We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction. ...Neither can this rule come to us from experience... This rule, inaccessible to analytic demonstration and to experience, is the veritable type of the synthetic a priori judgment. On the other hand, we can not think of seeing in it a convention, as in some of the postulates of geometry. ...it is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it.
Henri PoincaréRelated topics
act affirmation becoming conceiving contradiction convention escape experience geometry inaccessible indefinite intuition irreducible judgment mind occasion once possible power recurrence rule seeing synthetic usingRelated quotes
Human beings have faculties more elevated than the animal appetites, and when once made conscious of them, do not regard anything as happiness which does not include their gratification. I do not, indeed, consider the Epicureans to have been by any means faultless in drawing out their scheme of consequences from the utilitarian principle. To do this in any sufficient manner, many Stoic, as well as Christian elements require to be included. But there is no known Epicurean theory of life which does not assign to the pleasures of the intellect, of the feelings and imagination, and of the moral sentiments, a much higher value as pleasures than to those of mere sensation.
John Stuart Mill
It is one of the most beautiful characteristics of Theosophy that it gives back to people in a more rational form everything which was really useful and helpful to them in the religions which they have outgrown... in this teaching as to the immortality of the soul and the life after death, Theosophy...does not put forward these great truths merely on the authority of some sacred book of long ago; in speaking of these subjects it is not dealing with pious opinions, or metaphysical speculations, but with solid, definite facts, as real and as close to us as the air we breathe or the houses we live in - facts of which many among us have constant experience - facts among which lies the daily work of some of our students, as will presently be seen.
Charles Webster Leadbeater
Let true Christians then, with becoming earnestness, strive in all things to recommend their profession, and to put to silence the vain scoffs of ignorant objectors. Let them boldly assert the cause of Christ in an age when so many, who bear the name of Christians, are ashamed of Him: and let them consider as devolved on Them the important duty of suspending for a while the fall of their country, and, perhaps, of performing a still more extensive service to society at large; not by busy interference in politics, in which it cannot but be confessed there is much uncertainty; but rather by that sure and radical benefit of restoring the influence of Religion, and of raising the standard of morality.
William Wilberforce
I am almost amazed that you consider a professional philosopher capable of no confusion in concepts and definitions. Such things are nowhere more at home than among philosophers who are not mathematicians, and Wolff was no mathematician, even though he made cheap compen- diums. Look around among the philosophers of today, among Schelling, Hegel, Nees von Esenbeck, and their like; doesn t your hair stand on end at their definitions? Read in the history of ancient philosophy what kinds of definitions the men of that day, Plato and others, gave (I except Aristotle). But even in Kant it is often not much better; in my opinion his distinction between analytic and synthetic theorems is such a one that either peters out in a triviality or is false.
Carl Friedrich Gauss
Suppose the reasoning centers of the brain can get their hands on the mechanisms that plop shapes into the array and that read their locations out of it. Those reasoning demons can exploit the geometry of the array as a surrogate for keeping certain logical constraints in mind. Wealth, like location on a line, is transitive: if A is richer than B, and B is richer than C, then A is richer than C. By using location in an image to symbolize wealth, the thinker takes advantage of the transitivity of location built into the array, and does not have to enter it into a chain of deductive steps. The problem becomes a matter of plop down and look up. It is a fine example of how the form of a mental representation determines what is easy or hard to think.
Steven Pinker