Brian,
1) Re "You may want to postulate that this can all be explained in terms of algorithmic logic, etc. but it is unclear that this is enough. Indeed, it is unclear even whether mathematical proofs can be understood thus" i.e. Re creative leaps:
I never meant to imply that all aspects of outcomes can be logically explained in terms of algorithmic logic or mathematics. What I'm getting at is that all outcomes involve some aspects that are "creative leaps"; and that these creative leaps can't be represented as logical consequences of a complex mathematical/algorithmic system.
I would argue that it is these creative leaps that are driving the system forward to new outcomes, where the outcome is thought of as being representable by a set of numbers associated with fundamental variables, and where at least one of these numbers is due to a creative leap (i.e. not due to logical consequence). The creative leap itself can't be represented, but the outcome can be represented, and a "creative leap" outcome can be thought of as the assignment of a new number to a variable.
2) Re "language"/ perception:
One can never avoid using symbolic representations when trying to characterise something about the (e.g. fundamental) nature of the universe; and when forming conclusions about the (e.g. fundamental) nature of the universe from these symbolic representations.
The representations are usually mathematical, not "language". One can look at complex dynamic systems that might seem to evolve in time from the mathematical representations; or one can look at the mathematical representations themselves, and say that underlying every such representation there are categories, and relationships between such categories; and that therefore there is something fundamental about categories and relationships. I would argue that the fundamentals of perception are categories and relationships.