During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true
Mathematicians care no more for logic than logicians for mathematics.
I don’t quite hear what you say, but I beg to differ entirely with you.
Great fleas have little fleas upon their backs to bite ’em, And little fleas have lesser fleas, and so ad infinitum, And the great fleas themselves, in turn, have greater fleas to go on, While these again have greater still, and greater still, and so on.
Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.
All existing things upon this earth, which have knowledge of their own existence, possess, some in one degree and some in another, the power of thought, accompanied by perception, which is the awakening of thought by the effects of external objects upon the senses.
My opinion of mankind is founded upon the mournful fact that, so far as I can see, they find within themselves the means of believing in a thousand times as much as there is to believe in.
I was x years old in the year x2.
But the gambling reasoner is incorrigible: if he would but take to squaring the circle, what a load of misery would be saved.
Wrong hypotheses, rightly worked from, have produced more useful results than unguided observations.
Common integration is only the memory of differentiation.
The moving power of mathematical invention is not reasoning but imagination.
