Full Idea
Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions.
Clarification
The 'comprehension axiom' says that every property is collectivizing, or has an extension
Gist of Idea
NF has no models, but just blocks the comprehension axiom, to avoid contradictions
Source
report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.230
A Reaction
The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded.
Related Idea
Idea 13526 Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS]