Arledge, Christopher and Rynasiewicz, Robert
(2019)
On Some Recent Attempted Non-Metaphysical Dissolutions of the Hole Dilemma.
In: UNSPECIFIED.
Abstract
The hole argument of Earman and Norton (1987) is designed to establish a dilemma:
either give up the possibility of determinism in a wide class of spacetime theories, which they
believe substantivalists must do, or else embrace a principal called `Leibniz equivalence'
that identifies isomorphic models as representing one and the same physical situation, a
principle certainly necessary for relationalism but also thought by many to be sufficient
for relationalism. It would seem, then, that any resolution of the hole dilemma must
engage in major metaphysical maneuvering, as is typical of the enormous literature on
the hole argument. Recently, however, a number of authors have claimed metaphysical
excursions can be avoided and the dilemma dissolved if sufficient attention is paid to how
the mathematics used in the hole argument, and spacetime theories in general, applies
to the world2 (Weatherall 2018, Curiel 2018, Fletcher 2019). We think these attempts
are unsuccessful and intend to explain why, but not because we believe resolution of the
hole dilemma calls for metaphysical tinkering. For at the end we will suggest a resolution
that is non-metaphysical, at least to the extent that basic facts about reference are not
metaphysical.
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