FOM: Existential commitments in logic
Neil Tennant
neilt at mercutio.cohums.ohio-state.edu
Fri Oct 15 16:47:50 EDT 1999
Vaughan Pratt writes:
> under the (very reasonable)
> assumption that your language includes constants, all propositions
> true false or contingent become vacuously valid in the empty universe
> for lack of interpretations of those constants.
This is not so under the Russellian assumption that the truth of
any atomic predication P(t_1,...,t_n) requires each term t_i to
have a denotation.
In free logic one can express the Russellian assumption by adopting
the Rule of Denotation:
P(...t...)
__________ where P is an atomic predicate
E!t
Here E!t is short for (Ex)(x=t).
For the remaining rules of free logic, especially those for the
quantifiers (in natural deduction format) see my book Natural Logic, ch.
7.
Neil Tennant
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