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Single Idea 16189

[filed under theme 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula ]

Full Idea

Kripke's variable domain approach to quantified modal logic famously invalidates the Barcan Formula.

Gist of Idea

The variable domain approach to quantified modal logic invalidates the Barcan Formula

Source

report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Ori Simchen - The Barcan Formula and Metaphysics §3

Book Ref

-: 'Theoria' [-], p.9

A Reaction

[p.9 and p.16] In a single combined domain all the possibilia must be present, but with variable domains objects in remote domains may not exist in your local domain. BF is committed to those possible objects.

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 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 Converse Barcan: could something fail to meet a condition, if everything meets that condition? [Williamson]
13718 The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic [Sider]
13720 Converse Barcan Formula: □∀αφ→∀α□φ [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]
16186 The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
16187 The Barcan Formulas are orthodox, but clash with the attractive Actualist view [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]