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### Single Idea 19208

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

Full Idea

The Converse Barcan Formula has a startling result. Simple Quantified Modal Logic (SQML) has the following as a theorem: □∀xFx → ∀x□Fx. So 'everything exists necessarily' is a consequence of 'necessarily, everything exists'.

Gist of Idea

The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists'

Source

Trenton Merricks (Propositions [2015], 2.V)

Book Reference

Merricks,Trenton: 'Propositions' [OUP 2015], p.65

A Reaction

He says this is blatantly wrong. Williamson is famous for defending it. I think I'm with Merricks on this one.

Related Idea

Idea 19209
Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem **[Merricks]**