Ultimate components
[Wittgenstein] believed that language disguises thought, and that the real forms of our thoughts would become apparent only when the language in which they are expressed had been analysed and broken down into its ultimate components, which, according to him, are elementary propositions.
His idea was that the assertion of ordinary factual propositions is a gross move, which contains within itself a large number of minute moves. The grossness of ordinary factual propositions is a blessing [but] an exact account of what they mean could be given only if they were analysed into their ultimate components [...]
Wittgenstein did not claim to be able to give any examples of elementary propositions, because he thought that neither he nor any other philosopher had yet got down to the ultimate components of factual propositions.
In default of examples we have to rely entirely on Wittgenstein's specification of elementary propositions. He specifies them as a class of factual propositions which are logically independent of one another: the truth or falsity of one elementary proposition never implies the truth or falsity of any other elementary proposition.
To have a sense is to have a precise sense, and a factual proposition gets its precise sense only because its words represent things, just as a diagram says something only if its parts represent things [...] a factual proposition gets its precise sense only because its words either themselves represent existing things or are analysable into other words which represent existing things.
[...] to say that a proposition must have a precise sense is to say that it must be possible to draw a sharp line around everything that is necessarily the case if [the proposition] is true. [However] some factual propositions might be inherently vague. Wittgenstein himself makes this point [...] in Philosophical Investigations, and raises the interesting general question, whether logic idealizes the structure of language and, if so, to what extent.
A country, whose frontier was always a little further out than at any moment it was deemed to be, would not really have a frontier, and so would not be a territorial unit at all. Similarly, the aggrandizement of the sense of a proposition must come to a halt. There must be a definite limit to what is being asserted, and so there must be a definite limit to the view into reality which is presented by a picture or a factual proposition. Both may have a very fine grain, but in each case there must be a definite limit to the fineness of the grain.
This is an abstract argument, based on a general theory of meaning, and Wittgenstein did not claim to be able to produce any examples of complete analyses which might reinforce its conclusion, or even illustrate it. He merely specified elementary propositions as a class of logically independent factual propositions, and he left the precise nature of their elements, which he called 'names', shrouded in mystery.
Now these names were pure names, which, unlike the name 'Dartmouth', had no concealed factual content. So their meanings could only be the simple objects, or, as he puts it, leaving the qualification to be understood, the 'objects', which they represented. But what sort of thing is an object?
Elementary propositions lie at the centre of the system of factual discourse, and constitute its inner limit. The first stage of Wittgenstein's demarcation of the system was to fix this inner limit, because it was the point of origin from which he was to work outwards and calculate its outer limit, the maximum expansion of the bubble.
[David Pears]
Wittgenstein, p. 58-62, 66-7
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