Wittgenstein’s Tractatus: Now With Examples

Elliott Thornley · Essay, 2021

Ludwig Wittgenstein’s Tractatus Logico-Philosophicus is a century-old this year. It deserves its reputation as one of the most difficult books in modern philosophy.

Part of the difficulty is down to its subject matter. The book is about how language represents reality: how sentences like ‘The cat is on the mat’ manage to tell us something about the world. Exactly because we’re so accustomed to using these kinds of sentences, it can be hard to grasp just what Wittgenstein’s worry is. We’re like fish reading a book about the nature of water.

Another part of the difficulty can be chalked up to self-reference. Wittgenstein uses language to conduct his investigation into the nature of language. The book is thus a kind of ouroboros eating its own tail, with all of the trouble that involves.

A third part of the difficulty stems from the book’s length. It’s just 80 pages of cryptic, tweet-length remarks — sometimes precise, sometimes vague — covering everything from metaphysics to logic to ethics to theology.

But at least part of the difficulty is down to Wittgenstein’s stubborn refusal to give any examples of the kinds of things he’s talking about: names, objects, elementary propositions, atomic facts. His reluctance is understandable in a way. Wittgenstein claimed to establish the existence of these things on a priori grounds — via argument, rather than observation — and he thought that any examples he could give would be misleading. But his reluctance is peculiar in another way. As we’ll see, Wittgenstein is willing to write things that aren’t strictly true in order to help us understand him, so it’s strange that he didn’t extend this willingness to concrete examples and illustrations.

In this post, I’m going to do what Wittgenstein didn’t. I’m going to give a quick overview of the Tractatus that’s chock-full of examples and analogies. My exposition will be rough at some points and simplistic at others. Readers looking for maximum accuracy should consult the academic secondary literature. I’m writing this post because even the so-called ‘Introductions’ to the Tractatus can be hard-going.

Let’s begin. Wittgenstein’s main concern in the Tractatus is with propositions. Propositions are those things that can be true or false, the kinds of things that we express with declarative sentences. ‘The cat is on the mat’, for example, is a declarative sentence expressing the proposition that the cat is on the mat.

Some propositions have sense. Roughly, they tell us something about the world. More precisely, whether they’re true or false depends on how the world is arranged. ‘The cat is on the mat’ expresses a proposition with sense. It’s true if the cat is on the mat and false otherwise. Other propositions are senseless. They’re true no matter how the world is arranged, so they tell us nothing about the world. ‘Either it’s raining or it’s not raining’ expresses a senseless proposition. Still other propositions are nonsense. They also tell us nothing about the world, but not because they’re true no matter what. Instead, they tell us nothing because they’re neither true nor false. ‘Colourless green ideas sleep furiously’, for instance, expresses a nonsense proposition. Or, to take one of the rare examples in the Tractatus, ‘The good is more identical than the beautiful’ expresses a nonsense proposition.

These cases are pretty clear-cut, but others are less certain. Does the proposition expressed by ‘Murder is wrong’ have sense? Does it tell us anything about the world? How about the proposition expressed by ‘Time isn’t real’? Does that have sense? We can argue about each of these propositions individually, but that can be a long and tedious affair. It would be convenient if we had some formula to tell us which propositions are sensical, which are senseless, and which are nonsensical.

The Tractatus gives the outlines of such a formula. It presents ‘the general form of proposition’: a recipe for constructing propositions with sense. Wittgenstein’s claim is that all sensical propositions are of this same general form. Any proposition not of this form is nonsense. Wittgenstein is thus trying to do philosophers a huge favour. In philosophy, talking nonsense is an occupational hazard. You might well come to the end of a long career only to discover you were talking nonsense the entire time. The Tractatus is supposed to help us avoid that fate.

To see how Wittgenstein unearths ‘the general form of proposition’, let’s start with a particular example. Take the proposition expressed by ‘One of the Beatles was a bachelor.’ This proposition is sensical. It tells us something about the world. This proposition can also be analysed, by which I mean it can be broken down into parts. ‘One of the Beatles was a bachelor’ can be analysed into four propositions, connected by the word ‘or’: (1) John was a bachelor, or (2) Paul was a bachelor, or (3) George was a bachelor, or (4) Ringo was a bachelor. The symbol ‘bachelor’ can also be analysed, this time into two symbols connected by the word ‘and’. A bachelor is (1) unmarried, and (2) a man.

This process of analysis might well continue, but it can’t go on forever. Eventually, we’ll reach what Wittgenstein called elementary propositions: propositions that can’t be broken down. These elementary propositions are combinations of names: symbols that can’t be broken down.

Since our example proposition — One of the Beatles was a bachelor — has sense, each of its elementary propositions must also have sense. For these elementary propositions to have sense, each of the names in these elementary propositions must refer to something. The proposition expressed by ‘London is in England’ has sense because each of its terms refers to something. The proposition expressed by ‘London is in Flobertness’ is nonsensical, because ‘Flobertness’ doesn’t refer to anything. Wittgenstein thus concludes that names must refer to simple objects. These objects can’t be broken down. If they could be broken down, they might cease to exist. Then the corresponding name would have no reference, and any elementary proposition featuring that name would be nonsense. Wittgenstein’s enquiry into the nature of language has thus led him to a conclusion about the nature of reality: there must be simple objects forming the substance of the world.

Wittgenstein gives us no examples of objects, names, or elementary propositions. He establishes their existence through argument rather than observation, and so is happy to let others do the work of identifying them. He thinks that he can know that objects, names, and elementary propositions exist, even in the absence of examples. Think of it this way. I can know that you have an ancestor who spent their entire life underwater, even though I can’t point out any such ancestor. Take your parents and ask, ‘Did one of them spend their entire life underwater?’. If the answer is — as I suspect — ‘No,’ then take your parents’ parents: did one of them spend their entire life underwater? That’ll also be a ‘No,’ so take your parents’ parents’ parents, and so on. Eventually, the answer must be ‘Yes,’ because we all descended from sea creatures. I can thus know that you have at least one entirely aquatic ancestor, even though I know of no examples. Wittgenstein’s argument is analogous: if a proposition has sense, its analysis must end with elementary propositions made up of names referring to simple objects. Never mind that examples are hard to come by.

All that said, here’s one way of illustrating Wittgenstein’s view. Let the fundamental particles of matter — quarks, leptons, and the like — be our objects. Each such object is assigned a number, which serves as its name. Elementary propositions are then combinations of numbers. We might express them with lists, like ‘13, 28, 567, 435.’

(This illustration isn’t entirely faithful to the theory expressed in the Tractatus. Wittgenstein’s objects can’t be divided. They’re ‘unalterable and subsistent,’ and they exist in every world that we can imagine. Fundamental particles might lack some of these properties.)

Note that elementary propositions are just combinations of names, like ‘13, 28, 567, 435.’ They don’t say ‘28 is between 13 and 567’ or ‘567 crashes into 435’ or anything like that. How then can elementary propositions have sense? How can a mere combination of names tell us something about the world?

Wittgenstein’s answer is given by his famous picture theory of meaning. It’s an idea that’s said to have occurred to him in a Paris traffic-court, where he saw an accident reconstructed with toys. Those toys stood as proxies for the people and cars involved in the accident, and the way that the toys were arranged showed the way that the people and cars were arranged at the time of the accident. The toys together constituted a picture: ‘a model of reality.’ Wittgenstein claims that elementary propositions are also a kind of picture: an elementary proposition is a picture of an atomic fact. An atomic fact is a combination of objects, an elementary proposition is a combination of names, and the way that the names are combined in an elementary proposition shows how the corresponding objects are combined in an atomic fact.

With that last sentence, we’ve completed our descent from the top — an ordinary proposition expressed by ‘One of the Beatles was a bachelor’ — down to the very bottom: names, objects, elementary propositions, and atomic facts. Now to climb back up again. Wittgenstein’s claim is that all propositions with sense are founded on elementary propositions. More precisely, each proposition with sense is a truth-function of elementary propositions. To understand what’s meant by ‘truth-function,’ return to our Beatles example. The proposition expressed by ‘One of the Beatles was a bachelor’ is a truth-function of the following four propositions: (1) John was a bachelor, (2) Paul was a bachelor, (3) George was a bachelor, (4) Ringo was a bachelor. What that means is that the truth of ‘One of the Beatles was a bachelor’ depends only on the truth of the latter four propositions. Once you know whether each of the latter four propositions are true, you ~~can~~ know whether ‘One of the Beatles was a bachelor’ is true. More generally for Wittgenstein, if you know the truth of all the elementary propositions, you ~~can~~ know everything there is to know.

That gives us Wittgenstein’s formula for determining whether a proposition has sense. If a proposition could be true or false, depending on the truth of elementary propositions, that proposition has sense. If a proposition is true no matter which elementary propositions are true, that proposition is senseless. And if a proposition is not a truth-function of elementary propositions — if you couldn’t tell whether it’s true or false even if you knew all the elementary propositions — that proposition is nonsense.

This formula turns out to be bad news for philosophers. In Wittgenstein’s estimation, only scientific questions can be given answers with sense. The propositions of ethics (like ‘Murder is wrong’), aesthetics (like ‘Paris is beautiful’) and theology (like ‘God exists’) turn out to be nonsense. Indeed, all philosophical propositions turn out to be nonsense.

But hang on a minute! The Tractatus is filled to the brim with philosophical propositions. Does Wittgenstein think he’s been writing nonsense this whole time? Funnily enough, yes:

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright. — 6.54

But this answer only invites more questions: what’s the point of reading the Tractatus? How can a book full of nonsense help us ‘see the world aright’?

Wittgenstein’s answer is as follows: the Tractatus shows that any attempt to answer philosophical questions must be nonsense. There simply are no sensical answers to such questions. And so, in the words of Wittgenstein’s final proposition, ‘What we cannot speak about we must pass over in silence.’

But here one might object. Even if Wittgenstein’s propositions imply their own nonsensicality, that doesn’t prove that all philosophical propositions are nonsense. It doesn’t even prove that Wittgenstein’s propositions are nonsense. They might just be plain-old-false. Consider an analogy. The sentence ‘Any sentence consisting of more than five words is nonsense’ implies its own nonsensicality. But that sentence isn’t nonsense. It’s false.

Clearly, Wittgenstein didn’t think that his propositions were false. What might justify his own, more radical reading? Here’s one answer. Suppose that the propositions of the Tractatus strike us as the only viable answers to philosophical questions even after we recognise that these propositions imply their own nonsensicality. Then we might conclude that all philosophical propositions must be nonsense.

I’ll end with a metaphor. Imagine you’re in a clearing in a South American rainforest, searching for El Dorado. Many paths are open to you, and you don’t know which will take you there. You choose a path that looks promising, but after travelling a while you realise that you’re back where you started. You resolve to try again. But even knowing that the first path leads you back to the clearing, it still strikes you as the only way to reach your destination. In that case, you might conclude, there’s no need to try another path. There is no El Dorado.

On this interpretation, the Tractatus is a book to be read twice: first in innocence and then in experience. This reading also makes clear just how compelling Wittgenstein’s arguments must be in order for

On this reading, the Tractatus is a book to be read twice. First in innocence and then in experience. It also makes clear just how compelling Wittgenstein’s arguments must be in order for him to achieve his aims. Perhaps other paths will look more appealing the second time around.

Here’s a metaphor. Imagine you’re trying to journey to some destination — El Dorado. Many paths are open to you, and you don’t know which one will take you there. You choose one path, that you expect to be the best. After travelling, you realise you are back where you started. You resolve to try again. But even knowing that the path you’ve already took leads you back to where you started, it still strikes you as the only viable path that will get you to El Dorado. In that case, you might conclude that there is no way of getting to El Dorado.

One might claim that there is no point.

One thing you might say is that this just proves Wittgenstein’s theory is bad. Any theory that implies its own nonsensicality must be false. [Not necessarily nonsense! ‘Any sentence consisting of more than five words is nonsense.’] So we should reject W’s theory and look for a better one.

But here’s another possible interpretation.

Here’s one natural reaction to Wittgenstein’s Tractatus. Yes, if Wittgenstein’s propositions are true, then they are nonsense. But that just shows that Wittgenstein’s propositions are false. Some other propositions can answer our philosophical questions and remain meaningful.

The textual evidence indicates that Wittgenstein did not think this reaction correct. That must be because Wittgenstein’s propositions remain the most compelling as potential answers to philosophical questions even after we recognise their nonsensicality.

That is to say, each proposition with sense is equivalent to a set of elementary propositions united by logical connectives, like ‘and’ or ‘or’

whether a proposition with sense is true depends only on which elementary propositions are true. Once you know which elementary propositions are true, you know all there is to know.

Okay, so now we’ve gone from the top — an ordinary sensical proposition expressed by ‘One of the Beatles was a bachelor’ — and down to the very bottom: names, objects, elementary propositions, atomic facts. Now to swoop back up again. Wittgenstein’s claim is that all propositions with sense have, at their base, elementary propositions. More precisely, all sensical propositions are truth-functions of elementary propositions. [The proposition expressed by ‘One of the Beatles was a bachelor’ is a truth-function of the four propositions we identified above: (1) John was a bachelor, (2) …]. X is a function of Y iff the value of X depends only on the value of Y, so if you know what value Y takes, you know what value X takes. In our case, that means that, if you know for each elementary proposition whether it is true or false, you know whether each complex proposition is true or false. Any complex that is true no matter which elementary propositions are true is senseless. Any complex proposition that is not a truth-function of elementary propositions is nonsense.

This turns out to be bad news for philosophers. In Wittgenstein’s estimation, only scientific questions can be given answers with sense. The propositions of ethics (like ‘Murder is wrong’) and theology (like ‘God exists’) turn out to be nonsense. Indeed, all philosophical propositions are nonsense.

But hold on a minute.

All that said, I’ll give the following example to aid understanding. Imagine the Newtonian world of atoms. Every atom in the universe is assigned a number. That number is the atom's name. The atom itself is the object. Elementary propositions are combinations of names, like ‘13, 28, 567,435.’ They describe states-of-affairs (otherwise known as atomic facts), which are combinations of objects (in our example, atoms).

Wittgenstein gave no examples. But I'll give the following example to aid understanding. Imagine the Newtonian world of atoms. Every atom in the universe is assigned a number. That number is the atom's name. The atom itself is the object. States of affairs are these atoms standing in certain relations to each other. Elementary propositions are things like '13, 28, 567,435.' [USE WITT'S 'EXCALIBUR' EXAMPLE. PAGE 13 OF FANN].

Note that an elementary proposition is a list of names. It does not say, for example, '13 is between 28 and 567.' It just lists them. So how can an elementary proposition 'assert the existence of a state-of-affairs' (4.21)?

The answer: 'It is a picture of the state-of-affairs.' This is Wittgenstein famous picture theory of meaning. Paris traffic court. Page 15 of Fann.

‘What constitutes a picture is that its elements are related to one another in a determinate way.’ — T 2.14

‘The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way,’ — T. 2.15

‘What constitutes a propositional sign [the sentence] is that in it its elements (the words) stand in a determinate relation to one another.’ — T 3.14

This process of analysis might well continue, but it cannot go on forever. It has to stop at some point. Eventually, we’ll reach what Wittgenstein called elementary propositions: propositions that cannot be analysed into further propositions. These elementary propositions are combinations of names: words that cannot be analysed. The truth of an elementary propositions depends only on the existence of a particular state-of-affairs. The obtaining of a state-of-affairs is an atomic fact. An elementary proposition is true if that state-of-affairs exists and false if it does not.

Now as we saw above, if a proposition is to have sense, each of its constituent words must refer to something. The same is true of elementary propositions. Each name in an elementary proposition must refer to an object. These objects are simple. They cannot be divided.’ Objects make up the substance of the world.’ (T 2.021). If they could be divided, then their corresponding names could be analysed.

The bad news is that, in Wittgenstein’s estimation, much of past philosophy has been nonsense. Philosophers have failed to recognise the limits of language, and thus duped themselves into constructing nonsensical answers to nonsensical questions.

points the way towards such a formula.

These examples are clear-cut, but others are less certain. Does the proposition 'Murder is wrong' have sense? Does it tell us anything about the world? How about the proposition 'Time is not real’? We can argue about each of these individually, but that tends to be a long and difficult process. It would be good if we had some formula for determining which propositions have sense and which don't.

Wittgenstein’s Tractatus purports to give us this formula. He constructs ‘the general form of proposition’: a recipe for creating propositions with sense. His claim is that all sensical propositions are of this general form. If a proposition cannot be constructed from this general form, it’s nonsense. Wittgenstein is thus doing philosophy a huge favour. Talking nonsense is an occupational hazard. It would be nice to have a short book allowing us to ensure that we don’t waste our careers. The upshot, for Wittgenstein, is that it turns out a lot of philosophers have been talking nonsense. ‘Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) And it is not surprising that the deepest problems are in fact not problems at all.’ — 4.003

That’s a big claim. So, how does Wittgenstein establish that many philosophical propositions are nonsense?

Here's one way of talking nonsense: use a word that doesn’t refer to anything. The proposition 'London is in England' has sense. It tells us something about the world. The sentence 'London is in Flobertnessbess' is nonsense, because the word ‘Flobertnessbess’ does not refer to anything. Therefore, if a sentence is to have sense, each of its constituent words must refer to something. [SOURCE?]

Now note that most propositions can be analysed. By that I mean, they can be broken down into parts. Take, for example, the proposition ‘One of the Beatles was a bachelor.’ That proposition can be analysed into four propositions, connected by the word ‘or’: ‘Either (1) John was a bachelor, or (2) Paul was a bachelor, or (3) George was a bachelor, or (4) Ringo was a bachelor.’ Many words can also be analysed. The word ‘bachelor’ can be broken down into two parts, connected by the word ‘and’: (1) unmarried, and (2) man.

Wittgenstein gives us no examples of objects. He thought that was not his job, as a logician. He establishes the existence of objects on a priori grounds. That is, through argument, rather than sense evidence. Think of it this way. We know on a priori grounds that you have some last ancestor who spent their entire life underwater. Take your parents and ask, ‘Did one of them spend their entire life underwater?’. If the answer is — as I suspect — no, then take your parents’ parents. Did one of them spend their entire life underwater? Also no. So, take your parents’ parents’ parents. Eventually, we’ll reach a point where the answer is yes, because we all descended from sea creatures. So, we know that you have some last ancestor who spent their entire life underwater. We do not have to point them out to be sure.

The answer: 'It is a picture of the state-of-affairs.' This is Wittgenstein famous picture theory of meaning. Paris traffic court. Page 15 of Fann.

‘What constitutes a picture is that its elements are related to one another in a determinate way.’ — T 2.14

‘The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way,’ — T. 2.15

‘What constitutes a propositional sign [the sentence] is that in it its elements (the words) stand in a determinate relation to one another.’ — T 3.14

‘Elementary propositions are ’logical pictures’ of atomic facts — the basic kind of fact which cannot be further analysed; and all complex propositions are ‘truth-functions’ of the elementary ones.’ — Fann, p.8.

Propositions are truth-functions of elementary propositions.

Any proposition that is not a truth-function of elementary propositions is nonsense.

The totality of true propositions is the whole of natural science (or the whole corpus of the natural sciences). — 4.11

That means that ethics and theology are strictly nonsense. [MORE]

But philosophy too!

Philosophy is not one of the natural sciences. (The word ‘philosophy’ must mean something whose place is above or below the natural sciences, not beside them.) — 4.111

Philosophy does not result in ‘philosophical propositions’, but rather in the clarification of propositions. — 4.12

The problem is that TLP seems to be chock-full of ‘philosophical propositions’. So what’s going on?

The correct method in philosophy would really be the following: to say nothing except what can be said, i.e. propositions of natural science—i.e. something that has nothing to do with philosophy—and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions. Although it would not be satisfying to the other person—he would not have the feeling that we were teaching him philosophy—this method would be the only strictly correct one. — 6.53

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them—as steps—to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the world aright. — 6.54

What we cannot speak about we must pass over in silence. — 7

We’ve read the whole book and with his penultimate proposition Wittgenstein tells us everything so far has been nonsense? What a twist!

So what’s Wittgenstein been doing this whole time? It seemed like he’s giving a theory of how language represents reality. But now he says that any such theory is bound to be nonsense.

But here’s another possible interpretation.

0.1. Very rough

Ludwig Wittgenstein’s Tractatus Logico-Philosophicus deserves its reputation as one of the most mystifying books in twentieth-century philosophy.

Part of this is down to the subject matter. The book is about the nature of language, and that’s difficult to do because any extended investigation has to be conducted in language. It’s a bit like [wonky ruler? tuning an instrument?]. Part of it is down to the book's extreme brevity. It's about 80 pages, and it covers everything from metaphysics to logic to ethics to theology. But at least part of it is down to Wittgenstein’s near-steadfast refusal to give any examples of what he was talking about. That’s understandable in a sense, because Wittgenstein believed that any examples he could give would be misleading [?]. But it’s peculiar in another sense. As we will see, Wittgenstein was happy to say not-strictly-true things as a means to understanding. So it’s strange that he didn’t extend this willingness to concrete examples.

So here's my summary of the Tractatus, with lots of examples.

Sentences express propositions. The sentence 'My name is Elliott' and the sentence 'Je M'Appelle Elliott' are different sentences, but they express the same proposition. A proposition is a statement that tells us something about the world.[?]

Some propositions have sense. Roughly, they tell us something about the world. For example, 'the cat is on the mat.' Other propositions have no sense. They tell us nothing about the world. Some of these sentences are senseless. They are true as a matter of logic, so they do not tell us anything substantive. They only tell us the rules for using certain symbols.[?] For example, 'It is not the case that the cat is both on and off the mat.’ Other propositions do not even express logical truths. They are nonsense. For example, 'Colourless green ideas sleep furiously.' Or Wittgenstein’s own example, ‘Is the Good more or less identical than the Beautiful?’ (4.003).

These examples are clear-cut, but others are less certain. Does the sentence 'Murder is wrong' have sense? Does it tell us anything about the world? How about the sentence 'Time is not real’? We can argue about each of these individually, but that tends to be a long and difficult process. It would be good if we had some formula for determining which sentences have sense and which don't.

Now note that most propositions can be analysed. By that I mean, they can be broken down into parts. Take, for example, the sentence ‘One of the Beatles was a bachelor.’ That sentence can be analysed into four sentences, connected by the word ‘or’: ‘Either (1) John was a bachelor, or (2) Paul was a bachelor, or (3) George was a bachelor, or (4) Ringo was a bachelor.’ Many words can also be analysed. The word ‘bachelor’ can be broken down into two parts, connected by the word ‘and’: (1) unmarried, and (2) man.

The answer: 'It is a picture of the state-of-affairs.' This is Wittgenstein famous picture theory of meaning. Paris traffic court. Page 15 of Fann.

‘What constitutes a picture is that its elements are related to one another in a determinate way.’ — T 2.14

‘The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way,’ — T. 2.15

‘What constitutes a propositional sign [the sentence] is that in it its elements (the words) stand in a determinate relation to one another.’ — T 3.14

Wittgenstein claims that the Tractatus does not solve so much as dissolve all philosophical problems. He claims that philosophical questions arise only because we misunderstand the way our language works. Once we understand language, we recognise that all philosophical sentences are nonsense. Since a philosophical question can only be answered with a philosophical sentences, philosophical questions have no sensible answers. But Wittgenstein's work is not done if we still have the impulse to ask philosophical questions. Only once we've conquered the impulse have we fully understood.

As philosophers, talking nonsense is an occupational hazard.

Sentences express propositions. Propositions describe facts. And facts are the existence of states-of-affairs. A state of affairs is a combination of objects.

Whether a proposition has sense or not cannot depend on the way the world is. A proposition has no sense if one of its constituent names refer to an object that does not exist. Whether or not an object like a table exists depends on the way the world is. Therefore, in fully analysed propositions, names like ‘table’ will disappear. Instead, there will only be combinations of names referring to objects that exist in all ways the world could be. Again, we can suppose that atoms exist in all possible worlds. [see 2.02 to 2.023].

0.2. Correspondence

Name — Object

Elementary Proposition — State of Affairs/Atomic Fact

Proposition — Fact

0.3. Excalibur example

‘The word ’Excalibur’, say, is a proper name in the ordinary sense. The sword Excalibur consists of parts combined in a particular way. If they are combined differently Excalibur does not exist. But it is clear that the sentence ‘Excalibur has a sharp blade’ makes sense whether Excalibur is still whole or is broken up. But if ‘Excalibur’ is the name of an object, this object no longer exists when Excalibur is broken in pieces; and as no object would then correspond to the name it would have no meaning. But then the sentence ‘Excalibur has a sharp blade’ would contain a word that had no meaning, and hence the sentence would be nonsense. But it does make sense; so there must always be something corresponding to the words of which it consists. So the word ‘Excalibur’ must disappear when the sentence is analysed and its place be taken by words which name simples’. — Philosophical Investigations, section 39.

‘A name signifies only what is an element of reality. What cannot be destroyed; what remains the same in all changes.’ — PI, section 59.

0.4. Wittgenstein evaporates philosophical paradoxes. They are shown to be nonsense.

Initially inspired by Russell’s paradox.

Wittgenstein has apparently constructed an account of language and the way language relates to the world that resolves all the semantic paradoxes. He has not done so by providing a 'straight' resolution of the paradoxes, but by giving an account of the general form of proposition according to which the paradoxical sentences could not even be constructed, and are simply eliminated as nonsensical transgressions of the 'limits of language'. But in so doing he has led the discussion to a point that is every bit as paradoxical as the original paradoxes: once we have seen what the solution to the paradoxes is we realize that, by the same token, that solution cannot itself be stated. The paradox is clearly exacerbated by the fact that Wittgenstein seems to have been saying precisely what he is arguing cannot be said, and equally we seem to have been able to understand him, and argue for and against the positions he has apparently been putting forward. As Russell says:

0.5. Wittgenstein thought problems of philosophy were problems of language

Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes. — 4.002

Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) And it is not surprising that the deepest problems are in fact not problems at all. — 4.003

All philosophy is a ‘critique of language’ (though not in Mauthner’s sense). It was Russell who performed the service of showing that the apparent logical form of a proposition need not be its real one. — 4.0031

0.6. What is Wittgenstein doing?

0.6.1. The impossibility of explaining how language fits the world

There are several distinguishable trains of thought that lead to this paradoxical conclusion, which I shall detail when we come to look at 6.54 itself, but here we may consider two that are immediately relevant even at this introductory stage. The first is the idea that if our enterprise is to show how language fits the world, then what we would like to do is to describe the facts in the world and the propositions that are made true by those facts, and show the fit between them - and that apparently is what Wittgenstein is proceeding to do. The only way, however, to describe the facts that make a given proposition true is to use precisely the same form of words as is used in the proposition (or at best a logically equivalent proposition), so that we end up saying:' "It is raining" is made true by the fact that it is raining', which is scarcely the startling news we wanted. Wittgenstein is apparently attempting the impossible: adopting a vantage-point above language and the world, and describing the relation between them as seen from that perspective, which would require that 'we should be able to place ourselves with propositions beyond logic, that is, beyond the world' (4.12) and 'what we cannot think we cannot think, and so we cannot say what we cannot think' (5.61). In this way we finally recognize that the sentences we uttered in trying to describe that relation were in fact sentences to which no meaning could be given. The other, related, point is that it will prove to be impossible to speak meaningfully about the world as a whole (see 6.45), and that we cannot say such things as: These are all the facts there are', or These are all the objects [or e.g. propositions] there are'. But he in fact apparently begins by doing precisely that: The world is determined by the facts, and by their being all the facts'. — White

………

Finally, the one thing you cannot talk about on Wittgenstein's account is the one thing he has apparently been talking about throughout the book - the logical form of propositions that they share with reality (4.12). — White

In all these ways at least, Wittgenstein has apparently been saying things throughout the book which by his own lights cannot be said. The attempt to do so necessarily results in nonsense. In 6.53, he says that 'the only strictly correct method' of teaching philosophy would be a process of Socratic midwifery: you yourself say nothing philosophical, but only attempt to bring the pupil to see that they had failed to give any meaning to some of the signs they had used, whenever they tried to say 'something metaphysical'. In the Tractatus, he has, however, clearly departed from this method, and done something that is, on his own account, illegitimate. Where that leaves the way we should understand his book will be our next topic. — White

0.6.2. The impossibility of saying that ‘these are all the propositions’ or ‘these are all the facts’ or ‘this is everything that exists’

Suppose we start out with the elementary propositions p, q and r and form all their truth-functions. That will give us the limit of what can be said, if those three propositions are the only linguistic resources we have at our disposal. Given those resources, we shall have no way of expressing the idea that p, q and r either are or are not all the elementary propositions there are. That implies that if the general form of proposition is as outlined above, we can form no proposition that is tantamount to saying of a given set of propositions that they are all the elementary propositions. Similarly, we will be unable to say that a set of objects are all the objects there are, or a set of facts are all the facts there are, or for that matter, that the general form of proposition is the general form of proposition. But it is vital to Wittgenstein's purposes in this book, if he is to set the limits of language, that he should work with the idea of a 'totality of facts' (1.1) and the idea of 'all the elementary propositions' (4.52). His exposition consequently continually strays beyond the limits of what can be said. — White

0.6.3. Reductio ad absurdum

Although Wittgenstein clearly went into all this with his eyes open, and indeed saw it as one of his main objects to confront his readers with this paradoxical position, whatever he himself might have thought, what we have here is as clear a case as could be imagined of a reductio ad absurdum. What could be more absurd than espousing a theory that would, once fully worked out, imply that theory to be nonsense? — White

Despite the fact that this is a natural reaction that many readers may have, we shall look at it only briefly here. The main thing to say is that, at least as it stands, this is a shallow reaction. It should only command respect if it is accompanied by a serious attempt to rebut Wittgenstein's central arguments that lead him to the positions he has been advocating throughout the book. Here it should be noted that the arguments that lead up to Wittgenstein's saying what he does in 6.54 are among the strongest arguments in the book. There are, on any account, many minor flaws in the Tractatus and some of the ideas expressed, even if defensible, would not command widespread support. The ideas, however, lying behind Wittgenstein's insistence that there was something that could only be shown and not said are not only among those to which he is attaching most importance, they also have a deep philosophical point that cannot be set aside by any superficial objection. — White

0.6.4. El Dorado/Therapeutic reading

There has been large interest recently in the kind of reading that we now have to consider. This is the so-called 'New Wittgensteinian' reading of the Tractatus. In sharp contrast with the preceding reading, this makes 6.54 the key to the whole book. The book may be thought of as having two components - a 'frame' consisting primarily of the Preface and the 6.5s (6.54 in particular), and the rest of the book included within that frame - where the frame gives guidance to one's understanding of Wittgenstein's whole project. We take with full seriousness Wittgenstein's claim that the propositions in the main part of the book are nonsense, and stress that by nonsense is meant nonsense - gibberish - and that the point of the book is achieved (when the reader finally understands Wittgenstein, not the propositions of the Tractatus, since there is no such thing as understanding nonsense) when the illusion that those propositions make sense has been dispelled. The book has a 'therapeutic' purpose that seems to run along the following lines: the reader is initially seduced into reading the book 'straight', as an account of propositions and the way propositions relate to reality. This account finally falls apart and turns out to be nonsense in its own terms. Once the reader realizes this, they are disabused of the urge that led them to engage in the kind of enquiry they had apparently embarked on. They then 'see the world aright', in that they return to be content with our everyday language, without the wish to construct a metaphysical theory to underpin that language. The 'traditional' readings of the Tractatus have been engaged in a kind of double-think in which they somehow think it is both possible to accept the main tenets that the Tractatus apparently propounds and that the sentences expressing those tenets are nonsensical. We must take Wittgenstein to have been 'resolute' and that when he talked of 'throwing away the ladder', he meant precisely that - abandon any attempt to find any meaning in the sentences of the body of the book. In particular, we must overcome the illusion that there is anything that can be 'shown but not said'. — White

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How can we see the world aright by recognising the propositions of the Tractatus as nonsensical? • This recognition is supposed to expose the philosophical enterprise as illegitimate. • This requires that we have previously come to see the propositions of the Tractatus as providing the correct answers to philosophical questions. • And this impression needs to survive the realization of their nonsensicality. — Zalabardo

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The assessment that I have sketched in the previous section interprets Wittgenstein as making contributions to the philosophical enterprise—of finding solutions to philosophical problems and answers to philosophical questions. However, as I argued in the Introduction, for the author of the Tractatus engagement in the philosophical enterprise is only a means to an end. The end is to make manifest to his readers the illegitimacy of the enterprise. The means is to show that by following the rules that define the enterprise we reach the twin conclusions that the propositions of the Tractatus express philosophical doctrines that we should accept and that these doctrines entail that the sentences that seem to express them are actually nonsensical. — Zalabardo

It follows from my assessment of the Tractarian doctrines that Wittgenstein is very far from achieving his ultimate goal. The rules of the philosophical practice, as applied in the present book, fail to force upon us the conclusion that the sentences of the Tractatus express the right account of representation and reality. They also fail to enjoin the conclusion that the propositions expressed by the sentences of the Tractatus entail that these sentences are nonsensical. For even if we accepted these propositions, we would be able to resist the conclusions that Wittgenstein draws from them concerning the limits of propositional representation. — Zalabardo

Readers who accept the conclusions of the present book will have failed to complete the first stage of Wittgenstein’s programme. They will remain, with its author, in the grip of the illusion—if that’s what it is—that the philosophical enterprise addresses legitimate questions and problems.3 For them (for us) the value of the Tractatus has to lie in the contributions it makes to this enterprise, even if this isn’t quite what Wittgenstein intended. From my assessment of its achievements at this level it follows that the Tractatus amply deserves its reputation as one of the most significant works of contemporary philosophy. — Zalabardo

0.7. But self-refuting does not imply nonsense. At most it implies false.

The only answer seems to be that these propositions, taken seriously, are in some way self-refuting, or imply their own nonsensicality. But then there is just as much difficulty confronting this account as confronts the traditional reading in explaining what is meant by 'taken seriously' when applied to sentences that have no meaning whatever - and equally by what it means to talk of such propositions as implying anything. But even apart from that, the fact that sentences are self-refuting or imply their own nonsensicality does not show them to be nonsense: at most, it shows them to be false. — White

But even if a satisfactory answer can be given to those questions, the real question needs answering: 'How does the fact that the propositions of the Tractatus turn out, for what ever reason, to be nonsense have any therapeutic value?' After all, self-refuting metaphysical theories, even theories that turn out to be nonsense in their own terms, are hardly a rarity in the history of philosophy. The Verification Principle in particular was dogged by the difficulty of giving an account of its own meaningfulness in the terms for meaningfulness that it itself laid down - and no one has ever seen any therapeutic role for Logical Positivism analogous to the role that is here being assigned to the Tractatus. — White

Example: ‘Any sentence consisting of more than five words is nonsense.’

This sentence implies its own nonsensicality. But it is not nonsense. It’s false.

Sentences express propositions. Propositions describe facts. And facts are the existence of states-of-affairs. A state of affairs is a combination of objects.

1. Quotes

The world is all that is the case. — 1

The world is the totality of facts, not of things. — 1.1

The world is determined by the facts, and by their being all the facts. — 1.11

For the totality of facts determines what is the case, and also whatever is not the case. — 1.12

Each item can be the case or not the case while everything else remains the same. — 1.21

What is the case — a fact — is the existence of states of affairs. — 2

A state of affairs (a state of things) is a combination of objects (things). — 2.01

Objects are simple. — 2.02

Every statement about complexes can be resolved into a statement about their constituents and into the propositions that describe the complexes completely. — 2.0201

The configuration of objects produces states of affairs. — 2.0272

In a state of affairs objects fit into one another like the links of a chain. — 2.03

The totality of existing states of affairs is the world. — 2.04

The totality of existing states of affairs also determines which states of affairs do not exist. — 2.05

The existence and non-existence of states of affairs is reality. (We also call the existence of states of affairs a positive fact, and their non-existence a negative fact.) — 2.06

States of affairs are independent of one another. — 2.061

From the existence or non-existence of one state of affairs it is impossible to infer the existence or non-existence of another. — 2.062

We picture facts to ourselves. — 2.1

A picture is a model of reality. — 2.12

In a picture the elements of the picture are the representatives of objects. — 2.131

What constitutes a picture is that its elements are related to one another in a determinate way. — 2.14

A picture is a fact. — 2.141

The fact that the elements of a picture are related to one another in a determinate way represents that things are related to one another in the same way.// Let us call this connexion of its elements the structure of the picture, and let us call the possibility of this structure the pictorial form of the picture. — 2.15

Pictorial form is the possibility that things are related to one another in the same way as the elements of the picture. — 2.151

That is how a picture is attached to reality; it reaches right out to it. — 2.1511

The pictorial relationship consists of the correlations of the picture’s elements with things. — 2.1514

If a fact is to be a picture, it must have something in common with what it depicts. — 2.16

What a picture must have in common with reality, in order to be able to depict it — correctly or incorrectly — in the way it does, is its pictorial form. — 2.17

A picture depicts reality by representing a possibility of existence and non-existence of states of affairs. — 2.201

What a picture represents is its sense. — 2.221

The agreement or disagreement of its sense with reality constitutes its truth or falsity. — 2.222

It is impossible to tell from the picture alone whether it is true or false. — 2.223

It is impossible to tell from the picture alone whether it is true or false. — 2.224

In a proposition a thought finds an expression that can be perceived by the senses. — 3.1

What constitutes a propositional sign is that in it its elements (the words) stand in a determinate relation to one another — 3.14

The simple signs employed in propositions are called names. — 3.202

A name means an object. The object is its meaning. — 3.203

A name cannot be dissected any further by means of a definition: it is a primitive sign. — 3.26

A thought is a proposition with a sense. — 4

The totality of propositions is language. — 4.001

Language disguises thought. So much so, that from the outward form of the clothing it is impossible to infer the form of the thought beneath it, because the outward form of the clothing is not designed to reveal the form of the body, but for entirely different purposes. — 4.002

Most of the propositions and questions to be found in philosophical works are not false but nonsensical. Consequently we cannot give any answer to questions of this kind, but can only point out that they are nonsensical. Most of the propositions and questions of philosophers arise from our failure to understand the logic of our language. (They belong to the same class as the question whether the good is more or less identical than the beautiful.) And it is not surprising that the deepest problems are in fact not problems at all. — 4.003

All philosophy is a ‘critique of language’ (though not in Mauthner’s sense). It was Russell who performed the service of showing that the apparent logical form of a proposition need not be its real one. — 4.0031

A proposition is a picture of reality. A proposition is a model of reality as we imagine it. — 4.01

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it's got one (1) example in the form of the eye that does not see itself:

Where in the world is a metaphysical subject to be found? You will say that this is exactly like the case of the eye and the visual field. But really you do not see the eye. And nothing in the visual field allows you to infer that it is seen by an eye. — 5.633

Wittgenstein actually uses the phrase ‘for example’ quite a lot!

1.1. Extras

States of affairs are these atoms standing in certain relations to each other. Elementary propositions are things like '13, 28, 567,435.' [USE WITT'S 'EXCALIBUR' EXAMPLE. PAGE 13 OF FANN].

Note also that most sentences can be analysed. That means they can be broken down into constituent parts. Take, for example, the sentence 'One of the members of the Beatles was a bachelor.' That can be analysed into four sentences, connected together by the word 'or'. The term 'bachelor' can be analysed as 'unmarried man'. Now it seems as if this process of analysis must stop at some point. Eventually, you'll reach elementary propositions that cannot be broken down, and names which cannot be broken down.

And since, as we saw above, each of the constituents of a sentence has to refer to something if that sentence is to have sense, then names must refer to objects.

The answer: 'It is a picture of the state-of-affairs.' This is Wittgenstein famous picture theory of meaning. Paris traffic court. Page 15 of Fann.