Another characteristic of mathematical thought is that it can have no success where it cannot generalize.
Charles Sanders PeirceThe one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.
Charles Sanders PeirceWe shall do better to abandon the whole attempt to learn the truthunless we can trust to the human mind's having such a powerof guessing right that before very many hypotheses shall have been tried, intelligent guessing may be expected to lead us to one which will support all tests, leaving the vast majority of possible hypotheses unexamined.
Charles Sanders PeirceThird, consider the insistency of an idea. The insistency of a past idea with reference to the present is a quantity which is less, the further back that past idea is, and rises to infinity as the past idea is brought up into coincidence with the present.
Charles Sanders PeirceWe cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study ofphilosophy. These prejudices are not to be dispelled by a maxim, for they are things which it does not occur to us can be questioned. A person may, it is true, in the course of his studies, find reason to doubt what he began by believing; but in that case he doubts because he has a positive reason for it, and not on account of the Cartesian maxim. Let us not pretend to doubt in philosophy what we do not doubt in our hearts.
Charles Sanders PeirceThe real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you. Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of a definite increase of knowledge.
Charles Sanders Peirce