P.T. Barnum quote: “But however mysterious is nature, however ignorant the doctor, however imperfect the present state of physical science,…”

“Prophecy, however honest, is generally a poor substitute for experience.”

Benjamin N. Cardozo (1870–1938) United States federal judge

West Ohio Gas Co. v. Public Utilities Commission (No.2), 294 U.S. 79, 82, (1935)
Judicial opinions

“Science is a system of statements based on direct experience, and controlled by experimental verification. Verification in science is not, however, of single statements but of the entire system or a sub-system of such statements.”

Rudolf Carnap (1891–1970) German philosopher

Source: The unity of science, 1934/1995, p. 42

“Not only must philosophy be in agreement with our empirical knowledge of Nature, but the origin and formation of the Philosophy of Nature presupposes and is conditioned by empirical physics. However, the course of a science's origin and the preliminaries of its construction are one thing, while the science itself is another. In the latter, the former can no longer appear as the foundation of the science; here, the foundation must be the necessity of the Concept.”

Georg Wilhelm Friedrich Hegel book Encyclopedia of the Philosophical Sciences

Encyclopedia of the Philosophical Sciences (1816)

“The practice of physic is jostled by quacks on the one side, and by science on the other.”

Peter Mere Latham (1789–1875) English physician and educator

Book I, p. xxv
Collected Works

“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)

“Since, however, all multitude and magnitude are by their own nature of necessity infinite”

Nicomachus (60–120) Ancient Greek mathematician

Nicomachus of Gerasa: Introduction to Arithmetic (1926)
Context: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184

“Both pure and applied science have gradually pushed further and further the requirements for accuracy and precision. However, applied science, particularly in the mass production of interchangeable parts, is even more exacting than pure science in certain matters of accuracy and precision.”

Walter A. Shewhart (1891–1967) American statistician

Source: Statistical Method from the Viewpoint of Quality Control, 1939, p. 120

“A science, however, would arise to deal with something separated from each of them”

Nicomachus (60–120) Ancient Greek mathematician

Nicomachus of Gerasa: Introduction to Arithmetic (1926)
Context: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184

“You remain the more than natural figure. You
Become the soft-footed phantom, the irrationalDistortion, however fragrant, however dear.
That’s it: the more than rational distortion,
The fiction that results from feeling. Yes, that.”

Wallace Stevens (1879–1955) American poet

Notes Toward a Supreme Fiction (1942), It Must Give Pleasure

“One can show the following: given any rule, however "fundamental" or "necessary" for science, there are always circumstances when it is advisable not only to ignore the rule, but to adopt its opposite.”

Paul Karl Feyerabend book Against Method

Pg. 23.
Against Method (1975)

“But however mysterious is nature, however ignorant the doctor, however imperfect the present state of physical science, the patronage and the success of quacks and quackeries are infinitely more wonderful than those of honest and laborious men of science and their careful experiments.”

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P.T. Barnum 17

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