more on this theme     |     more from this thinker

Single Idea 16189

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

Full Idea

Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula.

Gist of Idea

The variable domain approach to quantified modal logic invalidates the Barcan Formula

Source

report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3

Book Ref

-: 'Theoria' [-], p.9

A Reaction

[p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects.

The 4 ideas from 'A Completeness Theorem in Modal Logic'

10760 With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg]
10163 Propositional modal logic has been proved to be complete [Kripke, by Feferman/Feferman]
16189 The variable domain approach to quantified modal logic invalidates the Barcan Formula [Kripke, by Simchen]
15132 The Barcan formulas fail in models with varying domains [Kripke, by Williamson]