On 28 May 2012, at 18:35, meekerdb wrote:

On 5/28/2012 1:37 AM, Bruno Marchal wrote:I am mute on the subject of whether p is true in any other world (unless I can use an axiom like the above).By the logicians notion of proof, if you prove a proposition, it istrue in all worlds/model/interpretation.But the 'worlds' are defined by the axioms and rules of inference.

`Not as such. the axioms and rules define only the truth common to all`

`models, when the theory is sound (and vice versa if the theory is`

`complete). Individual models have their lives of their own. They lives`

`in other theories or theories models. The models of PA exists in ZF's`

`model. Models (semantics) are beyond the theory.`

So you could change or add axioms and get different 'worlds'. Inthis logicians idea of 'world' it is not the case that you onlyprove things in the one world you're in.

`That was my point. We alway "prove" what is true in all worlds.`

`Proving is a trans-world notion. G proves <> t -> <>[] f, makes that`

`formula true in all worlds of all models based on all finite`

`irreflexive realist models, for example.`

`Here the world can be related to the models, but it leads to a very`

`special model. So different completeness theorem are being used in`

`that context, and we have to be cautious which one we are talking about.`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.