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| ``another question''
by rmilson on 2002-06-03 20:03:09 |
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| In regards to your structures entry, here is a
question that has been bothering me for a good long while:
Are empty models/structures allowed?
Of course, all foralls are true in an empty model,
and all "there exists" false.
Usually the standard texts say "no empty models allowed"
and I always wondered: "how come?"
The closest I've been able to come to an explanation,
is that people seem to want to be able to deduce
that
(For all x) (Px) |- (Exists x)(Px)
and to do this, you need to forbid empty models.
This always struck me as a question of convention,
an arbitrary decision someone made long ago.
Am I missing something? What is so abhorrent about
empty models that they must be forbidden? |
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