Symmetries, Indexicality and the Perspectivist Stance

ABSTRACT

I critically examine the assumption that the theoretical structure that varies under theoretical symmetries is redundant and should be eliminated from a metaphysical picture of the universe, following a ‘symmetry to reality’ inference. I do so by analysing the status of coordinate change symmetries taking a pragmatic approach. I argue that coordinate systems function as indexical devices, and play an important pragmatic role for representing concrete physical systems. I examine the implications of considering this pragmatic role seriously, taking what I call a perspectivist stance. My conclusion is that under a perspectivist stance, all symmetries (including local gauge symmetries) potentially have a direct empirical status: they point to dynamical aspects that are invariant under changes of operationalisation, and they constitute a guide not to reality, but to nomology and kinship.

Acknowledgement

I would like to thank Valeriya Chasova for her helpful comments on an earlier draft of this paper.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 van Fraassen (2008) has also applied the notion of indexicality to scientific representation, but in a different way. It is associated, for example, with self-location when using a map (‘I am here’). However, maps are not indexical representations in the sense proposed here, since in general, the symbols on a map always refer to the same objects whatever the context of use. Van Fraassen’s idea is that an ineliminable indexical is involved when using a representation (even a non-indexical representation) in context. This is a ‘deep’ but controversial idea (I will mention it again later). The idea that general scientific models are indexical because they only refer to concrete objects when applied in context is much more mundane, and should be less controversial.

2 I neglect the fact that, strictly speaking, the existence of a central force breaks the symmetries of Newtonian mechanics: I assume that the transformation applies to the force as well.

3 Strictly speaking, adopting this view from nowhere does not necessarily imply being able to represent the universe as a whole. So, an author such as Wallace (2019a) expresses doubts with regards to the idea that we should systematically interpret physical theories in cosmological terms. Yet he bases his defense of a version of the symmetry-to-reality inference on a consideration of models that incorporate measuring instruments as well as target systems. He remarks that no variant quantity of the target+instrument system can be measured by said instrument, and infers that variant quantities are unobservable. This reasoning amounts to eliminating perspectival aspects by invoking a larger model, taken to be more fundamental for interpretive purposes. As explained further, this is precisely the kind of move that PS resists.

4 As noted by an anonymous reviewer, this is a way of interpreting Baker’s (2010) proposal.

5 This is close to an inference from symmetry to reality, but not quite the same. It could be interpreted in terms of the symmetry-to-fundamentality mentioned before.

6 In some cases, this will require understanding possibilities in a fairly permissive way, for example when the transformation only concerns the remote past in a cosmological model. If we were to rule out such possibilities, some symmetries would lose their empirical status because of practical limitations due to our situation in the universe, but not for reasons of principle.