FOM: Functions before sets

[Moshe' Machover]

Randall Holmes writes:

> On a more general topic, the use of "function" as the primary
> foundational notion instead of "set" is not especially difficult (and
> is not a monopoly of category theory).  It is easier to explain sets
> as functions than it is to explain functions as sets ...

I agree.

>  A theory like ZFC in which sets could be interpreted as
> characteristic functions is certainly possible, but I'm not aware of a
> formal presentation of such a theory.

How about von Neumann's *An axiomatization of set theory*, 1925? I am
rather surprised that Holmes as well as others who have posted messages on
the set/function priority issue have ignored this well-known contribution
to se theory.

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