more from Saul A. Kripke

Single Idea 15132

[catalogued under 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula]

Full Idea

Kripke showed that the Barcan formula ∀x□A⊃□∀xA and its converse fail in models which require varying domains.

Gist of Idea

The Barcan formulas fail in models with varying domains


report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Timothy Williamson - Truthmakers and Converse Barcan Formula §1

Book Reference

-: 'Dialectica' [-], p.256

A Reaction

I think this is why I reject the Barcan formulas for metaphysics - because the domain of metaphysics should be seen as varying, since some objects are possible in some contexts and not in others. Hmm…

Related Ideas

Idea 15135 If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]

Idea 9449 The plausible Barcan formula implies modality in the actual world [Bird]