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Single Idea 13720
[filed under theme 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
]
Full Idea
The Converse Barcan Formula reads □∀αφ→∀α□φ (or an equivalent using ◊).
Gist of Idea
Converse Barcan Formula: □∀αφ→∀α□φ
Source
Theodore Sider (Logic for Philosophy [2010], 9.5.2)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.240
A Reaction
I would read that as 'if all the αs happen to be φ, then αs have to be φ'. Put like that, I would have thought that it was obviously false. Sider points out that some new object could turn up which isn't φ.
The
25 ideas
with the same theme
[formula relating possibility to existence]:
16519
|
No one can conceive of a possible substance, apart from those which God has created
[Arnauld]
|
14976
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Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds
[Cresswell]
|
16189
|
The variable domain approach to quantified modal logic invalidates the Barcan Formula
[Kripke, by Simchen]
|
15132
|
The Barcan formulas fail in models with varying domains
[Kripke, by Williamson]
|
18823
|
To say there could have been people who don't exist, but deny those possible things, rejects Barcan
[Stalnaker, by Rumfitt]
|
15415
|
The temporal Barcan formulas fix what exists, which seems absurd
[Burgess]
|
13728
|
The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability
[Fitting/Mendelsohn]
|
13729
|
The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity
[Fitting/Mendelsohn]
|
15130
|
If a property is possible, there is something which can have it
[Williamson]
|
15135
|
If the domain of propositional quantification is constant, the Barcan formulas hold
[Williamson]
|
15139
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Converse Barcan: could something fail to meet a condition, if everything meets that condition?
[Williamson]
|
13720
|
Converse Barcan Formula: □∀αφ→∀α□φ
[Sider]
|
13718
|
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic
[Sider]
|
13723
|
System B is needed to prove the Barcan Formula
[Sider]
|
19297
|
The two Barcan principles are easily proved in fairly basic modal logic
[Hale]
|
19301
|
With a negative free logic, we can dispense with the Barcan formulae
[Hale]
|
15023
|
The Barcan schema implies if X might have fathered something, there is something X might have fathered
[Sider]
|
19208
|
The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists'
[Merricks]
|
9449
|
The plausible Barcan formula implies modality in the actual world
[Bird]
|
18350
|
Truth-maker theorists should probably reject the converse Barcan formula
[Rami]
|
15380
|
Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging
[Vervloesem]
|
16187
|
The Barcan Formulas are orthodox, but clash with the attractive Actualist view
[Simchen]
|
16186
|
The Barcan Formulas express how to combine modal operators with classical quantifiers
[Simchen]
|
16190
|
BF implies that if W possibly had a child, then something is possibly W's child
[Simchen]
|
19036
|
The Barcan formula endorses either merely possible things, or makes the unactualised impossible
[Vetter]
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