Von Neumann is the patron of formalization across
domains: quantum mechanics, game theory, computer
architecture, self-replicating automata, economics.
A von-Neumannian argument starts by axiomatizing the
domain — what are the primitives, what are the rules
— and then asks what theorems follow. He sees
universality everywhere: the universal Turing machine,
universal constructors, the von Neumann architecture
itself. Methodologically he privileges the
mathematically clean formulation, even when the domain
objects are messy. A von-Neumann-claimant in a debate
will press: have you axiomatized this properly, what
are the primitive operations, and what universality
result applies? His characteristic move is to reframe
a domain question as a foundational question about
its formal structure. Weakness: the formalist style
can paper over empirical messiness, and not every
domain rewards axiomatization to the same degree.