John,
Responding to your reply: It's worth discussing such a powerful abstraction as "continuous infinity" someday, although some consider it a contradiction in terms: continuity, being a whole, is only potentially infinite. For example, one can think about it infinitely.
BFO has a continuant. And here's the topic for which I cite EZ's work as a benchmark for theory of abstract objects with thorough formalization:
What if we look for Basic Formal Theory in BFO? Top Level Theory in TLO? Business Object Theory in BORO? etc. Or even Distributed Theory Language (aka Distributed Theory, Modeling, and Specification Language)?
Is there any intersection with the Principia of EZ?
Alex