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 is true 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'. In this logicians idea of 'world' it is not the case that you only prove 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.



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 
For more options, visit this group at 

Reply via email to