The totality of all propositions is the sum total of what we are capable of expressing in language (4.001). Everyday language, however, does not break down neatly into distinct propositions. It has a logical structure, but this structure is disguised by the complicated conventions of ordinary speech, so much so that the logical structure beneath ordinary speech is difficult to ascertain. (4.002). Most of the problems of philosophy result from a misunderstanding of the logic of language. We can only answer such philosophical questions by pointing out that they are nonsensical (4.003).
A proposition is a picture of reality in the same way that notes in a score form a picture of a piece of music. And just as there is a general rule for translating notes on a page into music, there is also a general rule for translating written propositions into pictures of reality (4.0141). It is because of this correspondence between the form of a proposition and the form of reality that we can understand the sense of a proposition from the proposition itself: we don't need a further proposition to explain what one proposition means. "A proposition shows its sense. A proposition shows how things stand if it is true. And it says that they do so stand" (4.022). This is like saying a picture of a person shows what the person looks like. We don't need further explanations to tell us how we are supposed to correspond the marks on a piece of paper to a human face.
The logical connections between objects are not represented in a proposition. Propositions depict facts, not the logical structure of these facts, as expressed in connectives like "and" or "not," as well as more general logical concepts like those of class or relation. "My fundamental idea," Wittgenstein claims, "is that the 'logical constants' are not representatives; that there can be no representatives of the logic of facts" (4.0312).
Wittgenstein emphasizes that the truth-value of a proposition has no bearing on its sense. True or false, it still makes a picture of the world, and we can still draw logical inferences from that picture. The propositions p and ~p depict the same possible situation, only they have opposite sense (4.0621): one says that the picture presented is the case, and the other says that it is not the case.
"The totality of true propositions is the whole of natural science" (4.11). In this way, Wittgenstein sets philosophy apart as distinct from natural science. Natural science describes the world, whereas philosophy's aim is the logical clarification of thoughts (4.112). Philosophy itself is not a body of propositions; rather, it is the activity of clarifying the propositions of natural science. In clarifying the propositions of natural science, philosophy will not only render clear what can be said, but also show what cannot be said (4.114 and 4.115). Because it treats all the propositions of natural science equally, no branch of science (such as psychology or evolutionary theory) is more closely related to philosophy than any other branch (4.1121 and 4.1122).
The sense of a proposition is internal to the proposition, while the meaning of a name is external to the name. The meaning of a name is the object it denotes, and there is nothing in the name itself (as a written or spoken sign) that can tell us what object it denotes. Rather, we learn the meaning of a name by observing how and in reference to what it is used. The meaning of a name lies outside the name, and this meaning must be made clear by means of elucidations.