The picture theory of meaning

The picture theory is the idea, set out in the Tractatus, that a sentence works like a picture. A meaningful proposition is a model of a possible situation: its parts stand for things, and the way those parts are arranged shows how the things are arranged. If the world really is arranged that way, the sentence is true. If not, it is false, but it still makes sense.

That last point is the clever part. A sentence does not need to be true to be meaningful. "The cat is on the mat" means something even when the cat is in the garden, just as a drawing of a cat on a mat is still a drawing of that, wherever the cat happens to be.

In the animation above you see a ball resting on a box, and next to it the sentence "The ball is on the box". Thin lines run from each name in the sentence to the thing it names. Now let the ball roll off. The sentence is marked false, but nothing about it breaks: it still shows a perfectly clear possibility, one that simply does not match what is there. That is the picture theory in miniature.

Where did the idea come from?

According to a story Wittgenstein later told his friend Georg Henrik von Wright, the idea struck him during the First World War when he read about a Paris court case in which a road accident was reconstructed with toy cars and dolls. The model could represent the accident because its pieces corresponded to real cars and people, and their positions to real positions. His wartime notebook for 29 September 1914 already says that in a proposition a world is put together experimentally, like the Paris model. The idea grew into the opening remarks of the Tractatus logico-philosophicus, published in 1921 (German) and 1922 (English).

Wir machen uns Bilder der Tatsachen.

We make ourselves pictures of facts.

Tractatus 2.1

How does a sentence picture something?

Wittgenstein breaks it down into a few steps (Tractatus 2.1 to 2.225 and 4.01 onwards).

• Elements stand for objects. In a picture, each element goes proxy for a thing. In a fully analysed sentence, each name stands for an object (Tractatus 2.131, 3.203).
• The arrangement matters. A picture is not a heap of names. It is a fact in its own right: its elements are combined in a definite way, and that combination says that the things are combined in the same way (2.14, 2.15).
• Picture and world share a form. To be able to depict anything at all, a picture must have something in common with what it depicts. Wittgenstein calls the most general version of this shared structure logical form (2.18).
• Sense comes before truth. What a picture represents is its sense. Its truth or falsity lies in whether that sense agrees with reality (2.221, 2.222). You cannot tell from the picture alone whether it is true (2.224); you have to look.

Der Satz ist ein Bild der Wirklichkeit.

The proposition is a picture of reality.

Tractatus 4.01

Wittgenstein admits that ordinary sentences do not look like pictures. "The ball is on the box" is a string of sounds or letters, not a little drawing. But he points out that musical notation does not look like music either, and yet a trained musician can read a symphony from a score, and a gramophone groove holds the same music in yet another form (4.011, 4.014). What makes them all pictures of the same thing is a shared internal structure, not visual likeness.

Why did it matter so much to him?

The theory draws a sharp line around what can be said. A sentence makes sense only if it pictures a possible arrangement of objects. Everything else, including the claims of ethics, aesthetics, religion and much of traditional metaphysics, falls outside that line. Wittgenstein did not think those things were unimportant. On the contrary, he thought they could not be put into factual sentences at all.

The theory also explains logic. A tautology like "it is raining or it is not raining" pictures nothing, so it says nothing about the world, yet it is not nonsense: it shows something about the structure of language. And one thing a picture can never do is depict its own form. It can only display it (2.172). This is the root of the Tractatus distinction between saying and showing.

A common misunderstanding

The theory does not say that every sentence on the page is already a neat picture. Ordinary language, he wrote, disguises thought (4.002). Only after analysis into elementary propositions, made up of names in immediate combination, would the picturing become visible. Strikingly, Wittgenstein never gave a single example of an elementary proposition or of an object. Scholars still disagree about what he had in mind: physical particles, points in the visual field, or simply whatever analysis would end up with. The Stanford Encyclopedia entry on Wittgenstein's logical atomism lays out the options.

What did the later Wittgenstein think of it?

When Wittgenstein returned to philosophy around 1929, he soon began to criticise his own earlier view. The Philosophical Investigations opens by attacking a picture of language in which every word names an object, and it looks back on the Tractatus with a famous remark: a picture held us captive (PI §115). He came to see that describing facts is only one thing we do with words among many: giving orders, telling jokes, thanking, praying. That shift is what the ideas of language games and meaning as use try to capture.

Even so, the picture theory has not disappeared. The thought that a true sentence corresponds to a fact, that meaning has something to do with possible situations, and that a representation must share structure with what it represents, all live on in logic, in formal semantics and in debates about how models in science represent the world. For a broader overview, see the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy. The English text of the Tractatus is freely available at Project Gutenberg.