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" "By contrast, Galileo, the other legendary scientific figure of the era, not only published the most compelling critique of Aristotelian scholasticism in his Dialogues on the Two Chief World Systems, but in the process turned the issue of the epistemic authority of theology versus the epistemic authority of empirical science into a hallmark of modern times. Although Newton clearly sympathized with Galileo, he wrote virtually nothing critical of the Aristotelian tradition in philosophy, and the immense effort he devoted to theology was aimed not at challenging its epistemic authority, but largely at putting it on a firmer footing. Newton made no direct contributions to philosophy of a similar magnitude. Indeed, from his extant writings alone Newton has more claim to being a major theologian than a major philosopher.
I. Bernard Cohen (1 March 1914 – 20 June 2003) was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton.
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Galileo had the experience of beholding the heavens as they actually are for perhaps the first time, and wherever he looked he found evidence to support the Copernican system against the Ptolemaic, or at least weaken the authority of the ancients. This shattering experience—of observing the depths of the universe, of being the first mortal to know what the heavens are actually like—made so deep an impression... that it is only by considering the events of 1609... that one can understand the subsequent direction of his life.
The pioneering practitioners of the new science knew that they were producing a new kind of knowledge and so they declared this newness in the titles of their books and articles. Thus we have Galileo's Two New Sciences, Boyle's New Experiments, Kepler's New Astronomy, and Tartaglia's New Science. When Ben Jonson presented a masque entitled "News from the New World," his new world was not the newly found continent of North America, but the new world of science, the world revealed by the telescope of Galileo.
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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.