On the So-Called Argument of the Hole

Abstract

Th author submits to a critical analysis the argument of the hole, which has been formulated by Einstein and later developed by Earman and Norton. The aim of the analysis is an evaluation of the assumption made in the argument and the possibility of avoiding its indeterministic consequences. It turns out that it is a particular form of substantivalism assumed by Earman and Norton which is responsible for the indeterministic consequences of the argument. It follows that those consequences can be avoided by rejecting either substantivalism as a whole or its particular form accepted by both authors. None of the non-substantivalist interpretations proposed can be accepted, including also the one that Earman himself has tried to develop. The presented forms of the structural substantivalism and the substantivalism rejecting the transworld identification of points are hardly aceptable, either. Hence, there are two alternatives left: either one of the versions of essentialism or else instrumentalism, i.e. giving up doing ontology. Since the author regards instrumentalism as cognitively fruitless, he prefers the first option.