more from Michael Jubien

Single Idea 9967

[catalogued under 4. Formal Logic / F. Set Theory ST / 1. Set Theory]

Full Idea

Any set with a concrete member is 'impure'. 'Pure' sets are those that are not impure, and are paradigm cases of abstract entities, such as the sort of sets apparently dealt with in Zermelo-Fraenkel (ZF) set theory.

Gist of Idea

'Impure' sets have a concrete member, while 'pure' (abstract) sets do not


Michael Jubien (Ontology and Mathematical Truth [1977], p.116)

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.116

A Reaction

[I am unclear whether Jubien is introducing this distinction] This seems crucial in accounts of mathematics. On the one had arithmetic can be built from Millian pebbles, giving impure sets, while logicists build it from pure sets.