35. Cf. 1. Pollock, "Plantinga on Possible Worlds," in 1.Tomberlin and P. van Inwagen,
(Dordrecht: Reidel, 1985), 121-144.
.It is perhaps not obvious that this should be so in our fully perspectival semantics.
it seems clear that I don't stand in, e.g., the acquaintance-of relation with my friend
Lundstrom at a world
in which I don't exist, and that I do stand in its complement
is it clear that I don't stand in the identity relation with myself at
that I am better characterized as being identical with myself or not at worlds in w
fail to exist? My intuitions side with the latter, but the former is consistent. For its
cations on the logic, see note 39.
37. Failure to appreciate this point, I think, has led some actualists to deny serious ac
ism; see, e.g., Pollock's arguments in "Plantinga on Possible Worlds," 126ff, an
Salmon, "Existence," 91fT. I'd like to think that all they are
doing is denyin
as a logical principle.
38. These axioms ensure, in particular, that PRPs with distinct constituents or distinct}
cal forms are themselves distinct. Since it is rather tedious to introduce the defini
needed to express these axioms precisely, and since nothing hinges on their pr
expression for the purposes of this paper, I will avoid listing them here.
39. To incorporate into A3 the principle that contingent objects stand in the identity rel
with themselves even at worlds in which they don't exist we replace the axiom
83 with the axiom schema Id (so D,.
'Twill now be provable in A3) and drop
the stronger 'T
'T' becomes provable from Id, Nee, and Ind), repla
and replace Id in
with the axiom schema
for all noncomplex terms 'T.
40. My thanks toEd Zalta for typically incisive comments, and to John Gibbon an
colleagues at Texas A&M for their comments on a presentation based on an earl
of this paper. Thanks also to Chris Hill for numerous improvements stemming
meticulous reading of the penultimate draft of the paper, and also for his exe
disagree (of course) about whether nominalism is true. They
isagree about whether it's plausible. They even disagree about whether it's
orth discussing. And yet beneath this profound disagreement there exists
significant consensus about what kind of problem the problem of nomi-
ism is. According to this consensus, nominalism and its opposite, pla-
nism, are both intelligible, coherent claims about what exists.? In an older
abulary, they are both synthetic ontological hypotheses. This means the
spute cannot be settled a priori. All the reflection in the world will not tum
a contradiction in either proposal. At the same time, however, the dispute
not be settled by ordinary empirical means either. Both sides agree that
usally inert, non-spatiotemporal abstract objects would be radically unob-
rvable if they existed. Numbers and the rest, unlike neutrinos, do not leave
sorts of traces in the sensible world that a scientist can set about trying
find. What saves the dispute from being simply intractable is the recogni-