The Refutation of Nominalism

The Refutation of Nominalism - 35 Cf 1 Pollock"Plantinga on...

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35. Cf. 1. Pollock, "Plantinga on Possible Worlds," in 1. Tomberlin and P. van Inwagen, Alvin Plantinga (Dordrecht: Reidel, 1985), 121-144. 36..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 w in which I don't exist, and that I do stand in its complement him at w, is it clear that I don't stand in the identity relation with myself at w? Is it 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 i 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 really 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 S 83 with the axiom schema Id (so D,. = 'T will now be provable in A3) and drop the stronger 'T = 'T':::> D'T = 'T' becomes provable from Id, Nee, and Ind), repla axiom Vx(x = x) with VxE!x in G3, and replace Id in A3 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 editorial patience. 148 Refutation Nominalism (?)1 I. INTRODUCTION ~losophers 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 e 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-
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