One of the most popular extant kind of arguments for platonism about mathematical objects is indispensability arguments (IAs). In general, IAs take the following rough form: (1) We ought to be ontologically committed to all and only those entities indispensable to our best scientific theories; (2) Mathematical entities are indispensable to our best scientific theories; (3) Therefore, we ought to be ontologically committed to mathematical entities. IA-partisans have offered the following disambiguation of the notion of dispensability appearing in premise (2). Entity X is dispensable from theory T if and only if there exists a suitably attractive alternate theory T' such that T' makes no mention of Xs and is empirically equivalent to T. This intuitive conception of dispensability has generated a cottage industry for nominalists. The most famous (retroactive) example is Hartry Field's axiomatization of Newtonian gravitation in Science Without Numbers. The general hard-road nominalist strategy consists in providing 'nominalized' versions of scientific theories in hopes of showing that (2) is false. The Hungarian project of the Andréka-Németi school has been recently brought into this philosophical literature by Michèle Friend and Daniele Molinini. Molinini claims, pace Mark Colyvan, that the Hungarian project's axiomatization of special relativity is able to dispense with a certain mathematical object, the metric tensor, in its genuinely mathematical explanations of special relativistic phenomena. I will show that this poses a dangerous dilemma for nominalists. The upshot is a reassessment of what it means to dispense with some piece of ontological furniture in a scientific theory.
Date / Time / Place
June 21st / 12:05 / Aula 0A