Symmetry as an Epistemic Notion (Twice Over)

Symmetries in physics are a guide to reality. That much is well known. But what is less well known is why symmetry is a guide to reality. What justifies inferences that draw conclusions about reality from premises about symmetries? I argue that answering this question reveals that symmetry is an epistemic notion twice over. First, these inferences must proceed via epistemic lemmas: premises about symmetries in the first instance justify epistemic lemmas about our powers of detection, and only from those epistemic lemmas can we draw conclusions about reality. Second, in order to justify those epistemic lemmas, the notion of symmetry must be defined partly in epistemic terms. 1 Symmetry-to-Reality Reasoning 1.1 A rough introduction to symmetry 1.2 The symmetry-to-reality inference 1.3 Two questions 1.4 Two answers 1.5 Preliminary clarifications2 Against Redundancy 2.1 Redundancy 2.2 Is absolute velocity redundant? 2.3 Some redundancies3 Against Objectivity4 From Symmetry to Detection 4.1 The epistemic approach 4.2 The Occamist norm 4.3 From symmetry to detection5 The Meaning of ‘Symmetry’ 5.1 A framework 5.2 Formal definitions 5.3 Ontic definitions6 Epistemic Definitions 6.1 Taking observation seriously 6.2 How things look 6.3 Observation sentences 6.4 Observational equivalence7 Symmetry as an Epistemic Notion (Twice Over) 7.1 Observational equivalence and metaphysics 7.2 The Occamist norm revisted 7.3 Consequences8 Conclusion