On 14 Mar 2014, at 06:08, meekerdb wrote:
On 3/13/2014 9:54 PM, Bruno Marchal wrote:
which was my objection to writing <>t. In such a formula, t can
only be regarded as shorthand for some tautology.
If you want. Any simple provable proposition would do.
Then f also occurs in every world since (p & ~p) can be formed in
every world. But you say "we never meet f" in any world?
I meant that f, like (p & ~p), is FALSE in every world. By "met it" I
mean met it true.
Bruno
Brent
So <>t doesn't mean "There is some reality" it means "There is
some tautology: a proposition that is t in virtue of the
definition of relations "&", "V", "~", etc."
<>t means, in Kripke semantics, that there is a world in which t is
true (and as t is true in any world, it does mean that there is a
world.
Then when "<>A" is the diamond "consistency of A", it means that
there is a model verufying A, by Gödel's completeness theorem.
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