
7Berkeley, arguing against Barrow, claims that the infinite divisibility of finite lines is neither an axiom nor a theorem in Euclid The Thirteen Books of The Elements. Instead, he suggests that it is rooted in ancient prejudice. In this paper, I attempt to substantiate Berkeley’s claims by looking carefully at the history and practice of ancient geometry as a first step towards understanding Berkeley’s mathematical atomism.

88Is Geometry Analytic?Dianoia 1 (4). 2017.In this paper I present critical evaluations of Ayer and Putnam's views on the analyticity of geometry. By drawing on the historicophilosophical work of Michael Friedman on the relativized apriori; and Roberto Torretti on the foundations of geometry, I show how we can make sense of the assertion that pure geometry is analytic in Carnap's sense.