Single Idea 9879

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

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]