On Sun, May 27, 2012 at 06:20:29PM +0200, Bruno Marchal wrote:
> 
> On 27 May 2012, at 12:15, Russell Standish wrote:
> >I still don't follow. If I have proved a is true in some world, why
> >should I infer that it is true in all worlds? What am I missing?
> 
> I realize my previous answer might be too long and miss your
> question. Apology if it is the case.
> 
> Here is a shorter answer. The idea of proving, is that what is
> proved in true in all possible world. If not, a world would exist as
> a counter-example, invalidating the argument.

I certainly missed that. Is that given as an axiom? It seems like that
would be written p -> []p.

When I say p is true in a world, I can only prove that p is true in
that world. I am mute on the subject of whether p is true in any other
world (unless I can use an axiom like the above).

In what class of logics would such an axiom be taken to be true. (Of
course it is true in classical logic, but there is only one "world" there).


-- 

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Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au
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