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4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula

[formula relating possibility to existence]

25 ideas
No one can conceive of a possible substance, apart from those which God has created [Arnauld]
Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell]
The temporal Barcan formulas fix what exists, which seems absurd [Burgess]
The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn]
The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn]
If a property is possible, there is something which can have it [Williamson]
The Barcan formulas fail in models with varying domains [Williamson]
If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]
Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson]
The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
Converse Barcan Formula: □∀αφ→∀α□φ [Sider]
System B is needed to prove the Barcan Formula [Sider]
The two Barcan principles are easily proved in fairly basic modal logic [Hale]
With a negative free logic, we can dispense with the Barcan formulae [Hale]
The Barcan schema implies if X might have fathered something, there is something X might have fathered [Sider]
The Converse Barcan implies 'everything exists necessarily' is a consequence of 'necessarily, everything exists' [Merricks]
The plausible Barcan formula implies modality in the actual world [Bird]
Truth-maker theorists should probably reject the converse Barcan formula [Rami]
Barcan:nothing comes into existence; Converse:nothing goes out; Both:domain is unchanging [Vervloesem]
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
The variable domain approach to quantified modal logic invalidates the Barcan Formula [Simchen]
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
To say there could have been people who don't exist, but deny those possible things, rejects Barcan [Rumfitt]
The Barcan formula endorses either merely possible things, or makes the unactualised impossible [Vetter]