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2 ideas
19209 | Simple Quantified Modal Logc doesn't work, because the Converse Barcan is a theorem [Merricks] |
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. | |
From: Trenton Merricks (Propositions [2015], 2.V) | |
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. |
19208 | The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks] |
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'. | |
From: Trenton Merricks (Propositions [2015], 2.V) | |
A reaction: He says this is blatantly wrong. Williamson is famous for defending it. I think I'm with Merricks on this one. |