In the Notebooks 1914-16 Wittgenstein writes
The difficulty of my theory of logical portrayal was that of finding a connection between the signs on paper and a situation outside in the world. I always said that truth is a relation between the proposition and the situation, but could never pick out such a relation (19e-20e; quoted in Word and World, 71).
Language is first and foremost a representational system. It is with language that we ``make to ourselves pictures of facts'' (2.1). ``the picture is a model of reality'' (2.14). And in turn these pictures are themselves facts. This leads immediately to a notion of units, let's call them words, which stand for the objects. As the objects are linked in the world to form facts, the words are linked in language to form propositions. A sentence is meaningful if and only if it is a fact which corresponds to a possible fact in the world; it's true if it corresponds to an actual fact. But what does ``correspond'' mean?
This is Wittgenstein's ``picture theory of language.'' For Wittgenstein, propositions are pictures. Language is used to make these pictures. And it's not accidental that he uses the term ``picture,'' for Wittgenstein's theory of meaning is one which draws on the visual analogy precisely because the propositions are themselves facts, not mental representations.
2.13 To the objects correspond in the picture the elements of the picture.
2.131 The elements of the picture stand, in the picture, for the objects.
2.14 The picture consists in the fact that its elements are combined with one another in a definite way.
2.141 The picture is a fact.
2.16 In order to be a picture a fact must have something in common with what it pictures.
2.17 What the picture must have in common with reality in order to be able to represent it after its manner--rightly or wrongly--is its form of representation.
3.1431 The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.
The mutual spatial position of these things then expresses the sense of the proposition.
What are we to make of this? Let's start at the beginning and see what we can see.
At 3.1432, Wittgenstein writes: We must not say, ``The complex sign `aRb' says `a stands in relation R to b'''; but we must say, ``That `a' stands in a certain relation to `b' says that aRb.
This contains a key to understanding the picture theory of meaning. What do you think he means by this? He means that sentences aren't arbitrary signs of some content, proposition, but that they stand in an isomorphic relationship to that content--just as a photograph may be said to picture you by being mappable onto your features, so too a sentence pictures the fact it reports by being so mappable onto the proposition it means. `a' and `b' are the names of objects, `R' of a relation. Names are pieces of language. When names are concatenated appropriately, `aRb,' but not `RbR,' for example, the result is a sentence which is meaningful. And what it means is the fact which it pictures, viz., the fact that object-a is related to object-b by relation-R, or the fact that aRb. Another analogy might help: in pointillism, each dot on the canvas corresponds to a specific area in the scene depicted, for Wittgenstein, each unit in a proposition corresponds to a specific element in the state of affairs meant.
In an ideal language, every object and relationship would have a unique name (see 3.325). Thus every sentence would have an unambiguous meaning. As it is, we fall short of this, but that's not the worst problem.
For Wittgenstein `a,' which names object a, means not only that, á-la Locke, it is attached to the object as a name, but the sign, word `a' also represents the object a's possibilities of combination with other objects: i.e., it represents all of a's possibilities. Now as a start of the explanation of this let's say that just as the object a occupies a logical space--more accurately a cluster of metaphysical spaces--the word `a' must occupy a grammatical space which corresponds to the metaphysical spaces. Thus, if we say that one cannot come home in a flood of tears and a sedan chair because people are in such and such logical spaces, floods of tears in this and that logical spaces and sedan chairs in yet another set of logical spaces and the act of coming home in occupies yet another, and that the sets of spaces associated with floods of tears and sedan chairs and coming home in don't overlap, what our language must tell us is that the sentence `She came home in a flood of tears and a sedan chair' does not picture any fact, it is meaningless. And we must be able to read this off the grammatical spaces occupied by the words, names. So that by looking at the sentence `aHb & aHc' we will see that `a' standing in a certain relationship to `b' and `a' standing in that same relationship to `c' does not correspond to any possible fact: does not say that aHb & aHc.