2.173 A picture represents its subject from the outside (its standpoint is its form of representation), which is why pictures represent their subjects rightly or falsely.

A picture is a representation, a kind of claim, and so it can be true or false, correct or incorrect. Which is perhaps to say no more than: a proposition is a proposition, so it can be true or false. To "represent from the inside" would be simply to be, and existence is not true or false.

2.172 But a picture cannot picture its form of representation; it exhibits it.

So a picture has a discernible form, but cannot picture this. Otherwise I suppose it would be a picture of its own picturing activity, which is inconceivable. The inability of a picture to depict its own form, its own picturely essence, must be a logical inability after all. And that means, I think, that the idea just does not make sense.

2.171 A picture can picture every reality whose form it has.

A spatial picture [can represent] everything spatial, a color one everything colored, etc.

A spatial picture, I take it, need not itself be spatial. That is to say, we can represent three-dimensional space without building a three-dimensional model, just as we do not need to use colors to represent colors (we can use words, for instance, instead). But again I am talking here as if pictures were to be understood fairly literally. If they are propositions, then what is a spatial picture? A proposition to do with space? Perhaps a proposition belonging to the set of all (possible) propositions about space? And then 2.171 becomes obviously true.

2.17 What a picture must have in common with reality in order to be able to picture it in its way -- rightly or falsely -- is its form of representation.

See 2.151. This form is a possibility. For x to be a picture of y, x and y must share the possibility of being true or real (including, I suppose, being truly non-existent). One must be a logical possibility, the other must represent that logical possibility. It is that possibility that they must have in common. But what kind of thing is that? Are we reifying possibility? Making logic metaphysical? Surely not. So what is being said? Could it be: nothing?

Ostrow (p. 44): “Far from being imagined as a third element, stateable or unstateable, the pictorial form is no element at all, but rather part of the picture’s way of depicting. The picture “must” have in common with reality its particular pictorial form precisely because this form is constituted by this picture’s application to the world – just as the possibilities of length are given through the ruler’s use in measuring magnitudes.”

See also 2.033.

2.161 In the picture and the depicted there must be something identical so that one can be a picture of the other at all.

This might sound reasonable, but what does, say, "The cat sat on the mat" have in common with a cat's sitting on a mat? What is identical in the pictured and the picture? Perhaps we could say what is identical is a certain relation that they share. Otherwise nothing comes to mind. And remember we have not yet been given any examples of pictures. Are they literal pictures, as one might reasonably think? Or sentences, as is often thought? Or propositions? And how are we to decide exactly how they relate to "states of affairs" (whatever exactly they might be)?

Ostrow (p. 39) says of standard interpretations that: “Wittgenstein’s answer to the question of how the picture – and hence language – can always be about the world is thus supposedly to be: they share a form.” And yet: “the strategy of taking recourse in talk of an isomorphism is empty; it amounts to no more than the claim that depicting the world is possible because the world has the possibility of being depicted.”

Cf. 4.04.

2.16 A fact must have something in common with what it depicts in order to be a picture.

The line between facts and pictures is further blurred. A fact can be a picture, it is implied. Or else, Tatsache ("fact") does not mean here what it means elsewhere, in which case "fact" is less (good as) a technical term than it has seemed.

2.1515 These coordinations are as it were the feelers [antennae, “the things which a butterfly has” in Wittgenstein’s words] of the picture elements, with which the picture touches reality.

The picture/ruler/map is now imagined almost as a living being, adjusting itself to reality so as to correspond to it, like an invisible shadow that always matches its object.

2.1514 The picturing relation consists of the coordination of the elements of the picture and the things.

To picture something (i.e. to be a picture of something) is to share, deliberately I suppose, its order or internal structure.

2.1513 On this view the picturing relation that makes it a picture also belongs to the picture.

Black (p. 85) prefers ‘picturing relation’ here to P&McG’s ‘pictorial relationship. (Ogden has ‘representing relation,’ which is also OK with Black).

Cf. my comment on 2.13. Anscombe rejects Ogden’s translation in note 1, p. 68. I think her point is that Ogden allows for the misinterpretation that, as Ramsey puts it on p. 271 of Foundations of Mathematics, the elements of the picture “are co-ordinated with the objects by the representing relation which belongs to the picture.” The picturing relation is not a relation between picture and pictured, but between elements of the picture. As Anscombe says (p. 68): “only if significant relations hold among the elements of the picture can they be correlated with objects outside so as to stand for them.” A picture needs a certain kind of coherence to be a picture, just as a sentence needs a certain kind of structure to be a sentence, nonsensical or otherwise. The correlation with something else, in order to give the picture meaning, is something we do.

And yet, in light of what Wittgenstein says next, mustn't the picturing relation belong to both the picture and its relation to what it pictures? Not everything is a picture, so some kind of property or properties must be had in order for something to be a picture, we might think. But then not every picture is a picture of this, so something else would seem to be needed to make a given picture a picture of some given thing or things. If, on the other hand, correlating a picture with something else is something that we do, then couldn't the same be true of the seemingly essential properties of a picture? Couldn't anything be a picture? So perhaps what I've quoted Anscombe as saying here is wrong.

2.15121 Only the outermost points of the dividing lines [on the ruler] touch the object to be measured.

OK, but what else is there? How thick is this ruler supposed to be? If it is just a line (and why not?) then it all touches, like the map. Cf. 5.557.

2.1512 It is like a ruler laid against reality.

OK, so perhaps they are not one. But think of a map, to scale, laid right on top of reality. That is what a picture is like. And now recall that reality includes the non-existence of states of affairs and that pictures can represent the non-existence of states of affairs. So what is the relation between a non-existent state of affairs and a perfectly corresponding representation of it? Can we be sure that the relationship is not one of identity in fact (or in effect)?

Ostrow (p. 35) notes that a ruler does not use itself. We must apply it. He quotes Wittgenstein (Ludwig Wittgenstein and the Vienna Circle p. 185) saying to Waismann later that he might as well have called propositions measuring-rods as pictures.

2.1511 This is how a picture is tied to reality: it reaches right up to it.

How is language related to reality? They go right together. If they are not one, they are at least inseparable, with an entirely common border. There is no distance between them. It really sounds as though they might be one and the same.

(Cf. Schopenhauer Fourfold Root p. 81: “Indeed perceptions through sight ultimately refer to touch, and sight can be regarded as an imperfect touch extending to a distance and making use of the rays of light as long feelers.”)

2.151 The form of representation is the possibility that things are related to each other in the same way as the elements of the picture.

Ditto.

2.15 The elements of a picture's relating to each other in a specific way represents matters relating to each other just so.

Let us call this connection of the elements of a picture its structure, and its possibility the form of representation of the picture [i.e. the form of the picture's picturing].

‘Form of representation’ is what Ogden has, and is accepted by Black (p. 81), although he prefers ‘form of depiction.’ He rejects, though, P&McG’s ‘pictorial form.’

Pictures really are just like states of affairs. Perhaps we should not think of these "pictures" as literal pictures, e.g. paintings, written sentences, etc. Perhaps instead we should think of them as propositions, what sentences express or contain or mean. Then every possible proposition will not only represent but really be a possible state of affairs. To think of literal pictures would then be like confusing sentences with propositions, or metaphysics with logic.

2.141 A picture is a fact.

To represent a possibility space is, in a sense, to realize it. So pictures are facts, i.e. existing states of affairs.

2.14 A picture consists in its elements relating to one another in a specific way.

‘Specific’ could equally be ‘determinate’ (as in P&McG) or ‘definite’ (as in Ogden).

Echoes of 2.031 and 2.032 here. The essence of a picture is the same as the essence of a state of affairs. How then can a picture be anything other than a state of affairs? Its elements are different, I suppose. In a state of affairs they are possibility spaces. In a picture they are the representatives of such possibility spaces.

2.131 In a picture, the elements of the picture stand in for objects.

Again, more literally: The elements of a picture stand [in], in the picture, for objects. So objects now seem to be the kind of things that can be represented, which sounds metaphysical again. This, we might say, is the problem of language. It is hard to talk about something without making it sound like a thing, an object, a res. How can the elements of a picture stand for possibility spaces? Well, in a graph the points on the coordinates do. In a painting or sentence ..., what? Every possible content is represented by every possible content. And what are the contents of a sentence? Clauses, words, letters, letter-parts? It's hard to see how there can be a right answer.

2.13 In a picture, the elements of the picture correspond to objects.

This is a strange sentence: To the objects correspond in the picture the elements of the picture. Why not just: The elements of a picture correspond to objects? For two reasons, I think. The first is to emphasize the correspondence to objects. The second is that the correspondence takes place within the picture. The picture, that is to say, is not just a copy of reality, a double. A shadow corresponds to whatever casts the shadow, but the correspondence between this object and its shadow is, so to speak, external. A shadow is not a work of art, like a portrait, intended or presented as a copy. Pictures, though, are like portraits in this respect. The correspondence is internal in the sense that the picture 'claims' to represent certain things. Also, bear in mind that objects are possibility spaces. The elements of a picture do indeed correspond to these. A pencil sketch can represent only in shades of grey, while a sculpture can represent not really color but three-dimensions of space (so can a sketch, of course, but in a different way). How a representation represents depends on the kind of representation it is. In an oil painting red will usually be represented by red, whereas in a charcoal sketch red will have to represented in some other way. The possibilities for the picture correspond to possibilities for reality (objects). Perhaps in fact this is all that Wittgenstein means here.

2.12 A picture is a model of reality.

So a fact is a state of things/condition/state of things/status rerum in logical space which is a piece of reality. See 2.063 and 2.11. A picture represents a (purported) fact or existing state of affairs. In Wittgenstein and the Vienna Circle p. 185 he says: “I have inherited this concept of a picture from two sides: first from a drawn picture, second from the model of a mathematician, which already is a general concept. For a mathematician talks of picturing in cases where a painter would no longer use this expression.”

2.11 A picture presents a state of things in logical space, the existence and non-existence of states of affairs.

Fairly straightforward, it seems, although is the non-existence of a state of affairs now a fact too? Or is it simply that some pictures present as facts the non-existence of various states of affairs?

Ostrow (p. 35) compares this with 1.13 and says that, “From the start, it would seem, the world is understood always against a larger – logical – backdrop of what is not the case.” He also says (pp. 36-37) that it is a mistake to see Wittgenstein (rightly) as rejecting Frege’s idea that a proposition is a kind of name only then to wonder how a picture represents a state of affairs. Facts should not be reified. They are uses of pictures. Ostrow (p. 38): “positive and negative fact stand on the same level, a contrast between two uses of a picture.”

He also (pp. 80-81) compares this remark with 2.201, 2.202, and 2.203. His conclusion is that a picture presents [vorstellt] existent and non-existent atomic facts, and represents [darstellt] a possibility of such facts, a choice made from among the facts that it could be used to depict.

2.1 We make pictures of facts for ourselves.

This is the translation that Black (p. 76) calls the literal one.

Cf. Heinrich Hertz The Principles of Mechanics (New York: Dover Publications, 1956) p. 1: “We form for ourselves pictures or symbols of external objects…” Hertz is concerned with the question how scientists can represent nature in such a way as to allow for making predictions.

Here, apparently, is the start of the famous picture theory, which seems to be beginning on a very shaky foundation given my previous comment.

Schopenhauer on pictures, language, etc. says that language does not communicate perceptions or anything that needs to be translated into pictures in the imagination, at least not usually. Language deals with abstract conceptions, which is why animals cannot understand it even though they perceive as we do. Images can never do justice to the concepts they occasionally represent. “Now, although concepts are fundamentally different from ideas of perception, they stand in a necessary relation to them, without which they would be nothing. This relation therefore constitutes the whole nature and existence of concepts. Reflection is necessarily a copy, a repetition, of the original world of perception, albeit a special kind of copy in an entirely different material. Thus concepts may quite properly be called ideas of ideas.” (Everyman edition of Schopenhauer’s WWR, pp. 10-11.)

“[T]rue philosophy must always be idealistic; indeed, it must be so in order to be merely honest." (Ibid., p. 13) “To the empirical standpoint of the other sciences it is quite appropriate to assume the objective world as something absolutely given; but it is not appropriate to the standpoint of philosophy, which by its nature has to go back to what is first and original. Only consciousness is immediately given; therefore, the basis of philosophy is limited to facts of consciousness, i.e., it is essentially idealistic.” (Ibid.)

What is available to our immediate consciousness “is limited by our skin, or rather by the very tips of the nerves which emanate from the cerebral system. Beyond this lies a world of which we have no knowledge except through pictures in our head.” (Ibid., p. 17) According to Schopenhauer, thinking is a kind of reflection of the empirical world, but because it deals with abstract concepts, it is perhaps better compared with algebra. See Gardiner p. 111, and Schopenhauer’s Erslingsmanuskripte §34.

2.063 The total reality is the world.

Tricky. 1.12 says that the totality of facts determines both what is the case and what is not the case. 2.05 repeats this idea. But then 2.062 seems to contradict it. It is not the facts that tell us what the non-facts are, but their being all the facts that does so. So in addition to all the facts we need another fact, namely that these are all the facts. But don't we then get into an infinite regress? It cannot be a fact that these are all the facts, since "these" refers to a set that excludes that last, seemingly all-important, fact. The existence of states of affairs cannot itself be a state of affairs. Our attempt to define a logical space or world consisting of all that is possible and allowing for the possibility of specifying exactly which possibilities are actualized and which are not seems to have hit a wall. Cf. 4.12.

2.062 The existence or non-existence of a state of affairs cannot be inferred from the existence or non-existence of another.

This clarifies what it means to talk about dependence here. It is a logical relation, having to do with inference, not causation.

2.061 States of affairs are independent of one another.

Cf. 1.21.

2.06 The existence and non-existence of states of affairs is reality.

(We also call the existence of states of affairs a positive fact, their non-existence a negative one.)

Cf. 1.12. So there are negative facts, or at least “we” say there are, or reserve that name for something. The question of the relation between “the world” and “reality” comes up here. Ostrow (p. 34): “It is, it would seem, some version of the ancient problem of the nature of “what is not” that confronts us at the close of the 2.06s.” On this, see Anscombe (p. 13, footnote): “cf. Plato’s Theaetetus 189A: ‘In judging, one judges something; in judging something, one judges something real; so in judging something unreal one judges nothing; but judging nothing, one is not judging at all.’ Wittgenstein returned to the problem presented by this argument again and again throughout his life.”

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

Cf. 1.12. An existing state of affairs, the realization of that possibility set, is a fact. See 2, from which we have not progressed here. But also see 2.062. Black (p. 70) says that 1.12 expresses the same thought.

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

See above and 1.1, from which we have not progressed except in terms of the addition of definitions which may or may not prove to be useful.

Black (p. 69): “The chief novelty [in 2.04-2.063] is the introduction of the puzzling notion of reality (die Wirklichkeit).” Putting 2.04 and 2.06 together, we might expect a contrast between ‘the world’ and ‘reality,’ but 2.063 shoots that expectation down. Perhaps, Black suggests, the terms are synonymous, with ‘total reality’ emphasizing the negative aspects of the world.

2.034 The structure of a fact consists of the structures of the states of affairs.

More puzzling multiplication. So is a fact a state of affairs? Or a complex of states of affairs? Or is a fact the reality corresponding to (or realizing) the possibility that is a state of affairs? 1.112 and 2 suggest this last alternative is the correct one. Whatever states of affairs (or state of affairs) correspond to a fact must have the same logical structure as it, otherwise they would not be the states of affairs that correspond to it, by definition.

Black (p. 69): “This should be compared with 4.1. The ‘fact’ here is a complex fact (Tatsache): the ‘atomic facts’ (Sachverhalte) (‘states of affairs’ in P.-McG.) are those involved in the former.”