more from Charles Chihara

Single Idea 8758

[catalogued under 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory]

Full Idea

Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'.


An open sentence has a free variable in it

Gist of Idea

We could talk of open sentences, instead of sets


report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2

Book Reference

Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.239

A Reaction

As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets.