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Single Idea 13718

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

Full Idea

The Barcan Formula ∀x□Fx→□∀xFx is often regarded as a defect of Simple Quantified Modal Logic, though this most clearly seen in its equivalent form ◊∃xFx→∃x◊Fx.

Gist of Idea

The Barcan Formula ∀x□Fx→□∀xFx may be a defect in modal logic

Source

Theodore Sider (Logic for Philosophy [2010], 9.5.2)

Book Ref

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.238

A Reaction

[See Idea 13719 for an explanation why it might be a defect] I translate the first one as 'if xs must be F, then they are always F', and the second one as 'for x to be possibly F, there must exist an x which is possibly F'. Modality needs existence.

Related Idea

Idea 13719 Barcan Formula problem: there might have been a ghost, despite nothing existing which could be a ghost [Sider]

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]