Like many of their contemporaries Bernard Nieuwentijt (1654–1718) and Pieter van Musschenbroek (1692–1761) were baffled by the heterodox conclusions which Baruch Spinoza (1632–1677) drew in the Ethics. As the full title of the Ethics—Ethica ordine geometrico demonstrata—indicates, these conclusions were purportedly demonstrated in a geometrical order, i.e. by means of pure mathematics. First, I highlight how Nieuwentijt tried to immunize Spinoza’s worrisome conclusions by insisting on the distinction between pure and mixed mathematics. Next, I argue that the anti-Spinozist underpinnings of Nieuwentijt’s distinction between pure and mixed mathematics resurfaced in the work of van Musschenbroek. By insisting on the distinction between pure and mixed mathematics, Nieuwentijt and van Musschenbroek argued that Spinoza abused mathematics by making claims about things that exist in rerum natura by relying on a pure mathematical approach (type 1 abuse). In addition, by insisting that mixed mathematics should be painstakingly based on mathematical ideas that correspond to nature, van Musschenbroek argued that René Descartes’ (1596–1650) natural-philosophical project (and that of others who followed his approach) abused mathematics by introducing hypotheses, i.e. (mathematical) ideas, that do not correspond to nature (type 2 abuse)

As a supplement to John L. Heilbron’s account, I will argue that, although the label ‘experimental physics’ can be rightfully used to describe aspects of Petrus van Musschenbroek’s (1692-1761) work, the latter’s understanding of ‘physica’ is to be situated within a broader framework in which theological, philosophical and teleological considerations continued to play an important role. First, I will draw attention to Musschenbroek’s views on the scope of physica and especially to his conception of a law of nature. It will be shown that by radicalizing certain aspects of Isaac Newton’s methodological ideas van Musschenbroek no longer considered physics as the discipline that uncovered causes from effects, as Newton did, but as the discipline that studies the effects of unknown causes. In addition, I will show that van Musschenbroek endorsed the view that the laws of nature are contingent on God’s free will and that they are knowable due to his goodness. Second, it will be argued that for van Musschenbroek physics, alongside with teleology, had clear physico-theological repercussions. Along the way, van Musschenbroek’s views on the principle of sufficient reason will be discussed for the first time.