Single Idea 18830

[catalogued under 4. Formal Logic / F. Set Theory ST / 1. Set Theory]

Full Idea

Many set theorists doubt if the Generalised Continuum Hypothesis must be either true or false; certainly, its bivalence is far from obvious. All the same, almost all set theorists use classical logic in their proofs.

Gist of Idea

Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic

Source

Ian Rumfitt (The Boundary Stones of Thought [2015], 7.2)

Book Reference

Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.196


A Reaction

His point is that classical logic is usually taken to rest on bivalence. He offers the set theorists a helping hand, by defending classical logic without resorting to bivalence.

Related Idea

Idea 18827 If truth-tables specify the connectives, classical logic must rely on Bivalence [Rumfitt]