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Another characteristic of mathematical thought is that it can have no success where it cannot generalize.

Charles Sanders Peirce

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Charles Sanders Peirce
Age: 74 †
Born: 1839
Born: September 10
Died: 1914
Died: April 19
Geodesist
Linguist
Logician
Mathematician
Philosopher
Pragmatist
Statistician
University Teacher
Phillips Place
Cambridge
Massachusetts
Charles Peirce
Charles S. Peirce
Charles Sanders Santiago Peirce
CSP
Mathematics
Success
Science
Another
Cannot
Generalize
Thought
Characteristic
Thinking
Characteristics
Mathematical

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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.
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A quality is something capable of being completely embodied. A law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.
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It is certain that the only hope of retroductive reasoning ever reaching the truth is that there may be some natural tendency toward an agreement between the ideas which suggest themselves to the human mind and those which are concerned in the laws of nature.
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It is a common observation that those who dwell continually upon their expectations are apt to become oblivious to the requirements of their actual situation.
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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.
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The consciousness of a general idea has a certain unity of the ego in it, which is identical when it passes from one mind to another. It is, therefore, quite analogous to a person, and indeed, a person is only a particular kind of general idea.
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All the greatest achievements of mind have been beyond the power of unaided individuals.
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We do not really think, we are barely conscious, until something goes wrong.
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Truth is that concordance of an abstract statement with the ideal limit towards which endless investigation would tend to bring scientific belief, which concordance the abstract statement may possess by virtue of the confession of its inaccuracy and one-sidedness, and this confession is an essential ingredient of truth.
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In all the works on pedagogy that ever I read — and they have been many, big, and heavy — I don't remember that any one has advocated a system of teaching by practical jokes, mostly cruel. That, however, describes the method of our great teacher, Experience.
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Generality is, indeed, an indispensable ingredient of reality for mere individual existence or actuality without any regularity whatever is a nullity. Chaos is pure nothing.
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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.
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It is not knowing, but the love of learning, that characterizes the scientific man.
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The essence of belief is the establishment of a habit.
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Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics.
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The idea does not belong to the soul it is the soul that belongs to the idea.
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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.
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Mere imagination would indeed be mere trifling only no imagination is mere .
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... and it is probably that there is some secret here which remains to be discovered.
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It 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.
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