On Representational Redundancy, Surplus Structure, and the Hole Argument

Abstract

We address a recent proposal concerning 'surplus structure' due to Nguyen et al. [ 'Why Surplus Structure is Not Superfluous.' Br. J. Phi. Sci Forthcoming.] We argue that the sense of 'surplus structure' captured by their formal criterion is importantly different from-and in a sense, opposite to-another sense of 'surplus structure' used by philosophers. We argue that minimizing structure in one sense is generally incompatible with minimizing structure in the other sense. We then show how these distinctions bear on Nguyen et al.'s arguments about Yang-Mills theory and on the hole argument.

Is the classical limit “singular”?

“…23 Later on, we will establish that the classical limit can be interpreted as a functor that forgets stuff and structure*. We will provide additional discussion of these notions of forgetfulness in §9, but we note here that interpretations of these notions of forgetfulness have been discussed extensively already in the literature (Weatherall, 2017;Bradley and Weatherall, 2020). We encourage the reader to review those discussions for further introduction.…”

New Perspectives on the Hole Argument

“…Bradley and Weatherall [5], in their paper "On Representational Redundancy, Surplus Structure, and the Hole Argument," explore what it means to say that a physical theory exhibits "representational redundancy". They distinguish three different senses of "representational redundancy", and argue that each of these has importantly different consequences regarding, for instance, whether the models of a theory exhibiting such redundancy should be said to have "surplus structure".…”

“…The early literature on the hole argument, following on the heels of the landmark Earman-Norton paper, focused on metaphysical issues. 5 Is there a form of "substantivalism" that avoids indeterminism? Various authors defended versions of substantivalism-dubbed, with a distinctly perjorative flavor, "sophisticated substantivalism" by Belot and Earman [4], though this name has since been reclaimed by the sophisticates-according to which either (a) of the various isomorphic spacetimes generated by the hole argument and similar constructions, only one represents a "real" physical possibility (e.g.…”

Part 2: Theoretical equivalence in physics

“…In particular, a given functor may fail to be full, to be faithful, or to be essentially surjective (or more than one of these conditions may fail); such functors are sometimes said to be forgetful (Baez, Bartel, & Dolan, ). Studying the properties of such functors can allow one to say what is “forgotten” when moving from one theory to the other (Rosenstock & Weatherall, ; Weatherall, ; Nguyen et al, ; Bradley & Weatherall, ).…”