“The seventeenth century witnessed the birth of modern science as we know it today. The science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science—a dependence on numbers, on real numbers of actual experience.
…The ancients knew a few numerical laws… But prior to the Scientific Revolution, the goal of science (or the study of nature) was not to seek laws of nature expressed in terms of numbers or number relations. …the new science …not only found laws based on numbers but they were also willing to express these laws in terms of higher powers of numbers—squares and cubes.”

— I. Bernard Cohen

The Triumph of Numbers: How Counting Shaped Modern Life (2005)

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I. Bernard Cohen 9

American historian of science 1914–2003

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“All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon.”

John Theophilus Desaguliers (1683–1744) French-born British natural philosopher and clergyman

Source: Course of Experimental Philosophy, 1745, p. v: Preface
Context: All the knowledge we have of nature depends upon facts; for without observations and experiments our natural philosophy would only be a science of terms and an unintelligible jargon. But then we must call in Geometry and Arithmetics, to our Assistance, unless we are willing to content ourselves with natural History and conjectural Philosophy. For, as many causes concur in the production of compound effects, we are liable to mistake the predominant cause, unless we can measure the quantity and the effect produced, compare them with, and distinguish them from, each other, to find out the adequate cause of each single effect, and what must be the result of their joint action.

“The rise of new science in the seventeenth century laid hold upon general culture in the next century. The enlightenment… testified to the widespread belief that at last light had dawned, that dissipation of ignorance, superstition, and bigotry was at hand, and the triumph of reason was assured -- for reason was counterpart in man of the laws of nature which science was disclosing. The reign of law in the natural world was to be followed by the reign of law in human affairs.”

John Dewey (1859–1952) American philosopher, psychologist, and educational reformer

Time and Individuality (1940)

“Nothing carries so much authority today as science, but there is actually no such thing as ‘the scientific world-view’. Science is a method of inquiry, not a view of the world. Knowledge is growing at accelerating speed; but no advance in science will tell us whether materialism is true or false, or whether humans possess free will. The belief that the world is composed of matter is metaphysical speculation, not a testable theory. Science may succeed in explaining events in terms of causes and effects. In some accounts it may be able to formulate laws of nature. But what does it mean for something to cause something else and what is a law of nature? These are questions for philosophy or religion, not for science.”

John Gray (1948) British philosopher

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“Painting is a science and should be pursued as an inquiry into the laws of nature. Why, then, may not a landscape be considered as a branch of natural philosophy, of which pictures are but experiments?”

John Constable (1776–1837) English Romantic painter

Quote from 'The History of Landscape Painting,' fourth lecture, Royal Institution (16 June 1836), from John Constable's Discourses, ed. R.B. Beckett, (Ipswich, Suffolk Records Society, 1970), p. 69.
1830s, his lectures History of Landscape Painting (1836)

“Computer science is an empirical discipline. […] Each new machine that is built is an experiment. Actually constructing the machine poses a question to nature; and we listen for the answer by observing the machine in operation and analyzing it by all analytical and measurement means available. Each new program that is built is an experiment. It poses a question to nature, and its behavior offers clues to an answer.”

Allen Newell (1927–1992) American cognitive scientist

Source: Computer Science as Empirical Inquiry: Symbols and Search (1975), p. 114.

“To an increasing number of practitioners, computer simulations rooted in mathematics represent a third way of doing science, alongside theory and experiment.”

Ivars Peterson (1948) Canadian mathematician

Source: The Mathematical Tourist: New and Updated Snapshots of Modern Mathematics (1998), Chapter 1, “Explorations” (p. 10)

“[H]istorical science is not worse, more restricted, or less capable of achieving firm conclusions because experiment, prediction, and subsumption under invariant laws of nature do not represent its usual working methods. The sciences of history use a different mode of explanation, rooted in the comparative and observational richness in our data. We cannot see a past event directly, but science is usually based on inference, not unvarnished observation”

Stephen Jay Gould book Wonderful Life

you don't see electrons, gravity, or black holes either
Source: Wonderful Life (1989), p. 279

“The laws of thought are natural laws with which we have no power to interfere, and which are of course not to be in any way confused with the artificial laws of a country, which are invented by men and can be altered by them. Every science is occupied in detecting and describing the natural laws which are inflexibly observed by the objects treated in the Science.”

William Stanley Jevons (1835–1882) English economist and logician

Introduction, Lesson I: Definition and Sphere of the Science.
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“Pythagoras says that number is the origin of all things, and certainly the law of number is the key that unlocks the secrets of the universe. But the law of number possesses an immanent order, which is at first sight mystifying, but on a more intimate acquaintance we easily understand it to be intrinsically necessary; and this law of number explains the wondrous consistency of the laws of nature.”

Paul Carus (1852–1919) American philosopher

"Reflections on Magic Squares" in The Monist, Vol. 16 (1906), p. 139

“That from the outset they expect or even impose all the properties of finite numbers upon the numbers in question, while on the other hand the infinite numbers, if they are to be considered in any form at all, must (in their contrast to the finite numbers) constitute an entirely new kind of number, whose nature is entirely dependent upon the nature of things and is an object of research, but not of our arbitrariness or prejudices.”

Georg Cantor (1845–1918) mathematician, inventor of set theory

Letter to Gustac Enestrom, as quoted in Georg Cantor : His Mathematics and Philosophy of the Infinite (1990) by Joseph Warren Dauben ~ ISBN 0691024472

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I. Bernard Cohen 9

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