The thing about Shannon entropy is that it depends upon alphabets and symbol systems. I want to understand how it might be used to describe presymbolic computational systems.
What is a presymbolic computational system? Shannon entropy deals with alphabets in much the same capacity as Turing machines read symbols on a tape. Fundamentally it is about differentiating between states. I don't see how you can get a meaningful definition of information before starting with the notion of discrete states. Even fuzzy logic needs a semantic of states.
Presymbolic computation appears to me to be an invented term. Any theoretical or actual system can be framed in computational terms when analysed, but the properties provided through the use of symbols will still exist in a system, whether or not that analysis has been performed. The paper you cite appears to me to lean in the direction of cybernetics and control theory, that would naturally be able to translate into terms aligned to information theory. The same rules will apply to any physical system, no matter how complicated you believe it to be.
in any case, there seems to be a difference in describing a system with symbols and computational systems that use symbols for information processing. Some information processing seems possible in systems that don’t use symbols.
No, the interesting thing about Shannon entropy is that it is totally independent of how information is represented (as symbols, alphabets, numbers, structured objects, whatever).
Shannon entropy works for anything you can assign an alphabet of symbols to. It doesn't need the thing itself to be symbolic, just the description of the thing.
Maybe I’m not reading it properly, but in part 5, where he deals with transmission of continuous signals he doesn’t use his entropy formulation. He uses a distance metric, showing the difference between the sent signal and the received.