Dear Lev,
thanks for your comments. I am impressed by your framework and its rigorousity.
By contemplating the meaning of the term "information", it became clear, at least for me, that it has a very close relation to the term "definition". Information in my view is a *specific*, well-*defined* perspective of at least "interaction" (and maybe also of evaluation [and therefore "meaning" too]).
The most *specific* perspective that we know could be that of living beings, in the sense of qualia (meaning: *how* it is to perceive the color blue, red, green etc. or hear a sound out of a first-person-perspective).
This "how", which is related to our qualia, isn't describable mathematically in a numeric manner (in my opinion). But nonetheless it could be understood by some non-numerical framework like yours. Maybe it could be some day not only understood, but also be describable in a non-numeric framework. Your framework implies that one can't prove mathematically that there are certain things that aren't describable mathematically in the old-fashioned way (means in an objective manner). To be able to although re-present them, you must describe these *specific* things in another way to make obvious that there exist specific things as well as common properties of these specific things, that aren't describable mathematically. A hard task in my opinion but a promising, too, for the following reasons:
1. Presupposing "events" automatically inserts dynamics into a description and is in accordance with our perception of a dynamical universe.
2. Presupposing "classes" automatically inserts structure into a description and is in accordance with our perception of physical and mental structures.
3. Presupposing "classes" to have "common" formative, or generative history solves the puzzle of Gödel's undecidability-theorem, because the latter becomes *relative* and therefore relatively irrelevant for a certain *specific* perspective.
4. Presupposing "classes" that have "common" formative, or generative history also solves Bertrand Russell's famous antinomy of the set of all sets that do not contain themselves. Because the main *property* of a set that does not contain itself is the fact that it does not contain infinitely many times infinitely many objects. The latter would be the case if a set would contain itself as an element. Because that set would contain itself again as an element and so on. So, the formative criterion for the solution of this puzzle is to see that it differenciates between the finiteness of identity and the infiniteness of differences. And therefore Russell's set of all sets doesn't contain itself. It has to obey the structural rules that are valid for its own elements, namely not to contain infinitely many times infinitely many objects.
5. Presupposing "events" can only be more than an empty intellectual concept if they potentially could be experienced by "someone/something" without altering them (but altering the observer) or if the experiencer of the event is a specific part of the event. Otherwise the very notion of an event would be a meaningless term right from the start for human beings, because presupposing something that has no consequences for an observer and his observations can hardly have provable, or at least, can hardly have obvious consequences.
