Hermann Weyl and “First Philosophy”: Constituting Gauge Invariance

Abstract

The current vogue of naturalism – whether of a pragmatist, instrumentalist or realist variety – in philosophy of physics is largely attributable to a fiction promulgated by logical empiricism, but surviving the latter's demise. It states that relatively theory (especially general relativity) comprised a decisive refutation of Kant, and transcendental idealism more broadly. A closer look at the early years of general relativity reveals a considerably different picture. Here we trace how transcendental idealism informed Weyl's construction of a “purely infinitesimal geometry” whose additional (gauge) degrees of freedom enabled incorporation of electromagnetism into the spacetime metric.