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?
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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