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Single Idea 19209

[filed under theme 4. Formal Logic / D. Modal Logic ML / 1. Modal Logic ]

Full Idea

Logical consequence guarantees preservation of truth. The Converse Barcan, a theorem of Simple Quantified Modal Logic, says that an obvious truth implies an obvious falsehood. So SQML gets logical consequence wrong. So SQML is mistaken.

Gist of Idea

Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem

Source

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

Book Ref

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

A Reaction

I admire this. The Converse Barcan certainly strikes me as wrong (Idea 19208). Merricks grasps this nettle. Williamson grasps the other nettle. Most people duck the issue, I suspect. Merricks says later that domains are the problem.

Related Idea

Idea 19208 The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [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]