and to tell the enquirer the time are wholly different; for the inscription he tries to find a date, he does not look up the date for the time being in his calendar; in reply to the enquirer he looks at his watch straight away.

We must say ‘now’ always means the same, but a sentence containing the word ‘now’ does not say that what it says to be the case is the case now, unless it is uttered now. Sentences containing ‘now’ are uttered at various times; and we need to know when ‘now’ is or was being said in order to determine the truth of what is or was being said. And one answer to this question—which would hardly ever be asked when it was the answer—may be ‘it is being said now’. (It might be the answer when the question was asked about a piece of ticker tape.) Only if it is said now does the truth of a sentence p whose tense is significantly present imply that p. This pronouncement relates to things said now. It can be generalised thus: at any time, this can be truly said: ‘Only if it is said now, does the truth of a sentence p whose tense is significantly present imply that p.’

This shows the sense in which propositions cannot change their truth-value. If the expression ‘The truth-value of a significantly tensed proposition’ means: ‘The truth-value of a proposition at the time of its being stated, when that time is relevant to the question as to the truth-speaking of the sayer’, then that truth-value cannot change; and so also, when the specification of a date is included in a proposition, what it describes ceases to be significantly tensed; if the sentence is still significantly tensed, as in ‘The third world war will break out on October 1st, 1962’, it divides up into the dated, tenseless proposition ‘Outbreak of third world was, October 1st, 1962’ and ‘October 1st, 1962, is yet to come’.

Reichenbach† says that quoted ‘token reflexives’ are not used ‘token reflexively’, which is correct. But unless hearing and understanding are considered to involve either a token reflexive use of what is heard or understood, or a quotation of a token reflexive, as the case may be, the point does not enable us to succeed, by an analysis of ‘now’ as token reflexive, in getting rid of propositions whose truth-value changes. Those who are convinced that the analysis does succeed in doing this are possibly influenced by a feeling of what it is to mean ‘now’. One can be tempted to say to oneself ‘Said now, ‘now’ means now!’ The temptation arises partly from the idea that we can see what a word means by considering what we mean when we attentively go through the performance of meaning it; and partly from a supposition that it must be something meant by the isolated word ‘now’ that constitutes the meaning of a significantly tensed sentence whose time is the present. For it is quite correct to say ‘Only if it is said now, does the truth of a significantly present-tensed sentence p imply that p’.

If something was the case at a certain time, then at that time anyone who said of the thing in question ‘It is the case now’ would have been speaking truly. This is one reason for the pre-eminent role of the present tense. It means nothing to suppose that something was the case or is going to be the case, and to exclude ‘It is the case now’ from having been or from going to be the truth. There might seem to be an analogue to this for the past and future tenses: if something is the case, then ‘It will be the case’ was true to say, and ‘It was the case’ will be true to say. But here we can ask ‘When?’, to which a reply ‘Then!’ would raise the question ‘When is then?’. It makes no sense to ask ‘When is now?’ except (a) to ask the time or date it now is, or (b) using ‘now’ in quotes in connection, say, with an old letter in which ‘now’ occurs.

Propositions about changeable things are variable in truth-value, because in order to explain the sense in which they are invariable in truth-value, either you must give an incorrect account of ‘now’ and the present tense, or you must introduce the idea of ‘the truth value of a proposition at a time’; but that is to admit variability of truth-value. The invariability of the truth-value of a proposition is the trivial fact that a dated proposition cannot vary in truth-value. When I say that the truth-value of a proposition at the time of its being stated (supposing that to be relevant) cannot change, I only say that if it has a certain truth-value at the time of its being stated, it cannot come to have had a different one at that time; I do not say that it cannot cease to have the truth-value that it has at that time. On the contrary, if the time at which it is stated has any relevance to its truth-value, then it can come to have a different one. The universal denial of the variability of the truth-value of propositions is tantamount to a denial of change.

My account of ‘now’ may seem very slightly different—if at all— from Reichenbach’s: it is not clear that a single sentence I have written conflicts with what he says. It comes out that there is a difference of view involved if we consider a principle which he puts forward elsewhere in his book: ‘Two propositions have the same meaning if they obtain the same verification, as true or false, for all possible observations’. This is intended as an explanation of identity of meaning for propositions. I am saying that two propositions can be identical in every way, and hence one be merely the repetition of the other, and yet get different verifications as true and false.

Now since I should not call two identical sentences[1] therefore identical propositions, I have to give some account of propositional identity. Two identical sentences may not be identical propositions because, for example, identical names of different people might occur in them. This would make a difference of meaning, and hence, I should say, a difference of proposition. The view of ‘now’, and of tenses generally, that I have been attacking, is one in which two identical sentences containing tenses or ‘now’ have different meanings when said at different times; the difference being of the same kind as that between the differences of meaning between identical sentences containing a name ‘John’ when ‘John’ names a different man in each. That is to say, the difference is supposed to be a difference of reference in a sharp, technical, and very important sense of reference.

I do not have or desire any general account of the identity of propositions where the sentences to be considered are different. But where the sentences are the same, I should say that the propositions were the same so long as any proper name referred to the same bearers and the other words had the same meanings. Context may affect meaning—it is indeed context that shows which the bearer of a name is—but not just difference of time.

II

I now come to my second thesis: that a real proper name does not have to have a logically guaranteed bearer.

Russell’s idea of ‘logical proper names’ has a long history behind it; it will help us to understand it if we go back to Locke and Mill. Their views are very tangled, but of very great historical importance. Taking Mill first, we recall his doctrine that proper names have no connotation, only denotation, while predicates have both. Mill explains that the bearer of a proper name is its denotation; the denotation of a predicate is the list of things that it applies to. He cannot have it both ways; if the bearer is the denotation of a proper name, then the list of things that it applies to is not the denotation of a predicate; for these are the things that the predicate is true of, and a proper name is not anything that is true of its bearer; that, indeed, is a great part of the point of insisting that proper names have no connotation. And indeed in another place Mill inconsistently says that the denotation of a predicate is what it predicates of the things it is applied to. Now if proper names have only denotation, that is, only bearers, then it is natural to argue that when they have no bearers they must be without significance.

To this we should add the idea that a predicate, if it has application, would seem to demand the existence of things it is true of; for ‘having application’ = ‘being true of’, what Mill misleadingly called the denotation of the predicate. These things, that the predicate is true of, must in the end be signified by words which are not themselves in turn predicates, for if they are signified by words that are still predicates, these predicates in turn must have both connotation and ‘denotation’; and we shall only reach what predicates are true of when we give words that have only denotation. Why, one may ask, can one not name the things that a predicate is true of by means of a predicate? as e.g. in ‘Men are mortal’ and ‘I met a man’. There are several reasons against making this the end of the matter; in the first place, it is natural and surely correct to think that such propositions are true only in virtue of the holding of propositions of the form ‘ a ‘, i.e. in virtue of something’s holding of individuals who are named and not described; in the second place, these examples at any rate are examples of generality, which is best explained by using quantification; we need some account of the difference between ‘a man’ in ‘I met a man’ and ‘Each soldier killed a man’. It is a constant kind of difference, not a peculiar idiom; it is best set forth by using quantification; but the account we give using quantification will contain the function ‘x is a man’, and this is a pattern for the formation of propositions containing proper names—never predicates—where we put ‘x’.

I spoke also of a comparison between Russell and Locke. This comes out if we consider the following aspect of Russell’s ideas. He holds that

there are words which are only significant because there is something that they mean, and if there were not this something, they would be empty noises, not words. There must be such words if language is to have any relation to fact. The necessity for such words is made obvious by the process of ostensive definition. How do we know what is meant by such words as ‘red’ and ‘blue’? We cannot know what such words mean unless we have seen red and seen blue. If there were no red and no blue in our experience we might perhaps invent some elaborate description which we could substitute for the word ‘red’ as for the word ‘blue’. Any description which a blind man could understand would have to be in terms of words expressing experiences which he had not. Unless fundamental words in the individual’s vocabulary had this kind of direct relation to fact, language in general could have no such relation.

This is not like Mill’s terminology of connotation and denotation, because (a) Mill ascribes denotation to words that have connotation, but we can cut that out, having found fault with it, and simply say having connotation is the same thing as being a predicate, and (b) for Mill, ‘red’ has connotation, for it is a predicate. But the disagreement is then only about what ‘red’ is, not about the way words have meaning. For Russell says that he does not regard ‘red’ as a predicate for purposes of philosophical analysis. He prefers a language in which ‘red’ is a subject, i.e. a proper name. The predicates attaching to this subject would be descriptions of positions in space and time.

We can understand this better, I think, if we remember the things that Locke said about the names of simple ideas: that they ‘intimate some real existence, from which was derived their original pattern’ and that they ‘signify always the real as well as nominal essence of their species’. Any ‘essence’ according to Locke is an idea; real essence is the being of anything, whereby it is what it is; nominal essence would be given by the list of properties which give anything a right to a name; but since simple ideas have no definition, the list would only have one item, and that the name of the simple idea itself; the real and the nominal essence are one, and that one is given by the real existence which is the original pattern.

Individuals, such as John Locke, have according to Locke no nominal essence. If we compare Locke’s doctrine with Mill’s, we may at first sight be tempted to think that the names of individuals according to Locke are the very same as Mill’s ‘words which have only denotation and no connotation’. That is to take ‘connotation’ as partly involving the notion of ‘content’. But this would be wrong; for if we look at Mill again, we find him asserting that the abstract forms ‘whiteness’, ‘virtue’, ‘length’ are also words which have denotation and no connotation.

But it is absurd to speak of any name at all without a nominal essence; if a name can be without a nominal essence, there can be no right or wrong about its repeated use. Hence we can see why for Russell Locke’s simple ideas should assume the position of designata of real proper names. Russell might indeed give ‘this’ as an example of a name which does not have to have a nominal essence—and what goes with this is that for ‘this’ it does hold that it cannot be a misnomer and so not a correct ‘nomer’ either. But even if we accepted Russell’s view of ‘this’, a proposition running ‘This this this here now’ would seem profoundly unsatisfactory; we want some names with some content; and such words as ‘red’ would seem to satisfy our demand.

Although Russell’s ideas are more clear-cut than Locke’s or Mill’s, it is clear that there is a certain family resemblance among them all.

Locke’s thesis that proper names have no nominal essence attached to them is, as we have seen, not identical with Mill’s view that they have only denotation, since for Mill ‘having only denotation’ is not the same thing as ‘having no content’ (or nominal essence); but so far as Mill’s thesis about denotation concerns proper names it is fairly close to Locke’s; and attempts to make the same point are still to be found in many authors, who either repeat Mill’s formula, or say that in some sense proper names have no meaning. We are likely to be told, for example, that nothing about a proper name tells you what object it is a name of—as if anything about the word ‘blue’ told you what it meant! The following passage from Basson and O’Connor‡ is fairly typical:

If we require some further insight into the difference between a proper name and a description, we may consider the following example. The word ‘Palumbo’ is a proper name. But if you knew you were going to see Palumbo tomorrow, you would not know at all what to expect. It might be a man, a horse, a dog, a mountain, a river, a city, or numberless other things. The name ‘Palumbo’ does not give you the smallest clue as to the nature of the thing named. In other words it is not descriptive.

Compare with this:

The word ‘closh’ is a descriptive term. If you knew you were going to see something closh tomorrow, you would of course know exactly what to expect. The word ‘closh’ gives you all the clues you need as to the nature of the thing so called. In other words, it is descriptive.

Locke, explaining himself to the Bishop of Worcester, who had futilely protested against him ‘Peter, James and John are all true and real men’ said:

I beseech your lordship to consider whether ... by naming them Peter, James and John ... your lordship does not first suppose them men ... But if I should ask your lordship whether Wewena, Chuckery and Cousheda were true and real men or no, your lordship would not be able to tell me until I have pointed out to your lordship the individuals called by those names, your lordship, by examining whether they had in them those sensible qualities which your lordship has combined into that complex idea to which you give the specific name ‘man’, determined ... them to be of the species which you call ‘man’.§

In this passage Locke shows that he supposes it to be understandable what individuals are called Wewena, Chuckery and Cousheda without its yet being determined whether these are proper names of men or what. To point and say ‘That is Wewena—and I mean that “Wewena” is the proper name of that’ should prompt the question ‘That what is Wewena?’ Or, what comes to the same thing: ‘And how am I to go on using the name Wewena?’ Locke writes as if an intelligible reply would be ‘so long as it is the same individual’. And hence the question which often concerns philosophers: ‘What is an individual? What is a particular?’

That a word is a proper name is some information as to its meaning: it means that it has a very special kind of use; this is parallel to the information that a word is the name of a colour. The further enquiry ‘What kind of thing is it a proper name of?’ should elicit an answer such as ‘a city’, ‘a river’, ‘a man’, ‘a trumpet’, which we may reasonably say gives the full meaning, or connotation of the word. Thus Mill would have been nearer the truth if he had said that proper names have both denotation and connotation, but predicates only connotation. A small boy gave a moving spot of light that appeared in his room the proper name ‘Tommy Noddy’. Locke writes as if one could know what individual Tommy Noddy was without knowing that this was the proper name of a spot of light. To see the mistake in this, imagine that someone who had grasped that ‘Tommy Noddy’ was a proper name, asked to have Tommy Noddy pointed out to him. The child points to Tommy Noddy at a time when the spot of light is on a human being.

That is to say, with every proper name there is associated a predicate x, such that when a proper name is assigned to an x, the proper name is rightly used for the future to name the same x. The information ‘Tommy Noddy is the name of a spot of light’ thus gives the sense (meaning, connotation) of the proper name; and the difference which authors have striven to express between proper and common names is this: if you know the sense of a common name and are presented with that to which it applies you can apply it straight away; whereas you can know the sense of a proper name and be confronted with the individual whose name it is, and not know it is his name: you have to be introduced.

But what do I mean ‘to name the same x’? The explanation I have just given is very inadequate. To see this, consider that with ‘square’ there is associated a predicate ‘shape’, such that the word ‘square’ is rightly used always to name the same shape. But that does not turn ‘square’ into a proper name.

In order to explain what a proper name is, I therefore first introduce the notion of an ‘identifying predicate’: I shall henceforth use this expression in a technical sense. To be an ‘identifying’ predicate, a predicate φ must satisfy two conditions.

(1) The instruction ‘Count the φs’ must be a straightforwardly intelligible one: i.e. one which in ordinary circumstances does not stand in need of elucidation to someone familiar with the application of the predicate φ. To give a few specimens, the following predicates tend to satisfy this condition:

Human being.

Stroke of a gong.

Day.

Chess (token) piece.

Chess (type) piece.

Word (as spoken of by a printer or editor).

Prime number.

For most usually, the instruction to count the humans in a certain place, or the strokes of a gong on a certain occasion, or the days until such and such happens, etc., is straightforwardly intelligible. One would count chess (type) pieces that there were in a certain place by counting chess pieces, but not counting any of a type one had already counted. On the other hand the following predicates do not satisfy the condition:

Human.

Gold.

Red.

Dust.

Bigger than.

For ‘Count the xs such that x is human’, ‘… red’, ‘… dust’, or ‘… gold’, or ‘… that there is a y such that x is bigger than y’ is an instruction that would normally require elucidation if one was to do anything in obedience to it. Circumstances can be imagined in which the stage is so set, that e.g. ‘Count how many red things there are here’ has an obvious application—on a page of a picture book showing a number of toys some of which are red all over. That is because in this case there is an obvious predicate—‘pictured toys’—satisfying the condition, such that only things of which this predicate is true are red. No negative of a predicate yields an intelligible instruction ‘Count the not-φs’, except under conditions similar to those holding for ‘red’.

One can count the φs when one knows what counts as one, what as two φs. Thus in ordinary circumstances the instruction to count human beings is straightforward; it belongs to the technique of use of the word ‘human being’ to yield instances of the technique of applied counting. (I say ‘applied’ as opposed to counting ‘in the abstract’; counting in the abstract is when nothing is counted but the number series is gone over.) ‘Count what is human’, on the other hand is in ordinary circumstances an instruction that would need ad hoc elucidation. Is a human being and human skin one or two human things, and are a human footprint and a human cry to be counted one, two ...?

This, then, which I will call ‘countability’ for short, is the first requirement which a predicate must satisfy to be an identifying predicate. Note that it is not necessary, in order for a predicate φ to satisfy this requirement, that it should be impossible to find borderline and problematic cases, or to imagine circumstances in which we should not know how to count φs. (It is impossible that this should be impossible—except conceivably in mathematics: the ‘countability’ of prime numbers, say, is not something in connection with which I find it possible to conceive of borderline or problematic cases—but that may just be lack of knowledge and imaginative power on my part.)

Countables (i.e. φs, or xs such that φx where φ is a countable predicate) seem to correspond to the possible substituends for individual variables in symbolic logic. I will call the individual signs for the substituends quasi-names. But for the identifying predicates associated with proper names and so for a quasi-name to be a proper name there is a further requirement. Let φ be a countable predicate. Then in some cases the expression ‘the same φ’ is so used that we can speak of the same φ as now ψ, now not ψ. E.g. we can speak of the same day as now sunny and now not sunny, the same proposition as now true, now false; and so on. Now in these cases the identity of the φ that is and then is not ψ is formal. If a day is first sunny and then not, it is one part of the day that is sunny and another that is not, and the day is sunny and then not sunny because the parts constitute the day. An identifying predicate is a countable predicate whose application is such that the identity in question is not formal. E.g. ‘man’, ‘spot of light’, ‘hurricane’, ‘city’.

For Russell the identity associated with such predicates is formal; for a φ of this sort is part of space-time that falls, so to speak, within a certain outline within space-time and a φ will be first ψ and then not ψ because a part within this whole part of space-time that constitutes the φ in question is ψ, and another part not ψ. Suppose we have a proposition ψa where a is a quasi-name whose countable predicate is φ, then if we have ψa and then not ψa, on Russell’s view ψa and not ψa will not be complete propositions but propositional functions, just as ‘x is bald’ is a propositional function and not a proposition. The proposition is only completely specified by putting in the time at which ψa and not ψa: with the time specification in, the proposition will, if true, give a description of a cross-section of the four dimensional worm that is, say, a man. Thus the possibility of such a view stands or falls with the correctness of his account of the invariability of the truth-values of propositions, and hence with the correctness of his account of ‘now’.

A proper name is a word associated in the way I have described with an identifying predicate. If, as often happens, the same word has two associations of the kind in question with the same identifying predicate—e.g. if two men have the same name—there is no mistake; for the assignation is arbitrary, and the only sort of mistake occurring in connection with a proper name is misidentification: i.e. one makes a mistake in calling something John Smith if this implicitly goes with a mistake in the application of ‘the same man’.

Now it is possible to see in what sense a proper name logically demands the existence of a bearer. Suppose a sentence contains what appears to have the role of a proper name in it. This is partly a matter of grammar—i.e. that the word is in a place where a proper name might be, and partly a matter of words sounding like proper names. Consider the sentence ‘Enough is as good as a feast’, which someone ignorant of English might construe like ‘Bernhardt is as good as a feast’. Now, if we have such a sentence, then it is true if what its predicate means holds of a φ named by that name in the sentence, φ being an identifying predicate. Now the condition for a word to name a φ is that it shall have been assigned to a φ and is used in predications about the same φ. If there has not been any such assignment, there can be no predications about the same φ as the word was assigned to—for it never was assigned; there can however be a pretence of there having been such an assignment, i.e. a proceeding as if there had been such an assignment, as far as concerns the purpose of constructing narrative sentences; or again a mistaken conviction that such an assignment has been made. The first case is that of fictitious proper names, the second that of mistakes like those of the astronomers who thought there was an extra planet, which they called Vulcan, between Mercury and the sun. In such cases no real predications are made, for if predications appear to be made in connection with an ostensible proper name, the subject of predication is the thing named; hence if there is no such thing, since the name never received an assignment, we have no predications and so nothing either true or false, but pretense-predications or would-be predications. How is it, then, that such sentences could serve the purpose of explaining the notions of ‘subject’, ‘proper name’ and ‘predicate’? They can serve it as counterfeit money or toy money could be used in explaining the notions of buying and selling. On the other hand, if the fiction runs ‘Once there was a man called John, and John did so-and-so and such-and-such’, then the sentences of the story have a truth-value— they are most likely false, but since they are not supposed to be true, the question as to their truth does not engage our attention.

Now we readily become confused by the following facts: (a) any fiction could be cast into the form: once there was a man (fairy, god, etc) and this man did so and so and the same man did such and such ...; (b) the fact that people utter sentences under a mistaken conviction that an assignment of a proper name in it has been made, could be explained by saying e.g. ‘They think that there is a planet (which they call ‘Vulcan’) which is between Mercury and the sun, and that this planet was observed on such-and-such an occasion and the same planet was observed on such-and-such another occasion’; (c) an historical narrative might begin ‘In the third century B.C. there was a king, of such-and-such a state, called so-and-so, who …’ When we look at these three point (a), (b), (c), we can see how natural it is to suppose that the existence propositions (true or false) that we can associate with every ordinary ostensible proper name as it occurs in ostensible predications, stand to these proper names as similar existence propositions stand to descriptions (definite and indefinite in the Russellian theory). If, then, the form (φa) in some sense stands behind every proposition of the form (∃x) (φx), we can see why it should seem that the names ‘Vulcan’ (the non-existent planet), ‘Churchill’ (the former prime minister), ‘Themistocles’ (the Athenian statesman), ‘Pickwick’ (the fictitious character), could none of them be the real proper names, for they must all receive the same treatment, and propositions in which they occur can be represented as true and false propositions beginning ‘There is (or was) a …’. So the form (φa) which is fundamental to propositions of the form (∃x) (φx) is not truly represented by examples like Churchill, precisely because these have to be explained away as existential. In particular, any distinction between legendary and historical proper names is hard to make; for it is a disputed matter, in some cases, whether something is legend or history.

I fear the correct reply to this may seem to muddy the clear waters of logic; but that may be an illusion, and at any rate I have no doubt it is correct. We should distinguish between a formal and a real assignment of a proper name. The assignment is formal when it is simply an assignment to a bound variable in the narrative. King Arthur is a character of uncertain historicity: thus ‘There was a man—and only one—who was King in Britain such that the stories of the Arthurian cycle derive from or are embroideries on stories about him’ may be true, but it is not certain; and the assignment of the proper name is a formal assignment to the variable in ‘an x such that x was a man who was King etc’. (In ordinary language the bound variable is represented by ‘who’, ‘which’ and the personal pronouns when they have e.g. ‘someone’, ‘anything’, ‘no one’ as antecedents.) But when such narratives are (a) certain, (b) secondary to the use of the proper name itself, as in ‘There was a man called Churchill who was Prime Minister in England for the greater part of the Second World War’, then the assignment of the proper name is real and not formal and is prior to the existential narrative. An historical assignment can be real and not formal when we have the proper name by tradition from those who used it of its bearer.

Where the assignment, necessary for an ostensible proper name to be a real one, is real, then the proposition containing that proper name (or any sub-clause containing that proper name) is a genuine predication and is true or false if the predication makes sense for φs, where φ is the identifying predicate associated with the proper name. Where the assignment is pretended or clearly only formal, then there is no genuine predication (except within the scope of the existential quantifier) and no proposition either true or false. When the assignment is neither pretended nor real we can say that we do not know if a genuine predication has been made; and that an analysis of the proposition will show the relevant formal assignment.

Now when we turn to descriptions, so long as they do not contain any proper names lacking real assignment, the position is completely different. This is because propositions containing such descriptions set forth the situation they describe without any ambiguity beyond any that may be involved in the grammatical predicate. If it is under debate whether Themistocles was bald, we know of what man it is disputed whether he was bald. If it is asked ‘Was King Arthur (really) bald?’ it is reasonable to reply that we don’t yet know about whom the question is being asked. Analysis of the origin of the stories might reveal that we could not adhere to any distinct conception of what we meant, in this context, by a story’s being derived from or being an embroidery on stories about a particular man. It is, I suggest, a mark of (not certainly fictitious) proper names lacking real assignment, that the existential propositions, which must be true if the ostensible predications about the bearers of those ostensible names are to be true or false, have this kind of indeterminate character. And yet these existential propositions are all we can offer by way of an explanation of the supposed application of the ostensible proper name.

Now with descriptions it is quite otherwise: ‘The only son of the King of Saudi Arabia is bald’ is perfectly determinate in meaning, just as determinate as ‘Themistocles was bald at the end of his life’. But unlike such a proposition as ‘Themistocles is bald’, it has an external as well as an internal negation: ‘It is not the case that the only son of the King of Saudi Arabia is bald’ and ‘The only son of the King of Saudi Arabia is not bald’. The latter proposition shares some truth conditions with ‘The only son of the King of Saudi Arabia is bald’ and hence is not its contradictory.

What Russell’s analysis does for us is to remove the first impression that here, as in the case of a genuine proper name, we have a predication of a subject which is named, designated, referred to— whatever expression you prefer, it expresses the important relation of proper name to bearer. This relation is important in this way: if a genuine proper name is removed from a sentence (or sub-clause), what is left can be considered as a predicate expressing something affirmatively or negatively predicated of the bearer of the name. That is to say, we have here a distinctive and important form of proposition. Not the only form, nor yet necessarily the one fundamental form; it is not necessarily the case that all others (e.g. ‘2 × 2 = 4’; ‘The probability of p in the light of q is such-and-such’) are to be explained in terms of it; but certainly an important form. And the theory of descriptions shows how propositions containing definite descriptions in subject-positions (argument places) are not of this form.

 

* From an undated typescript with the author’s handwritten insertions and corrections. It appears to date from the 1950s. The explicit argument of the paper applies to definite descriptions only; to indefinite ones by implication.

† The reference presumably is to Hans Reichenbach, Elements of Symbolic Logic (New York: Free Press, 1947). [Ed.]

‡ A H Basson and D J O’Connor, Introduction to Symbolic Logic (London: University Tutorial Press, 1957).

§ John Locke, An Essay concerning Human Understanding, Bk.III, c.3, Note to section 11.

1 i.e. two propositional signs which are identical from the printer’s point of view. This is a rough indication of something that can and need be only roughly indicated. Handwriting, different fonts, etc., do not count against this identity.