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Single Idea 9449
[filed under theme 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
]
Full Idea
Modality in the actual world is the import of the Barcan formula, and there are good reasons for accepting the Barcan formula.
Gist of Idea
The plausible Barcan formula implies modality in the actual world
Source
Alexander Bird (Nature's Metaphysics [2007], 1.2)
Book Ref
Bird,Alexander: 'Nature's Metaphysics' [OUP 2007], p.6
A Reaction
If you thought logic was irrelevant to metaphysics, this should make you think twice.
The
25 ideas
with the same theme
[formula relating possibility to existence]:
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16519
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No one can conceive of a possible substance, apart from those which God has created
[Arnauld]
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14976
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Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds
[Cresswell]
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16189
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The variable domain approach to quantified modal logic invalidates the Barcan Formula
[Kripke, by Simchen]
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15132
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The Barcan formulas fail in models with varying domains
[Kripke, by Williamson]
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18823
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To say there could have been people who don't exist, but deny those possible things, rejects Barcan
[Stalnaker, by Rumfitt]
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15415
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The temporal Barcan formulas fix what exists, which seems absurd
[Burgess]
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13728
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The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability
[Fitting/Mendelsohn]
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13729
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The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity
[Fitting/Mendelsohn]
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15130
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If a property is possible, there is something which can have it
[Williamson]
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15135
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If the domain of propositional quantification is constant, the Barcan formulas hold
[Williamson]
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15139
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Converse Barcan: could something fail to meet a condition, if everything meets that condition?
[Williamson]
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13718
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The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic
[Sider]
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13720
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Converse Barcan Formula: □∀αφ→∀α□φ
[Sider]
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13723
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System B is needed to prove the Barcan Formula
[Sider]
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19297
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The two Barcan principles are easily proved in fairly basic modal logic
[Hale]
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19301
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With a negative free logic, we can dispense with the Barcan formulae
[Hale]
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15023
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The Barcan schema implies if X might have fathered something, there is something X might have fathered
[Sider]
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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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9449
|
The plausible Barcan formula implies modality in the actual world
[Bird]
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18350
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Truth-maker theorists should probably reject the converse Barcan formula
[Rami]
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15380
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Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging
[Vervloesem]
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16186
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The Barcan Formulas express how to combine modal operators with classical quantifiers
[Simchen]
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16187
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The Barcan Formulas are orthodox, but clash with the attractive Actualist view
[Simchen]
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16190
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BF implies that if W possibly had a child, then something is possibly W's child
[Simchen]
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19036
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The Barcan formula endorses either merely possible things, or makes the unactualised impossible
[Vetter]
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