Disregarding the 'Hole Argument'

TL;DR

This paper defends the validity of Einstein's hole argument against Weatherall's critique, arguing that Weatherall's restrictions on mathematical use are implausible and do not threaten the argument's validity.

Contribution

It provides a counter-argument to Weatherall's critique, reaffirming the philosophical significance of Einstein's hole argument.

Findings

Weatherall's restrictions are deemed implausible

The hole argument remains valid under standard mathematical use

The critique does not undermine the philosophical importance of the hole argument

Abstract

Jim Weatherall has suggested that Einstein's hole argument, as presented by Earman and Norton (1987), is based on a misleading use of mathematics. I argue on the contrary that Weatherall demands an implausible restriction on how mathematics is used. The hole argument, on the other hand, is in no new danger at all.