Saturday, November 25, 2006

When identity isn't identity, part 2

It just occurred to me that in the previous post on identity in intuitionistic logic, I made a bit of an error (one that survived the suggested correction). The problems with transworld identity are only problems in the context of modal logic. At least, I'm not sure of any problems that arise with identity of individuals across possible worlds in Kripke semantics for intuitionistic logic. There are enough structural similarities between the box and the universal quantifier that I imagine some formula could be cooked up. No clue what a version of Chisholm's problem with transworld identity would look like in terms of witnesses for intuitionistic formulas though. This is a roundabout way of saying that the conclusion of the previous post (about the apparent possibility of problems in classical logic) doesn't pan out. Since classical logic is validated on Kripke frames with only one world, there won't be transworld identity cause there is no transworld to speak of. Alas.

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