Luc, Joanna
(2023)
The Hole Argument without the notion of isomorphism.
[Preprint]
Abstract
In this paper, I argue that the Hole Argument can be formulated without using the notion of isomorphism and for this reason it is not threatened by the criticism of Halvorson and Manchak (2022). I divide the Hole Argument, following Earman and Norton (1987), into two steps: the proof of the Gauge Theorem and the transition from the Gauge Theorem to the conclusion of radical indeterminism. I argue that the Gauge Theorem does not rely on the notion of isomorphism, but on the notion of the diffeomorphisminvariance of the equations of local spacetime theories; however, for this approach to work, the definition of such theories needs certain amendments with respect to its formulation by Earman and Norton. In the analysis of the second step, I postulate that we should use the notion of radical indeterminism instead of indeterminism simpliciter and that we should not decide in advance what kind of maps are to be used in comparing models. Instead, we can choose tentatively some kind of maps for this purpose and check whether a given choice leads to radical indeterminism involving empirically indistinguishable models. In this way, the usage of the notion of isomorphism is avoided also in the second step of the Hole Argument. A general picture is that physical equivalence can be established by means of an iterative procedure, in which we examine various candidate classes of maps and, depending on the outcomes, we need to broaden or narrow these classes; the Hole Argument can be viewed as a particular instance of this procedure.
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The Hole Argument without the notion of isomorphism. (deposited 24 Nov 2023 02:17)
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