Philosophy must be of some use and we must take it seriously; it must clear our thoughts and so our actions. Or else it is a disposition that we have… - Frank P. Ramsey

Tautologies and contradictions are not real propositions, but degenerate cases. ...Clearly, by negating a contradiction we get a tautology, and by negating a tautology a contradiction. ...A genuine proposition asserts something about reality, and it is true if reality is as it is asserted to be. But a tautology is a symbol constructed so as to say nothing whatever about reality, but to express total ignorance by agreeing with every possibility.

[A]lthough my attempted reconstruction of the view of Whitehead and Russell overcomes, I think, many of the difficulties, it is impossible to regard it as altogether satisfactory.

[W]e shall be concerned with the general nature of pure mathematics, and how it is distinguished from other sciences. Here there are... two distinct categories of things of which an account must be given—the ideas or concepts of mathematics, and the propositions of mathematics. ...the great majority of writers on the subject have concentrated their attention on the explanation of one or the other... and erroneously supposed that a satisfactory explanation of the other would immediately follow.