On 13 Jun 2012, at 00:38, Russell Standish wrote:

On Tue, Jun 12, 2012 at 08:17:38PM +0200, Bruno Marchal wrote:On 12 Jun 2012, at 00:47, Russell Standish wrote:On Thu, Jun 07, 2012 at 01:33:48PM +0200, Bruno Marchal wrote:In fact we have p/p for any p. If you were correct we would have[]pfor any p.This is what I thought you said the "meta-axiom" stated? How else do we get p/[]p for Kripke semantics?Because if p is true in all worlds, then []p is true in all worlds OK?No. I didn't say that. p means p is true in a world. p true in all worlds would be written []p.

But in logic, if p appears in a deduction, p is true in all worlds.

`Take as example a formalization of classical propositional calculus.`

`The axioms have to be tautologies, and so are true in all worlds`

`(valuations, interpretation). The modus ponens concerves`

`tautologicalness, so all theorems (the formula appearing in the`

`deduction) are true in all worlds.`

`And p/[]p means that if p is true in all worlds (like if it is proved)`

`then []p is true in all worlds.`

`If you want to mean that p is true in a world, or the actual world,`

`you can say it, but not in deduction. Usually you will name that`

`world, by saying that p is true in alpha, at some meta level.`

Bruno

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