variably axiomatic. If the existential quantifier in play corresponds to the possibilist
mode of being, the following principle is necessarily true: for any F, if it is possible for
something to be F, then there is something that is F. However, if the quantifiers are
restricted to actual objects, this principle is not clearly true; it’s probably false, and if it is
true, it is merely contingently true.
The second version of possibilism is one inspired by (but not equivalent to or a
consequence of) necessitarianism, according to which everything necessarily exists,
and on which the Barcan formulas are accepted at face value.^68 The conjunction
of the two Barcan formulas is this: everyxis necessarilyFxif and only, necessarily,
everyxisFx.^69
On this kind of necessitarianism, although there is no actual entity that is my
brother, there is an entity that possibly is my brother. This is not a view Ifind
particularly attractive, and in fact a parallel view about tense will be critically
discussed in section 3.6. But the point here is not to assess which views are the
most attractive, but rather merely to present defensible views according to which
existence is systematically variably axiomatic. So let us consider a view according to
which the Barcan formulas are satisfied by entities enjoying one mode of being—the
mode of mere possibility—but not by entities enjoying actual existence.^70 On this sort
of view, which modal logic is appropriate to use depends on the kind of existence in
play, and hence existence is systematically variably axiomatic.
2.6 Mixed Views
Trivially, any feature that is systematically variably polyadic will be systematically
variably axiomatic. But there might also be more interesting connections between
doctrines that imply that existence is systematically variably polyadic and doctrines
that imply that existence is systematically variably axiomatic.
Consider, for example, the views defended in sections 2.4.1 and 2.4.2, and the
views defended in 2.5.2. (There we talked about existence at a time vs. absolute
existence, substantial existence vs. inherence, and necessary existence vs. contingent
existence respectively.) I’m inclined to hold that a substance is a necessary being only
if its mode of being is non-relative. Given this principle, it will follow that no material
substance is a necessary being if we accept the ontology explored in section 2.4.1,
according to which the being of a material substance is existence at a time. So if there
are any necessarily existing substances, we have a reason for holding that the mode of
being of such a substance differs from the mode of being of contingent material
(^68) This is the sort of view recently defended by Williamson (2013).
(^69) The Barcan formulas are named after Ruth Barcan Marcus, whofirst formulated them andfirst
defended their importance. Barcan Marcus (1995) is a collection of some of her famous papers, many of
which discuss the formulae named after her. 70
This sort of view was independently suggested to me by Maeghan Fairchild and Phil Corkum. I do
not know whether either has pursued such a view in writing as of yet.