20th WCP: On Naming and Possibility in Kripke and in the Tractatus

Raymond Bradley, in his book The Nature of All Being, has put forward an essentialist interpretation of the ontology of Wittgenstein's Tractatus Logico-philosophicus and aims to develop the modal dimensions that, in his opinion, are implicit in that work. (1) Among other theses, Bradley maintains that tractarian names can be interpreted as kripkean rigid designators, and this idea enables him to approach the Tractatus from the perspective of possible worlds semantics. The aim of this paper is to reassess this thesis of Bradley's, by examining the tractarian notion of name and the kripkean concept of rigid designator in Naming and Necessity, (2) with a view to answering the question as to whether an interpretation of tractarian names as rigid designators is possible, and to bringing to light some similarities and differences between the two theories of meaning.

1. The theory of naming in the Tractatus.

The tractarian notion of name ("Name") is the result of Wittgenstein's attempt to solve the problems arising out of the lack of reference, problems that he had inherited from Frege and Russell. (3) To this end, he proposes to analyze the conceptual expressions, relations and definite descriptions until simple homogeneous elements are reached. These ultimate constituents of language in which no differences can be found are the tractarian names. Wittgenstein postulates the existence of simple objects as references for the names so as to guarantee the reference and meaningfulness of language. It is essential to names that they are not analyzable any further, that they are indefinible.

Wittgenstein deals with the notion of name and discusses its indefinable nature in paragraphs 3.2-3.263 of the Tractatus. (4) A name is a simple sign ("einfache Zeichen") which stands for a simple object; it is the ultimate constituent of the proposition. A name is a primitive sign ("Urzeichen"), an indefinable sign (T 3.26-3.261). Simple signs are the elements of the propositional sign whose meanings are the objects (cfr T 3.2-3.221). The relationship between a name and an object is therefore merely referential: the name stands for the object; it is the representative of the object ("vertritt") (cfr. T 3.22-3.221). But a name gets its meaning only in the nexus of a proposition, that is, the fixation of the meaning is determined by the use of the sign, which makes the sign into a symbol (T 3.262, 3.3, 3.325-3.328). The meaning of names depends upon the grammatical rules that govern its use (T 3.327), upon its position in propositions and in language (T 3.3, 4.23). (5)

Tractarian names do not have sense; they have only reference. The sense of an expression is the way in which the content of its parts appears in the whole. However, in the order of tractarian names and objects, we cannot speak about sense, since they are simple and lack parts. It is useful to look more closely at two aspects of this notion of name. In the first place, if simple objects cannot be described, if meaning of names cannot be determined by means of sense, by analyzing it into parts, then, the answer to the question as to how names get their meaning can only be given by having recourse to their use: each simple sign contains virtually all the propositions of which it may form part.

Secondly, as the simple object does not have complexity, it does not have intelligibility. Therefore, the reference of a name cannot be understood as its content, as was conceived by Frege. The relationship between a name and an object is understood by Wittgenstein in terms of a replacing relation (T 3.22). The name replaces or takes the place of the object in the picture because it has the same form. As a result of the isomorphism between the language and the world, just as the name occurs in a proposition, but also can occur in others, so the object occurs in one state of affairs, but can also occur in other states of affairs, and the replacing connection is established in terms of those possibilities.

These paragraphs dealing with the notion of name seem to bring out two ideas that are not completely compatible. On the one hand, "the elements of the picture are the representatives of objects" (T 2.131) and they are correlated ("Zuordnungen") with objects (T 2.1514). In T 3.203 Wittgenstein explicitly states that "a name means an object. The object is its meaning." The object might be then considered as an isolated thing, as that thing which a name stands for, and the name would be the mark that enables us to identify an object. On the other hand, as "only in the nexus of a proposition does a name have meaning" (T 3.3), the meaning of names seems to be reduced to its contribution to the sense of propositions, and that contribution would lie in the ability to show how the objects might be combined in the world by showing how the names are combined in the proposition. The meaning of a name would therefore be relative to its position and role in the proposition.

To my mind, the right answer to the question as to how the tractarian names get their meaning involves the totality of language, and the role played by names in it (their logico-syntactical use); but it also requires finding a basis for the meaningfulness of language in the metaphysical constitution of the world. The projection establishes the pictorial relation between language and world. It is convenient to point out that such a projection is carried out by mapping one totality onto the other totality. For this reason, in the Tractatus the foundation lies in the notion of form; and form is considered within the framework of the relationship between name, proposition and language, and the corresponding relation between object, state of affairs and world. The condition of correlation between name and object, that the "connection of the propositional components must be possible for the represented things" (N 5.11.14), (6) does not concern the naming relation, but the pictorial one, and therefore it calls on the connection of objects in the state of affairs and of names in the proposition. (7)

2. Bradley's interpretation of tractarian names.

Bradley offers his interpretation of tractarian names by appealing to two principles, which he considers to be involved in Wittgenstein's picture theory: the Proxy Principle and the Form-Signalizing Principle. The Proxy Principle establishes that "a name 'goes proxy for' a simple object," and therefore takes account of the referential or semantical role of names; the Form-Signalizing Principle concerns the syntactical role of names, and establishes "that names 'signalize' the forms of objects for which they stand and thereby themselves take on corresponding forms" (B 131).

Bradley develops the Proxy Principle in detail, and applies it to technical tractarian names (B 132-135) and to ordinary names, or names of complexes (B 135-137), interpreting both kinds of names as rigid designators. He tackles the difficulties that arise regarding identity, and puts forward the solution that, in his view, Wittgenstein might have given to the problem (B 137-145).

Bradley defends the Proxy Principle by reference to N 25.12.14, 29.12.14 and T 4.0312, in which Wittgenstein seems to conceive the relation between a name and an object as the Proxy Principle declares. Bradley points out two characteristics of the tractarian naming relation. On the one hand, the relation between name and object is arbitrary, conventional (N 22.10.14, 3.11.14, T 3.34). On the other hand, names lack sense or descriptive content, and their function is therefore a merely referential one. This second characteristic enables Bradley to relate the tractarian theory of naming with Kripke's New Theory of Reference. According to Bradley, Wittgenstein opposes the descriptive theory of meaning in a triple sense: he rejects that names have sense, that any sense of names is given by the description of the object by means of the property or properties associated with the name, and that the reference of a name is identified precisely as the object satisfying the description of such properties (B 132).

I agree with Bradley in his understanding of the tractarian theory of naming as opposed to the descriptive theory; however, I do not concur with his reasoning, nor with the consequences he draws from it. As Bradley indicates, Wittgenstein's claims in N 26.5.15, 27.5.15 and T 3.221 offer enough textual support as to establish that names lack sense. But by saying that sense belongs to propositions, never to names, Bradley does not explain why that is so in the tractarian doctrine. It does not suffice to say that Wittgenstein would reject as an explanation of meaning any thesis concerning epistemological notions, such as the questions as to which description of the object by its properties we associate with a name, or how we identify the reference of a name (B 133). In my view, the reason lies in the absolute simplicity of objects and names. If names stand for absolutely simple objects, then they cannot be described by properties simply because they do not possess any properties. This is the reason why objects can only be named.

Once the tractarian theory of names has been introduced and has been opposed to the descriptive theory, Bradley regards Wittgenstein, together with J. S. Mill and Kripke, as a defender of a conception of names as rigid designators. Bradley introduces the kripkean doctrine of names and maintains that the theory of rigid designation implies the Proxy Principle as well as the claim that names designate the same objects in all possible worlds. Bradley accordingly defends the idea that the theory of rigid designation finds its basis in two intuitions: that objects can form part of states of affairs other than those in which they in fact occur, and that names can be used to stand for objects, regardless of the states of affairs in which they occur. According to Bradley's interpretation, Wittgenstein would have subscribed to both theses. The reason why he would have defended the second intuition is grounded merely in the plausibility of considering human beings to be able to invent and use names as marks of objects, without describing the properties of the corresponding objects (B 134).

Finally, Bradley defends the idea that names of complexes can also be interpreted as rigid designators. Nonetheless, Wittgenstein establishes in the Tractatus that ordinary names, names of complexes, mean via their definitions; that is, in order for the sense of propositions to be determined, it is necessary to analyze all the expressions in it. To my mind, paragraphs T 3.23-3.261, and in particular T 3.24, do not cast any doubts on this. As a consequence, it is even more controversial to interpret ordinary names as rigid designators, since the foundation of meaningfulness must be rooted in the tractarian simple elements (T 3.24).

3. Kripke's Theory of Names in Naming and Necessity, and the supposed rigidity of tractarian names.

The starting point of Kripke's development is the introduction of some difficulties in the descriptive theory of meaning. In order to overcome the problems underlying the descriptive theory, Kripke presents his own doctrine in the first lecture, and introduces his notion of rigid designator as the name that refers to the same object in every possible world (K 48). The second lecture contains a more detailed criticism of the descriptive theory of meaning, which leads him to establish the priority of the naming relation with respect to the descriptive relation, and to require an initial baptism or imposition of name on the object. In the third lecture, Kripke develops the thesis regarding necessity and essentialism, and applies the notion of rigid designator to natural kind terms, to definitions in scientific theories, and, finally, to the particular case of the mind-body identity thesis.

The key element of Kripke's theory of naming is the rigid nature of the naming relation. The basis for this rigidity lies in the primitive and immediate nature of the relation of the name to the object. The name is related to the object without any mediation. The kripkean doctrine of names requires an initial baptism in order to guarantee that no mediation of sense takes place. Kripke has recourse to the possibility of describing counterfactual situations in order to verify the rigidity of the designator. However, he makes it clear that it is because we can rigidly refer to an object, and speak about what might have happened to it under other conditions, that transworld identifications are possible (K 49). Therefore, transworld identity of reference is a consequence of the rigidity of the naming relation.

For this reason, the imposition of a name on an object is essential to the theory of rigid designators. This establishes what Kripke refers to as the relation of calling (K 70). This priority of the naming relation allows to overcome the circularity implied in the attempt at defining proper names. According to Kripke, the naming relation is prior to the descriptive relation, because no property can be attributed to an object unless there is some independent criterion to refer to it (K 88). In the initial baptism, the identification of the object to be named can be carried out by ostension, or by description of any of its properties (necessary or contingent), but the naming relation is directly established by imposing a mark on an object, and therefore it is possible to refer to an isolated object.

Some characteristics of tractarian names show certain similarities to those of kripkean names. On the one hand, the tractarian image of names as being like points and propositions like arrows (T 3.144) shows the main common feature, namely, the indefinibility of names and rigid designators. On the other hand, if rigid designators are defined simply as signs that denote the same object in every possible world, then tractarian names might be conceived of as rigid designators. (8)

Nevertheless, as has been shown, the rigidity of the name, as Kripke understands it, finds its basis in the priority and immediate connection of the name to the object. To my mind, this feature is alien to the Tractatus. Although tractarian names are also indefinable, the assignation of names to objects depends upon the whole language, upon the whole consideration of logical syntax, since projection and the subsequent pictorial relation are based on the isomorphism between language and world. In the picture theory there is no notion of sense of a name as presentation of its reference. However, the whole sense of language intervenes in the determination of reference, since objects can be determined only by their possible relations to all other objects. For this reason, whereas Kripke admits the possibility of referring to an object regardless of the states of affairs in which it can occur, Wittgenstein would not accept this. Kripke conceives of language as a set of signs that is being built up, and that can increase by the addition of new names as a consequence of new impositions of names on objects. However, in the Tractatus language and world are linked as totalities that share the same structure, so that the link between a name and an object depends upon the relation of that name to other names, and upon the relation of that object to other objects. That is the reason why an object cannot be named regardless of its possibilities of combination, since the correlation of the corresponding name with that object is the condition of possibility of the correlation of all other names with all other objects.

Kripke distinguishes between a description that gives the meaning of a name -definition- and a description that is used to fix its reference, without being a proper synonym of the name. However, in the Tractatus this distinction cannot be made, for the references of names are objects that, because of their simplicity, are absolutely empty. The net of combinatorial possibilities of an object enables us to identify it, and, similarly, the logico-syntactical use of a name enables us to identify it. For this reason, the question as to how to fix the reference, and the question as to which the meaning of names is are not two different questions, but the same one. Whereas in the kripkean theory the necessary properties of an object, those possessed by the object in every counterfactual situation, are not usually the properties used to identify the object in the actual world, in the Tractatus an object is identified by virtue of its possible relations to other objects, and these possible relations, in turn, are determined from the facts that constitute the actual world.

To sum up, Kripke does not share the logical atomism, (9) which forces Wittgenstein to reduce the meaning of names to their syntactical role within the whole language. Kripke defends the priority of the naming relation and the distinction between necessary and contingent properties, which implies some complexity in objects.

Other differences might be developed, such as those regarding counterfactual situations. Wittgenstein conceives of possible worlds as worlds that are thinkable from the actual world. (10) But to think of other worlds is to think that other states of affairs would have been the case. Once objects have been identified by the possible combinations they can form part of -by the conditions given in the logical space-, different combinations can be the case; but the possibilities of combination remain the same. This is where the peculiar rigidity of tractarian names is rooted. Given a specific logical space, and once the projection is carried out, then only those possible combinations of objects are thinkable, and therefore the designating relation remains unchangeable. Kripke's starting point, however, is the consideration of non simple objects that possess necessary and contingent properties. Given those actual objects, different situations can be described, by thinking of the objects lacking some of those properties or possessing different ones. Wittgenstein makes no difference between essential and accidental predication: everything that is allowed by logical syntax is possible.

4. Conclusions

These considerations allow us to conclude that although tractarian names somehow might be considered to be rigid designators, so far as the relation between a name and an object is constant and unchangeable, the basis for the peculiar tractarian rigidity is not the same as that for the rigidity of kripkean names. The nature of the relation between the name and the object is essentially different in these two accounts. Therefore, tractarian names, in spite of their peculiar rigidity, should not be regarded as kripkean rigid designators.

Bradley seems to found the relation between language and world on the naming relation. In his interpretation, the priority of the naming relation is part of his attempt to base what is thinkable on what is possible, by transferring the possibility of combination to the object. Nevertheless, the possibilist character of Bradley's approach to tractarian ontology is so intense that it leads him to leave aside an idea that is common to Wittgenstein and Kripke. Both of them take actuality as their starting point in order to open the way to possibility. In the Tractatus, logical space, the set of possibilities of combination of objects, is given; and, as a result of the the simplicity of objects, the set of possible combinations lacks any foundation at all. Kripke also builds descriptions of counterfactual situations from actualized objects (K 46, 53). Bradley, however, introduces factualness as subordinated to possibility. In my view, this absolute and foundational view of possibility is a consequence of the modal perspective of Bradley's approach, but it is not genuinely tractarian nor kripkean.