This chapter explores the development of Newton’s methodological thought up to c.1700, as well as that of his first followers. Newton’s caution in not antagonising Huygens in particular is highlighted. It was only in this decade that Newton started to emphasise the natural-theological significance of his natural philosophy, especially in manuscripts related to the Classical Scholia. But there was no metaphysical component; rather, Newton insisted on the analogical predication of the divine. Even more important was his reconsideration of the Hypotheses of the first edition, which eventually became the Rules of Philosophising of the second. It is shown that these were not abstract methodological principles, but rather a set of dialectical arguments designed to negate the possibility of weightless matter. Nonetheless, they shaped Newton methodological agenda and language for the rest of his life. His position was understood perfectly by his earliest follows: David Gregory and John Keill, both of whom were teaching in Oxford.

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This chapter argues for the centrality of the natural sciences in the Scottish Enlightenment. Beginning in the mid-seventeenth century, the activities of mathematical practitioners such as George Sinclair and virtuosi such as Sir Robert Sibbald laid the institutional foundations for the cultivation of natural knowledge in the Enlightenment era and incorporated the sciences of nature into Scotland s emerging public sphere. The restructuring of the Scottish universities in the decades following the Glorious Revolution enhanced the facilities for teaching and research in the sciences and, in doing so, fostered the rise of Newtonianism in Scotland. Newton’s writings inspired innovative work by Colin Maclaurin and other Scottish Newtonians across the many branches of mathematics and natural philosophy and also shaped the methods employed in the nascent ‘science of man’. The compatibility of the Newtonian system with religious belief, in turn, served to solidify the place of natural knowledge in Enlightenment culture, as did the harnessing of such knowledge to economic improvement. Even though the debate over James Hutton s theory of the earth in the 1790s challenged the alliance between science and religion, the natural sciences had by then established themselves as integral and vital components of the Scottish Enlightenment.