Newton's work and the philosophy that enshrines it are based on mathematical empiricism, which is the idea that mathematical and physical laws may be revealed in the real world via experimentation and observation.
For whatever is not deduced from the phenomena is to be called a hypothesis and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. The first edition of Principia features proposals about the movements of celestial bodies which Newton initially calls "hypotheses"-however, by the second edition, the word "hypothesis" was replaced by the word "rule", and Newton had added to the footnotes the following statement: they only rise in our estimation as we compare them with later attempts to improve on them." Mathematical philosophy
One hundred years later, however, Thomas Young would describe Newton's observations in Opticks as "yet unrivalled. Even so, the work was not considered revolutionary in Newton's time. The treatise, which features his now famous work on the composition and dispersion of sunlight, is often cited as an example of how to analyze difficult questions via quantitative experimentation. Newton's other seminal work was Opticks, printed in 1704 in Philosophical Transactions of the Royal Society, of which he became president in 1703. This method may be contrasted to the Cartesian method of deduction based on sequential logical reasoning, and showed the efficacy of applying mathematical analysis as a means of making discoveries about the natural world. The three books of Principia, considered a seminal text in mathematics and physics, are notable for their rejection of hypotheses in favor of inductive and deductive reasoning based on a set of definitions and axioms. Newton's Principia Mathematica, published by the Royal Society in 1687 but not available widely and in English until after his death, is the text generally cited as revolutionary or otherwise radical in the development of science. Newtonianism became an influential intellectual program that applied Newton's principles in many avenues of inquiry, laying the groundwork for modern science (both the natural and social sciences), in addition to influencing philosophy, political thought and theology. While Newton's influential contributions were primarily in physics and mathematics, his broad conception of the universe as being governed by rational and understandable laws laid the foundation for many strands of Enlightenment thought. Newtonianism is a philosophical and scientific doctrine inspired by the beliefs and methods of natural philosopher Isaac Newton.
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