All mathematics is tautology.

Could one imagine a stone's having consciousness? And if anyone can do so-why should that not merely prove that such image-mongery is of no interest to us?

Believers who have formulated such proofs [for God's existence] ... would never have come to believe as a result of such proofs

Logic is not a body of doctrine, but a mirror-image of the world. Logic is transcendental.

There can never be surprises in logic.

Ask yourself whether our language is complete--whether it was so before the symbolism of chemistry and the notation of the infinitesimal calculus were incorporated in it; for these are, so to speak, suburbs of our language. (And how many houses or streets does it take before a town begins to be a town?) Our language can be seen as an ancient city: a maze of little streets and squares, of old and new houses, and of houses with additions from various periods; and this surrounded by a multitude of new boroughs with straight regular streets and uniform houses.

Propositions show what they say: tautologies and contradictions show that they say nothing.