Studies in the Philosophy of Wittgenstein

Hidé Ishiguro

PEOPLE have often contrasted the picture theory of meaning of the Tractatus with the use theory of meaning of the Philosophical Investigations. Many have also argued that the picture theory of meaning is based on the concept of ‘naming’, since in the picture theory language catches on to reality through names which stand for objects. This has led people to talk as if the use theory of meaning was an expression of Wittgenstein’s later rejection of his Tractatus theory. I believe that talk of such contrast is highly misleading, and that it arises out of a misunderstanding of the Tractatus view of what it is for a name to refer to (bedeuten) an object. This misunderstanding is also responsible for the false and widely held belief that Wittgenstein’s theory of meaning and language renders conceptual change impossible and disables social criticism. It seems to me to be a truism that a word or a symbol cannot have the rôle of referring to a fixed object without having a fixed use. How could there be a philosophical doctrine of expressions and the objects to which they referred which was not at the same time a theory about the use of those expressions? No interesting philosophical question about the meaning of such expressions can be based on a contrast between ‘naming’ and ‘use’. The interesting question, I think, is whether the meaning of a name can be secured independently of its use in propositions by some method which links it to an object, as many, including Russell, have thought, or whether the identity of the object referred to is only settled by the use of the name in a set of propositions. If the latter holds, then the problem of the object a name denotes is the problem of the use of the name.

Contrary to widespread belief,¹ Wittgenstein rejected the former view throughout his writings and tried to work out various versions of the second. So far as this question is concerned, the main difference between the Tractatus and the Philosophical Investigations is not the presence or absence of the ‘use’ concept but that the Tractatus concept of ‘use’ is much less comprehensive than in the Investigations. That is to say, in the Tractatus Wittgenstein is interested in the problem of the rôle expressions play in a language, which he considers only in relation to the truth-stating purpose of language. He is not concerned with the various other things people may do by using such expressions—such as beseeching, promising, and so on.

The aim of this paper is twofold. The first is to examine and assess the view that it is only by determining the use of a name that one can determine its reference and to do so through an investigation of the reasons given in the Tractatus for this thesis. The second is to propose a new way of understanding the Tractatus theory of names, objects, and the relationship of referring which holds between them. This proposal follows from the first investigation. I will try to show that the Tractatus view of the logical independence of elementary propositions makes it impossible for ‘objects’ to have the criteria of identity we normally ascribe to particulars. The concept of a simple object in the Tractatus is that of an instantiation of an irreducible predicate where the question of individuation of different instantiations of the same predicate cannot arise. The ‘objects’ of the Tractatus are not particular entities in any normal sense, but entities invoked to fit into a semantic theory, so, when Wittgenstein later rejected the independence of elementary propositions, he was able to get rid of this peculiar notion of objects as well without altering his theory of names or reference in any fundamental manner.

What then is Wittgenstein’s theory of names? The key to the Tractatus view of the relation of objects and Names ² is expressed in the controversial 3.3, which says ‘Only propositions have sense (Sinn); only in the nexus of the proposition does a Name have reference (Bedeutung).’ It is well known that ‘Name’ is a technical word in the Tractatus. Not only can Names not be analysed further by any definitions, but the objects to which they refer are simple and cannot be given by a definite description. Like Russell and Quine, the Wittgenstein of the Tractatus thought that most of what we call proper names can be analysed further and can be treated logically as definite descriptions (3.24). Real Names cannot occur explicitly in ordinary, non-elementary propositions.³ What 3.3 expresses is a general thesis about expressions and the objects they designate, which plainly derives from Frege’s Foundations of Arithmetic, which does not advance such views about names. We will see that Wittgenstein’s notion of simple objects made him take this view even more seriously. One cannot look for the references of Names independently of their use in propositions.

It was in the context of his attempt in the Foundations of Arithmetic to explain his claim that numbers were objects rather than concepts, and that number words had objective reference (Bedeutung) and referred to objects, that Frege wrote ‘Only in a proposition have words really a reference (Bedeutung)…. It is enough if the proposition taken as a whole has a sense (Sinn); it is this that confers on its parts also their content’ (§ 60, repeated in § 62). One cannot refute the claim that numerals have objective reference just by saying that we cannot imagine numbers. Numbers are obviously not spatial objects. One cannot imagine, nor for that matter point to them—something which is specially evident if one thinks of the number zero or a million. Not only can we not picture or point to such numbers, we cannot even picture a million objects of whatever kind as distinct from a million and one of them, nor point to zero things. This might lead people to conclude that number words do not refer to anything. What Frege says in reply to such objections holds not only for number words but for all words. There are material objects we cannot point to or imagine, e.g. an elementary particle. Frege’s claim is that reference cannot be determined independently of how we settle and understand the sense of a proposition in which the word occurs. To understand this is nothing more nor less than to know the truth-conditions of these propositions. This is a view which Wittgenstein accepted completely. Throughout his later works, Wittgenstein discusses the temptation to look in the wrong direction for a mark which would tell us why a word refers to a certain object. We look for mental processes that go on as we utter the words rather than the rule governing the use of the words that we can come to grasp. And similarly in the Tractatus Wittgenstein is anxious to stress that we cannot see how the name refers to an object except by understanding the rôle it plays in propositions. Although the Foundations of Arithmetic was written eight years before Frege distinguished the sense (Sinn) and reference (Bedeutung) of expressions,⁴ and the word ‘Bedeutung’ is used here in a very general way, it seems nevertheless that Frege is using ‘Bedeutung’ in these passages to mean what he later meant by reference; in the sense in which the expressions ‘’ and ‘2’ have the same ‘Bedeutung’ and refer to the same number even if the manner in which each is presented is different. Throughout the Tractatus Wittgenstein makes a distinction between Sinn and Bedeutung in a manner roughly corresponding to Frege’s later works, and it seems clear that when Wittgenstein repeated this maxim of Frege’s Foundations of Arithmetic in Tractatus 3.3 and 3.314 he took ‘Bedeutung’ in the sense of ‘reference’.⁵ He uses ‘bedeuten’ and ‘vertreten’ (stand for) and ‘nennen’ (name) interchangeably in the Tractatus (3.221) and distinguishes them from ‘bezeichnen’ (to signify) which is used much more widely and loosely to cover all relations between expressions or signs and what they mean. For example, a sign ‘bezeichnet’ via the signs which occur in its definition (3.261). A variable ‘beizeichnet’ the formal concept (4.127) and propositions held to be true are propositions which are ‘betzeichnet’ with the assertion sign in Frege’s logic (4.442). In none of these cases do the expressions ‘bedeuten’ or refer. Later in the Philosophical Investigations, § 49, where Wittgenstein again refers to Frege’s passage, this time explicidy, he makes it clear that he takes ‘bedeuten’ in the sense of ‘name’ as distinct from ‘describe’.

It is a fundamental difference between Wittgenstein’s and Russell’s position that Wittgenstein holds that no expression, not even a name which cannot be further analysed, can be said to have reference out of the context of propositions. It is not a part of the Tractatus theory that if a symbol is logically simple and cannot be further analysed then it can be secured a reference independendy of and prior to its occurrence in a proposition, which for Wittgenstein is a ‘propositional sign in its projective relation to the world’ (3.12). Unlike Frege, Wittgenstein does not even think in terms of saturated and unsaturated sense, or complete and incomplete parts of thought. The only basic distinction he makes is between the way in which defined signs signify and undefined signs signify. In general the Tractatus talks of sense only with regard to propositions. The sense of a proposition is the thought which it expresses. All that sense amounts to for constituent expressions is their use. That is to say, they play a part in making up propositions which have sense. We therefore “cannot give a sign the wrong sense’,⁶ since the sense a sign has is nothing more than the rôle it has been assigned in language. We know the use of such signs, and as 4.03 says, must use old expressions to communicate a new sense. Names and predicates can be said to have the rôle of referring when they occur in propositions. Names refer to objects, and predicates (whether monadic or relational) refer to what holds of the objects. Strictly speaking one can do without predicate expressions in any subject predicate proposition, since one can always express the predicates that are true of objects by the ordered concatenation or pattern of the Names of the objects.⁷ A name then has a reference only in the sense that we know how to use the name in sentences to refer to an object about which we can say true or false things. Thus, although it makes sense to talk of the object which a name refers to without using the name in any particular proposition, this is so only because we know in general the kind of propositions in which the name can occur. We do this by thinking of the class of propositions obtained by treating the name as a constant and treating the other expressions which make up the proposition as variables (3.312).

Is this view of Wittgenstein a defensible one, or is it ‘clearly wrong’ as e.g. Professor Geach argues in his Reference and Generality?⁸ I think we will gain insight into the point Wittgenstein is making by comparing it with some of Russell’s views. It is perfectly true that one can use a name by itself, e.g. in the vocative to hail a person as Geach writes, but the fact that we can use names in such ways seems to me to depend on names obtaining the references they do have by their use in propositions, as Frege and Wittgenstein claimed.

Russell’s notion of ‘meaning’ seems in his earlier works to carry many Meinongian or Bradleian undertones. In his article ‘On Denoting’,⁹ Russell assumes that an expression used as a grammatical subject in the verbal expression of a proposition does not have any meaning by itself unless its meaning, which he equates with the object denoted, figures intact in a proper analysis of the proposition. Thus for Russell not only do words like ‘everything’, ‘nothing’ and ‘something’ have no independent meaning; phrases such as ‘a man’ or even ‘the king of France’ have no meaning. These are called incomplete symbols.¹⁰ For Russell, to say of a word that it has meaning by itself is tantamount to saying that the meaning of the word is an object such that if we express a proposition using the word, the proposition will be about the object. ‘John Smith is fat’ would express a proposition about John Smith if the meaning of the phrase ‘John Smith’ is the man John Smith.

Thus, although Russell in this article refers to Frege’s ‘Sinn’ as meaning, and ‘Bedeutung’ as denotation, Russell’s own notion of the meaning of an expression is quite different from Frege’s notion of ‘Sinn’. If anything it is closer to Frege’s ‘Bedeutung’. The very phrases which for Frege have ‘Sinn’ but no denotation like ‘the least convergent series’ or ‘the king of France’, have in Russell’s view no meaning on their own. But in what sense could the meaning of a word ever be the object referred to? At a pinch one might say that the meaning of ‘Karl Marx’ is that it is the name of the man Karl Marx, but hardly that the meaning is the man. The Tractatus is right when it says that I can only speak about objects. I cannot express (aussprechen) them (3.221).

In the Tractatus words or signs have their use, i.e. their fixed rôle in logical syntax, and when used in propositions many of them refer to objects, or properties that are true of objects, but they do not have a sense or meaning which they express in addition to this. Signs which refer to objects (as distinct from properties or relations which are true of objects) are called names.¹¹ Quine says that to be is to be a value of a variable. Similarly the Tractatus says that to be an object (thing, entity, etc.) is to be a value of a variable name (4.1272). To be an object, or a function, or a fact, is not a classification of things in the sense in which to be solid or to be coloured or to be moving is. It is a purely logical notion, as it was for Frege, which the Tractatus calls a ‘formal concept’. We cannot properly ask in isolation whether John is an object or whether a colour is an object, or relations are objects. Nor is the question whether ‘objects’ are physical things or mental objects appropriate. If we forget the fact that only the absolutely simple are to be called objects in the strict sense, and allow ourselves the relative or ‘shifting’ use of the word ‘object’, as Wittgenstein does in 4.123, the proposition ‘that table is red’ is about the object table, the proposition ‘John is the father of Paul’ is about the objects John and Paul, and the proposition ‘that colour is darker than this’ is about the objects colours, and ‘being a father is an asymmetric relation’ is about the object ‘being a father’.

But then what is the logical criterion of an expression being a name? How does one establish that an expression, say ‘a’, is a name of an object? Not by someone pointing to something and uttering ‘a’. One would not know whether ‘a’ is being used to describe, to name, to count. Even if one could somehow make it clear that ‘a’ is being used as a name rather than a predicate or as a sentence, one would not have settled what was being named by pointing. Is it the place? The material thing? The surface? An aspect? Or what is it? Russell wrote as if names get attached to their bearers by the speaker’s intention. According to him, at any given moment there are certain things of which a man is ‘aware’, which are ‘before his mind’. ‘If I describe these objects, I may of course describe them wrongly: hence I cannot with certainty communicate to another what are the things of which I am aware. But if I speak to myself, and denote them by what may be called “proper names” rather than by descriptive words, I cannot be in error. So long as the names which I use really are names at the moment, i.e. are naming things to me, so long the things must be objects of which I am aware, since otherwise the words would be meaningless sounds, not names of things.’ (‘On the Nature of Acquaintance’, 1914.) Such a private act would not for Wittgenstein make a sound into a name of an object although a man can privately commit himself to a consecutive use of an expression, and thereby give an object a name for his own purpose. The aspect or the surface of the thing which is before my mind has shape, colours, as well, and it is only the consecutive use of the name that will establish which of all those things I did name. I cannot therefore ‘communicate to another what are the things of which I am aware’ by uttering the sounds. The Tractatus view is that if one uses names in propositions and one understands the syntactical rôle they play, then the proposition would not have a definite sense unless the names obtained a definite reference. This means that if people take ‘f(a)’, ‘g(a,b)’ as stating a definite state of affairs,¹² then they do see that ‘a’ ‘b’ are used to refer to the objects which the proposition is about. (‘g(a,b)’ will express a state of affairs involving two not three objects.)¹³ In the case of ordinary proper names we identify the bearer by a definite description or indicate the kind of thing we are talking about and use a demonstrative to point out which one of that kind we mean. But if the objects cannot be identified by a definite description, nor be picked out by pointing, since they are ‘independent of what is the case’, how can one see that the word or sign refers to a fixed object?

This is done according to Tractatus 3.263 by ‘elucidations’. An elucidation does not give a definite description of the object denoted by a Name—as this is claimed to be impossible—nor is it a definition of the Name. Elucidations are propositions in which the Names are used rather than mentioned. I take it that in making an elucidation we are to assert the propositions containing the Name. When we catch on and understand what is asserted, we have grasped what the proposition is about and we know what the object is which is referred to by the Name. For example, in Peano’s axioms, O, number and successor are treated as primitive signs—i.e. they are not defined in terms of other terms. In Peano’s axioms these signs are used, so that one can come to see the mutual relationship of the references of these signs. When we understand what Peano’s axioms say, we have already identified, O, the successor of O, the successor of the successor of O, and so on. Miss Anscombe, who has so correctly dissociated the Tractatus from the empiricist epistemologies and reductionisms with which it has often been wrongly identified, seems to be mistaken when she writes that although ‘Wittgenstein pretended that epistem-ology had nothing to do with the foundations of logic and the theory of meaning, with which he was concerned, the passage about the “elucidation” of names, where he says that one must be “acquainted” with their objects, gives him the lie’.¹⁴ 3.263 is no more committed to any particular theory of epistemology than any other part of the Tractatus. 3.263 says ‘The references (Bedeutungen) of primitive signs can be accounted for by means of elucidations. Elucidations are propositions that contain the primitive signs. So these propositions will only be able to be understood if the references of the signs are already known (bekannt).’

Wittgenstein is not saying in the last sentence that we must already be acquainted with what the primitive sign refers to by itself, and that it is only because of this that we understand propositions containing these signs. Such an interpretation will make the claims made by these three sentences completely circular and unilluminating. Surely Wittgenstein is here claiming that when one comes to understand these elucidations, one is already identifying what the primitive signs which occur in them refer to. Identifying the reference of the primitive signs, and understanding the elucidations are not two separate epistemological steps because the identity of the references of names and the sense of the elucidations are not logically separable. This identification need not be done in the presence of the object. Even when the object is a perceptible one it need not be present. The object may not even be a perceptible one at all. This is obviously the case with ordinary names. We can grasp the identity of the person named ‘Pablo Picasso’ without ever having perceived him. We can learn what ‘π’ refers to and know that it is an unterminating decimal although we cannot perceive numbers, and although any decimal expansion we have seen expressing π would have been of finite length. Why should the situation change with names of simple objects? Russell believed that if we understand what a word ‘means’, we should either be able to describe it or be acquainted with it (in an empirical sense). We can only learn the meaning of a logically proper name by being acquainted with the object and linking the name to the object in the presence of it. But there is no reason to believe that Wittgenstein, who did not require that Names have reference or ‘meaning’ independently of this use in propositions, shared this view. Just as what is described by a complex symbol can be all kinds of things, so the reference of Names may be all sorts of objects. The identification of an object need not have anything to do with having a sensory experience of the object or being able to point to the object. The word ‘bekannt’ used by Wittgenstein need not mean ‘acquainted’ in the sense in which something is given to the senses. I think that it means ‘acquainted’ in the sense in which we may be said to be acquainted with a foreign language (as in ‘die Sprache ist ihm bekannt’) or with literary works. When Russell wrote in Mysticism and Logic, page 219, that ‘Every proposition which we can understand must be composed wholly of constituents with which we are acquainted’ he did mean ‘acquainted’ in a special empiricist sense. Whereas the Tractatus 3.263 is saying that one cannot understand a proposition without understanding what the proposition is about. Thus although we need not have come across the objects referred to by the Names used in a proposition before, if we do come to understand the sense of the proposition then at that moment we already know what the Names refer to.

If the elucidations contradict each other, and no consistent use of the Names which occur in them has been specified, then the Names have not been successfully given the rôle of referring to an object. Thus 3.328 says ‘if a sign is without use, it is without reference’. Again if two Names have exactly the same use—and one can always be substituted for the other, then, the two signs refer to the same object. 5.47321 explains why this is. ‘Occam’s maxim is, of course, not an arbitrary rule, nor one that is justified by its success in practice; its point is that unnecessary units in a sign-language do not refer to anything. Signs that serve one purpose are logically equivalent, and signs that serve none have, logically speaking, no reference.’

In the Tractatus one does not decide that one can substitute one expression for another expression because they refer to the same object. If two names are used in such a way that one can be substituted for the other, then the names do refer to the same object. Thus 4.241 says ‘ “a = b” means that the sign “b” can be substituted for the sign “a” and 4.242 adds that expressions of the form ‘a = b’ are mere devices to show the rôle of the signs and state nothing about the reference of the signs ‘a’ and ‘b’ (Strictly speaking, the equation does tell you that the object referred to has these two names.) An equation (or any so-called identity statement) is, according to the Tractatus, a way of showing something about two sets of signs or expressions, i.e. that they are used to refer to the same object. It is not an assertion about the object referred to by the expressions. ‘It is impossible to assert the identity of the reference of two expressions. For in order to assert anything about their reference, I must know what their reference is without knowing whether the expressions refer to the same thing or not.’¹⁵ In other words, one can show that expressions refer to the same object, but one cannot informatively say of the reference of expressions that they are one and the same. This is because ‘to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all’.¹⁶

The Tractatus view is, it seems, very close to what the often misunderstood Leibnizian principle ‘eadem sunt quorum unum alteri potest substitui salva veritate’ asserts. Leibniz was laying down the criterion of identity of terms—(which are concepts expressed by words or phrases, and not the objects which fall under the concepts,¹⁷ whereas for the early Russell terms were the objects). Terms (not things) t₁ and t₂ are to be considered identical if t₁ can be interchanged for t₂ in every proposition in which it occurs without affecting the truth-value of the proposition. That is to say, two expressions are to be treated as expressing the same concept if one can be replaced by the other salva veritate. Similarly in the Tractatus it is not that we know that two words name the same object and then conclude that they are allowed to be interchanged. Rather, if we treat all the propositions where one expression is substituted for the other as having the same truth-value as the original proposition, then we are using the two expressions as having the same reference. It goes without saying that equations containing the expressions are not to be treated as one of these propositions, since, according to Wittgenstein, they are not proper propositions at all.

It might be thought that in order to decide that ‘a’ and ‘b’ have the same truth-value, I have either already to know that a and b are one and the same object, or else know that ‘a’ and ‘b’ have the same sense or express the same concept in some independent way—perhaps by definition (a common concern of Leibniz and of Frege in his Begriffsschrift). If the former is true, then substitutivity does not provide any criterion of identity of reference, and if the latter is true, then, as Frege writes in his Grundlagen, § 67, ‘all identities would then amount simply to this, that whatever is given to us in the same way is to be reckoned as the same … a principle so obvious and so sterile as not to be worth stating’. Whereas, as Frege goes on to say, identity claims are not sterile precisely in that we are able to recognize something as the same again even though it is given in a different way.

For the Tractatus the second alternative is ruled out because a Name is a simple symbol which is not defined via other signs. The sign itself is completely conventional and displays no logical structure. But why does not the first alternative hold? It is more difficult and more important to see why it does not hold and why the objection as a whole falls down.

In order to do this let us forget about simple objects for a moment, and examine what it is in ordinary contexts to know that a and b are the same object. It often happens that two people are using expressions believing that they are referring to the same thing or person and then suddenly realize that as a matter of fact they were talking about different things. For example A is talking about the point a meaning the tiny dot—or tiny black spot on the paper, and B is using ‘the point a’ to mean the geometrical position of the spot, which itself has no colour. Asked to point to the object they are referring to, they both point to the same area of the paper before them. Asked to fix their minds on the object they are thinking about, they would both fix their attention on the particular locus on the paper in which, as a matter of fact, the black spot is. But they come to realize that they are talking about different things when one person claims that a is black, for example, and the other person disagrees, because he is talking about something which cannot have any colour.

When such disagreement arises, how do they settle the question whether they are disagreeing about what is true of one and the same object or whether they are talking about different objects? And how do they decide whether they are talking about different kinds of objects, or about different particulars of the same kind? This is not a clear-cut question. But it seems that there must be some set of propositions about any object whose truth has to be agreed by anyone who is talking about an object of that kind, or at least a set of coherent attitudes or reactions to the object which are shared by anyone referring to it, which might be expressed by others as a belief in the truth of a certain set of propositions. For example, if ‘m’ is used to refer to a natural number, a person has to know how to go on counting and how to manipulate numbers in certain ways. He must in some way have a criterion of re-identifying the same number when he encounters it again and know how numbers differ from other kinds of objects even if he cannot formulate verbally the claim that m is either O or a successor of another number. If ‘a’ is used as a name of a geometrical point, the person must be able to work with points in all sorts of ways without being taken in about the physical features of the dot which shows the point; even if the person does not know Euclid’s first definition. Similarly with any empirical object. If ‘a’ is used as a name of an individual cell, the person would need to have grasped a certain network of theories which enables him to trace or reidentify cells through their changes.

I suspect that the ‘elucidations’ of the Tractatus are a set of propositions of this kind. The elucidations make us see what the object is by showing its internal properties.¹⁸ By making us grasp the kind of object which is in question they make us see in what sort of state of affairs the object could occur. What kind of propositions the elucidations are depends on the nature of the particular object in question. Whatever kind of propositions elucidations are, if it is only by grasping the truth of the elucidations that we understand what objects we are talking about, then it cannot be the case that we have to know that ‘a’ and ‘b’ refer to the same object before we can decide of any ‘a’ and ‘b’ that they have the same truth-value. The objection raised against the Tractatus view that expressions have the same reference if we treat them as having the same use collapses. That is why, if we take the Tractatus view that Names cannot be further analysed seriously, then as Wittgenstein says, an identity claim cannot be about the objects which Names stand for, but is a way of showing how Names are to be used.

In the case of ordinary names, we cannot identify the reference merely by grasping what kind of object it is. We will have to know that the object is that particular rather than another one of a given kind. I will try to show later that in the case of the simple objects of the Tractatus the question how one can distinguish an object of one kind from another object of the same kind cannot be properly raised. To summarize what we have seen up to now about the relation of the use of names and the identity of their reference: (i) We settle the identity of the object referred to by a name by coming to understand the sense, i.e. the truth-conditions of the proposition in which the names occur. (ii) Two names refer to the same object if the names are mutually substitutable in all propositions in which they occur without affecting the truth-value of the propositions. (iii) In order to be able to do this and understand that the truth-conditions of propositions containing name ‘a’ or ‘b’, we have already to agree about the truth (not just the truth-conditions) of a certain sufficiency of propositions in which ‘a’ and ‘b’ occur. Thus the identity of the object referred to by a name cannot be settled prior to or independently of the sense of the propositions in which they are used, and agreement about the truth of some of these propositions.

I will now examine some of the consequences of this Tractatus view of meaning. The Tractatus view entails that it is the use of the Name which gives you the identity of the object rather than vice versa. We cannot give a name a meaning and use by linking it to an object unless the object is already identified by the use of other names or definite descriptions. If the object is already identified as the bearer of another name, the problem of the name and object is still there unsolved. If the object can be identified by a description we can learn the reference and use of a name by correlating it to the object picked out by the definite description, as indeed we normally do. The Tractatus mistakenly assumes that in such cases we are correlating a name with a definite description rather than with the object which falls under the description—and therefore refuses to consider the correlated symbol as a name in a logical sense. As Wittgenstein was to realize later, even if a complex could only be given by its description,¹⁹ it does not of course follow that one cannot refer to the complex by a name. The Tractatus theory of names is basically correct, however, in so far as it is a refutation of views which assume that a name is like a piece of label which we tag on to an object which we can already identify. A label serves a purpose because we usually write names—which already have a use—on the label. The labelling by itself does not establish the use of the label. If a label is pasted on a bottle, one does not even know whether the label is correlated with the owner of the bottle, the contents of the bottle, the bottle itself, or a particular property, e.g. poisonous, of the contents. Russell seems to have assumed that logically proper names were like token labels since he talks as if by uttering ‘this’ in the presence of ‘what one is acquainted with at the moment’, or ‘what one sees at a given moment’, you give the word ‘this’ a meaning and turn it into a name. The word ‘this’, at the moment, he claims stands for an actual object of sense and is therefore a logically proper name.²⁰

But what kind of a name is ‘this’? In the Tractatus catching onto the use of a Name is grasping the identity of the reference of the Name. When we establish the use of a Name we establish the reference of all token signs of a given type when the signs are used in propositions. As Wittgenstein wrote in Notes on Logic, ‘names are not things but classes’. Each token sign of ‘this’ or ‘A’ is a different token sign or thing from another ‘this’ or ‘A’, but the use or sense is attached to the whole class of signs or expressions of the same type. Thus ‘A’ is the same sign as ‘A’,²¹ and likewise ‘this’ is the same Name (if it is a Name at all) as ‘this’. If the meaning of ‘this’ changes for Russell on every occasion of its use, then as he also believes that the meaning of a name is a particular, every token ‘this’ ought to be a different name, not the same ambiguous proper name as Russell claims. Names would not then be a class of similar word tokens with an identical use as they are for the Tractatus. The same argument applies to Russell’s notion of ordinary proper names. Russell thought that each person can attach a different definite description to the same ordinary proper name at different times. We may then ask him why should the name be considered the same one if various tokens of it are used with diverse meanings. On the other hand if we try to defend Russell’s stated position and claim that every logically proper name is an ambiguous proper name and claim that ‘this’ is always one and the same name which somehow gets a different meaning every time it is used, then we have to assume that the word already has some general meaning which tells us why a different particular object is meant by the word on each occasion of its use. This general meaning would be something like ‘the object the speaker is pointing to’ or ‘the object in front of me’. (Russell was to argue this later in his discussion of ‘egocentric particular’.) This again would make the word ‘this’ quite different from any Tractatus Name since the word ‘this’ would then have to be replaceable by these descriptions. It could not then be a primitive sign.²²

In the Notebooks, Wittgenstein wrote ‘What seems to be given us a priori is the concept: this—Identical with the concept of the object.’²³ And indeed if one does not take objects as necessarily and absolutely simple, but as things which we treat as simples by referring to them and saying this about them (as Wittgenstein did here), then indeed if we are in a position to refer to an object by a name or definite description we can always refer to it by using the expression ‘this’. For every entity that we can individuate can be referred to as ‘this’ or ‘that’, regardless of whether the object is present or absent, or given or not given to the senses. Once we have a way of identifying the number 2, for example, we can refer to it and say ‘this is smaller than 3’. If we can pick out a particular shape from other shapes we can say things about it like ‘This is asymmetrical’. It does not follow, however, that the word ‘this’ is a name. No more than it follows from the claim ‘to be an object is to be a value of a name variable’ that the variables of quantification are names. The first consequence then of the Tractatus view of Names is that a Name is not like an individual tag or a paper label. A Name is a class of similar token expressions, each of which is used in propositions to refer to the same object. It is not like a pronoun or like a Russellian logically proper name. It is at least more like an ordinary proper name than it is like any pronoun.

The second consequence I want to discuss of the Tractatus view of Names is a feature which distinguishes them from normal proper names; that Names refer to simples and that complexes cannot be named but only described. This is based on a false assimilation in the Tractatus of the relation of propositions and the facts they express and the relation between an expression and a complex object which it signifies.

As I have already said, there is no reason why we cannot name a complex object which we can also identify by a description. Nor need the name be a mere abbreviation of the description. This wrong view comes, I think, from a combination of a correct insight Wittgenstein had about the impossibility of naming facts with his general talk about ‘complexes’, which failed to distinguish between facts and complex objects which we can specify extensionally and which are ‘things’. There are facts that are true of complex objects, but the object, however complex it may be, is not a fact. I will begin by defending the view that not only facts but states of affairs cannot be named. Although facts (Tatsachen) are what the world consists of (1.1), their identity is too intimately dependent on language or thoughts expressed by some projective method for them to be treated extensionally. A proposition, whether true or false, describes an atomic state of affairs (Sachver-halt), and if the proposition is true and the atomic state of affairs obtains we identify a fact. Suppose two cubes a and B are in front of me. If the following propositions: ‘a is bigger than b’, ‘a is to the right of b’, ‘a is of a darker red than b’, ‘there are two cubes’, ‘there are 12 square surfaces’, ‘there are 16 vertices’, are all true, then they all express different facts. None of these propositions is logically equivalent to any of the others, and thus according to the Tractatus they do not have the same sense. The facts described by the propositions cannot be said to be identical simply because they concern one and the same arrangement of two material objects. There are as many elements in the fact described as there are referred to in the proposition, i.e. as there are articulated by the proposition. And if we follow the Tractatus view the properties or relations which are ascribed to these elements must, I believe, be considered intensionally: a point I will discuss later on. Thus although one can raise the question whether a fact expressed by one proposition is the same or different from that expressed by another (by a discussion of the logical equivalence relationship etc.), one cannot say of a verbally unidentified fact, f₁, unexpressed by any projectional method, whether it has n elements, or whether it is the same as fact f₂, because as yet we have not settled the identity of the ‘it’ that we are talking about. Pointing, or naming, or even naming all the elements of the fact we have in mind, will not identify the fact. There may be an indefinite number of facts involving the same elements. Thus as 5.5423 says, if we have a figure on the page which can be seen in two ways as a cube we are seeing two different facts. In this case we are looking at the same drawing, and we have distinguished the same number of lines but we can see two different facts represented, depending on how we supply the rules of projection. It is because of their referentially opaque nature that states of affairs can be described but not named (3.144). If I use names or simple signs to talk about states of affairs—as when I use letters like p or q to mean ‘a is to the right of b’ or ‘a is bigger than b’, then ‘p’ or ‘q’ are abbreviations of the sentences, and not names of the states of affairs. Similarly, if I decide to call the fact that Rome is to the north of Naples ‘Ivan’, ‘Ivan’ will be, as it were, the code name of the proposition ‘Rome is to the north of Naples’, since it is only via the proposition (expressed verbally, or by some sign or diagram, with its rule of representation) that I can specify the fact. As Wittgenstein says, propositions can describe states of affairs because they are articulate. We understand what the proposition describes by understanding the constituents (4.024). And by constituents, Wittgenstein means (unlike the early Russell) the words, or the signs, or the pictorial elements which make up the propositional sign. That is why he also claims that a proposition is a function of the expressions contained in it (3.318). This is what the picture theory of meaning comes to.

The Wittgenstein of the Tractatus (like Russell) is, however, wrong to talk about all complex objects in the same way as he does about facts. For although the identity of a fact cannot be settled except by settling the identity of the proposition which describes it, the identity of complex objects such as General de Gaulle does not depend on our articulating any one particular description. It is of course true, as we have seen, that the question of identity of objects cannot be raised unless we see what kinds of propositions about them make sense and we cannot do this unless we agree about the truth of some propositions. But, as has been correctly argued by many recent writers on this subject, there is no one individuating description which has to be equated to the names or presupposed by all who refer to General de Gaulle or Istanbul. Thus, even if, Russell says, what appears to be a proper name of a complex object could be replaced by a definite description of the form ‘(x) x’ salva veritate, it is not the case that the complex object can be identified only by this particular definite description. One need not analyse it into any particular existential proposition, and therefore one need not understand the constituents (which, in the case of Wittgenstein, are the constituent expressions or signs) of any particular proposition. Therefore 3.24 is wrong when it says ‘A proposition about a complex stands in an internal relation to a proposition about a constituent of the complex’. Even if we were to call an object which can be given by some complex description ‘a complex’ it does not follow that all of the descriptions which identify it stand in an internal relation to the complex. Thus it does not follow either—so long as analysis of propositions involves replacing the proper names of complex objects by definite descriptions—that ‘A proposition has one and only one complete analysis’ as 3.25 says. For, if many of the definite descriptions which pick up one and the same complex object such as General de Gaulle do not even have a semantic or logical relationship to each other, there is no reason to think that, if we replace ordinary proper names by different definite descriptions, the end stage of the complete analysis would necessarily be the same. This would be so only if one assumes, as Leibniz did for example, that an ordinary proper name of a (complex) object is an abbreviation of the sum of all the predicates which are true of the object. This means that if ‘a sign that has a definition signifies via the signs that serve to define it’ (3.261), then an ordinary proper name cannot be treated as a sign which has a definition. A name need not be taken as a function of the constituent expressions of a particular description and, consequently, a proposition containing ordinary names need not be taken as a function of these constituent expressions. It would then not be true in general that ‘the sense of a truth-function of p is a function of the sense of p’ as 5.2341 says. Wittgenstein criticizes Frege for calling a proposition a composite name (3.143); Wittgenstein makes the opposite mistake of treating names of complex objects as propositions.

And here I come to the third and most important consequence, which is that the notions of ‘Bedeutung’ (reference) and ‘bedeuten’ (refer) are intensional ones in the Tractatus and, therefore, that the simple objects whose existence was posited were not so much a kind of metaphysical entity conjured up to support a logical theory as something whose existence adds no extra content to the logical theory. A point I will argue now. It has often been claimed that according to the Tractatus the meaning of a Name is its bearer, since 3.203 says that a Name refers to an object and that the object is its reference. And since the Tractatus says that an elementary proposition is a concatenation of Names, it has been claimed that Tractatus offers an extensional basis of semantics. I do not think that this claim is quite right. Later in the Philosophical Investigations Wittgenstein criticized the view which confuses the reference (Bedeutung) of a name with its bearer. The reference of the name ‘Nothung’ is the sword Nothung. If the sword is broken the bearer of the name ‘Nothung’ no longer exists. If the bearer of a name and the reference of a name are identical, the name should no longer have a reference either. But the sentence ‘Nothung has a sharp blade’ has sense, and one would want to say that in the proposition ‘Nothung’ has a reference. As if to avoid the difficulty, the Tractatus claimed that ordinary names such as ‘Nothung’ could not be names in the strict logical sense. I think this shows not that Wittgenstein wrongly identified the notions of bearer and reference in the Tractatus but rather that although he was not articulate about this, he had already realized that talk about references of names is not like talk about the bearers of ordinary names. ‘Reference’ is a semantic category with its peculiar logic. The bearer of the name ‘Socrates’ no longer exists, but the name has reference. So long as the name plays the rôle of identifying the man that once existed, it will always have reference. Just as references of names are permanent in our language, so according to Wittgenstein objects are unalterable and persistent (bestehend) (2.0271). Just as we use the same noun in affirming or denying or questioning, so objects persist independently of what is the case (2.024). These features of the objects, combined with their logical simplicity, in turn imbue Names which refer to them with very peculiar features.

Wittgenstein’s belief that Names must be possible if propositions are to have definite sense ²⁴ is based on two logical theories which he holds in the Tractatus. One is the view mentioned earlier, which I think is basically right, that propositions about objects, that is to say, propositions in which one ascribes certain properties to objects or says that objects stand in a certain relation to one another, which one might express as ‘fx’, ‘(x.y)’ can in principle be expressed without predicate expressions or relational expressions. As Professor Copi and Miss Anscombe have said, one can express them by a certain pattern or arrangement of the names of the objects. Thus ‘(x.y)’ could be expressed and ‘fa’ could be expressed (where ‘a’ is written upside down). That is to say, in any subject-predicate proposition which we can write as function of the subject names it is essential to have constituents which stand for the subjects but it is not necessary to have a function sign. What particular function of the names it is can be indicated by a specific concatenation of the names of the objects, which is not to be treated as a list of names.²⁵ So although in normal logical notation we do actually use function signs or relational expressions such as ‘f’, ‘’ or ‘R’, they are not essential in order to express what they do express.²⁶ The second theory is that so long as there are defined signs then there must be undefined signs. If not we will have an infinite regress and the propositions which we form by using signs which have meaning via definitions will not have a definite sense. As we can express propositions which have definite sense—i.e. definite truth-conditions, these two theories lead Wittgenstein to say that it must be possible that there should be irreducible singular terms—i.e. Names. It is because of this that Wittgenstein claims that all propositions are truth-functions of elementary propositions (5). Not only propositions in which truth-functional connectives occur, and which have surface syntactical complexity, but all propositions are derivable from elementary propositions by logical operations.

The requirement of Names in the Tractatus might then seem like the claim for the indispensability or irreducibility of ‘singular terms’ of which one of the most persuasive recent defenders has been P. F. Strawson. I think, however, that, paradoxical as it might seem, Wittgenstein’s request for the possibility of Names does not entail the indispensability of ‘singular terms’. In her explanation of the Tractatus demand for Names, Miss Anscombe has written that Names are required if we are to be able to construct propositions and understand their sense (as we do) without already knowing what is true and what is false. For to understand the sense of a proposition is to understand its truth-conditions, and this means that there must be propositions which are false in only one way, and this is so only if there are Names.²⁷ That is to say, according to Miss Anscombe, if we have

(1) fA where ‘A’ is of the form ‘the ’

the truth-condition of (1) will involve the truth-condition of

(2) There is an x such that x, and for all y, y only if y = x.

(1) can be interpreted as saying fx of this x, and can thus be false in two different ways, namely either when it is not the case that there is only one x which is , or when there is such an x, but which is not f. But (2) will only be true if

(3) b

for some B where ‘b’ is a Name (or where ‘b’ can be paraphrased as ‘the ψ’ and so on until we arrive at some χc where ‘c’ cannot be paraphrased any more). And (3) can be false in one way only—when the object B does not have the property . Thus if propositions do have definite sense and their having sense does not depend on the truth of another proposition, then there must be propositions of the form ‘b’ where ‘b’ is a name. But does (1) entail (3) and is Wittgenstein really committed to maintaining this?

It has already been shown that names of complex objects need not be reducible to one particular definite description. But so long as the use of a name of a complex object presupposes the use of some definite description, (1) would seem to entail (2). But why does it entail (3)? There seems to be no logical difficulty in supposing that in the final analysis one realizes that the truth-conditions of (1) involve the truth-condition of (2). And as Miss Anscombe rightly says, this involves understanding that (2) can be false in two different ways, one of which is the falsity of an existential proposition. But we do not have to know the truth-value of the existential proposition in order to give a definite sense or truth-conditions to (1). We need only know the truth-con-ditions of the existential proposition. To understand the sense of ‘fA’, where ‘A’ is of the form ‘the ’, is to understand the sense of ‘(∃x) x’ as well as ‘fx’ We must understand what it is for there to be one and only one x which is (without having to know its truth or falsity), and we must understand what it is for such an x to be f if there is such an x. Thus even if our analysis ended at (2) it would not be the case that ‘whether a proposition had sense would depend on whether another proposition was true’, which 2.0211 says would be true if there were no substances. It would of course not follow that because we stopped our analysis at (2), we have proved that substances do not exist. Wittgenstein clearly claims that there must be simple objects in order that propositions have definite sense. But to say that there are objects, and to say that one must arrive at their Names at the end of logical analysis, are two different claims. As far as Names are concerned he writes that they must be possible. I will try to show that within the framework of the logical atomism of the Tractatus it hardly makes any difference at all whether one claims that final analysis leads to elementary propositions or to existential statements logically equivalent to them. This equivalence itself seems to be maintained by Wittgenstein when he says ‘We can describe the world completely by means of fully generalized propositions, i.e. without first correlating any Name with a particular object’ (5.526).

Let us examine this question a bit more carefully. 5.47 says quite clearly that ‘fa’ says the same thing as ‘(∃x) fx . x = a’. This would suggest that ‘fa’ could never be equivalent to an existential proposition since it is an existential proposition plus something more: namely the identity claim that x = a. For example, to claim that there is a man who killed Caesar, and that he is Brutus, is quite different from just asserting that there is a man who killed Caesar. And indeed if ‘a’ is an ordinary proper name, ‘fa’ always says something more than ‘(∃x) fx’. ‘a’ plays the rôle of identifying or specifying a particular object which the proposition is about. We read in the Notebooks that ‘Names are necessary for an assertion that this thing possesses that property and so on. They link the propositional form with quite definite objects.’ It must be remembered however that Names which occur in elementary propositions are different from names like ‘Brutus’. The references of Names are simple objects which ‘can only be named’ and not given by definite descriptions. So in the proposition ‘[∃x] fx . x = a’ where ‘a’ is a name, a is merely identified as an object which is f. I cannot imagine it excluded from the possibility of combining with others (2.0121)—so in order to know a I must know what it would be for it to be true that g(a.b), h(a.b.c) etc. but not that they are true; and a itself has no material or contingent features which allow me to identify it by a description. Thus to say ‘(∃x) fx . x = a’ comes to the same as ‘an object is f’ Strawson has argued convincingly that ‘the identificatory function of singular terms should be acknowledged …, and clearly distinguished from the operation of asserting that there is just one thing answering to certain specifications.’²⁸ And indeed in ‘fa’ or ‘(∃x) fx . x = a’, one is not asserting that there is just one thing which is f. (In fact, there may be many things that are f.) One is talking about a particular object a. But as I have said, so long as ‘a’ is a Name, the object a in fa has no contingent properties which would enable one to identify it by a definite description. To identify a would be nothing more than identifying an f. And for the Tractatus, propositions which have the same truth-conditions have the same sense.

It might be objected that in order for ‘fa’ even to have sense before it is true or false, there must be an object named by ‘a’, whereas ‘(∃x) fx’ has sense even when it is false—when there is no object. But what is it to require that there must be an object a which might or might not be f? Let us take seriously Wittgenstein’s claim in 5.526 that Names can be dispensed with in our description of the world. He argues this point in greater detail in his Notebooks of 16 October 1914. ‘Yes the world could be completely described by completely general propositions, and hence without using any sort of names or other designating (betzeichnendes) signs. And in order to arrive at ordinary language one would only need to introduce names etc. by saying, after an “(∃x)”, “and this x is A” and so on.’ We realize that in this example since we introduce the name ‘A’ by saying (∃x) fx and this x is A, it would be quite impossible to envisage the A as not having the property f. There is no other criterion for A to be identified as an object. ‘A’ is here what we call a dummy name. We realize also the truth of the claim, hinted previously, that properties or relations in the Tractatus be treated intensionally. The irreducible properties or relations which are ascribed to objects in elementary propositions cannot be identified extensionally as the class of objects which have the property, or which stand in the relation. If it is only via the properties which it has that an object is introduced, the properties in turn cannot be defined by the objects which have them. According to my interpretation, the objects of the Tractatus are as far removed as can be from ‘bare particulars’ which people like Professor Copi have claimed they are. They are necessarily instantiations of some properties, although Wittgenstein cannot say what kind of properties they are instantiations of. He merely tells us that the properties concerned are not material properties like being of a particular colour.

In proofs in elementary geometry we often ascribe dummy names to objects which are assumed to have no properties except those which are ascribed to them in the proofs. For example, we say ‘Let a be the centre of the circle C’ and go on to deduce the various relations it has to other things. We cannot however go on to suppose that a is not the centre of the circle, for a has no identity other than that of being just that. We may come to decide, after using a dummy name ‘a’, that ‘a’ did not secure a reference. But as long as we use ‘a’ and talk of object ‘a’ it is the centre of the circle C—and an object necessarily has to have a property other than being an object, since, as the Tractatus says, object is a formal concept. I hope it is clear that I am not claiming that every proposition of the form ‘fa’, ‘gbc’ where ‘a’, ‘b’, ‘c’, are Names, must be true. In the example of the geometrical proof, the proposition ‘a is on line L’ may well be false. Some elementary propositions are true, some are false (4.25). It seems nevertheless the case that, if some proposition of the form a is necessarily true in order for us to be able to identify a at all, and, as an elementary proposition of the form a is claimed to be logically independent of any other elementary proposition, then the condition of the use of the Name ‘x’ is nothing more than the conditions which enable us to say ‘(∃x) x’ It is because of this that Wittgenstein could not, strictly speaking, require that Names exist, but only that Names be possible: that we would be able to use Names.

If, as I have argued, Names in the Tractatus are like dummy Names, the relationship of bedeuten or referring which holds between Names and objects is also of a very special kind, as also is the nature of objects themselves. We have already seen that the identity of an object can be determined only by settling the sense of the propositions in which the Names occur. But the sense of an elementary proposition of the form ‘fa’ is exactly the same as the sense of a proposition of the form ‘fb’ where ‘f(x)’ expresses the same property, and ‘a’ and ‘b’ are different Names. Just as in the geometrical proof mentioned earlier, saying ‘Let a be the centre of the circle C’ is exactly the same as saying ‘Let B be the centre of the circle C’, if ‘a’ and ‘b’ are dummy names. What the dummy names are used to identify are nothing more nor less than an instantiation of the description or predicate which follows. If the conditions of using a dummy name are the conditions of saying ‘there is a so and so which …’, then dummy names cannot fail to refer to an object so long as the set of propositions in which they occur make sense. Referring to an object here means that the dummy names have use. When we identify two human beings by their proper names and predicate something of them—as when we say ‘Bernard Shaw and Oscar Wilde are Irish’, we identify the two men not merely as different Irishmen, and so naturally their names are not interchangeable. Dummy names are interchangeable so long as we interchange them consistently, and so I believe are Names in the Tractatus.

I am not claiming that Wittgenstein explicitly thought that his Names behave like dummy names, but only that in effect they are made to do so. The objects Names refer to are entities which have a criterion of identity quite different from those according to which we normally identify and distinguish spatio-temporal objects. However simple a spatio-temporal object is, as a particular it only belongs to this world and not to all possible imaginary worlds as the objects are said to do (2.022). The simplest spatio-temporal objects not only have the possibility of occurring in various states of affairs, but do occur in many. They are instantiations of many properties. The tiny fleck of snow on my palm is made of H₂O; it fell at a particular time in January 1968 in a particular spot in London, etc. etc. Even if one takes the view that there is no logical necessity for the object to have some or most of these properties, and even if one believes that it could have had various other external properties under different circumstances, the fact remains that the object has all these external properties. If an object lacks any of the properties that A has, or has any property that A does not have, then it simply is not A: thus no spatio-temporal object of this world identified in the normal way could be a constituent of any other imagined world. The identity of any particular spatio-temporal object is not determined by its ‘possibilities’. Many philosophers have therefore been tempted to take the ‘objects’ of the Tractatus as either being properties or sense data. I have already given reasons why predicate expressions are not considered as Names in the Tractatus, and thus why the properties or relations (that are true of objects) to which predicate expressions refer when they occur in propositions or which are expressed by a structure of the concatenation of the Names of objects are not to be treated as objects. Sense data theory will not by itself provide us with objects which are common to all worlds either. Each token sense datum is not only bound to this world but also to the person who has the experience. If we are referring not to token sense data but to types of sense data, then we are considering properties which are true of certain areas of our visual field, which again are not objects. To suppose either that objects of the Tractatus are spatio-temporal things, or that they are sense data, lands us in similar difficulties. To ask what kind of familiar entities correspond to the objects of the Tractatus seems to lead us nowhere. The alternative here attempted has been to ask what kind of criterion of identity objects can have to enable them to be ‘independent of what is the case’ (2.024), and constitute an imaginary world as well as our real one.

As we have seen, the reference of a Name which has as its form the possibility of occurring in various atomic states of affairs is identified nevertheless in an existing atomic state of affairs; i.e. only as an instantiation of a certain property, monadic or relational. At the same time every atomic state of affairs is independent of every other (2.061, 2.062). We can understand what it is for states of affairs to be independent of each other if each state of affairs is described by a general proposition. That there is a red object might be independent of the fact that there is a square object, and so on. But what is it for elementary propositions in which Names occur to be logically independent of each other? If an object A is identified as the reference of ‘A’ in ‘FA’, this is so independently of the existence or non-existence of any other atomic state of affairs involving A; independently of whether we are to treat A as the instantiation of any other properties at all. This could not be the case where ‘A’ is the name of any particular individual. A then is not an object in any extensional sense. If we think of a world different from our own in which the same atomic state of affairs holds as in ours, then one can say in the language of the Tractatus that this imaginary world and ours have the same objects. In less eccentric philosophical speech this would be expressed by saying that there are instantiations of the same predicate in the different worlds, or that these different worlds have members of the same set.

The claim, in the Tractatus that objects exist should then be understood to mean that there are instantiations of certain irreducible properties which for Wittgenstein are different from any material properties. (In understanding, for example, that here is an instantiation of the property red, we also understand that there could here be instantiations of the property being square, being hard and so on.) It is not a claim that there are properties or relations, but nevertheless a claim about properties and relations all the same. It is not a claim about the existence of individual concepts in any Leibnizian sense, since any individual concept is a highly complex one including an infinite number of predicates, whereas the claim that objects exist in the Tractatus is the assertion that there are instantiations of simple irreducible properties. And it is the combination of the view that the identity of objects referred to by a Name can be determined only by settling the use of the Name, with his view that all elementary propositions must be logically independent of one another that leads him to this position.

My interpretation of the Tractatus view of objects may appear to be eccentric. But I would like to end this paper by drawing attention to three important facts which I believe indicate the plausibility of my interpretation. The first is the commentary which Wittgenstein himself gives in the Philosophical Investigations, §§ 46–8 about the objects of the Tractatus. After writing that the objects of the Tractatus are like the simples of the Theaetetus, Wittgenstein goes on to give an example of a language-game for which the Theaetetus account is valid. The language serves to describe various combinations of squares on a surface which are red, green, white or black. Each coloured square is a simple, and is given the name ‘R’, ‘G’, ‘W’, or ‘B’, depending on the colour. Each sentence in this language consists of a sequence of these names, e.g. ‘RRBGGGRWW’, which describes a particular arrangement of the coloured squares. Here we see clearly that every different square of the same colour is given the same name, and is regarded as the same simple. The fact that they are different token squares does not endow them with different names. The names are not claimed by Wittgenstein to correspond to colours, but to coloured squares. Yet, different token squares of the same colour have the same names. In other words, the use of a name identifies an instantiation of a property, and does not distinguish between different instantiations of the same properties. This is exactly what I have claimed the Names of the Tractatus do. The point I am making is also supported by Waismann’s notes of Wittgenstein’s comments where it is pointed out how wrong it is to ask whether objects are ‘thing-like’ or ‘property-like’. This is the second point I wish to refer to. Objects, Wittgenstein says here, are elements of presentations (Darstellungen). In other words, to say that there are objects is nothing more than to say that there is something described, or presented by a diagram, picture, etc. And to say that there is something described or pictured does not, of course, mean that the thing described or pictured exists.

The third point to which I would like to draw attention is certain areas of Model theory, where, as in the Tractatus, some logicians have talked of objects which could be common to different possible worlds. In order to be able to specify a possible world by e.g. a model consisting of an ordered pair A, R where A is a non-empty set and R is a relation, and a different possible world by another model A, R′; where A is said to be the same non-empty set as in the former and R′ a different relation, one has invoked a notion of objects different from our normal notion of particulars. For the objects which are members of the set A have been given an identity which is independent of the relations they satisfy in different worlds. (This peculiarity would not arise if one made the models specify descriptions of possible worlds, rather than the worlds themselves.)

It has been suggested by Stenius, Stegmüller and Hintikka that we might obtain a better understanding of the ‘objects’ in the Tractatus by invoking model theoretical concepts. Although I disagree with various aspects of Stenius’s and Stegmüller’s views about the Tractatus, which amongst other things fail to distinguish between what are to count as properties and objects in a given state of affairs, it seems to me to be correct that the objects of the Tractatus which merely determine the possibility of their occurrence in various states-of-affairs have logical features close to those exhibited by those objects in Model theory which can occur in different models.

Let me summarize the main conclusions of this paper. The Tractatus does not, as has sometimes been thought, offer an extensional foundation of semantic analysis. The objects of the Tractatus are not like things (however simple) in the empirical world which can be individuated extensionally. The concept of a simple object is more like that of an instantiation of an irreducible property. This concept was a logical requisite for the Tractatus theory, and followed from the combination of a basically correct theory about names, of a mistaken assimilation of complex things and facts, and of a wrong and unnecessary claim about the independence of elementary propositions. The Tractatus theory of Names, which claims that the problem of the identity of the reference of names and the problem of the use of Names in propositions are inseparable, is closely connected with the picture theory of meaning and contains much that is right and illuminating even for those who reject talk about simple objects and mutually independent elementary propositions—as Wittgenstein himself did in his later years.

¹ As an example of this view, which I think is misleading, see Max Black, A Companion to Wittgenstein’s Tractatus, pp. 114–15, ‘Wittgenstein considers the question of how the meaning of names can be communicated. His disturbing answer is that it is impossible to explain a name’s meaning explicitly; the only way to convey the meaning is to use the name in a proposition, thereby presupposing that the meaning is already understood. On this view, the achievement of common reference by speaker and hearer becomes mysterious.’

² I will write Name with a capital to indicate the technical sense the word has in the Tractatus—a name which cannot be further analysed by definitions.

³ Tractatus 4.23. ‘The name occurs in the proposition only in the context of the elementary proposition.’

⁴ ‘Über Sinn und Bedeutung’, 1892, Zeitschrift für Philos. u. philos. Kritik. It is clear from a letter Frege wrote to Peano in 1896, where he still makes the point about words having ‘Bedeutung’ and ‘Sinn’ only in the context of a proposition in ordinary language, that he maintained the maxim ‘Only ask for the “Bedeutung” of a word when it is used in a proposition’ even after he made the ‘Sinn’ and ‘Bedeutung’ distinction.

⁵ Unless we distinguish Wittgenstein’s use of ‘Bedeutung’ and ‘Sinn’ carefully, and take the former as ‘reference’, as Miss Anscombe rightly says in Introduction to Wittgenstein’s Tractatus, we will not be able to make sense of the following claims.

3.331,	where he criticizes Russell’s formulation of the Theory of Types because Russell had to mention the ‘Bedeutung’ of the sign when establishing the rules for them. Wittgenstein is referring to Russell’s talk about individuals, or classes, or classes of classes which different kinds of signs ‘denote’ and which Russell calls ‘terms’ of propositions, and not to meanings of signs in any ordinary sense.
4.126,	that the sign which distinguishes a formal concept is a characteristic feature of all symbols whose ‘Bedeutungen’ fall under the concept. Wittgenstein is here talking about the way in which e.g. we express that the signs refer to objects, by using ‘a’ ‘b’ ‘c’ … as signs, or that the signs refer to functions by using ‘f’ ‘g’ ‘h’ as signs—i.e. the references of different kinds of symbol fall under different concepts.
5.02,	where Wittgenstein criticizes Frege’s theory about the ‘Bedeutung’ of propositions—it is clear that he is talking about Frege’s view that propositions refer to truth-values, and not about Frege’s view of the sense of propositions.

Again, we will fail to see the point of one of the important theses of the Tractatus that logical constants do not stand for anything (and have no reference), unless we make the Sinn/Bedeutung distinction. Of course logical constants have sense in that they have a use and become constituent signs of complex propositions, which have a sense—but Wittgenstein wants to say that unlike names or predicates (even relational predicates) they do not refer to anything. ‘… nothing in reality corresponds to the sign “~”.’(4.0621).

⁶ 5.4732.

⁷ Even in the case where there is only one object involved, as in ‘A is red’, one can have a convention whereby one expresses that an object is red by writing the name of the object sideways. Then the above proposition could be expressed as .

⁸ Reference and Generality, first edition, pp. 25–6. After reading this paper in manuscript form, Professor Geach has kindly shown me his revised version of the same passage, written for the second edition due to come out in Autumn 1968. He makes clear that even when names are used independently, e.g. to call someone, or on labels, the use is not independent of the language system to which the names belong.

⁹ ‘On Denoting’, Mind, 1905.

¹⁰ ‘By an “incomplete” symbol we mean a symbol which is not supposed to have any meaning in isolation, but is only defined in certain contexts. In ordinary mathematics, for example and are incomplete symbols…. Such symbols have what may be called a “definition in use”. This distinguishes such symbols from what we may call proper names.’ (Priticipia Mathematica p. 66.)

¹¹ vide 4.24, 4.1211.

¹² Wittgenstein misleadingly talks of propositions describing states-of-affairs, and of propositions representing states-of-affairs—instead of saying as he should that propositions state states-of-affairs.

¹³ It has been a standing controversy whether predicates or properties are included in the objects of the Tractatus or not. It is true that if properties do not count as objects it is difficult to see how in the state of affairs expressed by ‘fa’, ‘objects fit into one another like the links of a chain’ as they are said to do in states of affairs in 2.03. But not only do other passages of the Tractatus go against the view that predicates are objects; it seems to me to be a central thesis of the Tractatus that subject-predicate propositions, i.e. propositions in which properties are ascribed to objects, can be expressed as a function of the objects. It is better to acknowledge the difficulty Wittgenstein has in explaining the limiting case of a state of affairs in which there is only one object involved, than to render the thesis empty (see note 2, p. 41). As Strawson has argued, the word ‘about’ may be unable to carry the burden of distinguishing objects and properties mentioned in a proposition. Wittgenstein nevertheless thought, with Frege, that if ‘fa’ is a proposition, we have an intuitive grasp of the difference between the rôles of ‘f’ and ‘a’.

¹⁴ G. E. M. Anscombe, An Introduction to Wittgenstein’s Tractatus, p 28.

¹⁵ 6.2322 Wittgenstein simplifies the problem by supposing that either one knows the reference of both expressions, or knows neither; which is wrong.

¹⁶ 5.5303.

¹⁷ ‘… sive Termino sive notioni’ p. 85. ‘Per Terminum non intelligo nomen sed conceptum seu id quod nomine significatur, possis et dicere notionem, ideam.’ p. 243. ‘… et ita distinguendum erit inter Terminum et Rem seu Ens’ p. 393. Opuscules et Fragments Inedits de Leibniz, edits par Couturat 1903. Leibniz is confused at times in other works as to whether terms are concepts expressed by words, or whether they are verbal expressions of concepts.

¹⁸ 2.01231 ‘If I am to know an object, though I need not know its external properties, I must know all its internal properties.’

¹⁹ 3.24.

²⁰ ‘Philosophy of Logical Atomism’ in Logic and Knowledge, p. 201

²¹ 3.203.

²² In Philosophical Investigations, §§ 38, 39, 45, Wittgenstein gives a detailed criticism of the theory that the word ‘this’ is a name. This might be taken as a refutation of his own view in the Tractatus since he is arguing in these pages against the view that there must be simple objects which can only be named, which was claimed in the Tractatus as well as in Russell’s Philosophy of Logical Atomism. It is clear that he is criticizing Russell’s theory when he talks of the ‘conception of naming as an occult process’ and of the ‘philosopher who tries to bring out the relation between name and thing by staring at an object in front of him and repeating a name or even the word “this” seven times’. Such views were never a part of the Tractatus.

²³ Notebooks, 16, 5. 1915.

²⁴ 3.23. ‘The requirement that simple signs be possible is the requirement that sense be determinate.’

²⁵ 4.22. See also footnote 2, p. 28. And, similarly, generalized propositions with quantifiers can be expressed without function signs, e.g. by expressing ‘(∃y)y is red’ by ‘(∃y) λ’ y, ‘(x) (y) f (xy)’ by ‘(x) (y)’. And just as we learn the conventional meaning of each different predicate in ordinary language, we can learn the convention of expressing various properties by different patterns of name variables.

²⁶ 3.1432 ‘Instead of “The complex sign ‘aRb’ says that a stands to B in the relation R”, we ought to put, “that ‘a’ stands to ‘b’ in a certain relation says that aRb”.’

²⁷ G. E. M. Anscombe Introduction to Wittgenstein’s Tractatus, p. 47.

²⁸ P. F. Strawson ‘Singular Terms and Predication’, Journal of Philosophy, Vol. 58, No. 15, 1961. Reprinted in Philosophical Logic, O.U.P., p. 77.