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Wittgenstein, Frege & The Context Principle

Susan Lucas on how words gain meaning from their context.

Wittgenstein’s Tractatus Logico-Philosophicus is perhaps one of the most startlingly original pieces of philosophy ever written. It has been likened to a philosophical poem; but on another level, it is a very abstract, remote and precise analysis of the logic of language and how we succeed in ‘picturing’ reality in language. Yet for all its originality, the Tractatus evolves from the weaving together of a number of contemporary philosophical threads; and for all its apparent remoteness, at times we see the concerns with the human and the everyday that were to emerge so powerfully, particularly in the Philosophical Investigations, as Wittgenstein’s thinking developed. On the one hand, then, the Tractatus emerged out of the turn towards philosophical logic begun in the last years of the nineteenth century; on the other, the influence of what we would now call ‘continental philosophy’, perhaps particularly the work of Schopenhauer, can be felt, for example in the remarks on ethics towards the end of the book.

Wittgenstein’s predecessors in philosophical logic, Bertrand Russell and Gottlob Frege, both sought to set mathematics on rock-solid foundations in formal logic. In the course of this project both came to see their work as having wider ramifications, suggesting that logical analysis was a way both of doing metaphysics and of demystifying it. Controversial and abstruse questions about the fundamental nature of things could perhaps be domesticated by approaching them as questions about the logic of language. The project ultimately foundered, even in its narrower sense – but not before it had a lasting influence on analytic philosophy.

In this article I shall trace just one thread of the influence of Frege on Wittgenstein; in the use Wittgenstein makes of Frege’s ‘Context Principle’. This allows us to at least partly make sense of what Wittgenstein says about simple objects in the Tractatus, and of how he sees language picturing reality. Moreover, his adherence to the Context Principle remained constant through the developments in his thinking. Even in the Tractatus, the Context Principle represents a first inkling of Wittgenstein’s later conviction that in order to understand how language is meaningful, we need to explore how people actually use it.

The Context of the Context Principle

The Context Principle was one of three principles that Frege introduced at the beginning of his 1884 book The Foundations of Arithmetic. In it Frege was trying to argue for what we might call the objectivity of mathematics. According to such a view, any mathematical proposition – such as Goldbach’s Conjecture that every even number is the sum of two primes – is either objectively true or objectively false, even if we never in fact discover which, and even if in principle we could never discover which it is. However, Frege was equally concerned to reject one kind of account of mathematical objectivity, which we might call mathematical Platonism – the view that mathematical statements are made true by reference to abstract mathematical objects that are in some way real, even though we can’t see, touch or feel them. In other words, mathematical objects such as numbers are ‘real things’, and it is in virtue of this that the truths of mathematics are objective, independent of us – there to be discovered.

Such a view has its attraction – doing mathematics can feel like discovering what is already there – but there are difficulties with it too. In particular, what kind of account are we to give of these abstract objects? Consider the number 11 as an abstract object. How might we know about it? For in contrast to the familiar types of object that are the furniture of our everyday lives, abstract objects do not impact on our senses or change the world in any way (this is what is meant by ‘abstract’). Frege wants to hold on to the objectivity of mathematics, even to say that numbers actually are objects, whilst rejecting this Platonic kind of view. To try to do so he introduces these three principles at the beginning of his book:

• Anti-Psychologism: always separate the logical from the psychological.

• The Context Principle: never ask for the meaning of a word in isolation, but only in the context of a proposition.

• The Concept/Object Distinction: always keep in mind that concepts are distinct from the objects that fall under that concept.

The first principle is directed against psychologism, the doctrine that logical truths are dependent on human awareness, which both Frege and Wittgenstein consistently opposed. The third principle says that concepts and objects are distinct from one another. Frege makes the distinction in semantic terms, that is, in terms of the different roles played by different aspects of a sentence. So, names (such as ‘John’, ‘the cat’, etc) refer to objects, and predicates (such as ‘is good’, ‘was unhappy’, etc) to concepts.

These two principles are immediately linked to the Context Principle, which is central to Frege’s project. According to the Context Principle, the basic unit of sense is the proposition, or sentence. The sentence is the smallest unit of language which can be used to say anything at all. The meaningfulness of names and predicates is a matter of the place they occupy in the sentence, and also whether the sentence is true. Whether or not a name refers to an object, then, is a matter of the contribution the name makes to the truth of the whole sentence.

For Frege then, the Context Principle removes the difficulties of Platonism by asserting that the existence of objects comes down to whether sentences that contain terms referring to them are true. Questions about what exists, and how, are then approached as questions about the truth of sentences. Or in other words, for Frege, it is the linguistic behaviour of numerical expressions together with the truth of the propositions in which they are found that settles the fact that numbers are objects. Because mathematical expressions are meaningful, this shows to Frege that there is no possibility that the scales might drop from our eyes and we might find that there are no natural numbers in reality. Rather, once we have settled that terms referring to numbers are singular terms (that is, they operate like names), and that mathematical sentences using them are by ordinary, sensible criteria true, there is no further intelligible question about whether numbers are objects.

To accept the Context Principle is to accept that the meaning of a name cannot be secured independently of its use in a sentence. Meaning is already to some extent recognised by Frege as turning on the role expressions play in a language – the use that is made of expressions – albeit that he understands this fact in a rather formal, structural way.

Wittgenstein’s Understanding of Context

In the Tractatus, Wittgenstein accepts the Context Principle and so rejects the traditional view that things exist prior to language: that is, he does not think the world is divided up independent of the classifications of the world we make in using language. So as in The Foundations of Arithmetic, the metaphysics that emerges from the Tractatus does so as a result of what can make language meaningful.

As its title suggests, the Tractatus Logico-Philosophicus is concerned with philosophical logic. In particular, it’s concerned with the way in which the underlying logic of language represents the logic of reality. Classical logic is taken for granted in the Tractatus, and it sets the limit on possible states of affairs – meaning, on what can be said or thought. Logic is what makes it possible for us to say anything about the world; it is what makes representation possible. Logic makes it possible for a sentence to be structured so as to have any sense at all, and so to be able to say anything.

You can see this clearly in the way Wittgenstein explains negation. In the Tractatus, for a proposition to have sense is for it to picture a possible state of affairs – which means, define what it would be like for that proposition to be true. If I understand ‘the cat is sitting on the chair’, what I understand is what it would be like if Tibbles were indeed sitting on the chair. But for Wittgenstein, understanding what it is like for a proposition to be true can’t be separated from understanding what it would be like for it to be false – what the world would be like if Tibbles were not sitting on the chair. The fixing of the sense of a proposition includes the negative as well as the positive. That is, the possibility of the proposition’s being false does not result from its having a sense; rather, its possible negation is integral to its sense – part of what it means. A meaningful proposition can be true or false; and if it is false, its sense is the same, but the facts are different. Like all the logical operations (eg conjunction, disjunction and implication), the negation sign applied to a proposition does not represent the facts: rather, it shows the sense of a proposition by giving it its form – that is, by combining the simple propositions in it in a particular way. Here, we get to the sense in which, for Wittgenstein in the Tractatus, logic is the possibility of representation.

Both of these must be possible for the statement ‘Tibbles is sitting on the chair’ to be meaningful

In a number of places in the Tractatus, Wittgenstein quotes the Context Principle almost verbatim from Frege’s Foundations of Arithmetic. For example, “Only propositions have sense: only in the nexus of a proposition does a name have a meaning” or “An expression has meaning only in a proposition” (Tractatus 3.3, 3.314). Wittgenstein is here making much the same use of the Context Principle as Frege: acknowledging the fundamental role of the sentence (proposition) within language – that it is only with a sentence that one can say anything; and also that the reference of the parts is a matter of their contribution to the truth of whole propositions. Moreover, it is only in language that certain states of affairs are allowable and certain others are ruled out, so that, for example, ‘the book is red’ represents a possible state of affairs, but ‘the number 7 is red’ does not.

What is this?

We also find Wittgenstein criticising the primacy of ostensive definition (e.g. pointing to an object and saying “That’s a penguin”) as a way of picking out objects in much the same way that Frege does. An ostensive definition yields a simple proposition – which is a proposition whose names directly refer to things in the world. Wittgenstein never does give an example of a simple proposition, but they seem to be basic subject/predicate phrases, such as “Popper is stupid.” However, it is not the case that in simple propositions names are connected with objects in easy word-to-world connections. Instead, Wittgenstein uses the Context Principle to suggest that primitive signs – names for simple objects – can only be understood by explaining the simple propositions containing them: “The meanings of primitive signs can [only] be explained by means of elucidations. Elucidations are propositions that contain the primitive signs. So they can only be understood if the meanings of these signs are already known.” (Tractatus, 3.263). In other words, you only know what I mean in saying “That’s a penguin” if you already have a good idea from other explanations what sort of thing a ‘penguin’ is: compare my pointing to the thing and saying “That’s a bird.”

Here then, we get to the positive use that Wittgenstein makes of the Context Principle in the Tractatus. His endorsement of the Context Principle suggests that the Tractarian simple objects to which names in simple propositions refer are what exist primarily or in their own right, not in some obscure metaphysical sense, but rather in the way that numbers are objects for Frege: they exist because they are necessary for the determinate sense of simple propositions and hence for meaningful language.

We begin to grasp how simple objects function: they are not the ordinary objects we encounter in everyday life, that impact upon our senses in causal ways. Rather, Wittgenstein’s embracing of the Context Principle makes him see objects in a technical sense: they are the referents of names in simple sentences, which names, when put together with predicates using the ‘scaffolding’ of logic, give us the structure of our world in language.

Future Contexts

Wittgenstein, then, accepts the Context Principle in the same form as Frege, makes essentially the same critical use of it, and shares with Frege a conception that the best way to find out what sort of things exist is to reflect on the nature of language. In the famous passage at the beginning of the Tractatus, Wittgenstein states, “The world is the totality of facts not of things” (1.1). If, as Wittgenstein claims at 2.063, “the sum total of reality is the world,” then it is only language that gives us reality, since it is only language that gives us facts. And the way language pictures reality in the Tractatus cannot be understood without a background understanding of Wittgenstein’s assent to Frege’s Context Principle and the use he makes of it.

Despite their common conception of ontology, of what exists, Wittgenstein and Frege differ from one another in significant ways. Whilst Frege, like Russell, yearned to provide a language more logically perfect than ordinary language, Wittgenstein does not believe that there is anything fundamentally wrong with ordinary language; rather it is that the surface form of an ordinary language proposition can sometimes mislead about its actual logical form. Therefore he thinks there is a need to reveal the structure of propositions more perspicaciously than ordinary language always allows.

Wittgenstein’s assent to the Context Principle continued long after the Tractatus. He remained committed to it while developing his mature conception of ‘meaning as use’ in the Philosophical Investigations, where he again quotes the Context Principle verbatim (§49). In the Tractatus, as we have seen, the Context Principle is essentially used in a structural way. However, it already contains in embryonic form the idea of the Philosophical Investigations that there is a ‘philosophical grammar’ to our claims about the world that is embodied in our practice of using language meaningfully. At the time he was writing the Tractatus, Wittgenstein could only understand this notion of ‘background’ – what was later to become ‘grammar’ – in terms of an abstract structure underlying our language-use but independent of it. It was only when the lessons of his mature conception of linguistic use had been absorbed that the full concept of ‘grammar’ emerged, and Wittgenstein saw that our most fundamental practical commitments as human language-users are an intimate part of what it means to characterise reality in language. So in the Investigations, although the Context Principle continues to be affirmed, the context shifts from propositions to include the entire language game and ourselves as competent language-users in the various forms of life we pursue. Yet to the extent that Frege recognised that the linguistic characterisation of reality is always contextual, and the Wittgenstein of the Tractatus endorsed Frege’s insight, it is possible to represent the origins of Wittgenstein’s mature conception of language in the Investigations and beyond as already there in the Context Principle as it emerges in the Tractatus, and in the work of Wittgenstein’s illustrious forebear, Gottlob Frege.

Susan Lucas is Priest-in-Charge at St Faith, Great Crosby, Liverpool.