Single Idea 14235

[catalogued under 5. Theory of Logic / G. Quantification / 6. Plural Quantification]

Full Idea

If the rule is asserted 'Given any well-determined objects, they can be collected into a set by an application of the 'set of' operation', then on the usual account of 'they' this is a tautology. Collection comes automatically with this form of reference.

Gist of Idea

Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection


James Cargile (Paradoxes: Form and Predication [1979], p.115), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? Intro

Book Reference

'Metaphysics (Philosophical Perspectives 20)', ed/tr. Hawthorne,John [Blackwell 2006], p.124

A Reaction

Is this a problem? Given they are well-determined (presumably implying countable) there just is a set of them. That's what set theory is, I thought. Of course, the iterative view talks of 'constructing' the sets, but the construction looks unstoppable.