“There are, in fact, as I began to say above, not a few principles which are the special property of mathematics, such principles as are discovered by the common light of nature, require no demonstration, and which concern quantities primarily; then they are applied to other things, so far as the latter have something in common with quantities. Now there are more of these principles in mathematics than in the other theoretical sciences because of that very characteristic of the human understanding which seems to be such from the law of creation, that nothing can be known completely except quantities or by quantities. And so it happens that the conclusions of mathematics are most certain and indubitable.”

Vol. VIII, p. 148
Joannis Kepleri Astronomi Opera Omnia, ed. Christian Frisch (1858)

Adopted from Wikiquote. Last update Sept. 14, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "There are, in fact, as I began to say above, not a few principles which are the special property of mathematics, such p…" by Johannes Kepler?
Johannes Kepler photo
Johannes Kepler 51
German mathematician, astronomer and astrologer 1571–1630

Related quotes

Galileo Galilei photo
Lysander Spooner photo

“If justice be not a natural principle, it is no principle at all. If it be not a natural principle, there is no such thing as justice. If it be not a natural principle, all that men have ever said or written about it, from time immemorial, has been said and written about that which had no existence. If it be not a natural principle, all the appeals for justice that have ever been heard, and all the struggles for justice that have ever been witnessed, have been appeals and struggles for a mere fantasy, a vagary of the imagination, and not for a reality.

If justice be not a natural principle, then there is no such thing as injustice; and all the crimes of which the world has been the scene, have been no crimes at all; but only simple events, like the falling of the rain, or the setting of the sun; events of which the victims had no more reason to complain than they had to complain of the running of the streams, or the growth of vegetation.

If justice be not a natural principle, governments (so-called) have no more right or reason to take cognizance of it, or to pretend or profess to take cognizance of it, than they have to take cognizance, or to pretend or profess to take cognizance, of any other nonentity; and all their professions of establishing justice, or of maintaining justice, or of rewarding justice, are simply the mere gibberish of fools, or the frauds of imposters.

But if justice be a natural principle, then it is necessarily an immutable one; and can no more be changed—by any power inferior to that which established it—than can the law of gravitation, the laws of light, the principles of mathematics, or any other natural law or principle whatever; and all attempts or assumptions, on the part of any man or body of men—whether calling themselves governments, or by any other name—to set up their own commands, wills, pleasure, or discretion, in the place of justice, as a rule of conduct for any human being, are as much an absurdity, an usurpation, and a tyranny, as would be their attempts to set up their own commands, wills, pleasure, or discretion in the place of any and all the physical, mental, and moral laws of the universe.

If there be any such principle as justice, it is, of necessity, a natural principle; and, as such, it is a matter of science, to be learned and applied like any other science. And to talk of either adding to, or taking from, it, by legislation, is just as false, absurd, and ridiculous as it would be to talk of adding to, or taking from, mathematics, chemistry, or any other science, by legislation.”

Lysander Spooner (1808–1887) Anarchist, Entrepreneur, Abolitionist

Sections I–II, p. 11–12
Natural Law; or The Science of Justice (1882), Chapter II. The Science of Justice (Continued)

Lysander Spooner photo
Bion of Borysthenes photo

“Bion insisted on the principle that "The property of friends is common."”

Bion of Borysthenes (-325–-246 BC) ancient greek philosopher

As quoted by Diogenes Laërtius, iv. 53.

Diogenes Laërtius photo

“Bion insisted on the principle that "The property of friends is common."”

Diogenes Laërtius (180–240) biographer of ancient Greek philosophers

Bion, 9.
The Lives and Opinions of Eminent Philosophers (c. 200 A.D.), Book 4: The Academy

Vladimir I. Arnold photo

“At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering.”

Vladimir I. Arnold (1937–2010) Russian mathematician

"Will Mathematics Survive? Report on the Zurich Congress" in The Mathematical Intelligencer, Vol. 17, no. 3 (1995), pp. 6–10.
Context: At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste... Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics.

Albert Einstein photo
Bernard Le Bovier de Fontenelle photo

“The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there… If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little.”

Bernard Le Bovier de Fontenelle (1657–1757) French writer, satirist and philosopher of enlightenment

Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)

Aristotle photo

Related topics