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Prior to the publication of The ''Principia'', the philosophy of motion and change in the universe was largely a theoretical and non-mathematical enterprise. The dominating methodological approach to natural philosophy both in the Aristotelian-scholastic and Cartesian mosaic, was one in which truths about the natural world were proposed as conjectural hypotheses. Newton explicitly rejected the method of hypotheses, and instead demanded that all propositions be deduced from the phenomena and then converted into general principles via induction. In the second edition of The ''Principia'', Newton states:
“I <blockquote>I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies and the laws of motion and law of gravity have been found by this method. And it is enough that gravity should really exist and should act according to the laws that we have set forth and should suffice for all the motions of the heavenly bodies and of our sea.[[CiteRef::Newton (1999)]]</blockquote>
Newton called his method the experimental philosophy, because theories about the behavior of empirical objects can only be refuted via experimental procedures.[[CiteRef::Smith (2002)]] He expressed the core beliefs from which he derived his method in a set of four “rules for the study of natural philosophy,” which he stated in book III of The ''Principia'' as follows:
"1<blockquote>#) No more cause of natural things should be admitted than are both true and sufficient to explain their phenomena 2#) Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same 3#) Those qualities of bodies that cannot be intended and remitted (i.e. qualities that cannot be increased and diminished) and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally 4#) In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true nonwithstanding any contrary hypothesis, until yet other phenomena make such propositions either more exact or liable to exceptions.[[CiteRef::Newton (1999)]]</blockquote>
Out of these four rules a new, engaged method for conducting science emerged that stood in stark contrast the previous passive and theoretical Cartesian and Aristotelian-scholastic methods. Propositions are born from natural sources and placed back into the natural world to be tested empirically.[[CiteRef::Smith (2002)]] As the four rules were absorbed into the ensuing mosaic, the calculus became deeply incorporated in the experimental method, as it was used to mathematically calculate from natural laws an empirical prediction, and then evaluate how exactly the prediction matched the observed reality.