FOM: Existential commitments in logic

[Neil Tennant]

Vaughan,
if one treats the empty universe as one of the universes quantified over
in the normal definition of validity (S is valid iff in every universe and
under every interpretation in that universe, S is true) then the resulting
notions of validity and logical consequence for free logic, under the
Russellian assumption the truth of any atomic predication requires
denotations for all the singular terms involved, call for the rules of 
inference that I mentioned.
I know that it seems terribly counterintuitive to consider an (the) empty
universe; but some logicians (I am not one of them) insist that logic
should be absolutely neutral on ontological matters. That is, logic should
not even commit one to the claim that something exists. 
Best,
Neil

___________________________________________________________________
Neil W. Tennant
Professor of Philosophy and Adjunct Professor of Cognitive Science
230 North Oval
The Ohio State University