FOM: Existential commitments in logic

[Neil Tennant]

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