Combining Philosophers

Ideas for Irenaeus, Gideon Rosen and W Kneale / M Kneale

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2 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II

18851

Pairing (with Extensionality) guarantees an infinity of sets, just from a single element [Rosen]

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V

10051

The axiom of infinity is not a truth of logic, and its adoption is an abandonment of logicism [Kneale,W and M]