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Pictures and Nonsense

Mark Jago looks at Wittgenstein’s first theory of language, in the Tractatus. One of the conclusions of this theory is that the theory in the Tractatus is nonsense…

In this article I am going to describe Wittgenstein’s famous picture theory of language. The aim of this theory is to set out an account of what sentences mean and just as importantly, to give us a way of distinguishing sense from nonsense. The theory is found in Wittgenstein’s first book, the Tractatus Logico-Philosophicus, which ranks as one of the hardest-to-read of all the great works of philosophy. It is an unusual book, written whilst Wittgenstein was serving in the Austrian army during the First World War and finished whilst he was a prisoner of war in Italy. It is remarkably short for a great work of philosophy; this is in part due to Wittgenstein's condensed writing style, which has put off many readers and confused a good number of philosophers. But Wittgenstein’s aim was not to confuse his readers: he simply wanted to express himself as precisely and as logically as possible.

So the picture theory of language is an attempt to discover the essence of language. In its simplest form, the theory says the function of language is to allow us to picture things.

In itself, this doesn’t tell us all that much. Pictures can have many purposes – just think of the differences between hieroglyphics and modern artworks. Therefore it is helpful to consider a very basic type of picture, such as a diagram I might draw to show a friend the way to my house. I do not have to sketch every detail of the route my friend should take, such as what the view will look like along the way. Rather, I need to show my friend where to turn, and perhaps mark some prominent landmarks along the route.

Suppose that my diagram indicates that my friend should take the second right after the lights. Of course, the situation that the diagram presents to my friend need not be true to the facts; my diagram might be part of a practical joke on her, in which I send her to someone else’s house. In constructing a picture such as this, I am not constrained by the actual facts. Although my house is on the second road on the right, I am perfectly able to draw a diagram in which the house is pictured on the second road on the left.

Wittgenstein is keen to emphasize that what a picture means is independent of whether it is a truthful representation or not. But if a diagram can be misleading or downright false, so that it does not picture the facts, what does it picture? Wittgenstein says that what a diagram or picture represents exists in logical space. One way to understand this is to see that the way the world has turned out is not the only way that it could have turned out. Had things turned out differently, my house could have been on the second left, even though it is actually on the second right. So a picture represents something that is the case, or alternatively, could have been the case had the world turned out differently.

What is it that makes the arrangement of lines on my diagram a picture, whereas a scribble produced at random (say, by a crab crawling around in the sand) is not counted as a picture? According to Wittgenstein, it is that the lines in the diagram are related together in a way that mimics the way the things they correspond to are related. For example my diagram has symbols for roads and houses, which if true, are arranged in a way which mimics their arrangement in reality.

Our diagram is a good example of what Wittgenstein had in mind when talking about pictures, for its usefulness relies on the way in which the parts of the picture are arranged, rather than relying on it being a lifelike artistic depiction of the facts. The important point is that the structure of the picture mirrors (represents) the structure of a possible situation. The possible situation is what the picture means. This is why we can know what a picture means without knowing whether it is true or false. The picture is true when the situation it pictures is the actual situation. To find out if it is, we have to look and see how the world actually is.

Wittgenstein’s theory of language holds that sentences work like pictures: their purpose is also to picture possible situations. It must be pointed out that Wittgenstein is not concerned with mental pictures, ie the images we conjure up in our minds. The thesis is not that the meaning of a sentence is what we picture in our minds when we hear or think the sentence. That was the theory of language advocated by John Locke, the 17th century empiricist philosopher. Rather, Wittgenstein is concerned with a more abstract notion of a picture, as something that either agrees or disagrees with any way the world might have been, and which says, this is the way things actually are.

Logical Analysis

The next element of Wittgenstein’s first theory of language concerns how sentences are built up from simpler sentences (or propositions, as Wittgenstein calls them, meaning a sentence that’s unambiguously either true or false). His idea is that whenever a sentence contains one of the logical connectives ‘not’, ‘and’, ‘or’, or ‘if … then’, we can work out the truth-value of that proposition (ie whether it’s true or false) if we know the truth-values of the sentences that make it up. This is seen most easily by giving an example. Suppose I say, “If it isn’t raining, then we will go to the park and have a picnic.” This sentence is made up from the following simpler sentences:

1. It is raining

2. We will go to the park

3. We will have a picnic

We build our complex sentence in three stages. First, we negate sentence 1 by adding ‘not’ to it; then we join sentences 2 and 3 with ‘and’; finally, we join these two new sentences using ‘If … then’. Wittgenstein gives us a method of determining the truth-value of our complex sentence in terms of the truth or falsity of sentences 1 to 3. Negated sentences ‘not …’ are true when the sentence that occupies the ‘…’ place is false. Sentences built by joining two sentences with ‘and’ are true when each of the original sentences are individually true. Finally, conditional ‘if … then’ sentences are false when the first sentencein the complex sentence is true but the second is false, and true otherwise. These conditions correspond to the truth tables any philosophy student learns in their first logic classes. Combine these rules together and you discover the truth conditions for the compound sentence.

Having given this analysis of complex sentences in terms of simpler ones, Wittgenstein then says that there must be sentences that are completely free of logical complexity. He calls these elementary propositions. These are not simply sentences in which ‘not’, ‘and’, ‘or’ or ‘if … then’ do not appear, for Wittgenstein holds that sentences can contain hidden logical complexity which does not show up in everyday English. An example of this is given by definite descriptions such as “the present King of France is bald.” According to Wittgenstein’s teacher Bertrand Russell, this actually means “there exists exactly one person who is both the present King of France and bald.” According to Russell, the existential ‘there exists’ is hidden in everyday English use, but can be brought out through logical analysis.

Meaning and Nonsense

We can now turn to Wittgenstein’s more general remarks on what counts as sense (ie what is meaningful) and what is nonsense. In the introduction to the Tractatus, Wittgenstein says that he set out to draw a boundary between thinking something meaningful and thinking nonsense. He does not discuss thought at any length, for he claims that the boundary between sense and nonsense can be drawn only in language.

To recap, Wittgenstein argues that the meaning of a sentence is just what it pictures. Its meaning tells us how the world is if the sentence is true, or how it would be if the sentence were true; but the picture doesn’t tell us whether the sentence is in fact true or false. Thus we can know what a sentence means without knowing whether it is true or false. Meaning and understanding are intimately linked. When we understand a sentence, we grasp its meaning. We understand a sentence when we know what it pictures – which amounts to knowing how the world would be in the case of the proposition being true.

This is a truth-conditional theory of understanding: we understand a sentence when we grasp the conditions in which the sentence would be true. Truth-conditional theories of understanding have a counterpart in the theory of meaning: ‘the meaning of a sentence is a condition on how the world would have to be for that sentence to be true.’ The truth-conditional theory of meaning has been popular in recent years because it provides a realist theory of meaning, on which one can say what a sentence means without appealing to what anyone might or might not know to be the case.

Now we turn to Wittgenstein’s analysis of what counts as a meaningful sentence, and by the same token, what counts as nonsense. As we have seen, Wittgenstein holds that meaning rests on a sentence being a picture of a possible situation, and so meaning is linked to truth conditions. Therefore without truth conditions, a sentence cannot be meaningful.

Let us look at what this implies. All elementary propositions purport to describe a basic fact about the world, and so an elementary proposition is true if that fact exists and false otherwise. As a consequence, all elementary propositions are meaningful. According to Wittgenstein, a sentence can only be meaningful if it is an elementary proposition or else is built from a number of elementary propositions using ‘not’, ‘and’, ‘or’ and ‘if … then’. (We might also allow sentences beginning ‘for all’ or ‘every’.) Every sentence that does not fit this template is meaningless, according to Wittgenstein.

This does not guarantee that all the sentences that are built in this way are meaningful. A sentence can be built from elementary propositions in this way but because of the way it is put together, the meaning drops out of the sentence. This loss of meaning happens when we arrive at a sentence that just has to be true or just has to be false. This is the case for tautologies, which logic guarantees to be true, and logical falsehoods, which could not possibly be true. “Either it’s raining or it’s not” is a tautology, because however the world might have turned out, it would be true. Accordingly, saying “either it’s raining or it’s not” does not tell us anything about the world: it does not allow us to distinguish the actual situation from any situation that might have been. On the other hand, “It’s both raining and not raining” is a logical falsehood. It could not be or have been true, however the world might have turned out. So this too tells us nothing abut how the world is.

According to Wittgenstein, tautologies and logical falsehoods do not picture anything and so cannot be meaningful sentences. But they lack meaning in a different way to sentences not built from elementary propositions using the logical connectives. Those sentences are utterly nonsensical (Wittgenstein’s term was unsinnig), whereas tautologies and logical falsehoods merely lack a meaning (they are sinnloss).

It is logic, then, that sets the limits of meaning. When logic itself tells us that a sentence is true or false, the sentence lacks meaning. Such sentences lie on the boundary between meaningfulness and meaninglessness. Inside the boundary, sentences picture a way the world could be, or the way that it is, if they are true. Outside the boundary, therefore, we find sentences that do not picture a way the world could be at all.

But what about the remarks I’ve just made? Do they picture a way the world could be? They do not. They concern how language works, and so they say what would be the case however the world might have turned out. The logic underpinning language is common to all the ways the world [logically] might have been, so saying that language works like this or that does not tell us anything about the world: it does not picture anything. As a consequence, all talk about language and its meaning lies on the far side of the sense/nonsense boundary.

This conclusion applies just as strongly to the Tractatus itself as it does to this article. Given Wittgenstein’s theory of sense and nonsense, that very theory turns out to be meaningless! This is not an unforeseen consequence of Wittgenstein’s theory, something he realized at a later date. By the time we get to the end of the Tractatus it appears that Wittgenstein intended all along to show that what he had written is nonsense. If this is so, why did he write the Tractatus at all? And if the Tractatus is nonsense, what about the rest of philosophy?

The Purpose of Philosophy

Included in Wittgenstein’s list of nonsense, as well as the logic of language, is any talk about ethics, aesthetics, religion and mathematics. In fact, all philosophical reflection is meaningless.

To many, this conclusion is incredible. Many philosophers devote their efforts to discussing ethical arguments, for example; why would they do this if all they say is meaningless?

On one way of reading the Tractatus, Wittgenstein’s main message is the meaningless of philosophy in general. So the picture ‘theory’ I discussed above should not be called a theory at all, for a theory can be stated meaningfully. However, even though philosophical sentences are meaningless, philosophy as an activity can show us certain things – things, that is, that cannot be said meaningfully.

This distinction between saying and showing is vital to the Tractatus. The aim of the Tractatus is to show us things: for example, to show us that philosophical or mathematical sentences do not picture anything, and to show the logical structure that language must have. Wittgenstein viewed this activity of showing what cannot be said as of prime importance for philosophy. This conception of philosophy contrasts with many traditional views, dating back to ancient times, which seek to use rational thought to discover the most basic and fundamental features of reality. Indeed, this is how the Tractatus begins, with an examination of the logical structure of the world. But as the investigation develops, we begin to realize that Wittgenstein’s aim is actually far more radical.

In reading the Tractatus, we are not being presented with arguments which attempt to establish a conclusion, for to do so would rely on the subject matter being the kind of thing that can be talked about meaningfully. But the aims of the Tractatus, and of philosophy in general, are not the same as the aims of science. Instead, for Wittgenstein, philosophy aims at the clarification of our thoughts. Through pursuing philosophy as an activity, we come to realize the boundaries of sense.

The Tractatus ends on a mystical note, a term Wittgenstein did not shy from (unlike many analytical philosophers). Traditional philosophical problems such as the will, the soul, God and scepticism, cannot be resolved by appealing to the facts of our world. This is why they are mystical. In fact, it is not even correct to call these ‘problems’, for only issues that can be settled by appealing to the facts, such as the problems of physics or psychology, should be counted as problems to Wittgenstein.

The logical positivists of the Vienna Circle were attracted to the Tractatus. They too held that metaphysical propositions are meaningless, and agreed with Wittgenstein that philosophers should demonstrate that such speculations are nonsense. But according to Wittgenstein, any allegiance to the logical positivist’s verification principle – which says that only those sentences that can be verified count as meaningful – is itself meaningless. The logical positivists wanted to align philosophy with scientific method, but Wittgenstein would regard this as misguided.

Wittgenstein takes the activity of philosophy seriously. Participating in philosophy can allow us to see the world rightly. To understand the Tractatus, we have to go through the kind of thought process that Wittgenstein went through in writing it. He says that it can be understood only by those who have already had the thoughts it contains. Anyone who comes to understand the Tractatus, understands that it is senseless; but since understanding has then been achieved, the sentences written in it are no longer needed. In this way, it does not matter that they are meaningless, for they have brought understanding.

Wittgenstein offers us a wonderful and notorious metaphor for this process. He compares someone reading the Tractatus to someone climbing a ladder to reach higher ground. Once she reaches it she can throw the ladder away, since it is no longer needed. Similarly, once understanding has been achieved, we can throw the Tractatus away, as we no longer need it to support our understanding. The value is in the activity, not the content.

The main thrust of the Tractatus, then, is that there is sense and there is nonsense, but we cannot talk meaningfully about this distinction nor about which side of the divide a sentence belongs to. Talking about nonsense is itself nonsense. This is something we cannot say meaningfully, but which nevertheless shows itself in language. Or as Wittgenstein says in his own inimitable style, whereof one cannot speak, thereof one must be silent.

© Mark Jago 2006

Mark Jago is a lecturer at the Department of Philosophy at Nottingham University, where he is completing his PhD. He is currently compiling an introductory book on Wittgenstein.

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