On 3/6/2015 7:24 AM, Bruno Marchal wrote:
That might depend on the context. Usually, in our computationalist context it means true
in the standard model of arithmetic, which is "this reality" if you want.
In the modal context, it means true in this world (which in our arithmetical context is
NOT necessarily among the accessible world, because we don't have []p -> p). With the
logic of provability, we cannot access the world we are in. p does not imply <>p
I wonder about such definitions of modal operators. WHY doesn't p imply <>p? We */could/*
define <> so that it did. Is there some good reason not to?
Brent
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