Another characteristic of mathematical thought is that it can have no success where it cannot generalize. Charles Sanders Peirce More Quotes by Charles Sanders Peirce More Quotes From Charles Sanders Peirce We should chiefly depend not upon that department of the soul which is most superficial and fallible (our reason), but upon that department that is deep and sure, which is instinct. Charles Sanders Peirce instinctsoulreason ...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 Peirce dreammathscience If we are to define science, ... it does not consist so much in knowing, nor even in "organized knowledge," as it does in diligent inquiry into truth for truth's sake, without any sort of axe to grind, nor for the sake of the delight of contemplating it, but from an impulse to penetrate into the reason of things. Charles Sanders Peirce knowingscienceknowledge A hypothesis is something which looks as if it might be true and were true, and which is capable of verification or refutation by comparison with facts. Charles Sanders Peirce mightfactslooks A true proposition is a proposition belief which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended. Charles Sanders Peirce disappointmenttruthlong There is not a single truth of science upon which we ought to bet more than about a million of millions to one. Charles Sanders Peirce gamblingtruthscience Mathematics is purely hypothetical: it produces nothing but conditional propositions. Charles Sanders Peirce ontologylogicmathematics All the progress we have made in philosophy ... is the result of that methodical skepticism which is the element of human freedom. Charles Sanders Peirce progressatheismphilosophy ... and it is probably that there is some secret here which remains to be discovered. Charles Sanders Peirce mathematicalmathematicssecret There never was a sounder logical maxim of scientific procedure than Ockham's razor: Entia non sunt multiplicanda praeter necessitatem. That is to say; before you try a complicated hypothesis, you should make quite sure that no simplification of it will explain the facts equally well. Charles Sanders Peirce simplicityrazorstrying The a priori method is distinguished for its comfortable conclusions. It is the nature of the process to adopt whatever belief weare inclined to, and there are certain flatteries to the vanity of man which we all believe by nature, until we are awakened from our pleasing dream by rough facts. Charles Sanders Peirce dreammenbelieve The truth is, that common-sense, or thought as it first emerges above the level of the narrowly practical, is deeply imbued with that bad logical quality to which the epithet metaphysical is commonly applied; and nothing can clear it up but a severe course of logic. Charles Sanders Peirce common-sensequalitylevels Truly, that reason upon which we plume ourselves, though it may answer for little things, yet for great decisions is hardly surer than a toss up. Charles Sanders Peirce decisionanswersmay The woof and warp of all thought and all research is symbols, and the life of thought and science is the life inherent in symbols; so that it is wrong to say that a good language is important to good thought, merely; for it is the essence of it. Charles Sanders Peirce importantessencescience It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty. Charles Sanders Peirce brainmenideas Every man is fully satisfied that there is such a thing as truth, or he would not ask any question. Charles Sanders Peirce askssatisfiedmen Upon 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 Peirce wallblockphilosophy Notwithstanding all that has been discovered since Newton's time, his saying that we are little children picking up pretty pebbles on the beach while the whole ocean lies before us unexplored remains substantially as true as ever, and will do so though we shovel up the pebbles by steam shovels and carry them off in carloads. Charles Sanders Peirce beachlyingchildren Our whole past experience is continually in our consciousness, though most of it sunk to a great depth of dimness. I think of consciousness as a bottomless lake, whose waters seem transparent, yet into which we can clearly see but a little way. Charles Sanders Peirce lakespastthinking The third class consists of men to whom nothing seems great but reason. If force interests them, it is not in its exertion, but in that it has a reason and a law. For men of the first class, nature is a picture; for men of the second class, it is an opportunity; for men of the third class, it is a cosmos, so admirable, that to penetrate to its ways seems to them the only thing that makes life worth living. These are the men whom we see possessed by a passion to learn. Charles Sanders Peirce naturesuccesslife
