4.013 And if we delve into the essence of this imagery then we see that it is not disturbed by apparent irregularities (like the use of # and Ь in musical notation).

Because even these irregularities picture what they are meant to express; only in another way.

(Sharp and flat are what I mean to indicate here, of course.)

What matters is not how a notation or language looks, but how its signs function.

‘Pictoriality’ is suggested by Black (p. 163) for Bildhaftigkeit. Ogden has ‘pictorial nature,’ P&McG have ‘pictorial character.’ I use ‘imagery’ because that is how Wittgenstein translated the same word in 4.015.

4.012 It is obvious that we perceive a proposition of the form “aRb” as a picture. Here the sign is obviously a likeness of the signified.

Again: really? A proposition of the form “Putnam respects Quine” strikes us as being a picture, or representation, of Putnam’s respecting Quine? Sentences in languages we do not know do not strike us in this way, it seems to me. If by proposition we mean thought, i.e. understood proposition, then does the meaning represent Putnam’s respecting Quine? Surely not. The meaning is that Putnam respects Quine. The sentence represents, but does not do so obviously. Does the understood sentence obviously represent? It indubitably represents, if by "represents" we mean means. Does what is understood in the sentence, the proposition or meaning ‘contained in’ the sentence, represent Putnam’s respecting Quine? Does that Putnam respects Quine (the meaning of the sentence “P respects Q”) represent Putnam’s respecting Quine? The concept of representation just seems to have no application here. What might be a likeness of pRq? What might obviously be a likeness of pRq? I have no idea.

4.011 At first glance a sentence – as it exists printed on paper perhaps – seems not to be a picture of the reality with which it deals. But so too do written notes seem at first glance not to be a picture of music, nor our written signs for sounds (letters) to be a picture of our spoken language.

And yet these symbolisms prove to be pictures – even in the ordinary sense of the word – of what they represent.

Really? A written sentence is a picture, in the ordinary sense, of a spoken sentence? Notes picture music? They represent these things, I think we can say that. So perhaps “Bild” is better translated as representation than as picture. Then propositions represent reality as we conceive of it, or imagine it, or take it to be. This sounds fair enough, albeit perhaps not very interesting.

Black (p. 163) says that the bit about pictures even in the ordinary sense “can hardly be defended.” On the same page, above this, he quotes Moore Papers p. 263 to the effect that Wittgenstein admitted that when he wrote the TLP he had not noticed that the word ‘pictures’ was vague, but that, nevertheless, “he still … thought it “useful to say ‘A proposition is a picture or something like one’” although … he was willing to admit that to call a proposition a “picture” was misleading; that propositions are not pictures “in any ordinary sense”.” So something odd is going on here. According to Moore, Wittgenstein said that he merely wished to stress a similarity between the grammar or use of ‘proposition’ and that of ‘picture.’ Why, though?

4.01 A proposition is a picture of reality.

A proposition is a model of reality as we think it is.

“Wirklichkeit” might equally be translated as truth here, but standardly isn’t. Not much apparent advance on 3.

4.0031 All philosophy is “critique of language.” (Though not in Mauthner’s sense.) Russell’s merit is to have shown that the apparent logical form of a proposition need not be its true form.

So Russell’s philosophy is not all nonsense, but perhaps most of it is, especially if this is the only idea of merit in Russell’s work.

Separate point: and yet, see 5.5563. Any apparent inconsistency between these two remarks is, I think, cleared up by the reference here to Russell’s point.

Mauthner was skeptical about the ability of language to convey truth because, he thought, it only pictures reality, never actually coinciding with nature. See Nordmann pp. 117-121. For Mauthner, language is conventional and based on metaphor, so it can never really grasp the real world. See Stokhof pp. 25-27.

4.003 Most sentences and questions that have been written about philosophical things are not false but rather nonsensical. So we cannot answer questions of this kind at all, but only ascertain their nonsensicality. Most questions and propositions of philosophers are based on our not understanding the logic of our language.

(They are of the same kind as the question whether the good is more or less identical than the beautiful.)

And it is not surprising that the deepest problems are really no problems at all.

Ogden wrongly has ‘senseless’ for unsinnig.

This echoes the preface and reminds us to be on our guard against nonsense in the Tractatus itself. However, Wittgenstein only says that most philosophy is nonsense, not that it all is. So the possibility, as far as 4.003 alone goes, is distinctly open that the Tractatus is not nonsensical at all. But then why would he mention this idea here? Presumably, if the Tractatus is not nonsense, because what he is doing here is determining the nonsensicality of other philosophical ideas. Those of Russell and Frege, presumably, since it is primarily their ideas that are addressed in the Tractatus. These are implied to be no better than the worst kind of metaphysical claptrap.

Schopenhauer, in the midst of something of a rant about the state of German philosophy, which he regards as dishonest, pretentious, and empty, says in the Fourfold Root p. 169 that: “Moreover, “the Good, the True, and the Beautiful” are much in favour, especially with the sentimental and tender-hearted, as pretended Ideas, although they are simply three very wide and abstract concepts, in that they are drawn from innumerable things and relations, and are consequently very poor in substance, like a thousand other abstracta of a similar kind.”

4.002 Man possesses the ability to construct languages, whereby every sense can be expressed, without having any inkling how and what each word means. – As one speaks without knowing how the particular sounds are produced.

Ordinary language is a part of the human organism and not less complicated than it.

It is humanly impossible to gather the logic of language immediately from it.

Language disguises thought. Indeed so much so that from the outer form of the clothes one cannot infer the form of the thoughts they clothe; because the outer form of the clothes is made for a wholly different purpose than to let the form of the body be known.

The unspoken, silent agreements for understanding ordinary language are enormously complicated.

Russell on ordinary language (from 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) Frege says his Begriffsschrift is a tool invented for “certain scientific purposes” and that it ought not to be condemned “because it is not suited to others.” He makes no claim, then, that it is better than ordinary language for ordinary purposes. See Weiner, p. 156 in Reck (ed.) From Frege to Wittgenstein. Weiner gives the reference to Frege as BEG, p. 6/BS, p. xi.

My first reaction: This sounds important, but can it be right? Is “complicated” the right word here? If we accept that ordinary language contains a hidden order or logic that logicians must unearth, then there does seem to have to be something complicated and unconscious going on in ordinary language. Jerry Fodor and Noam Chomsky might be interested in this. But how can we know there is such a thing to find, especially if it is humanly impossible to gather it immediately? What medium might be useful to us? Then again, much of this passage sounds quite Fregean, and Wittgenstein is not necessarily out to attack the “great works of Frege” (see the preface) at every turn. He could be in earnest here.

4.001 The totality of sentences is language.

Another definition.

4 A thought is a meaningful proposition.

I.e. a sinnvolle Satz.

3.5 An applied, thought, propositional sign is a thought.

Another definition, this time of a thought (“der Gedanke”).

3.42 Although a proposition may determine only one place in logical space, at the same time the whole of logical space must already be given by it.

(Otherwise negation, logical sum, logical product, etc. would introduce ever new elements – in coordination.)

(The logical scaffolding around a picture reaches through the whole logical space. The proposition reaches through the whole logical space.)

A set of coordinates determines only one figure, but the coordinates themselves imply a set of axes, a space or dimension (or set of dimensions) in which the figure can be. Similarly with propositions and logical space. Since logical space applies to all things, all possibilities, as such then any possibility implies it. Remember, in case this sounds controversial, that we are pretty much still dealing with definitions here, and that there might yet prove to be no cash value whatsoever to any of this.

3.411 Geometrical and logical place agree in that both are possibilities of existence.

That is, each is the possibility of an existence, and in that they are the same. The difference is that geometrical space is more limited than logical space. Geometrical space covers geometry. Logical space covers everything.

3.41 The propositional sign and the logical coordinates: That is the logical place.

There you are.

3.4 A proposition determines a place in logical space. The existence of this logical place is guaranteed by the existence of the constituent parts alone, by the existence of the meaningful proposition.

That is, by the existence of “des sinnvollen Satzes.”

Noteworthy here is the apparent equation of the constituent parts and the meaningful proposition. But this might not be surprising if the proposition has been whittled down to an imperceptible commonality among various sentences and “the constituent parts” are simply possibility spaces. What we seem to have are possibilities, and of course each possibility guarantees the existence of a space for it in logical space. Because what follows “of course” in that sentence is a tautology.

3.3442 The sign for a complex is not arbitrarily resolved by analysis in such a way that its resolution would be different in each sentence structure.

(P&McG have ‘proposition,’ Ogden has ‘propositional structure’ here for Satzgefüge.)

Analysis must be consistent, I suppose.

3.3441 One can, e.g., express the common feature of all notations for truth-functions thus: It is common to them that they all— e.g. —can be replaced by the notation “~p” (“not p”) and “p v q” (“p or q”).

(This shows [gekennzeichnet] the way that a specific possible notation can give us general insight.)

A specific kind of logical notation or concept-script can show us something general, namely that a general range of bits of language can be translated into them. We seem to learn nothing about the world in this way though, except that different bits of it have this in common, which we could have known already, without the symbolism.

3.344 That which signifies in a symbol is the common feature of all symbols that can take its place following the rules of logical syntax.

Essentially nothing, in other words. No thing. What matters is the role within logical syntax, the place that is taken there.

3.343 Definitions are rules for translation from one language into another. Every right sign-language must allow of translation into every other by means of such rules: This is what they must all have in common.

There is no ostensive definition in this sense. To define is to determine one bit of language as equivalent to another. Any adequate language will be able to cope with all such possible translations (perhaps just by having a means for importing foreign words and phrases, so that the English for Brie is “Brie” for instance). Again, what is had in common by bits of language is just this relation between them, not anything metaphysical.

3.3421 A particular way of symbolizing may be unimportant, but it is always important that this is a possible way of symbolizing. And it is like this in philosophy generally: the particular proves unimportant time and again, but the possibility of each particular gives us an insight into the essence of the world.

What matters is not what happens to be so, but the possibilities. These constitute the essence of the world that we are concerned with. So these are what matter to the philosopher. Nothing really new here, despite the exciting reference to gaining information or clarity on the essence of the world.

3.342 In our notations there is indeed something arbitrary, but this is not arbitrary: if we have determined something arbitrarily then something else must be the case. (This stems from the essence of the notation.)

Or: This depends on the essence of notation. The best candidate for something arbitrary in a notation would seem to be the signs used, that “dog” (rather than “chien” or “Hund” say) means dog, and so on. But from this arbitrary designation, once the meaning has been defined or determined, any necessary truths about dogs (that they are animals, say) will then be necessarily true of “dogs.” It is the designation or determination or definition that produces the necessity. The essence of notation then seems to have something to do with definition, which sounds right and certainly fits the general Tractarian view of language as representing designated objects in states of affairs.

3.3411 Thus one could say: The actual name is that which all symbols that signify an object have in common. It would then follow that no composition at all is essential for a name.

P&McG are simply wrong here, as Black (p. 152) points out.

What is essential to a name is that it names the particular thing it names. If it is the name of a Tractarian object, a point in logical space, then it is as simple as a name can be. It is simply a name that simply names a simple object. Anything complex in the name would be inessential. On the other hand, the actual name referred to here would, or at least could, have no discernible features at all. No sound, or appearance, for instance. While it becomes simpler it also becomes invisible. Could it be a phantom?

3.341 The essential in a proposition is thus that which all propositions that can express the same sense have in common.

And likewise in general the essential in a symbol is that which all symbols that can fulfill the same purpose have in common.

What is common to all propositions that can express the same sense? The ability to express just that sense. Must this ability depend on some other common feature? Not that I can see. The same goes for symbols. So 3.341 seems to be quite empty, its only purpose being to confirm the suspicion about 3.34 that it was not an important metaphysical truth.

3.34 A proposition possesses essential and accidental features.

The accidental are those features that come from the particular way of producing the propositional sign. The essential are those which alone enable the proposition to express its sense.

The accidental features would then seem to be what it sounds like, if spoken, or how it looks, if written, etc. The essential would belong not to the sentence but to the proposition. What could those be? Not its sense, since they are said to be whatever it is that enables the proposition/sentence to express its sense. They are presented as non-physical sense-making powers or prerequisites. Is this metaphysics, or have we strayed into nonsense?

3.334 The rules of logical syntax must be self-evident if one only knows how each one of the signs signifies.

Are the rules of logical syntax identical with the ways of signification?

3.333 A function can therefore not be its own argument, because a functional sign already contains the prototype of its argument and it cannot contain itself.

Let us suppose that the function F(fx) could be its own argument; there would then therefore be a proposition: “F(F(fx))” and in this the outer function F and the inner function F must have different meanings, because the inner has the form ø(fx), the outer the form ψ(ø(fx)). Only the letter “F” is common to both functions, but that in itself has no significance.

This becomes clear immediately if instead of “F(F(u))” we write “(Eø) : F(øu) . øu = Fu”.

Thus Russell’s Paradox is laid to rest.

Black (p. 149) says of this reference to Russell’s paradox that Wittgenstein “presumably [means] the variant concerning functions (rather than classes) that are not themselves included in the set of their own values.”

Having rejected Russell’s solution in 3.332, here Wittgenstein rejects his problem too. (The “E” here should, by the way, be the existential quantifier.)

Ostrow (p. 67) compares this remark with 3.1432. “Wittgenstein’s aim is once more to bring out how our hold on a notion of logical form is parasitic on how we speak, on what it makes sense to say.” Russell’s belief that a theory of types is needed suggests that he confusedly thinks something like the opposite of this, Ostrow thinks.

3.332 No proposition can express something about itself, because a propositional sign cannot be contained in itself (this is the whole “Theory of types”).

Russell has made a mistake analogous to mixing up concepts and objects, in Frege’s sense of the terms.

3.331 From this remark we get a comprehensive view of Russell’s “Theory of types”: Russell’s error is shown by his having to speak of the meaning of a sign when putting together his rules for signs.

Black (p. 146) suggests ‘get a comprehensive view of’ for sehen wir in Russell’s ‘Theory of Types’ hinüber while P&McG have ‘turn to’ and Ogden has ‘get a further view – into Russell’s …’ ‘Hinüber’ means ‘over’ and ‘in’ means ‘in,’ so we are seeing into Russell’s theory, getting insight, but also getting an oversight, either looking beyond it or, as Black suggests, looking over the whole thing (but at it, not to something on the other side).

Russell’s system is impure, therefore, in the sense of TLP 3.33.

In Principles of Mathematics (1903) Russell proposed his first, simple version, and in “Mathematical Logic as Based on the Theory of Types” (1908) he proposed the ramified version. The basic idea of the theory of types is that classes are not objects. This makes for a simpler ontology, and means that it is nonsense to talk about a class being a member of a class in the way that an object (a spoon or a barber, say) can be a member of a class. But the simple version does not get rid of all paradoxes. The ramified theory of types is based on the vicious circle principle, i.e.: “Whatever involves all of a collection must not be one of that collection'; or 'If, provided a certain collection had a total, it would have members only definable in terms of that total, then the said collection has no total.” (see Principia Mathematica, 1 (1910), Introduction, ch. 2, p.1). In the simple theory, there are types of objects (real objects, classes of objects, classes of classes, and so on). In the ramified theory there are also types of properties (properties, properties of properties, etc., e.g. shyness is nice or red is a property of objects).

The theory of types is developed in order to avoid certain paradoxes, e.g. those involving infinity (how it seems possible to come up with an infinite number of objects from a finite collection, and thus prove a priori that the world contains an infinite number of objects—i.e. prove the axiom of infinity) and the class of all classes that are not members of themselves. “Now the theory of types emphatically does not belong to the finished and certain part of our subject: much of this theory is till inchoate, confused, and obscure. But the need of some doctrine of types is less doubtful than the precise form the doctrine should take.”[1]

Classes are logical fictions, and if they are treated as being real objects, whose names have real signification, then the sentences in which they are treated this way will be devoid of meaning. “The supposition that a class is, or that it is not, a member of itself is meaningless in just this way.”[2] Since we cannot know whether the axiom of infinity is true, we cannot know whether the world is infinitely or, on the contrary, finitely divisible. If the latter is the case, then logical analysis has a chance of finding the real simples or particulars that make up the world.

F. P. Ramsey, following Wittgenstein, objects to this theory. Propositional functions are symbols, while individuals are objects. So talk of functions of functions is not like talk of functions of individuals. “For the range of values of a function of individuals is definitely fixed by the range of individuals, an objective totality which there is no [getting?] away from. But the range of arguments to a function of functions is a range of symbols, all symbols which become propositions by inserting in them the name of an individual. And this range of symbols, actual or possible, is not objectively fixed, but depends on our methods of constructing them and requires more precise definition.”[3]

Wittgenstein’s criticism in the Tractatus begins (3.331) with the observation that formal logic is supposed to be purely formal, yet Russell has to refer to the Bedeutungen of the signs in the drawing up of his symbolic rules. This shows that something has gone wrong with the introduction of the theory of types. But what? The theory of types amounts to just this: “No proposition can say anything about itself, because the propositional sign cannot be contained in itself.” (3.332, Ogden).

It is, it seems, a bit like Frege’s distinction between concept and object. Talking about concepts and functions makes them sound like objects, but we need to look at their role in the system to understand them properly. The fact that ‘The class of classes’ looks and sounds like ‘The class of spoons’ does not mean that they are the same. In Frege’s terms, ‘The class of classes’ can be analyzed into the function ‘The class of ( )’ and the argument ‘classes’. Functions are not arguments. A good system of symbols will show this distinction. It does not need to be explicitly stated in a seemingly ad hoc way.

Russell’s paradox shows that there are concepts that do not determine a course of values (or value-range). It shows that Basic Law V is false. Neither Russell nor Frege really managed to rescue logicism from this problem though.

Mounce (p. 56) puts Wittgenstein’s objection to Russell’s theory of types this way: “one cannot in a correct symbolism construct a proposition which refers to itself without making it evident that the contained proposition has a different function from the proposition which contains it. But then it will be evident that one cannot construct a proposition which refers to itself. For, given such a misguided attempt, it will be evident that what one has is not one proposition, referring to itself, but different propositions. In short, a theory of types is entirely unnecessary.”

Black (p. 146): ‘It is hard to account for Wittgenstein’s evident animus in this digression. For Wittgenstein’s own programme for ‘logical syntax’ can properly be viewed as an attempt to accomplish what Russell was reaching for in his theory of types. Wittgenstein himself once said that philosophical grammar or logical syntax was ‘a theory of types’ (Phil. Bem. 3, 2). An improved version of Russell’s theory of types might well be a part of logical syntax in Wittgenstein’s conception.”

---

[1] Introduction to Mathematical Philosophy p. 135.

[2] Ibid., p. 137

[3] Ramsey “Predicative Functions and the Axiom of Reducibility” in Klemke, pp. 355-368, p. 358, originally in Chapter 1 pp. 32-49 of his The Foundations of Mathematics.

3.33 In logical syntax the meaning of a sign should never play a role; it must be able to be established without anything thereby being said of the meaning of a sign, only the description of the expressions being presupposed.

McManus calls this and the following remark about Russell obscure. On p. 77 he writes: “That we should simply strive to make more apparent the difference between different symbols, rather than (per impossibile) stating what the difference between the symbols is (for instance, by discussing the different kinds of things to which they refer), helps explain” this obscure criticism of Russell.

Meaning (Bedeutung) here again seems to be used in the sense of object referred to or something like that, as we find in Frege. Logical syntax is thus independent of the world, just as algebra is independent of anyone’s bank account.

3.328 If a sign is not used then it is meaningless. That is the meaning of Occam’s razor.

(If everything behaves as if a sign had meaning, then it has meaning.)

Ogden has ‘not necessary’ and P&McG have ‘useless’ for nicht gebraucht. Black (p. 134) points out that the true meaning is ‘not used.’

Ockham’s razor is generally quoted as: Entities are not to be multiplied beyond necessity. It is a kind of metaphysical principle, a rule for generating economical theories about reality. So why link it with meaning? Perhaps this is nonsense. Or perhaps Bedeutung (“meaning”) is here used in a Fregean way, indicating something referred to or signified. When a sign in fact signifies nothing, does nothing at all, there is no point positing something as its reference. But then the fundamental question about meaning is not does a sign refer? but does it have a use? So Frege-ish questions of metaphysics become at least somewhat irrelevant. As the parenthetical comment seems to emphasize.

3.327 A sign determines a logical form only together with its logico-syntactical use.

That is, only taken together with this use does it determine a logical form.

3.326 In order to recognize the symbol in the sign one must look to the meaningful [sinnvollen] use.

To know the (meaningful, significant, or ‘sensical’) use is, it seems, to know the symbol. In Letters to Ogden, p. 59, Wittgenstein writes: “The meaning of this prop[osition] is: that in order to recognize the symbol in a sign we must look at how this sign is used significantly in propositions. I.e. we must observe how the sign is used in accordance with the laws of logical syntax. Thus “significant” here means as much as “syntactically correct”.” I have ‘meaningful’ instead of ‘significant’.

3.325 In order to avoid such errors, we must use a symbolism that excludes them by not using the same sign for different symbols and by not using signs that signify in different ways in what appears to be the same way. A symbolism then that obeys logical grammar – logical syntax.

(The concept-script of Frege and Russell is one such language, though admittedly it does not yet exclude all errors.)

Cf. 5.5563.

A thought: Wouldn’t it be ironic if right here Wittgenstein were to make just the kind of mistake he has just warned about? The first sentence seems fine. But what is “logical grammar”? Could grammar possibly be illogical? No. He means the grammar of logic, the syntactical rules of logic. But what are these? Just the rules of logic, surely. And, just as surely, grammar already obeys these. Perhaps he means a language that more clearly follows the laws of logic. But it is clear already that all grammar must, can only, do this, and the laws of logic are just generalizations (hypothetical ones, we might say) derived from natural language. So the language described might be both impossible to create satisfactorily and unnecessary anyway.

3.324 Thus the most fundamental confusions (of which the whole of philosophy is full) easily arise.

So if philosophy is full of nonsense and the point of the Tractatus is to solve this/these problem(s) then 3.323 seems to be crucial. The book presumably aims to show either how we should use words/language, or that misuse of words/language leads to confusion.

3.323 In colloquial language it is common for the same word to signify in different ways – and thus belong to different symbols --, or for two words, that signify in different ways, to be applied in a proposition in ways that are the same externally.

Thus the word “is” appears as the copula, as the sign of equality, and as the expression for existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak about something [an object], but also about something happening [an event].

(In the proposition “Green is green” – where the first word is a person’s name and the last is an adjective – these words do not simply have different meanings but they are different symbols.)

Russell in Logical Atomism: “The is of “Socrates is human” expresses the relation of subject and predicate; the is of “Socrates is a man” expresses identity. It is a disgrace to the human race that it has chosen to employ the same word “is” for these two entirely different ideas—a disgrace which a symbolic logical language of course remedies.” (p. 172)

Some clue here about Wittgenstein’s use of “external.” It refers to the extra-logical, the merely physical, the superficial. Why not say simply that “Green” and “green” have different meanings? See PI §558 and §561.

3.322 A common characteristic of two objects can never be indicated by our symbolizing them with the same signs, but by two different ways of symbolizing. Because the sign is indeed arbitrary. One could thus also choose two different signs and where would then be what was common in the symbolization?

So, for instance, that we both call something by the name “God” does not at all mean that we are talking about the same thing. The word used is arbitrary, just as it would (probably, etymological curiosities aside) be pure coincidence if a word in two historically unrelated languages looked or sounded exactly the same. What matters is the way in which the word means. What matters, one might say, is its use.

3.321 Two different symbols can thus have the same sign (written or audible etc.) in common with one another – they signify then in different ways.

Fair enough. Two words might sound and look alike but have different meanings, as the word ‘bank’ can be the side of a river or a likely target for robbers. And the same might be true of signs/symbols other than words.