Is everything a set? Quine and (Hyper)Pythagoreanism

Kemp, G. (2017) Is everything a set? Quine and (Hyper)Pythagoreanism. Monist, 100(2), pp. 155-166. (doi: 10.1093/monist/onx001)

Abstract

Every student of Quine knows that his ontology consists in physical objects plus the entities required by mathematics, i.e., sets or classes. He came to this view after trying out nominalism, the view that there are only physical objects, and concluding that it cannot be made to work. Less well known is his having tried out, and ultimately rejected, the seemingly outlandish view that everything is a set or class, called “Pythagoreanism” or “(Hyper)Pythagoreanism.” I think he should not have rejected this view but embraced it, and I try to defend it by appealing only to premises that Quine accepted. Of course students of Quine also know that he came to think of ontology as having less scientific importance than he did in “On What There Is” and Word and Object. The scientific cash value of our whole theory of nature, he came to think, is measured not so much in what it says exists but rather in its structure. I think that Quine’s view on this point is immaterial to the fortunes of Pythagoreanism.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Kemp, Dr Gary
• Authors: Kemp, G.
• College/School: College of Arts > School of Humanities > Philosophy
• Journal Name: Monist
• Publisher: Hegeler Institute
• ISSN: 0026-9662
• ISSN (Online): 2153-3601
• Published Online: 11 April 2017
• Copyright Holders: Copyright © 2017 The Authors
• First Published: First published in Monist 100(2):155-166
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher