Unpacking “For Reasons of Symmetry”: Two Categories of Symmetry Arguments

Abstract

Hermann Weyl succeeded in presenting a consistent overarching analysis that accounts for symmetry in (1) material artifacts, (2) natural phenomena, and (3) physical theories. Weyl showed that group theory is the underlying mathematical structure for symmetry in all three domains. But in this study Weyl did not include appeals to symmetry arguments which, for example, Einstein expressed as “for reasons of symmetry” (wegen der Symmetrie; aus Symmetriegründen). An argument typically takes the form of a set of premises and rules of inference that lead to a conclusion. Symmetry may enter an argument both in the premises and the rules of inference, and the resulting conclusion may also exhibit symmetrical properties. Taking our cue from Pierre Curie, we distinguish two categories of symmetry arguments, axiomatic and heuristic; they will be defined and then illustrated by historical cases.

What Keeps the Earth in Its Place? The Concept of Stability in Plato and Aristotle

“…This received view, with which Brading and Castellani concur, underlies interpretations of certain Greek texts and affects their translations. Given the historical fact that symmetry arguments are based on the modern concept of symmetry, which is essentially a 19th‐century development, we do not accept the received view that there are symmetry arguments in antiquity (see Hon and Goldstein, 2006, pp. 426–429).…”

“…He then links this principle with symmetry considerations, a move which Leibniz did not take for the simple reason that the concept of symmetry, as we know it today, was not available to him (see, e.g. Hon and Goldstein, 2006, pp. 426–427; cf.…”

“…Moreover, Sambursky identifies the condition of homoiotes (equability) with a state of indifference. Symmetry considerations, however, do not underpin the principle of sufficient reason, which requires an agent, unlike the concept of indifference (see Hon and Goldstein, 2006, pp. 426–428).…”

“…By symmetry argument we mean that symmetry may enter any or all of the three components that comprise an argument. Typically, a symmetry argument has premises that refer to symmetrical properties whose consequences with respect to some structure can be seen in the conclusion of the argument mediated by a rule of inference (for a discussion of symmetry arguments, see Hon and Goldstein, 2006; cf. van Fraassen, 1989, p. 233).…”