The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.

[Leibniz] was always engaged in trying to construct such as mathematical logic as we have now... and he was always failing because of his respect for Aristotle... Whenever he invented a really good system, it always brought out that [Aristotle's logic] is fallacious... He could not bring himself to believe that it is fallacious, so he began again. That shows that you should not have too much respect for distinguished men.

I am sorry that I have to leave so many problems unsolved. I always have to make this apology, but the world really is rather puzzling and I cannot help it.

[The] belief in the physical world has established a sort of reign of terror. You have got to treat with disrespect whatever does not fit into the physical world. But this is really unfair to things that do not fit it. They are just as much there as the things that do.

The longer one pursues philosophy, the more conscious one becomes how extremely often one has been taken in by fallacies, and the less willing one is to be quite sure that an argument is valid if there is anything about it that is at all subtle or elusive, at all difficult to grasp.

I believe the only difference between science and philosophy is that science is what you more or less know and philosophy is what you do not know. Philosophy is that part of science which at present people choose to have opinions about, but which they have no knowledge about. Therefore every advance in knowledge robs philosophy of some problems which formerly it had.

The philosopher has an adventurous disposition and likes to dwell in the region where there are still uncertainties.

[Mathematical logic] makes [philosophy] dry, precise, methodical, and in that way robs it of a certain quality that it had when you could play with it more freely. I do not feel that it is my place to apologize for that, because if it is true, it is true. If it is not true, of course, I do owe you an apology; but if it is, it is not my fault, and therefore I do not feel I owe any apology for any sort of dryness or dullness in the world.

Acquire a taste for mathematics, and then you will have a very agreeable world.

Bertrand Russell, Philosophy of Logical Atomism, 1918