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.
Of the many references to Newton in 18th-century electrical writings only a small number were to the Principia, the greater part by far were to the Opticks. This was true not alone of the electrical writings but also in other fields of experimental enquiry…. [The Opticks] would allow the reader to roam, with great Newton as his guide, through the major unresolved problems of science and even the relation of the whole world of nature to Him who had created it…. in the Opticks Newton did not adopt the motto… —Hypotheses non fingo; I frame no hypotheses—but, so to speak, let himself go, allowing his imagination full reign and by far exceeding the bounds of experimental evidence.
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.