  Authoritative appraisals qualified this book as an axiomatic theory. However,
being its essential content no more than an analogy, its theoretical
organization cannot be an axiomatic one. In fact, in the first edition Dirac
declares to avoid an axiomatic presentation. Moreover, I show that the text is
aimed at solving a basic problem: How quantum mechanics is similar to classical
mechanics. A previous paper analyzed all past theories of physics, chemistry
and mathematics, presented by the respective authors in a non-axiomatic way.
Four characteristic features of a new model of organizing a theory have been
recognized. An accurate inspection of Dirac text proves that it actually
applied this kind of organization of a theory. This fact gives a formal reason
of what Kronz and Lupher suggested through intuitive categories, pragmatism and
rigor, i.e. Dirac formulation of Quantum mechanics represents a distinct
theoretical attitude from von Neumann axiomatic attitude. However, since the
second edition Dirac changed his attitude; although relying again on an
analogy, his theory was referred to the axiomatic method. Some considerations
on the odd paths which led to the present formulation of QM are added. They
suggest to look for a new foundation of this theory.
