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MrMind comments on Open Thread, November 15-22, 2013 - Less Wrong Discussion
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Because then any model of the full quantum category would describe the same reality: instead of the infinite-dimensional Hilbert space you could just choose say a much looser ontology with sets and relations between them (as in Spekken's toy model of quantum physics).
This arbitrariness would undermine the raison d'etre of the present model.