Abstraction and Epistemic Economy

Marco Panza (1)

1 IHPST - Institut d'Histoire et de Philosophie des Sciences et des Techniques

Most of the arguments usually appealed to in order to support the view that some abstraction principles are analytic depend on ascribing to them some sort of existential parsimony or ontological neutrality, whereas the opposite arguments, aiming to deny this view, contend this ascription. As a result, other virtues that these principles might have are often overlooked. Among them, there is an epistemic virtue which I take these principles to have, when regarded in the appropriate settings, and which I suggest to call `epistemic economy'. My present purpose is to isolate and clarify this notion by appealing to some examples concerning the definition of natural and real numbers. I shall also try to make clear that complying with this virtue is essentially independent of complying with existential parsimony or ontological neutrality.

Mots clés: Mathematical Understanding; Natural Numbers; Epistemic Economy; Philosophy of Mathematical Practice; Philosophy of Mathematics; Frege Arithmetic; Real Numbers

Domaines: Histoire, Philosophie et Sociologie des sciences; Philosophie

Marco Panza. Abstraction and Epistemic Economy. 2015. ⟨halshs-01131191⟩