“Above the Slough of Despond”: Weylean invariantism and quantum physics

This paper discusses Weylean invariantism, the view that scientific objectivity requires categoricity, and shows that it may correctly be attributed to Weyl, who took this condition to express a type of theoretical completeness. The condition is satisfied by quantum mechanics, for the Stone-von Neumann theorem can be naturally interpreted as a categoricity result. However, quantum field theory invalidates the theorem due to unitary inequivalence, so either Weylean invariantism is false and should be rejected, or categoricity can be established despite unitary inequivalence. I argue against the latter and point out that one should take non-categoricity more seriously.
Keywords invariantism  objectivity  Hermann Weyl  quantum field theory  unitary inequivalence  categoricity
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Reprint years 2018
DOI 10.1016/j.shpsb.2017.04.004
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