This paper argues that, for Bernard Nieuwentijt, mathematical reasoning on the basis of ideas is not the same as logical reasoning on the basis of propositions. Noting that the two types of reasoning differ helps make sense of a peculiar-sounding claim Nieuwentijt makes, namely that it is possible to mathematically deduce false propositions from true abstracted ideas. I propose to interpret Nieuwentijt’s abstracted ideas as incomplete mental copies of existing objects. I argue that, according to Nieuwentijt, a proposition is mathematically (...) deducible from an abstracted idea if it can be demonstrated that that proposition makes a true claim about the object that idea forms. This allows me to explain why Nieuwentijt deems it possible to deduce false propositions from true ideas. It also implies that logic and mathematics are not as closely related for Nieuwentijt as has been suggested in the existing secondary literature. (shrink)

In this essay I reassess Willem Jacob ‘s Gravesande's Newtonianism. I draw attention to ‘s Gravesande's a-causal rendering of physics which went against Newton's causal understanding of natural philosophy and to his attempt to establish a solid foundation for the certainty of Newton's natural philosophy, which he considered as a powerful antidote against the theological aberrations of Descartes and especially Spinoza. I argue that, although ‘s Gravesande clearly took inspiration from Newton's natural philosophy, he was running his own scientific and (...) intellectual agenda and that he was combining Newtonian and non-Newtonian elements. (shrink)

Baruch Spinoza’s (1632–77)Tractatus theologico-politicus (1669 or 1670) caused outrage across the Dutch Republic, for it obliterated the carefully installed separation between philosophy and theology. The posthumous publication of Spinoza’s Ethica, which is contained in his Opera posthuma (1677), caused similar consternation. It was especially the mathematical order in which the Ethica was composed that caused fierce opposition, for its mathematical appearance gave the impression that Spinoza’s heretical teachings were established demonstratively. In this essay, I document how the Dutch physician, local (...) politician, and amateur mathematician and experimenter Bernard Nieuwentijt (1654–1718) attempted to physico-mathematically and methodologically counter the threats posed by Spinoza’s program. Nieuwentijt tried to defend the authority of the scriptures in times at which they came under attack by the new philosophy and by the emerging sciences that were gradually winning terrain. The crux of his defense consisted in delineating a modest epistemology, a “learned ignorance,” that would cure Spinoza’s followers of their pansophical aspirations, on the one hand, and remove the conflict between the Bible and reason, on the other. The specific way in which he sought to accomplish this distinguished him from Dutch Reformed thought, or so I will argue. (shrink)