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Single Idea 19208

[filed under theme 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 Ref

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]

The 17 ideas from 'Propositions'

19200 Propositions are standardly treated as possible worlds, or as structured [Merricks]
19201 Propositions can be 'about' an entity, but that doesn't make the entity a constituent of it [Merricks]
19202 Propositions are necessary existents which essentially (but inexplicably) represent things [Merricks]
19203 A sentence's truth conditions depend on context [Merricks]
19204 True propositions existed prior to their being thought, and might never be thought [Merricks]
19205 'Snow is white' only contingently expresses the proposition that snow is white [Merricks]
19207 Sentence logic maps truth values; predicate logic maps objects and sets [Merricks]
19206 'Cicero is an orator' represents the same situation as 'Tully is an orator', so they are one proposition [Merricks]
19209 Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks]
19208 The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks]
19210 The standard view of propositions says they never change their truth-value [Merricks]
19211 Early Russell says a proposition is identical with its truthmaking state of affairs [Merricks]
19212 Unity of the proposition questions: what unites them? can the same constituents make different ones? [Merricks]
19213 We want to explain not just what unites the constituents, but what unites them into a proposition [Merricks]
19214 In twinning, one person has the same origin as another person [Merricks]
19217 I don't accept that if a proposition is directly about an entity, it has a relation to the entity [Merricks]
19215 Arguers often turn the opponent's modus ponens into their own modus tollens [Merricks]