From the ALWS archives: A selection of papers from the International Wittgenstein Symposia in Kirchberg am Wechsel

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It is a well-known fact that TPLA by Russell is influenced by Wittgensteinian stimuli. In the brief foreword to the first three lectures, Russell states his debts with some well-known words (Russell 1918, p. 160). It is far less known that those words are almost literally taken from the third lecture. In their original context, the debt appears to be quite specific and to concern an issue that is prima facie surprising: theory of relations and its connections with theory of types. Why is this issue surprising? We know that Russell and Wittgenstein debated for a long time about some aspects of the theory of relations; but these aspects are usually identified with those relations involved in the theory of judgement, as Russell had expounded it in the unpublished “Theory of Knowledge” (Russell 1982).

On the contrary, the context of the quoted acknowledgement in the third lecture is radically different: Russell is going to talk about predicate semantics, its ontological commitments and the importance of a correct understanding of such notions, in order to catch the philosophical significance of theory of types. In particular, one feature is common to relations (and properties too, since properties are conceivable as monadic relations) and their linguistic counterparts and is fundamental for the theory of types: relations have in their essence the class of objects of which they can hold, predicates are essentially connected with the class of names which can saturate them and the mirroring of these combinatorial properties between relation and predicate is a necessary condition for the semantic connection between them. It is not prima facie clear what is Wittgensteinian here, insofar as we look at the Tractarian or pre-Tractarian theory of relations. This theory is notoriously difficult. However, it seems quite sure that Tractarian relations and their elusive linguistic counterparts do not have features similar to those which TPLA gives to relations and predicates.

In this paper, we suggest a plausible solution to this puzzle. We proceed by theoretical comparison, since historical reconstruction seems powerless here. We compare theory of relations and predicates in TPLA and theory of names and objects in the TLP.

Russell expounds the following thesis immediately after the mentioned acknowledgement to Wittgenstein.

Understanding a predicate is quite a different thing from understanding a name. By a predicate, as you know, I mean the word that is used to designate a quality such as red, white, square, round, and the understanding of a word like that involves a different kind of act of mind from that which is involved in understanding a name. To understand a name you must be acquainted with the particular of which it is a name, and you must know that it is the name of that particular. You do not, that is to say, have any suggestion of the form of a proposition, whereas in understanding a predicate you do. To understand „“red“, for instance, is to understand what is meant by saying that a thing is red. You have to bring in the form of a proposition. You do not have to know, concerning any particular “this”, that “this is red” but you have to know what is the meaning of saying that anything is red. You have to understand what one would call “being red”. The importance of that is in connection with the theory of types. (Russell 1918, p. 182)

In the TLP we do not find any dichotomy between two categories of designators whose semantic features are different. On the contrary, this dichotomy is clearly purported in the Russellian excerpt above. Thus, it is problematic to understand in which sense this theory is Wittgensteinian, insofar as Russell pretends it is Wittgensteinian.

Our proposal is that the semantics for predicates in TPLA is analogous to the Tractarian semantics for names, i.e. the only kind of linguistic expressions which the TLP admits as designators. If this is the case, then it is possible to make sense of the acknowledgement. In fact, the semantics for relations was the real novelty in this phase of development of Russell’s thought. The semantics for names – apart from the trickier issue of the concrete identification of proper names – is still grounded in the notion of knowledge by acquaintance: a long-term Russellian theme. This is not the case for predicate semantics. Therefore, it is plausible that Russell declares his debt about what was actually new.

Let us draw the comparison. Concerning objects, which are the meaning of names, Wittgenstein wrote:

2.01231 If I am to know an object, though I need not know its external properties, I must know all its internal properties. (Wittgenstein 1921)

Thus, the knowledge of an object does not require to know, for any other object, if it is connected or not in an actual fact with the first one (these are its external properties). On the contrary, we need to know which other objects can be combined with it (its internal properties). The analogy with the TPLA excerpt is strong: in order to understand the word “red”, I do not need to know, for any particular, if it is red or not, but I need to know what can be said to be red.

Obviously, a difference is apparent as the analogy : the comparison between the knowledge of an entity and the understanding of a linguistic expression could seem hazardous. However, this difference is only specific to the quoted excerpts. Both the authors have corresponding theses on three different levels: ontology, semantics and syntax. We can qualify these three connected sub-theses with quite traditional labels:

• (i) on the ontological level, both Russellian relations and Wittgensteinian objects have essential combinatorial properties; Wittgenstein calls these combinatorial properties “logical form” of the objects;
• (ii) on the syntactical level, both Russellian predicates and Tractarian names have analogous combinatorial properties, i.e. they are essentially connected with the propositions where they can occur;
• (iii) on the semantic level, the two linguistic categories share a sort of “context principle”, such that they have meaning only in the context of a proposition.

Regarding Russell, many formulations suggest this exegesis. However, the Russellian inclination to alternate syntactical and ontological lexicon with great freedom makes it difficult to quote a specific passage. This freedom in itself partially legitimates our extensive exegesis. Nonetheless, look at this excerpt from “The logical atomism”, a later essay, notoriously close to TPLA on these themes:

Attributes and relations, though they may be not susceptible of analysis, differ from substances by the fact that they suggest a structure, and that there can be no significant symbol which symbolizes them in isolation. (Russell 1924, p. 172)

Relations, in this Russellian ontology, are simples (i.e., they can not be further analysed), but are different from substances (i.e., the particulars which are the meanings of names), insofar as they suggest a structure: thus, our analogy is legitimate on the ontological level. Moreover, nothing can symbolize them standing alone: thus, the Russellian predicates respect the semantic context principle.

On the Wittgensteinian side, it is not difficult to show that the TLP maintains not only the quoted thesis about the independence and not-independence of objects on the ontological level, but also that:

1) names have meaning only in the context of a proposition (the semantic thesis), as Wittgenstein explicitly affirms in a well-known, Fregean flavoured section (Wittgenstein 1921, T 3.3);

2) names, mirroring the logical form of objects, are essentially connected with the propositions which can include them (the syntactical thesis). It is not by chance that this last point is developed by Wittgenstein in the sections commenting the context principle in 3.3. They are quite famous, thus I can avoid to analyse them here.

I quote only a previous section, which states the connection between the two levels of non-independence (ontological and syntactical). The syntactical non-independence of words is here a parenthetical comment to the non-independence of objects:

2.0122 Things are independent in so far as they can occur in all possible situations, but this form of independence is a form of connexion with states of affairs, a form of dependence. (It is impossible for words to appear in two different roles: by themselves and in propositions.) (Wittgenstein 1921)

The only remaining asymmetry is determined by Russell’s reference to the “understanding” of names and relations. Under this only point of view, one may legitimately think that Tractarian names are more close to Russellian names of particulars than to predicates. In fact, though knowledge by acquaintance of the designated object is not required, it is plausible that in order to understand a Tractarian name we only need to know which object is its meaning, without any need to know the logical form of name and object. It is surely a tricky issue involving the possibility of seeing Russell and Wittgenstein as precursors of the so-called direct reference theories. We can avoid facing this issue, renouncing to pose the comparison on this particular level, which perhaps Wittgenstein would have ignored as merely psychological. The relevant semantic level is not the understanding of meaning of names, but the general conditions under which a name can be a name of an object. On this level, the comparison is successful. According to the TLP, a name can be a name of an object under this necessary (though not sufficient, insofar as there are many objects sharing the same form) condition: a name has to mirror the logical form of the object (“signalizing form” principle).

The TPLA semantics for predicates provides for a similar necessary condition. Is it sufficient too? Though TPLA tells us nothing about this aspect, it is theoretically plausible that this condition is not sufficient, as the corresponding condition concerning Tractarian names is not sufficient either. In fact, it is plausible that there exist different predicates, which designate different relations, but are nonetheless connected with the same class of propositions. We can use the Russellian example: the predicate “red” does not designate the same monadic relation that the predicate “green” designates; nonetheless, the predicates “red” and “green” can be in the same class of propositions.

Thus, also on the semantic level, the analogy seems convincing. The exclusion of the “understanding” issue does not affect the other levels. Russell himself often faces the semantic level with a lexicon compatible with the Tractarian point of view. E.g.:

[...] the relation of a predicate to what it means is different from the relation of a name to what it means. (Russell 1918, p. 233)

We have legitimated the comparison on all the levels which seem relevant: ontology, syntax, semantics.

Now, we should pass to theory of types, insofar as Russell claims that his Wittgensteinian theory of relations is important in order to catch the philosophical significance of theory of types. I have not the time to enlighten here the connection between theory of relations and theory of types in TPLA. In general, I propose that the connection is deeply similar to the way in which theory of types is grounded on the combinatorial properties of objects – through the notion of “propositional functions” - in the relevant Tractarian section.

I leave this aspect aside and draw some brief conclusions. The main problem concerns Russell and his interpretation of Wittgensteinian suggestions. Russell claims in TPLA to adopt this theory of relations because of certain Wittgensteinian suggestions. However, he seems to misunderstand something and underestimate something else. It is difficult to trace the limits to his misunderstanding and underestimation, since we do not dispose of adequate historical sources. We do not know what Wittgenstein thought of these issues before 1914. Therefore the historical reconstruction is unavoidably speculative. Anyway, Russell adopts ontological, syntactical and semantic theories about relations and predicates strongly similar to the corresponding Wittgensteinian theories about names and objects. These Russellian theories are built on a core thesis: relations and predicates have determinate combinatorial properties. However, this theory of relations does not seem to determine the logical syntax as a whole. Russell develops only those consequences which are pretheoretically required by the theory of types and the anti-paradoxical aims of it. The remaining picture is not clarified. The respective role of objects and relations – having so different ontology and semantics – is quite obscure. About theory of types, Russell does not seem to see that the Wittgensteinian tool is strongly uneconomical, when conceived as a tool for the foundations of theory of types.

On the Wittgensteinian side, the shown comparison can give some integrative contribution to a vexata quaestio: which is the ontological role of universals? This contribution is only integrative, because of the already mentioned difficulties in giving a persuasive account of the dependence relations between Wittgensteinian suggestions and TPLA. Anyway, it seems that Russell applied to properties and relations what Wittgenstein refers to objects. And this transfer seems undeclared and quite natural from Russell’s point of view. Obviously, one can imagine many ways to fill the historical gaps in such transition. However, a quite natural way to give an account of the transition is to admit that Tractarian objects are not as extraneous to universals as it has been often thought.

In 1983, Merrill and Jaakko Hintikka (Hintikka 1982) proposed that both universals and particulars are objects, though their names function in a different way. A recent proposal by Pasquale Frascolla (Frascolla 2004) claims that all objects have to be conceived as phenomenicqualia, therefore as universals. We do not aim to discuss here difficulties and problems in such proposals. From our limited point of view, we can only remark that both these proposals are a plausible basis to make sense of the strong analogy with TPLA we tried to show here.

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