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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
Thought
Characteristic
Thinking
Characteristics
Mathematical
Mathematics
Success
Science
Another
Cannot
Generalize

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Some think to avoid the influence of metaphysical errors, by paying no attention to metaphysics but experience shows that these men beyond all others are held in an iron vice of metaphysical theory, because by theories that they have never called in question.
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Doubt is an uneasy and dissatisfied state from which we struggle to free ourselves and pass into the state of belief while the latter is a calm and satisfactory state which we do not wish to avoid, or to change to a belief in anything else.
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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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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.
Charles Sanders Peirce
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Mere imagination would indeed be mere trifling only no imagination is mere .
Charles Sanders Peirce
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Mathematics is purely hypothetical: it produces nothing but conditional propositions.
Charles Sanders Peirce
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... and it is probably that there is some secret here which remains to be discovered.
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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
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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.
Charles Sanders Peirce
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Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus theoretically, is to uselanguage in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.
Charles Sanders Peirce
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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.
Charles Sanders Peirce
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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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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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I define a Sign as anything which is so determined by something else, called its Object, and so determines an effect upon a person, which effect I call its Interpretant, that the latter is thereby mediately determined by the former.
Charles Sanders Peirce
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It is not knowing, but the love of learning, that characterizes the scientific man.
Charles Sanders Peirce
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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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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.
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But the extraordinary insight which some persons are able to gain of others from indications so slight that it is difficult to ascertain what they are, is certainly rendered more comprehensible by the view here taken.
Charles Sanders Peirce
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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