more on this theme     |     more from this text


Single Idea 14976

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

Full Idea

If one wants the quantifiers in each world to range only over the things that exist in that world, and one doesn't believe that the same things exist in every world, one would probably not want the Barcan formula.

Gist of Idea

Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds

Source

Max J. Cresswell (Modal Logic [2001], 7.2.2)

Book Ref

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.151


A Reaction

I haven't quite got this, but it sounds to me like I should reject the Barcan formula (but Idea 9449!). I like a metaphysics to rest on the actual world (with modal properties). I assume different things could have existed, but don't.

Related Idea

Idea 9449 The plausible Barcan formula implies modality in the actual world [Bird]


The 7 ideas from Max J. Cresswell

Normal system K has five axioms and rules [Cresswell]
D is valid on every serial frame, but not where there are dead ends [Cresswell]
S4 has 14 modalities, and always reduces to a maximum of three modal operators [Cresswell]
In S5 all the long complex modalities reduce to just three, and their negations [Cresswell]
A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell]
A de dicto necessity is true in all worlds, but not necessarily of the same thing in each world [Cresswell]
Reject the Barcan if quantifiers are confined to worlds, and different things exist in other worlds [Cresswell]