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

Introduction

Some of Wittgenstein’s early remarks on the connection between logic and the world leave a highly anti-conventionalist impression. For example, in the Tractatus, he says that the world is “in logical space” (TLP 1.13) and that logic “pervades the world” (TLP 5.61). At a first glance, this seems to imply that the rules of logic are determined by the way the world is. And this, in turn, seems to be something that is not dependent on convention. Consider, for example, a passage from the Notebooks 1914-16, where Wittgenstein says:

And it keeps on forcing itself upon us that there is some simple indivisible, an element of being, in brief a thing … And it appears as if that were identical with the proposition that the world must be what it is, it must be definite. (NB, 62)

Further statements favouring an anti-conventionalist interpretation can be found in the Tractatus. According to 5.4731, language “prevents every logical mistake”, and what makes logic a priori is the fact that one “cannot think illogically”. And according to 6.124, logic “is not a field in which we express what we wish with the help of signs, but rather one in which the nature of the absolutely necessary signs speaks for itself”.

These passages have lead Ishiguro to the claim that there is no trace of conventionalism about the rules of logic in the Tractatus (Ishiguro 2001, 129–31). However, Ishiguro’s claim does not take into account important evidence from the pre-Tractatus writings. The aim of this paper is to argue that construction and convention play a significant role in the formation of Wittgenstein’s thought. Some aspects of these early developments show considerable influence on the philosophy of the Tractatus. Moreover, the role of construction and convention leads to an explanation for some aspects of the Tractarian conception of subjectivity.

1. Logic, Ontology, and Construction

Wittgenstein introduces the issue of construction in the context of his theory of tautologies. This theory of tautologies has its roots in Wittgenstein’s theory of the bi-polarity of propositions. According to the theory of bi-polarity, a meaningful proposition must be able to be true or false (NB, 94). The “poles” of the proposition, symbolized by “a” and “b” in Wittgenstein’s notation, correspond to the case of the truth and the case of the falsehood of the proposition (NB, 98). In the Notes dictated to Moore, Wittgenstein makes use of the theory of the bi-polarity of meaningful propositions in order to characterize tautologies. Tautologies are propositions that do not have two poles (NB, 113). In a letter to Russell of 1913, Wittgenstein analyses the nature of propositions of logic with the help of this conception of tautologies:

It is the peculiar (and most important) characteristic of non-logical propositions, that their truth cannot be seen in the propositional sign itself. (…) But the propositions of logic – and they alone – have the property of expressing their truth or falsehood in the very sign itself. (…)

The great question is now: How should a notation be constructed, which will make every tautology recognizable as a tautology in one and the same way? This is the fundamental problem of logic. (NB, 128–9)

Here, this question is answered with recourse to the application of the ab-notation to more complex propositions. Already at this place, complex propositions are conceived of as truth-functionally dependent on elementary sentences. Finally, the Notebook entry of 21 November 1916 answers the same question in a more technical way:

We now need a clarification of the concept of the atomic function and the concept “and so on”.

The concept “and so on”, symbolized by “….” is one of the most important of all and like all the others infinitely fundamental.

For it alone justifies us in constructing logic and mathematics “so on” from the fundamental laws and primitive signs. (NB, 89)

On the side of the constitution of the world, the idea of construction plays a very similar role. Already in the Notebooks, Wittgenstein puts forward a theory of simple objects. Although he considers different possibilities for what these objects might be like (e.g. minima sensibilia or points in visual space; NB, 45; 50; 64), he ultimately is confronted with the impossibility of giving convincing examples. Therefore, he says:

If I can imagine a ‘kind of object’ without knowing whether there are such objects, then I must have constructed their archetype (Urbild) for myself. (NB, 74)

The notion of object, therefore, is to be seen as the result of construction similar to the way rules of logic are conceived of as the result of construction. More generally, Wittgenstein writes: “we can foresee what we have constructed” (NB, 71), which holds for the rules of logical notation as well as for the conception of simple objects. Construction in logic and construction of the archetype of objects, moreover, seem to be tied to each other. For example, the question around which much of the early sections of the Notebooks turn is: “can we manage without simple objects in LOGIC?” (NB, 46). Thus, logic and ontology in Wittgenstein’s earliest writings are both to be seen as results of construction, and the construction of ontology is immediately connected with the construction of logic.

2. Construction, Convention, and Adequacy Conditions

The obvious question arising at this point concerns the role of convention in construction. In the context of his first formulation of the theory of tautologies in the Notes dictated to Moore, Wittgenstein says:

What is unarbitrary about our symbols is not them, nor the rules we give; but the fact that, having given certain rules, others are fixed = follow logically. (NB, 114)

He takes this thought up explicitly at TLP 3.342. Again, the logical notation shows arbitrary features, whereas the consequences of these arbitrary decisions follow in a non-arbitrary way. As Wittgenstein says, this has to do with the “nature” (“Wesen”) of logical notation.

This does not mean that construction in logic, in Wittgenstein’s view, would be completely unrestricted. Already in the Notes dictated to Moore, he says:

It is true, in a sense, that logical proposition are “postulates” – something which we “demand”; for we demand a satisfactory notation. (NB, 118).

This point is repeated in TLP 6.1223. Here, again, logical truths are characterised as something we can “postulate”, in the sense that we can “postulate” a sufficient logical notation. At both places, Wittgenstein clearly takes a conventionalist line of thought. However, the role of convention in logic at the same time is qualified by conditions of adequacy: Convention has to yield a “satisfactory” or “sufficient” logical notation. For a specification of these adequacy conditions, we have to turn to various passages of the Tractatus and the pre-Tractatus writings. An important requirement is that a satisfactory notation must be constructed in a way that the self-referential paradoxes cannot occur. According to TLP 3.333-3.334, logical syntax must preclude the possibility that a function can be its own argument. This adequacy condition is already part of the early Notes on Logic, where Wittgenstein says:

No proposition can say anything about itself, because the symbol of the proposition cannot be contained in itself; this must be the basis of the theory of logical types. (NB, 107)

In fact, Wittgenstein sets up a much more extravagant catalogue of conditions of adequacy. In his 1913 letter to Russell mentioned above, there is the requirement that an adequate logical notation has to provide means of proving the tautological character of logical truths in a uniform way (NB, 129). The theory of the bi-polarity of propositions also leads to the requirement that an adequate logical notation must be based on the idea that elementary sentences are true-or-false pictures of reality and, for this reason, logically independent from each other (TLP 2.021-2.0212). A further requirement is that logic has to be constructed in a way that accounts for the determinateness of sense (TLP 3.23), a requirement that leads to a form of semantic atomism. It may not be surprising that Wittgenstein, despite of his conventionalist attitude, was convinced that a logic constructed along the lines of his early philosophy is the only one that is able to meet all these criteria of adequacy (see NB, 17).

3. Construction, Convention, and Subjectivity

From this perspective, the seemingly anti-conventionalist statements quoted by Ishiguro can be seen in a different light. It is interesting that one of these statements (TLP 5.61) is taken from Wittgenstein’s discussion of solipsism. The fact that “logic pervades the world” there is connected to the view that the world is “my world” and that “that language which alone I understand” is “my language” (TLP 5.62). Seen from this perspective, the facts that “my” world is in logical space (TLP 1.13) and that “my” language prevents illogical thought (TLP 5.4731) do not provide a convincing argument against a form of conventionalism restricted by a set of adequacy conditions.

Quite to the contrary, aspects of Wittgenstein’s view of subjectivity can be seen as a consequence of his views about construction and convention. Subjectivity, for Wittgenstein, does not come in by way of a commitment to the phenomenological character of simple objects, or, correspondingly, to a phenomenological language (see Blank 2001). It is exactly the insight that it might prove impossible to identify any satisfactory examples of simple objects that introduces the theme of construction into Wittgenstein’s conception of ontology (see NB, 74). Rather, constructing logical rules and “archetype” of objects is subjective in the sense that it is something that we do. Thus, there are no de re necessities, no given structure of the world which, in turn, determines the structure of language. Language is “my” language, and the world “my” world, because both logic (which “pervades” language and the world) and the conception of simple objects (whose configurations constitute the world) are to be seen as results of construction. The only necessity at work here is a kind of necessity resulting from the set of adequacy conditions for a sufficient logical notation.

This does not mean that the role of construction and convention would provide an exhaustive account of all Wittgenstein has to say about subjectivity. Quite to the contrary, some aspects of his remarks about solipsism cannot be explained without a consideration of the influence of authors such as Schopenhauer and Weininger (see, Sluga 1981; McGuinness 2001). This holds especially for some of the aspects of Wittgenstein’s view of subjectivity that are more closely tied to the issue of individuality, e.g. the issues of will, happiness and death (see TLP 6.43-6.4312). However, there also is a strongly, and explicitly, impersonal aspect in his conception of subjectivity. Consider, for example, the Notebook entry of 23 May 1915, where Wittgenstein says:

The limits of my language constitute the limits of my world. There is only one world soul, which I for preference call my soul and as which alone I conceive what I call the souls of others. (NB, 49)

A few days later, in the entry of 29 May 1915, he cautiously, in the form of questions, puts forward the idea that, in some sense, there is only one language (NB, 52). The at the same time personal and impersonal character of subjectivity implied by this account of language can, at least in part, be explained by the role of construction and convention in Wittgenstein’s early views on logic and language. The personal aspect of subjectivity is, partly at least, due to the fact that each individual makes use of a language that is based on the construction of logical rules and ontological assumptions (and not on an independently given structure of the world). The impersonal character of subjectivity is due to the fact for all individuals the logical and ontological construction underlying language, due to the set of adequacy conditions, is the same. In this sense, in TLP 5.62 Wittgenstein characterizes “my” language at the same time as the only language there is (“that language alone”).