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