In propositions of the form "A says that p" or "A believes that p," it would seem that the proposition "p" is being used in a larger proposition without having any bearing on that larger propositions truth or falsity. For instance, the proposition "John hopes that it will rain tomorrow" can true or false regardless of whether or not it does actually rain tomorrow. This would seem to problematize Wittgenstein's claim that all propositions are truth-functions of elementary propositions. If "John hopes that it will rain tomorrow" is a composite of, among other things, the proposition "p," then p would have to have some bearing on the truth or falsity of the overall proposition.
Wittgenstein answers that a proposition of the form "A believes that p" does not actually involve a relationship between A and the proposition "p." "'A believes that p,' 'A has the thought p,' and 'A says p' are of the form '"p" says p'" (5.542). For A to think, believe, or say that p is the case, the words that constitute the verbal utterance of p must occur to A. It is then not A but these words that are related to p, and the internal similarity between the words and the proposition is obvious. Wittgenstein further infers that there is no such thing as a "soul" where thoughts and beliefs reside (5.5421).
We cannot learn a priori what kinds of objects or elementary propositions there are. Logic is prior to any particular experience, but not prior to the fact of experience itself: it is the shape experience takes. Logic can teach us that there are objects and elementary propositions, but it is a matter of applying logic that we come to learn about the varieties of objects and elementary propositions that there are. There is no such thing as "logical experience" that we can consult regarding the various forms of elementary propositions (5.552).
"The limits of my language mean the limits of my world" (5.6): the limits of language are determined by the totality of elementary propositions, and the limits of the world are determined by the totality of facts. There is a one-to-one correspondence between facts and elementary propositions, so we cannot say what lies outside the limits of the world (5.61).
This observation leads Wittgenstein to reflect on the limited truth of solipsism. Where, within the limits of my world, do I fit? Wittgenstein draws the analogy between the relationship between the metaphysical subject and the world on one hand, and the relationship between the eye and the visual field on the other (5.633). I cannot see my eye anywhere in my visual field, but the existence of a visual field presupposes the existence of the eye. Similarly, my self is not something I encounter in the world, but the existence of the world (my experience of the world) presupposes that there is a self to experience it. However, I cannot talk about this self because it is outside the limits of the world, and hence outside the limits of language. The only way the self appears in philosophy is in the fact that "the world is my world" (5.641).
The term "solipsism" defines a number of related philosophical positions, all of which claim that the objects and people in the world only exist as objects of my awareness, that only I, as a thinking consciousness, truly exist. No philosopher has seriously defended this position (although there is a story about a woman who wrote to Bertrand Russell, claiming she was a solipsist and wondering why there weren't more people like her), but it has fascinated philosophers as a doctrine that is very difficult to refute. How can we convince a solipsist that we, or the objects around him, exist? What proof can we give him?