Seventy pages, written mostly in the trenches, published in German in 1921 and in English in 1922 with a translation Wittgenstein disliked and an introduction by Russell he thought had missed the point. He believed it had solved every philosophical problem, and left the subject.

The numbering, which is the structure

Almost nobody explains this and it is the first thing to know.

There are seven main propositions, numbered 1 to 7. Everything else is a decimal expansion: 1.1 comments on 1, 1.11 comments on 1.1, 2.0121 comments on 2.012. The number tells you the logical weight of the remark. A proposition with a short number is load-bearing; one with a long number is a gloss on a gloss.

So the book can be read at any depth. Read only the seven and you have the skeleton. Read to two decimal places and you have the argument. The full text is the argument with its supports.

The seven:

1. The world is everything that is the case. 2. What is the case, the fact, is the existence of states of affairs. 3. The logical picture of the facts is the thought. 4. The thought is the proposition with a sense. 5. A proposition is a truth-function of elementary propositions. 6. The general form of a truth-function is given. 7. Whereof one cannot speak, thereof one must be silent.

Note that 7 has no expansion. It is one line with nothing under it.

What reading it is like

Short, and among the hardest things in philosophy, in a specific way: the sentences are simple and the connections are missing. Wittgenstein compresses to the point of omitting the reasoning, on the view that a reader who has had the thoughts will recognize them.

Do not read it straight through first. Read the seven propositions. Then read 1 through 2.063, which sets up the ontology. Then jump to 6.4 onward, which is the ethics and the conclusion and is the part that is actually about something. The middle — the logic, 4 through 6.1 — is technical, was the part Russell cared about, and is the part that has dated most.

Ogden's 1922 translation is the famous one; Pears and McGuinness (1961) is more accurate and less beautiful. The Ogden has "whereof one cannot speak"; the Pears has "what we cannot speak about".

The picture theory

A proposition is a picture of a possible state of affairs.

The story he told is that he got the idea from a Paris law report of a traffic accident presented with model cars. The model represents because its parts stand for things and their arrangement stands for the arrangement of the things. A sentence works the same way: its elements go proxy for objects, and the way they are combined says how the objects are combined.

Three consequences.

A proposition has sense independently of being true. The picture shows a possibility; whether the possibility obtains is a separate question.

What a picture cannot do is picture its own form of representation. To say how a picture represents, you would need a picture of the relation between picture and world, which would need the same again.

The limits of language are the limits of the world. Whatever cannot be pictured cannot be said. That includes logical form, ethics, aesthetics, the self as subject, and God.

Saying and showing

The distinction the whole book turns on, and the one Russell missed.

Some things cannot be said and nonetheless show themselves. That a proposition has the logical form it has is not a further fact it could state; it is displayed in the proposition. The value of the world does not lie inside the world and cannot be stated as a fact within it.

This is why the concluding remarks are not dismissive of ethics. 6.421 says ethics cannot be put into words and that ethics is transcendental. He wrote to a publisher that the book's point was ethical, and that the important part was the one he had not written. The Vienna Circle read the same text as verificationism — meaningful statements are the verifiable ones, so the rest is nonsense to be cleared away — and took him as their founder. He thought they had inverted him: what cannot be said is not the unimportant remainder, it is everything that matters. He responded to their invitations by reading them Tagore's poetry with his back to the room.

The ladder

6.54, and one of the strangest moves in philosophy.

He says that anyone who understands him will recognize his propositions as nonsense — that they are a ladder to be thrown away after you have climbed it. The book's own sentences try to say what by its own doctrine cannot be said: they are about the relation between language and world, and that relation shows and does not speak.

So the Tractatus declares itself meaningless in its second-to-last remark, and then closes with 7.

What to make of that is the central question in the scholarship. The traditional reading treats the nonsense as illuminating — it conveys something by failing in the right way. The resolute reading, from Cora Diamond and James Conant, says that is having it both ways, and that he meant plain nonsense, with the book a therapeutic exercise that leaves you with nothing but the recognition that you wanted to say something unsayable.

Key passages

1–1.21 — the world as facts rather than things.

2.1–2.225 — the picture theory.

4.003 — most philosophical propositions are not false but nonsensical.

4.116 — whatever can be said can be said clearly.

5.6 — the limits of my language mean the limits of my world.

6.41–6.421 — value lies outside the world; ethics is transcendental.

6.44 — not how the world is, but that it is, is the mystical.

6.522 — there is indeed the inexpressible; this shows itself.

6.54 — the ladder.

7 — the last line.

What is contested

Whether the nonsense is illuminating or plain. The traditional and resolute readings divide on this and the dispute has run for thirty years. It decides what the book is.

Whether logical atomism has any content. The simple objects at the base are never given an example. Wittgenstein says it is not the philosopher's business to supply one, and critics say a theory whose basic entities cannot be instanced is not saying anything.

Whether he later refuted it or extended it. The Investigations attacks the picture of language as naming, which is the Tractatus's picture. The commitment to dissolving problems rather than solving them is continuous. See Wittgenstein.

How much Frege and Russell are in it. The sense-reference distinction and the theory of descriptions are both presupposed, and Wittgenstein's debt is larger than the book's tone admits — he thanks them in the preface in a single sentence.