3.32 A sign is what is sensibly perceptible of a symbol.

Cf. 3.11. So “2” would be the sign, but it would be a different symbol in first 23 and then 102. In “23” the sign “2” means “twenty-,” whereas in “102” it means “-and 2.”

3.318 Like Frege and Russell, I take a proposition to be a function of the expressions contained in it.

So propositions are being treated here as functions. But it does not follow, Anscombe points out (p. 103), that Wittgenstein thinks propositions just are functions. We can speak of 8 as a function of 2, she notes, without meaning that 8 just is a function and nothing else, or that thinking of it this way is the right way to think of it. So Wittgenstein is not here saying anything incompatible with Frege’s view that a proposition is not a function.

3.317 Fixing the values of a propositional variable is specifying the propositions whose common characteristic the variable is.

The fixing is a description of these propositions.

The fixing will therefore deal only with symbols, not with their meaning.

And the only thing essential to the fixing is that it is only a description of symbols and tells nothing of the symbolized.

How the description of the propositions occurs is unessential.

Black (p. 129) says that ‘signs,’ here and in 3.33, would be better for Symbolen than ‘symbols.’

Me: Saying that X = 2 or -2 tells us that any proposition containing 2 or -2 (which the proposition “201 – 23 = 178” does not) has the variable X in common. A statement such as “X = 2” does not tell us the meaning of X. This might be easier to see with a statement of the same form in which we do not already know the meanings of the words, e.g. “A boojum is a snark.” This does not tell you what a boojum is. It simply tells you that the signs “boojum” and “snark” can be used interchangeably. (This might not be true in fact, at least in all cases. The expressions “that evil tyrant” and “your worshipful majesty” might refer to the same man, but this does not make them interchangeable exactly. Still, to whom you were referring would probably be clear enough were you to make the mistake of mixing these expressions up.) Attempts to clarify language by means of logical analysis seem likely to tell us nothing at all about the world, therefore.

3.316 What values a propositional variable may accept is fixed.

The fixing of the values is the variable.

There seems to be an interesting combination here of agreement (arbitrariness) and absolutism (non-arbitrariness). A variable may be replaced by any range of values, determined by whoever introduces the variable. But once a variable is defined, the definition fixes the range completely. X can mean anything, but if I say “X² = 4” then its meaning is settled (as either 2 or -2). “X” on its own has no meaning, and so is not a variable. In a proposition such as “X² = 4” it is a variable and has a meaning. And its meaning, its possible values, is set.

Cf. 5.501. Black (p. 128) says the procedure referred to is that described in 3.317, not 3.315.

3.315 If we convert a component of a proposition into a variable, then there is a class of propositions which are all the values of the resulting variable proposition. This class still depends in general on what we, by arbitrary agreement, mean by the parts of that proposition. But if we convert into variables all those signs whose meaning is arbitrarily determined then a class like this will still always remain. This however is now dependent on no agreement, but only on the nature of the proposition. It corresponds to a logical form – a logical prototype.

Take the proposition: Bad monkeys like good bananas. Now replace “bananas” with the variable x. We can now generate a class or set of propositions in which x is replaced by something suitable, something that fits (“apples,” say, but not “green”). This set depends on the arbitrary meanings we have given to words like “bad” (we could have used “mal” or “schlecht” instead). Now what if we replace all the arbitrary words with variables? For all m, if m is b and b is g then m likes b. Or perhaps: For all w and all y, if w is x and y is z then wLy. Something like that. Now there is still a class of propositions for which this could stand, to be generated by filling in the place of w, x, y, z, and L with grammatically appropriate words (or proposition parts of some kind). This set or class though does not depend on arbitrary agreement, the conventional meanings of words (or other symbols). Rather it depends on what I (following the later Wittgenstein) am here calling grammar, what Wittgenstein calls logic or logical form.

Mounce (p. 30): “In the Tractatus, logical form is something which, as it were, underlies the rules of language and guarantees its intelligible usage. In the Investigations, he thinks of logical form as being a kind of formalization of the rules of language and these arise out of its use; they do not underlie and guarantee its intelligibility. Common to both works, however, is the view that meaning is not some special entity or psychological process.”

3.314 An expression has meaning only in a proposition. Every variable can be taken as a propositional variable.

(Even a variable name.)

So we are really not getting away from propositions here. Perhaps just as talk of propositions does not really get us away from sentences.

3.313 An expression is thus presented by way of a variable whose values are the propositions that contain the expression.

(In the limiting case the variables become constants, the expression a proposition.)

I call such a variable a “propositional variable.”

We seem to be multiplying logical entities beyond necessity, but we’ll see where we get with all this.

3.312 It is thus presented by way of the general form of the propositions that it characterizes.

Moreover in this form the expression is constant and everything else is variable.

OK, but what is this general, unchanging form? Presumably we are dealing with logic here, not metaphysics. So does talk about constancy and variation really belong? How could a matter of logic not be constant?

3.311 An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic feature of a class of propositions.

An expression (or symbol) is thus something like a meaning. In the way that a proposition can be thought of as what various sentences with the same meaning have in common, so too an expression is what various propositions with (or containing) the same meaning have in common. So do we need the concept of an expression? Do we need the concept of a proposition?

3.31 Every part of a proposition that characterizes its sense I call an expression (a symbol).

(The proposition itself is an expression.)

The expression is all that is essential for the sense of a proposition that propositions can have in common with each other.

An expression marks a form and a content.

OK. More definitions. And how do expressions differ from propositions? Well, a proposition is an expression, so there cannot be much difference. An expression is also any part of a proposition that is proposition-like too, but this might also be called a proposition surely. So we don’t seem to have gained much here.

Black (p. 123): “Wittgenstein is not defining this sense of ‘symbol’ but merely adding that an expression is a symbol.”

3.3 Only a proposition has sense; only in the context of a proposition does a name have meaning.

Wittgenstein here echoes Frege in Foundations § 62.

There is no knowing the meanings of primitive signs before one understands propositions in which they occur. So perhaps 3.263 just means that to understand an elucidation is to understand the primitive signs it contains. Perhaps. This might also throw some light on 3.1432. Propositions are primary.

Cf. Schopenhauer Fourfold Root p. 95: “It is like a word of two meanings; only from the context can we infer what is meant.”

3.263 The meanings of primitive signs can be explained through elucidations. Elucidations are propositions which contain primitive signs. They can thus only be understood if the meanings of these signs are already known.

What the…?! This sounds circular and pointless. Don’t know the meaning of a primitive sign? An “elucidation” will help. But you will only understand it if you already know the meaning of the relevant primitive sign! So either knowledge of meaning is not the same thing as understanding when it comes to signs, which seems unlikely (but who knows?). Or explanation of meaning is quite impossible (in the terms presented by the Tractatus up to now). See p. 44 and pp. 49-50 of Joan Weiner’s essay in Future Pasts.

Anscombe (p. 26) suggests that this passage, along with 3.261, provides the best evidence for thinking that the elementary propositions of the Tractatus are simple observation statements, such as “This is a red patch.” Names and only names are primitive signs. Logical signs, as he indicates elsewhere, are not primitive signs. But (see p. 27) what elucidates a name need not be an elementary proposition. And from 6.3751 it follows directly that “This is a red patch” cannot be an elementary proposition. Anscombe concludes that elementary propositions are not simple observation statements, and that this explains why Wittgenstein did not refer to observation in connection with them. What they are he cannot say, but they must exist. See, for instance, 5.5562, 3.23, 2.021, 2.0211, and 4.221.

See also 5.526.

3.262 A sign’s application shows [zeigt] whatever is not expressed in the sign itself. What signs slur over, their application speaks out.

James Conant argues that the distinction between zeigen and erläutern is important.[i] The former applies only to meaningful propositions, while the second can apply to nonsense. Without wishing to prejudge the issue, I will use ‘show’ only for zeigen. McManus also mentions this issue in footnote 8, p. 36.

The application of a sign seems almost to be working against the sign itself here. Is this slurring over a deliberate attempt to hide something? Perhaps it could be, but probably not. It might be worth asking whether signs do express anything themselves. Maybe all the meaning/signifying/saying/showing is done by the application of the sign.

The application of a sign is here linked with its meaning. In Chapter 1, §2 of Schopenhauer’s Fourfold Root (p. 2) he talks of the different applications of the principle of sufficient reason and says that the principle acquires a different meaning in each such application.

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[i] See James Conant “What ‘Ethics’ in the Tractatus is Not,” in D. Z. Phillips and Mario von der Ruhr (eds) Religion and Wittgenstein’s Legacy Ashgate, 2005, pp. 39-88, p. 82, note 49.

3.261 Every defined sign signifies via the signs through which it can be defined; and the definitions show [weisen] the way.

Two signs, one primitive and one defined by primitive signs, cannot signify in the same way. One cannot analyze names through definitions. (Nor any sign that has meaning on its own, independently.)

Working backwards through this: Signs have meaning only in the context of propositions, so there are no such signs anyway (see 3.22). Names cannot be analyzed by means of definitions or by any other means, since they are quite simple. Primitive signs (names) signify (get meaning) by some means other than definition, since they cannot be defined. Others have the meaning they are defined as having. So can primitive signs have meaning at all? It is hard to see how they could, and so hard to see how the other signs supposedly defined by means of them could be defined either.

It is hard at this point, in the terms the Tractatus gives us, to see how meaning is possible at all. Language (signs, etc.), conceived as something distinct from the world, seems to be incapable of being hooked up to it.

The “Nor any” in the last sentence is Wittgenstein’s translation. See Letters to Ogden p. 59.

Consider in this connection the fact that Frege’s goal is to get away from the ambiguities and misleading qualities of ordinary language. Hence he cannot say precisely in ordinary language what the terms of his system mean. We have to look at the system and see how they operate there. Can a sign have meaning on its own? In Frege’s view, the meaning of a word is not the mental picture associated with it, nor anything merely psychological. We should not consider the meaning of a word in isolation, but within the context of a proposition. If the proposition makes sense, then the words that make it up do. See Foundations of Arithmetic. Also see Russell’s Logical Atomism: “It is exceedingly difficult to make this point clear as long as one adheres to ordinary language, because ordinary language is rooted in a certain feeling about logic, a certain feeling that our primeval ancestors had, and as long as you keep to ordinary language you find it very difficult to get away from the bias which is imposed upon you by language.” (p. 205)

3.26 A name cannot be analyzed further by a definition: it is a primitive sign.

Propositions are complex, names are simple.

3.251 A proposition effects [expresses] what it expresses in a definite, clearly assignable way: a proposition is articulated.

Propositions are as precise as the states of affairs they describe, and as structured.

3.25 There is one and only one complete analysis of a proposition.

Obviously, since a complete analysis is an analysis into simple signs, which correspond to objects, i.e. points in possibility-space. To say an analysis is complete is to say it has been completely disambiguated or defined. If this can be done, it can be done in only one way.

3.24 A proposition that deals with a complex stands in an internal relation to a proposition that deals with a component of the complex.

A complex can only be given through its description, and this will match it or not match it. A proposition, in which there is mention of a complex, will, if this complex does not exist, be not nonsensical [unsinnig] but simply false.

One can see that a propositional element signifies a complex by a vagueness in the propositions in which it occurs. We know by this proposition that something is not yet definite [determinate]. (The notation for generality indeed contains a prototype.)

The abbreviation of the symbol of a complex in the form of a simple symbol can be expressed by a definition.

See 4.123 for the meaning of ‘internal.’ See 4.241 for the meaning of ‘definition.’ There is a logical relation between propositions about complexes and propositions about parts of complexes, presumably taking these propositions to be about complexes qua complexes and propositions about complex-parts to be about them qua complex parts (see my comment on 2.0201). In the next paragraph of 3.24 Wittgenstein seems to agree with Russell about the (non-existent) King of France. To say that the King of France is bald, when there is no King of France, is to say something that is simply false, not nonsensical. There can indeed be vagueness in propositions, something corresponding to indeterminacy. There is a sort of implication here that this vagueness might be eliminable, but there is certainly no claim that this will be so. Indeed, if the notation for generality (for all x, if x etc., I suppose) already contains a prototype for indeterminacy, then perhaps it is not dispensable from logic.

3.23 The requirement of the possibility of simple signs is the requirement of the definiteness of sense.

So if sense is to be definite and not vague then there must be, or it must be possible for there to be, such things as simple signs. See my comment on 3.2 for why we might not insist that sense be definite. But if what can be said can be said clearly, mustn’t sense be definite? I don’t think so. A vague sentence can be quite clear, as the later Wittgenstein certainly realized. If I say “Stand near the door” this is vague but, possibly, quite clear.

This connects with Frege. See Basic Laws of Arithmetic 1903, v. 2, §56 and §62. Bearn discusses this on pp. 51-53. See also Notebooks p. 62.

See also Mounce, on what the point of a logical system is for Wittgenstein (this comment might be better elsewhere). (p. 48) “it is not the purpose of a logical system to provide a language more perfect logically than the ordinary. Such a project, on his view, is entirely incoherent. One thing cannot be more logical than another. A thing is either logical or it is not; it is either meaningful or it is meaningless. Thus, the purpose of a logical system is not to provide the logic that ordinary language lacks; rather it is to display the logic of ordinary language more perspicuously than ordinary language does itself. But then it follows that the cardinal sin in a logical system will be lack of perspicuity, vagueness, ambiguity.”

3.221 I can merely name objects. Signs stand for them. I can only speak them, I cannot express them. A proposition can only say how a thing is, not what it is.

The third sentence is puzzling. I can speak signs but not express them? What's the difference? Perhaps what this means is: I cannot mean things, since meaning in the relevant sense is not personal or psychological. “The cat sat on the mat” means what it means, regardless of me. It is signs that mean things, not people that do so. We can only use or utter signs. I can say “By ‘cat’ I mean dog” and then say “The cat sat on the mat” meaning “The dog sat on the mat,” but ‘my’ meaning this is done by the words themselves. I cannot mean something without words, i.e. without signs or tokens of some kind, be they (mental or physical) pictures or words or whatever. But this seems like a stretch.

What about the last sentence of 3.221? A sentence consists of signs, not of objects. It can say, in effect, “The thing designated by ‘cat’ sat on the mat.” It cannot incorporate a non-linguistic object into itself and say this is what ‘cat’ or ‘Fluffy’ stands for. Why not? Because to do so is to treat or make the object in question part of language, hence linguistic in the relevant sense. Holding up a cat and saying “This is Fluffy,” meaning “The meaning of ‘Fluffy’ is this,” is giving a definition, performing a linguistic act (an act, that is, within or belonging to language). It is, in effect, a kind of equation: Fluffy = ö. And equations tell us nothing, including what a thing is. I can of course say that Fluffy is a cat, is seriously overweight, is cowardly, and so on. But this tells you how Fluffy is, not what Fluffy is like.

What else is there to say though? What would it be to say what something is in some other sense? Nothing at all. That is why it cannot be done. The “impossibility” is logical, i.e. there is no such thing as doing that, i.e. the very idea is plain nonsense. This reminds me of Berkeley. We can say that the apple is red, mealy, soft, and so on, but we are not adding anything to say then that it is matter. Or, for that matter, idea.

3.22 In a proposition a name stands for an object.

And outside a proposition it doesn’t? I was going to say "surely not," but perhaps this is right after all. Outside a proposition is it a name at all? Does it stand for anything when not in the context of a proposition? Quite possibly not.

3.21 The configuration of the simple signs in a propositional token corresponds to the configuration of objects in a state of things.

No real surprise here, given 3.2 and so on.

3.203 A name means an object. The object is its meaning. (“A” is the same sign as “A”.)

Not the most helpful parenthetical comment, surely. Perhaps again the striking or puzzling remark is a sign of irony or something unobvious going on. See PI § 39 and 40, where the meaning of a name is distinguished from the bearer of a name.