(source) 
Charles Sanders Peirce
(10 Sep 1839  19 Apr 1914)

Science Quotes by Charles Sanders Peirce (21 quotes)
Among the minor, yet striking characteristics of mathematics, may be mentioned the fleshless and skeletal build of its propositions; the peculiar difficulty, complication, and stress of its reasonings; the perfect exactitude of its results; their broad universality; their practical infallibility.
— Charles Sanders Peirce
Another characteristic of mathematical thought is that it can have no success where it cannot generalize.
— Charles Sanders Peirce
Every work of science great enough to be well remembered for a few generations affords some exemplification of the defective state of the art of reasoning of the time when it was written; and each chief step in science has been a lesson in logic.
— Charles Sanders Peirce
For example, there are numbers of chemists who occupy themselves exclusively with the study of dyestuffs. They discover facts that are useful to scientific chemistry; but they do not rank as genuine scientific men. The genuine scientific chemist cares just as much to learn about erbium—the extreme rarity of which renders it commercially unimportant—as he does about iron. He is more eager to learn about erbium if the knowledge of it would do more to complete his conception of the Periodic Law, which expresses the mutual relations of the elements.
— Charles Sanders Peirce
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
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
It is by no means hopeless to expect to make a machine for really very difficult mathematical problems. But you would have to proceed stepbystep. I think electricity would be the best thing to rely on.
— Charles Sanders Peirce
It is not knowing, but the love of learning, that characterizes the scientific man.
— Charles Sanders Peirce
It is the man of science, eager to have his every opinion regenerated, his every idea rationalised, by drinking at the fountain of fact, and devoting all the energies of his life to the cult of truth, not as he understands it, but as he does not understand it, that ought properly to be called a philosopher. To an earlier age knowledge was power—merely that and nothing more—to us it is life and the summum bonum.
— Charles Sanders Peirce
Kepler’s discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler—such penetrating minds as Descartes and Pascal—were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.
— Charles Sanders Peirce
Mathematics is distinguished from all other sciences except only ethics, in standing in no need of ethics. Every other science, even logic—logic, especially—is in its early stages in danger of evaporating into airy nothingness, degenerating, as the Germans say, into an anachrioid [?] 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
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
Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.
— Charles Sanders Peirce
The one [the logician] studies the science of drawing conclusions, the other [the mathematician] the science which draws necessary conclusions.
— Charles Sanders Peirce
The pragmatist knows that doubt is an art which has to be acquired with difficulty.
— Charles Sanders Peirce
The rudest numerical scales, such as that by which the mineralogists distinguish different degrees of hardness, are found useful. The mere counting of pistils and stamens sufficed to bring botany out of total chaos into some kind of form. It is not, however, so much from counting as from measuring, not so much from the conception of number as from that of continuous quantity, that the advantage of mathematical treatment comes. Number, after all, only serves to pin us down to a precision in our thoughts which, however beneficial, can seldom lead to lofty conceptions, and frequently descend to pettiness.
— Charles Sanders Peirce
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
There is one thing even more vital to science than intelligent methods; and that is, the sincere desire to find out the truth, whatever it may be.
— Charles Sanders Peirce
True science is distinctively the study of useless things. For the useful things will get studied without the aid of scientific men. To employ these rare minds on such work is like running a steam engine by burning diamonds.
— Charles Sanders Peirce
[For] men to whom nothing seems great but reason ... nature ... 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 ... Those are the natural scientific men; and they are the only men that have any real success in scientific research.
— Charles Sanders Peirce
[Mathematics is] the study of ideal constructions (often applicable to real problems), and the discovery thereby of relations between the parts of these constructions, before unknown.
— Charles Sanders Peirce
Quotes by others about Charles Sanders Peirce (1)
Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
See also:
 10 Sep  short biography, births, deaths and events on date of Peirce's birth.