Categoria: Curriculum Episteme
Philosophical Debates About Infinitesimals —
Barrow, Boyle, Berkeley, Hume (and Fontenelle)
Abstract
Debates about infinites and infinitesimals in early modern mathematics are more often than not presented as being essentially limited discussions concerning mathematical rigour among a few mathematicians—with Berkeley’s criticism as the-exception-that-proves-the-rule. Infinitesimals, however, were a prevalent philosophical concern. My talk starts with Isaac Barrow’s first ‘demonstration’ of the existence of infinitesimals to focus on the appropriation of Barrow’s discussion by natural philosophers Robert Boyle and John Keill, and then by philosophers Hume and Berkeley. The ubiquitous presence of philosophical language and arguments in this literature goes a long way to explain some of the debates between Leibniz and his early followers, and also the background to Fontenelle’s failed magnum opus. I shall argue that what counted as logically acceptable for mathematicians and natural philosophers changed in a matter of decades to make room for new objects they were introducing into mathematical practice.
