FOM: Existential commitments in logic

Vaughan Pratt pratt at CS.Stanford.EDU
Fri Oct 15 17:46:08 EDT 1999

Pratt> under the (very reasonable)
Pratt> assumption that your language includes constants, all propositions
Pratt> true false or contingent become vacuously valid in the empty universe
Pratt> for lack of interpretations of those constants.

Tennant>This is not so under the Russellian assumption that the truth of
Pratt>                                                          ^^^^^
Tennant>any atomic predication P(t_1,...,t_n) requires each term t_i to
Tennant>have a denotation.

Hi, Neil.  The phenomenon I pointed out for the empty universe makes the
validity of any proposition independent of its truth in that universe.
How does an assumption about the truth of propositions affect validity
in this situation?

The plaintive cry "There's nothing here" is, taken literally, paradoxical:
how could it even have been uttered, let alone heard?  Whether the
negation of this proposition is analytic or contingent depends on the
details of one's semantics.

A sensible semantics might leave that question undecided.  My point was
that at least one traditional semantics makes it analytic.  If your point
is that free logic makes it contingent you need to say something about
validity in order to show why my argument does not apply to free logic.


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