The really useful education is that which follows the direction of the child's own instinctive interests, supplying knowledge for which it is seeking, not dry, detailed information wholly out of relation to its spontaneous desires.

A priori Logical propositions are such as can be known a priori without study of the actual world.

The fact that an opinion has been widely held is no evidence whatever that it is not utterly absurd; indeed in view of the silliness of the majority of mankind, a widely spread belief is more likely to be foolish than sensible.

Logic must no more admit a unicorn than zoology can.

History is valuable, to begin with, because it is true; and this, though not the whole of its value, is the foundation and condition of all the rest. That all knowledge, as such, is in some degree good, would appear to be at least probable; and the knowledge of every historical fact possesses this element of goodness, even if it posses no other.

But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.

To think I have spent my life on absolute muck.