4.0312 The possibility of a proposition is based on the principle of the representation of objects by signs.

My fundamental thought is that the “logical constants” represent nothing. That the logic of facts does not allow of representation.

Mounce (p. 12) says of this “fundamental idea” that: “logic … reflects, on Wittgenstein’s view, by showing not by saying. This indeed is the central doctrine of the Tractatus. Logic differs from all the other sciences because the other sciences say something about the world whereas logic only shows something.” There is no representation, but there is reflection, in other words.

Ostrow (p. 87): “We are meant to see that, contrary to Frege’s contention, the logical functions cannot be construed along the lines of genuine (material) functions, that it makes no sense to suppose a domain of entities which form the special province of the logician. Nor is this a point directed merely at Frege. Russell is even more explicitly committed to the assumption of a definite logical subject matter, as is evident in his … claim that “the chief part of philosophical logic” is “the endeavor to see clearly the entities” that mathematics regards as indefinable (Principles xv).” On this, see note to 2.01. In Letters to Ogden p. 20, Wittgenstein rejects the suggested title for the TLP of Philosophic Logic saying that this title would be “wrong. In fact I don’t know what it means! There is no such thing as philosophic logic.” It seems clear that his objection was not merely that it should be Philosophical Logic instead.

My initial reaction: The fundamental idea. This must be important. So, there being propositions depends on the principle that objects can be replaced by signs that go proxy for them. But this principle seems to be false. Propositions are essentially representative in a way that objects are not. A cat sitting on a mat has no meaning. “The cat sat on the mat” has. And “The [picture of a cat] sat on the ___" has no meaning at all, although you might guess what I have in mind. Objects are not replaced by signs. They are represented by them, which is quite a different thing. Let’s assume that this is what Wittgenstein means. Propositions depend on the representation of objects, not of the logic of facts. But weren’t objects something like possibility points? And isn’t logic all about possibility? Maybe the logic of objects can be represented but not the logic of facts. But facts are made of objects, so why should there be a difference? This is a little obscure. Perhaps though the implication is that propositions as described in the Tractatus really are not possible.

4.0311 A name stands for a thing, another for another thing, and they are connected with each other, so the whole – like a tableau vivant – stands for a state of affairs.

Why a tableau vivant and not a normal picture? For what does a tableau vivant stand? The picture, or the pictured? That is, a tableau vivant of the death of Socrates could be seen as a representation of the death of Socrates or of The Death of Socrates (a painting). Is Wittgenstein saying that a proposition is like a name, only for a state of affairs rather than for an object?

4.031 In a sentence a state of things is as it were put together by way of a test.

Instead of, This sentence has such and such a sense, one can say, This sentence represents such and such a state of things.

A proposition is here spoken of as an unasserted thought in Frege’s terms. It is a possible assertion, so to speak. Nordmann (pp. 108-114) discusses various possible translations of this remark, and their various implications. It is ambiguous in the German, the first sentence allowing for the interpretation that a sentence puts together a situation experimentally, or as an experiment, or for the sake of experiment, or in order to be put to the test.

4.03 A sentence must communicate a new sense with old terms.

A sentence communicates a state of things to us, so it must be essentially connected with the state of things.

And the connection is just that it is its logical picture.

A sentence says something only insofar as it is a picture.

So propositions picture states of things. This is not new. It must be essentially connected with the relevant state of things, which sounds metaphysical, but in fact the connection in question is precisely, merely, that it pictures it. Logically, whatever exactly that might mean.

4.027 It is of the essence of a sentence that it can communicate a new sense to us.

We can learn new words, and use these to mean new things, but the credit should go not to words but to the sentence. If I become strong by taking steroids, it is a mistake to think that the steroids are doing all the work. Rather, my body is such that it converts steroids to muscle. It is of the essence of a sentence that it can absorb new words and use them to make a new sense.

Could there be anything here that could be used to solve the 6.54 puzzle? (Not that I can see, but this would seem to be a good place, in terms of the number scheme, to look.)

Original comment: A new sense in the sense that this combination of signs has not been seen before, at least by us. But how do we know the meanings of words except through sentences? And we just do not understand sentences on their own, as even 4.026 can be taken to imply.

4.026 The meanings of simple signs (words) must be explained to us for us to understand them.

We make ourselves understood, though, with sentences.

Black (p. 172) offers this rather free paraphrase: “The meanings of words have to be explained for us, have to be shown, but once this has been done, we use propositions to make ourselves understood, to communicate thoughts.” It seems to me, though, that the meaning might be more that, while words need to be explained, the explanations offered can only take the form of sentences. Meaning and understanding take place in the medium of sentences, not words (even though, in a sense, sentences are made up of words). Sentences consist of words in the way that the human body consists of such things as carbon and water. You can break the one down into the other, but you cannot produce the greater simply by adding or mixing the ingredients.

Compare with 6.54. Wittgenstein there seems to contrast understanding a person's sentences with understanding the person, so that we can understand him yet see that his sentences are nonsensical. According to 4.026, though, we could only understand him by means of his sentences. If these sentences are nonsensical, it is obviously difficult to see how we could understand him by means of them.

My initial reaction: You need to learn the meanings of words, but once you know them you can understand new combinations of them in sentences. The sensible components of language are arbitrary and so must be learned, but the senses (meanings0 expressed by means of them are, what, already intelligible? This would be very different from the later Wittgenstein, perhaps even the Wittgenstein who comes later at 5.62, for instance. If “senses” are “intelligibilities” then this is uncontroversially true, I suppose, but hardly as informative as it sounds.

4.025 The translation of one language into another does not proceed by one’s translating each sentence of one into a sentence of the other, but only by translating the constituent parts of sentences.

(And the dictionary translates not only substantives but also verbs, adjectives, and conjunctions, etc.; and it treats them all the same way.)

Yes, but translation software does not work very well. Translation is not as simple or mechanical as 4.025 suggests. Wittgenstein, who helped with the translation of the Tractatus, surely knew this. Cf. Philosophical Investigations §§1-23.

4.024 To understand a proposition means to know what is the case if it is true.

(One can therefore understand it without knowing whether it is true.)

One understands it if one understands its constituent parts.

The first two sentences here seem straightforward enough. The last is problematic, because you might think you do not understand “The cow milks the boy” even though you understand the individual words. But knowing what milking (a cow) is does not tell us what is meant here. So we do not understand the constituent parts of this sentence. We understand parts of other sentences that look the same, that is all.

4.023 Reality must be fixed by a proposition except for a yes or a no.

Therefore it must describe reality completely.

A proposition is a description of a state of affairs.

As the description of an object goes by its external properties, so a proposition describes reality according to its internal properties.

A proposition constructs a world with the help of a logical scaffolding and therefore one can actually see in the proposition all the logical features of reality if it is true. One can draw conclusions from a false proposition.

So propositions must be quite definite or determinate about something (not the whole of reality, presumably, although maybe that) and not at all vague. A proposition describes the internal properties of a state of affairs. Why? And what are these? If internal properties are logical properties, then do propositions describe these? Presumably. And so a true proposition will describe the logic of a part of the world, of a state of affairs. Since it shows its sense, one will be able to see from it what this logic is. If the proposition is false one will have to think a bit, perhaps just by affixing a mental “not” to the picture presented by the proposition.

4.022 A proposition shows its sense.

A proposition shows what is the case if it is true. And it says that this is the case.

Puzzling, since a proposition considered as a sentence does not show its sense, and considered as a proposition or understood thought then the concept of showing does not seem to fit it. A proposition, we might say, is a sense. 4.022 suggests that a proposition is like a Fregean assertion sign followed by a literal picture, one that is impossible to misinterpret because it requires no interpretation. It (somehow) shows its sense (correct interpretation). Is this a reduction of Frege’s philosophy of language?

Others are puzzled by this remark too. Black (p. 165) quotes Wisdom calling it “a mistake.”

4.021 A proposition is a picture of reality: Because I know the state of things it represents if I understand the proposition. And I understand the proposition without its sense having been explained to me.

Tricky. How can I know or be acquainted with a state of things/state of things that does not exist (consider false propositions)? I think 4.021 must be taken as a tautology. To know the state of things a proposition represents simply is (i.e. means) understanding the proposition.

4.02 We see this from our understanding the sense of a proposition without its being explained to us.

Splutter! We might understand a string of pictographs (women drink beer, say, or bird fly to pharaoh) but we hardly understand a sentence in the same way. We need to know the meanings of the signs. The same is true with pictographs, of course, but they could sometimes be guessed. We could, I suppose, guess the meaning of a sentence, but what could this show us about the essence of propositions? The reason we can understand the sense of a proposition without its being explained to us is that we know the correct use of its signs. In this I include letters as well as words and punctuation marks, since “The dog went Hav! Hav!” is intelligible (that’s the sound the dog made) whereas “The dog went hav hav” would take more guesswork (does “hav hav” mean “pee pee”? is it a place?, etc.). Consideration of the use of writing, including hieroglyphic writing, in fact seems to show that the essence of propositions is not picturing in any simple sense at all. And neither 4.016 nor 4.02 actually denies this.

Proops (pp. 103-105) argues that Wittgenstein is in fact referring back to 4.01 here, when he says ‘this.’ He bases this claim on the fact that it does not make much sense otherwise, and in the Prototractatus 4.02 refers to 4.01 and some related remarks. Presumably Wittgenstein inserted other material without noticing that he needed to change the wording of 4.02.

4.016 In order to understand the essence of the proposition, let us consider hieroglyphic writing, which depicts the facts it describes.

And from it came the alphabet, without losing the essence of picturing.

Real (Egyptian) hieroglyphic writing is in fact alphabetic and does not simply depict, image, or map the facts it describes. We might imagine the kind of writing Wittgenstein describes here, but it is possible that he knows we could not get very far this way. Writing does seem to have started with pictographs, but of course spoken language came before this, and is thought to have emerged from gestures (in the beginning was the deed, all very later Wittgensteinian). So it might be true that the (written) alphabet came from pictographs, and hence that (written) sentences began this way. This tells us nothing philosophically, surely, since logic is not concerned with such empirical matters. But the history lesson might be helpful all the same, as a kind of metaphor. The idea seems to be that the essence of propositions is to represent.

4.015 The possibility of all similes, of all the imagery of our language, rests on the logic of picturing.

The clause “of all the imagery of our language” is Wittgenstein’s translation.

This clearly looks to be a key statement for the picture theory. Language is pictorial or representative, and the possibility of its being so depends on the logic of representation. So: the logic of representation is fundamental to the possibility of similes (representation?), which might in turn be taken to be a prerequisite for representation itself.

But is this resting or necessity or dependence meant to be metaphysical (factual)? Presumably not. It is logical. So the image of resting, etc. is quite misleading here. Can the logic of picturing really be anything other than the possibility of picturing? Does anything rest on anything else? Is anything at all really being said?

4.0141 In the fact that there is a general rule by which the musician is able to read the symphony out of the score, and that there is a rule by which one could reconstruct the symphony from the line on a gramophone record and from this again – by means of the first rule – construct the score, herein lies the internal similarity between these things which at first sight seem to be entirely different. And the rule is the law of projection which projects the symphony into the language of the musical score. It is the rule of translation of this language into the language of the gramophone record.

This is all Wittgenstein’s translation. See Letters to Ogden p. 26. Cf. 3.11.

I have wondered whether the last sentence could possibly be a joke. What could the rule be by which one reads music from a score? Of course people do this, just as we can read aloud from a printed script. But I'm not sure what there is apart from the printed word and the sounds we make. There is something, seemingly, but what is hard to say. Rules are not easy to understand, and nothing here seems to help very much.

4.014 A gramophone record, a musical thought, musical notation, and sound waves, all stand to one another in that internal picturing relation that holds between language and world.

The logical form is common to all of them.

(As in the fairytale with the two youths, their two horses and their lilies. They are all in a certain sense one.)

‘Logical form’ is suggested by Black (p. 163) for logische Bau, which literally means something more like Ogden’s ‘logical structure.’ Since Wittgenstein contrasts structure and form, and refers to logische Bau nowhere but here, Black argues that ‘form’ is more appropriate than ‘structure’ here.

If they are one then they do not really have anything in common. They simply are the same thing. And yet they are not really the same thing. A musical score and a musical recording are not the same, although both may be referred to as, say, Beethoven’s Fifth. They have a kind of interchangeability, though, and insofar as they are interchangeable (which is by no means completely) they are one. But the interchangeability is purpose-dependent, seemingly. In the fairy story it is symbolic, and depends on our being able to see it as such. It is not, it seems, real in a platonic, metaphysical sense.

The fairytale in question appears to be the story “Golden Children” by the brothers Grimm. See Nordmann p. 114, note 47, where Jim Klagge is credited with this discovery. In this story, Nordmann says, “two youths, two horses, and two lilies mirror each other and yet, in a fairy-tale sense, are “literally” one.” In another case of two being one, he says that “the definite article points to Goethe’s Märchen, which revolves around a lily and a youth who are in many ways one.”