‘Shut up and contemplate!’: Lucien Hardy׳s reasonable axioms for quantum theory

• Gives a simple, compact version of Hardy׳s reconstruction of quantum mechanics from “natural axioms”.
• Discusses the nature of Hardy׳s axioms and justifies some of them through correspondence arguments.
• Compares Hardy׳s reconstruction with earlier and later attempts of the same kind.

Since the beginning of quantum mechanics, attempts were made to derive it from simple natural axioms or assumptions. These reconstructions suffered from various defects, including the questionable naturalness or the overabundance of the axioms, the mathematical difficulty of the derivation, and the inclusion of a wider range of theories than just quantum mechanics. Recently, in 2001, Lucien Hardy propounded “five reasonable axioms” that seem to elude such criticism. The present paper purports to give a simplified version of this new foundation, to discuss Hardy׳s original version and subsequent variants by others authors, and to investigate the nature of the relevant axioms in light of their possible connection with correspondence arguments.