Single Idea 18827

[catalogued under 5. Theory of Logic / A. Overview of Logic / 6. Classical Logic]

Full Idea

If we specify the senses of the connectives by way of the standard truth-tables, then we must justify classical logic only by appeal to the Principle of Bivalence.

Gist of Idea

If truth-tables specify the connectives, classical logic must rely on Bivalence

Source

Ian Rumfitt (The Boundary Stones of Thought [2015], 7)

Book Reference

Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.184


A Reaction

Rumfitt proposes to avoid the truth-tables, and hence not to rely on Bivalence for his support of classical logic. He accepts that Bivalence is doubtful, citing the undecidability of the Continuum Hypothesis as a problem instance.

Related Idea

Idea 18830 Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt]