more from Bernard Bolzano

Single Idea 9987

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

Full Idea

An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'.

Gist of Idea

An aggregate in which order does not matter I call a 'set'


Bernard Bolzano (Paradoxes of the Infinite [1846], 4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.56

A Reaction

The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate.