Logic must look after itself. In a certain sense, we cannot make mistakes in logic.

Is it even always an advantage to replace an indistinct picture by a sharp one? Isn't the indistinct one often what we need?

I don't know why we are here, but I'm pretty sure that it is not in order to enjoy ourselves.

When one is frightened of the truth then it is never the whole truth that one has an inkling of.

With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.

For a large class of cases - though not for all - in which we employ the word meaning it can be explained thus: the meaning of a word is its use in the language.

The child learns to believe a host of things. I.e. it learns to act according to these beliefs. Bit by bit there forms a system of what is believed, and in that system some things stand unshakeably fast and some are more or less liable to shift. What stands fast does so, not because it is intrinsically obvious or convincing; it is rather held fast by what lies around it.