3.202 The simple signs used in a proposition are called names.

Another definition.

3.201 I call these elements “simple signs” and the proposition “completely analyzed”.

Black (p. 108) points out that, since we have no way to know when we have reached a complete analysis, this remark does not usefully define ‘simple sign.’

3.2 In propositions thoughts can be so expressed that the objects of the thought match the elements of the propositional token.

My first attempt to comment on this was: Really? What then are the elements of the propositional token (sentence)? Not letters, presumably, or sounds. Words perhaps, or phrases. If I say “The chair was quite soft” then the words “the chair” will correspond not with one particular possibility space (or point in logical space, or object) but with many (however many such points there are in a chair, as it were, or chair-possibility). The same goes for the words “quite soft”. Do they cover a specific range of possibility-spaces? Surely not. There is vagueness here, or so it would seem. An analysis of such a propositional token as “The chair was quite soft” results in vague and infinite sets of ‘objects’. (Infinite because, by 2.0131, at least some objects exist in an infinity of objects of a similar kind.) Nothing really gets clarified or made determinate.

On a second look, I'm inclined to emphasize the word "can" in Wittgenstein's remark.

3.144 One can describe states of things, but not name them.

(Names are like points, whereas propositions, having sense, are like arrows.)

In mathematics and, I think, in German, ‘sense’ (Sinn) can mean direction, as well as meaning.

Is “name” being implicitly defined here as a word that applies to simples only? If so, is the only “impossibility” implied by the first sentence of 3.144 a definitional one, a logical one?

3.1432 Not: “The complex sign ‘aRb’ says that a stands in relation R to b” but rather: That “a” stands in a certain relation to “b” says that aRb.

Aren’t these equivalent? Perhaps that is the point. An explanation only puts the same thing another way, a way that is, in itself, neither better nor worse. On the other hand, what Wittgenstein seems to be saying is that the second of his sentences is actually preferable to the first. Why would that be? Perhaps because the first treats ‘aRb’ as needing explanation or unpacking or articulation, whereas in fact it is already fully articulate. For those who understand a sentence or proposition, its analysis is quite useless (i.e. uninformative).

Mounce says, on pp. 24-25, that it might help to substitute some actual relation for aRb. Thus, we could say “Not: ‘The complex sign ‘the painting hangs on the wall’ says that the painting stands in the relation of hanging to the wall’ but rather: That the painting stands in the relation of hanging to the wall says that the painting is hanging on the wall.” Mounce (p. 25): “In other words, the relation between a proposition and its sense is an internal one. The sense of a proposition is to be found in an arrangement of physical signs; it is not to be found in something that corresponds to that arrangement, some entity over and above it, whether in the empirical or some quasi-empirical world.” (If you understand “The painting hangs on the wall” then it does you no good at all to be told the longer version that is the alleged meaning of this complex sign.)

A proposition is not a name, and the meanings of its elements are not independent of it, are not really, we might say, elements, in the sense that the proposition consists of bits that can be understood more clearly or fully when taken apart. Cf. 3.3.

Black (p. 105): “I take W. to be denying that the complex sign is a name of the situation described: a fact is needed to refer to a fact.”

Fahrnkopf discusses a nominalistic interpretation of this passage and a realistic one. Nominalist readings (e.g. Copi's and Anscombe's) take the key point to be that 'R' would have no place in an ideal symbolism. Thus relations are not real, and whatever 'aRb' tells us might just as well be expressed by, say, 'ab' or 'ba'. On p. 29 Fahrnkopf writes: "according to Wittgenstein's decimal notation, 3.1432 is a comment on 3.143, and this latter passage is concerned only to make the point that a propositional sign is a fact, not a name; this is also the context of the remark in the "Notes on Logic" which corresponds to 3.1432. On my interpretation, then, the purpose of 3.1432 is only to contrast symbolizing facts with names, and the nominalist tone of this passage--which could have been avoided altogether had Wittgenstein specified that the relation in which 'a' stands to 'b' consist in their respective relations to 'R'--is in any case minimized by the realization that the status of 'R' as a name is implied in many other contexts in the Tractatus."

Fahrnkopf also points out (p. 35) that in the Notebooks Wittgenstein wrote on 16/6/15 that relations and properties are objects.

3.1431 The essence of a propositional token becomes very clear if we think of it as made up of spatial objects (such as tables, chairs, books) instead of written signs.

The reciprocal spatial position of these things then expresses the sense of the proposition.

Ogden here has ‘mutual spatial position,’ which Black (p. 103) calls the literal translation. But ‘mutual’ can imply shared, as in “our mutual friend,” and here the spatial position is not meant to be the same.

Relative position, syntax, seems here to be presented as all that is needed for sense, although of course you need some tokens to arrange too. What about semantics?

3.143 The usual form of expression in writing or printing disguises a propositional token’s being a fact.

Because in a printed sentence, e.g., no essential difference appears between a propositional token and a word.

(This is how it was possible for Frege to call a sentence a complex name.)

‘Complex’ here is suggested by Black (p. 103). The others have ‘compounded’ (Ogden) and ‘composite’ (P&McG).

Grammar is invisible. Note also that Wittgenstein thinks it necessary to come up with an explanation for how Frege could have made a mistake.

3.142 Only facts can express a sense, a set of names cannot.

A class or set is both hypothetical and, what seems to be the point here, unstructured. Sense depends on structure, i.e. syntax or grammar. It also, as we have seen, seems to depend on what has meaning being more than merely hypothetical, i.e. on its being in some sense real.

3.141 A proposition is not a mixture of words. – (In the same way that a musical theme is not [just] a mixture of notes.)

A proposition is articulated.

Wittgenstein says (Letters to Ogden, p. 24) that the main point is that a proposition is a structure, not a mixture. Obviously the order is essential in each case. To be a proposition, to have a meaning or sense, words must be combined grammatically (at least approximately). This is the precise way in which words must be combined to have a meaning. That is to say: “The dog bit the man” means something different than “The man bit the dog.” The meaning depends on the way in which the words are combined, and which combination means what depends on grammar.

3.14 A propositional token consists in its elements, the words, relating to each other in a definite way.

A propositional token is a fact.

See 2. A sentence (propositional token) is a state of affairs that exists. True enough. It can also be a picture (see 2.16) and a thought. So the distinction between world and representation is further blurred or erased. A sentence not only expresses a thought (see 3.1), it actually is one, or at least can be. We seem to able to cut thoughts and propositions from our metaphysics, if we have one, and see that these terms are logical terms of art, no more. And, by this point, perhaps scarcely even that for Wittgenstein.

3.13 To a sentence belongs all that belongs to the projection, but not what is projected.

Thus the possibility of what is projected belongs to it, but not it itself.

Its sense is therefore not yet contained in a sentence, but [perhaps?] the possibility of expressing it is.

(“The content of a sentence” means the content of a significant [meaningful, sinnvollen] sentence.)

The form of its sense is contained in a sentence, but not its content.

I’m following Black (p. 100) here in translating Satz as ‘sentence’ rather than ‘proposition.’

You would think that only what is projected (the sense or meaning) is what belongs in common to both a proposition and the sentence that is its projection. But here Wittgenstein says that propositions are really something like potential sentences. Not only do we encounter propositions only in the form of sentences, but propositions exist only as sentences. Because until they are sentences, propositions have no content, no sense. And a proposition without sense is hardly a proposition at all, is it? If a proposition has only form then it certainly has no real existence. It is a logical fiction or hypothetical ‘entity’ used for thinking about logic. Its ‘existence’ is purely logical, not metaphysical at all.

Alternatively, the first sentence of 3.13 might be read as saying that propositions and sentences (tokens) have everything in common except the physical manifestation that is the sentence (token). That (the physical stuff) is what is projected. Thus the possibility of being communicated belongs to a proposition, but not the perceptible properties necessary for communication themselves. It therefore has no use yet (so sense is use?), but only the possibility of being used. This doesn’t sound too implausible, but what would be “the possibility of expressing the sense of a proposition” if this sense were itself the expression of a proposition/thought/sentence? The second half of 3.13 seems incompatible with the reading offered in this paragraph. So we are back with my previous paragraph. What now to make of the first sentence of 3.13, which does sound odd? I think oddness often indicates irony in the Tractatus. To a proposition belongs nothing, in other words, because what is projected exists only in sentences. (Or thoughts ‘embodied’ in some perceptible medium. I don’t see why this has to be physical and not, say, the stuff of a Cartesian mind.)

Black (p. 100) says that what belongs to the projection means “all that is internal to the representing relation, i.e. the logical form that the sentence has in common with the state of affairs it represents (2.18)” and what is projected means the sense. He also says (same page) that: “form of its sense = ‘form of the possible state of affairs presented’ = ‘the logical form’.”

3.12 I call the token through which we express a thought a propositional token. And a proposition is a propositional token in its projective relation to the world.

So a Denken is a Gedanke, it seems, and we must take 3.11 logically, not metaphysically, just as I suggested. And what I said about sentences and their relation to propositions seems to be confirmed here too.

3.11 We use the physically perceptible token (audible or written, etc.) of the proposition as a projection of a possible state of things.

The method of projection is the thinking of the proposition’s sense.

This is tricky and important. How do we use sentences (sensibly perceptible representatives of propositions) as projections (representations?) of possible states of things? A possible state of things is a state of affairs. A proposition is a picture of a state of affairs. A sentence is a physical version of a proposition, i.e. (I suppose) a proposition with additional, physical characteristics. Since this is the form in which (it seems) we must deal with propositions, we could identify the two, but the proposition is the sentence conceived under the aspect of logic. Its external features (font, language, etc.) are irrelevant. Perhaps this is where the earlier talk of “external properties” of objects comes in. If objects are quasi-fictional ‘entities’ that we get by analyzing propositions, and we only ever encounter propositions in a form where they have external properties, then perhaps one might talk of the external properties of objects. To do so would surely be at best misleading though, since to think of a sentence as a proposition is precisely to think of it without its external properties, or not to think of those properties, or to think of it as if they were irrelevant.

Anyway, the first sentence of 3.11 seems to say no more than that we use sentences in place of (or as) propositions. The second equates doing this with thinking (of) the sense of the proposition. If thinking means doing something with (or having) a thought (as this term has been used and understood up to now) then this cannot be a psychological matter. But Wittgenstein could be using das Denken (“the thinking”) to mean something other than the thought (der Gedanke). So let’s not jump the gun. If thinking in a psychological (metaphysical, not logical) sense is a method for using sentences to get at or convey propositions, then 3.11 tells us that sentences get hooked up to propositions by means of a psychological act. There are multiple problems with this idea. Some have to do with Wittgenstein’s Fregean opposition to psychologism. But perhaps saying so begs the question. More obviously, the theory under consideration is massively implausible. If I use a sentence to convey a thought to another, how does that person know what I’m thinking? Language use (i.e. successful language use) would seem to not only require but be a kind of telepathy. Surely Wittgenstein cannot have meant this.

The other way to take the second sentence of 3.11 is as an equation or definition: thinking of the proposition’s sense is (means, equals) using the sentence that expresses or corresponds to it. What I say or write, I also (thereby) think. This seems to make insincerity impossible, but it does not do so if “thinking” is simply being (re-)defined in this way.

Anscombe says (p. 69, note 1) that “Wittgenstein’s use of ‘projection’ is a metaphorical extension of the mathematical use, which may be explained thus: ‘The drawing of straight lines through every point of a given figure, so as to produce a new figure each point of which corresponds to a point of the original figure.’”

3.1 In a sentence a thought is expressed perceptibly.

Ogden’s “through the senses” is surely wrong, unless it means “through the senses and into the mind.” P&McG have “an expression that can be perceived by the senses.” Black (p. 99) notes that this is “somewhat laboured,” and suggests “In a sentence the thought expresses itself perceptibly.”

3.05 We could only know a priori that a thought was true if its truth could be known from the thought itself (without any object of comparison).

Because we are talking about a priori truth here and because, it seems to be implied, no other thoughts can be involved, either because they would not help (because the truth of each is independent of the truth of others) or because other thoughts themselves would count as objects of comparison.

3.04 An a priori correct thought would be one such that its possibility implied its truth.

Cf. 2.202.

3.0321 We could well represent spatially a state of affairs that went against the laws of physics, but not one that went against the laws of geometry.

Because the idea is quite empty: a geometric representation of anti-geometry.

3.032 One can no more in language present “the logically contradictory” than one can in geometry present through its coordinates a figure that contradicts the laws of space; or give the coordinates of a point that does not exist.

The “impossibility” is logical, not metaphysical. There is not something that one cannot do, just as there is no such thing as a geometric figure that contradicts geometry (not geometry as we know it, but geometry as such). Talk of such things is gibberish.

3.031 It used to be said that God could create everything, only nothing that would be contrary to the laws of logic. – That is [?], we could not say of an “illogical” world how it would look.

I wonder whether Wittgenstein commented on the translation of this. Both Ogden and P&McG have “The truth is…” for the start of the second sentence, but I see nothing corresponding in the German. It looks literally to be: “We could of course not say of an “illogical” world how it would look.”

We cannot picture it, we cannot conceive of it, even God could not create it. These are all ways of saying (in a misleadingly metaphysical-sounding way) that the idea has no sense. I could add “for us”, but then all pictures are made by us and for us, or so at least it seems so far for Wittgenstein.

McManus (p. 59, note 24) cites the first sentence of this remark as an example (others are in 3.323, 4.002, 4.003, and 5.02) of straightforwardly empirical claims that could not possibly be interpreted as nonsensical, even if they are false. That is, it is evidence that not every sentence in the book is meant to be simply nonsensical.

3.03 We cannot think anything illogical, because we would then have to think illogically.

Cf. 5.4731. "Thinking illogically" is a contradiction in terms if "thinking" is understood as Wittgenstein means it. That is why we cannot do it. There is no such thing to do. And so what is illogical is utterly inconceivable. There cannot, as a matter of logic, of sense, be an illogical state of things. The word "cannot" here sounds metaphysical, but it can't be. It would be absurd to say that that which is unthinkable or inconceivable cannot occur in the world. Why on earth not, after all? And what are we talking about? What is the reference of "the unthinkable"? Asking this starts to sound metaphysical and mystical, but here that is plainly a mistake. “Thinking illogically” is self-contradictory, neither possible nor impossible, that is why we ‘cannot’ “think anything illogical,” because that too is, or implies, a contradiction. What could it mean to have a thought of “an illogical state of things”? It would mean to have a logical picture, a kind of copy or representation of, the logic of an illogical thing, the internal structure of something with no internal structure. This is, again, neither possible nor impossible but sheer nonsense.

3.02 A thought contains the possibility of the state of things that it thinks. What is thinkable is also possible.

So the limits of the thinkable are determined by possibility, i.e. by logic, not by any psychological limits of thinkers.