The ideal strategy to secure the foundations of an empirically successful theory is to provide physical postulates on which it can then be unambiguously reconstructed. Identifying such postulates, especially when one wants them to be indisputable, may however prove difficult. Such is notoriously the case of quantum mechanics. What are then the alternative strategies to provide nonetheless the theory with some kind of foundational legitimacy? When its formalism is mature enough, one can try to supplement to foundational rigor showing that the mathematical structure underlying the theory is in some sense “necessary”. To reach this aim, one puts requirements on how the physical systems or situations are to be formally handled. One attempts then to show that the formalism of the theory is a solution, hopefully unique, of the latter. To achieve the proper sense of necessity and to avoid ad hoc justification, the requirements have to be as general as possible. On the other hand, they also have to be “natural” and no wonder that eventually the frontier between physical postulates and such formal requirements gets blurred.
This strategy has been used in the various axiomatizations of quantum mechanics. The talk will examine the rise of such approaches in the history of quantum theory and the (sometimes heated) debates that the latter prompted. Special attention will be given to the rise of the so-called Geneva School.
