for the world does not presuppose anything about the world, not any "rationality" of it, or whatever it may be called. It has nothing to do with any properties of the universe; it is concerned with the expression of facts by propositions (i. e. by other facts), and more particularly with the equivalence of different expressions. There an no conditions for the validity of logic.
Perhaps I should remark, in passing, that there are certain conditions for the possibility of speaking about the world at all — but that is quite a different matter. In order to use language there must be occasion for employing words (or the equivalent of words), and this occasion does not exist unless there are similarities in the world, for if every object or event occured just once, there would be no sense in giving a name to it, for the name could never be used. There would not be one world, in fact, however changing, but there would be continually new worlds having nothing to do with each other. There would be no possibility and no need of expressing anything, and we could not ask any questions. But as soon as we are able to ask questions there is the possibility of expression, and there is logic. It is even misleading, although I have done it myself for the sake of argument, to speak of the "validity of logic", for an invalid logic would not be logic, it would be nonsense.
Once more : the world cannot be logical or irrational — such phrases are nothing but excuses for bad philosophy. Whatever the universe is like — we can describe it by true propositions. The world consists of facts, the facts have a structure, and our propositions will picture the facts correctly — they will be true if they have the same structure.
In this simple way we must give account of the notion of truth; there is not much more to be said about it. The older philosophers were quite right when they declared that truth was a kind of correspondence between the judgment and that which is judged, although it was impossible for them to recognize the nature of the correspondence, which is simply identity of structure.
The phrase "identity of structure" must not be misinterpreted. When there is a ring lying on a book, for instance, this is an extremely complicated fact in nature, in which an indefinite number of details could be discerned: there are innumerable different ways in which a ring can lie on a book ; both objects may have innumerable different shapes and may be in innumerable different physical conditions. No heed is taken of all these possibilities in
