...mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic, especially in its early stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such danger for pure mathematics; for that is precisely what mathematics ought to be.
Charles Sanders PeirceUpon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy: Do not block the way of inquiry.
Charles Sanders PeirceIt is a common observation that a science first begins to be exact when it is quantitatively treated. What are called the exact sciences are no others than the mathematical ones.
Charles Sanders PeirceIt has often been argued that absolute scepticism is self-contradictory; but this is a mistake: and even if it were not so, it would be no argument against the absolute sceptic, inasmuch as he does not admit that no contradictory propositions are true. Indeed, it would be impossible to move such a man, for his scepticism consists in considering every argument and never deciding upon its validity; he would, therefore, act in this way in reference to the arguments brought against him.
Charles Sanders PeirceNo general description of the mode of advance of human knowledge can be just which leaves out of account the social aspect of knowledge. That is of its very essence. What a thing society is! The workingman, with his trade union, knows that. Men and women moving in polite society understand it, still better. But Bohemians, like me, whose work is done in solitude, are apt to forget that not only is a man as a whole little better than a brute in solitude, but also that everything that bears any important meaning to him must receive its interpretation from social considerations.
Charles Sanders Peirce