Some 17th-century discussions on the grounds of mathematical knowledge

Antoni Malet

UPF Barcelona (and Max Planck Institute for the History of Science (Berlin

Properly speaking there were no debates about the foundations of mathematics in early modern Europe, nor were there specific sets of axioms and postulates circulating and being compared as to which one was to be preferred to ground mathematics. It is nonetheless true that on occasion some authors got entangled on discussions related to the nature and status of mathematical definitions and first principles. We will focus on the debates between Isaac Barrow, John Wallis, and Thomas Hobbes. We will pay particular attention to the ways in which they considered (or failed to do so) metaphysical foundations to be essential for the task of putting mathematical knowledge on a sound basis.