Abstract. In this paper I discuss Jonathan Bain’s answer to the argument against
radical ontic structural realism (OSR) based on the idea that a structure is an
isomorphism class and thus cannot be the only thing that exists. I examine Bain’s
proposal of replacing the set-theoretic approach to OSR with a categorial
approach and argue that several of his argumentative moves are deficient. First,
Bain seems to define wrongly some of the mathematical concepts involved in
category theory, for instance that of ‘maximal ideal’, and he also attempts to use
these concepts in ways that would be detrimental to OSR itself. Both of these
deficiencies undermine his claims. Second, the very form of Bain’s argument is, to
some point, self-defeating, since defining any category whatsoever presupposes
some fixed set-theoretic framework.
Keywords: ontic structural realism, mathematical structuralism, category
theory, set theory.
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