The object of these pages is to give a common framework for discussing
mathematics; it is not to specify a rigorous foundation (analogous to the
Zermelo-Fraenkel axiomatisation of set theory, for example). My intent is
that the concepts and denotations I introduce should be usable by contexts
building on such a foundation and, for the most
part, expressible in terms of any reasonable foundation. It is to be
expected that any such foundation shall impose some restrictions on what
entities may be entertained as values
, which shall cause some of the
entities I discuss to be inexpressible – indeed, not only expected but
hoped, as the toolkit I develop here is eminently capable of expressing
entities that, if accepted as values, would yield paradoxes. To help ensure
at least enough survives that filter to leave us with some useful mathematics,
I delineate a core of constructible
entities which, I hope, all foundations should be able to allow as
values.
My goal, in packaging the foundations, is to provide a general notation and language for the exposition, that captures the essence without the encumbrance of the pedantic details needed by any particular foundation.
Written by Eddy.