Mathematical Responses to the Hole Argument: Then and Now

@article{Bradley2021MathematicalRT,
  title={Mathematical Responses to the Hole Argument: Then and Now},
  author={Clara Bradley and James Owen Weatherall},
  journal={Philosophy of Science},
  year={2021},
  volume={89},
  pages={1223 - 1232}
}
Abstract We argue that several apparently distinct responses to the hole argument, all invoking formal or mathematical considerations, should be viewed as a unified “mathematical response.” We then consider and rebut two prominent critiques of the mathematical response before reflecting on what is ultimately at issue in this literature. 
View on Cambridge Press
cambridge.org
4 Citations
Background Citations
4

4 Citations

Representation and Spacetime: The Hole Argument Revisited

ABSTRACT Ladyman and Presnell have recently argued that the Hole argument is naturally resolved when spacetime is represented within homotopy type theory rather than set theory. The core idea behind…

The Hole Argument and Beyond, Part I: The Story so Far

In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical…

Reopening the Hole Argument

The aim of this expository paper is to argue that although Weatherall (2018) and Halvorson & Manchak (2022) claim to ‘close the Hole Argument’, its philosophical thrust may be resurrected by…

Between a Stone and a Hausdorff Space

We consider the duality between General Relativity and the theory of Einstein algebras, in the extended setting where one permits non-Hausdorff manifolds. We show that the duality breaks down, and…

35 References

On the mathematics and metaphysics of the hole argument

    O. PooleyJ. Read
    Philosophy
    The British Journal for the Philosophy of Science
  • 2021
We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article by Weatherall. Broadly speaking, we defend the mainstream philosophical literature from…

Closing the hole argument

The hole argument purportedly shows that spacetime substantivalism implies a pernicious form of indeterminism. Here we attempt to answer the question: what is the mathematical fact that is supposed…

Regarding the ‘Hole Argument’

    J. Weatherall
    Philosophy
    The British Journal for the Philosophy of Science
  • 2018
I argue that the hole argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the hole argument is…

The Hole Argument

    J. Norton
    Philosophy
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
  • 1988
I give an informal outline of the hole argument which shows that spacetime substantivalism leads to an undesirable indeterminism in a broad class of spacetime theories. This form of the argument…

Holes and Determinism: Another Look

    S. Leeds
    Philosophy
    Philosophy of Science
  • 1995
I argue that Earman and Norton's familiar "hole argument" raises questions as to whether GTR is a deterministic theory only given a certain assumption about determinism: namely, that to ask whether a…

Is There a Syntactic Solution to the Hole Problem?

After some background setting in which it is shown how Maudlin's (1989, 1990) response to the hole argument of Earman and Norton (1987) is related to that of Rynasiewicz (1994), it is argued that the…

New Perspectives on the Hole Argument

This special issue of Foundations of Physics collects together articles representing some recent new perspectives on the hole argument in the history and philosophy of physics. Our task here is to…

On Some Recent Attempted Non-Metaphysical Dissolutions of the Hole Dilemma

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…

Spacetime and Holes

    Carolyn Brighouse
    Philosophy
    PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association
  • 1994
John Earman and John Norton have argued that substantivalism leads to a radical form of indeterminism within local spacetime theories. I compare their argument to more traditional arguments typical…

What Price Spacetime Substantivalism? The Hole Story

    J. EarmanJ. Norton
    Philosophy, Physics
    The British Journal for the Philosophy of Science
  • 1987
Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument…