The way up is the way down: the mos geometricus and first principles in late antiquity

Lecture by Marije Martijn (VU Amsterdam), organized by the Department of the History of Philosophy and the Roots of Deduction research group (led by Catarina Dutilh Novaes).

The method for which Euclid’s Elements are the paradigm, i.e. the so-called exposition more geometrico, is generally considered an axiomatic-deductive method. In this lecture, I will show that this characterization does not fit the actual use made of the method by its arguably most influential late ancient fan, Proclus – that is, if we take ‘deductive’ to refer to “the way down”, i.e. the route from starting points to conclusions, only. For Proclus, any work more geometrico starts with presenting “the way up,” i.e. the acquisition of first principles.