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'.
Clarification
An open sentence has a free variable in it
Gist of Idea
We could talk of open sentences, instead of sets
Source
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.