Rüdiger Schack and Gabriele Carcassi on The Character of Physical Law

11:10 on Frequencies and Repeated Trials. Gabriele Carcasssi just posted another essay: Ensembles all the way down. See also Quantum de Finetti Theorems as Categorical Limits, and Limits of State Spaces of C*-algebras by Sam Staton and Ned Summers:

De Finetti theorems tell us that if we expect the likelihood of outcomes to be independent of their order, then these sequences of outcomes could be equivalently generated by drawing an experiment at random from a distribution, and repeating it over and over. In particular, the quantum de Finetti theorem says that exchangeable sequences of quantum states are always represented by distributions over a single state produced over and over. The main result of this paper is that this quantum de Finetti construction has a universal property as a categorical limit. This allows us to pass canonically between categorical treatments of finite dimensional quantum theory and the infinite dimensional. ...

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I also listened to this talk on Pragmatism that Hilary Putnam gave in 2013. The pragmatists gave a definition of truth which was literally once and for all, and then hardly ever mentioned it again!


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