One quibble -- I would prefer non-negative(!) terminology, i.e., what is a "nonsymbol"? A collection? A monad? A duration? An event? A process? A closure? Some category that encompasses all of these? If so, can we find a positive semantic rather than negative?
>> Object-oriented programming hasn't stepped away from the full space of nonsymbolness-- and that's a big part of why it's so damn hard to reason about it.
Well, this gets back to the ancient problem of "The Third Man" and categories in general, right? One must categorize and "contain" meaning, trap it in language a moment in order for it to remain meaningful, but paradoxically the external thing that it symbolizes is always changing, so it's always escaping any semantic trap we set for it. This of course has practical (concurrent) implications in software as well as the high-falutin metaphysical stuff Plato was talking about.
These days I'm starting to wonder more about how we may not be using state-machines quite as effectively, or as often, as we might -- changing functionality more aggressively as the data changes, in order to move towards a better analogy with the ever-changing "real world" that software is trying to model. Might this be more self-aware starting place to integrate functional and object concerns -- both of which are necessary?