Well, you rose to the challenge, so I should respond in an appropriate way (defined by the ends of educating and learning). The answer to the chronologically first question ought to simplify the matter. How is it possible to encode a description of an event in multiple ways? A possibly less interesting answer is that (in your way of thinking of events) sentences does not just describe events, they also describe the nature of existents (presumably) relevant to the event. There are many facts about cats, tables and actions which could be mentioned in the description, but are not. Maybe you are required to provide such information, maybe not. Maybe that decision is elevated to the status of grammar, maybe that is merely social convention that people rarely violate. The second answer is that descriptions of states via natural language is conventional, not natural, and languages differ in those conventions. For example, English has requirements for using determiners that are not part of Russian grammar.
I accept the cognitive premise the “simpler” structure is a desideratum, and that we ought to use logic to live our lives. Simplicity is meaningless in a vacuum, it is only useful as a comparative tool – use the simplest means possible to achieve an end. The measure of simplicity is, what…? Shortness. Of what? It could be process (involves fewer steps); it could be physical output (measured how?). Anyhow, we have rules of language.
I’m afraid that I was not able to comprehend a lot of the things you said. I don’t know what you mean by “real things” versus “non real things”. If it's not real, it's not a thing. Are you talking about physically tangible objects versus mental representations (which may have only a remote relation to a tangible object). If so, in what way is it “ugly” that there is a relationship between actual cats and tables, versus mental representations of cats and tables? On the contrary, I would say it would be very ugly if there were no such relationship. At any rate, I think you are saying that there are numerous ways of classifying existents, and since linguistic structure exist, they too can be classified. Hence we have facts (in some languages) that we subsume under the notion “case”, also “preposition”, “tense”, “aspect” and so on.
Let’s move to the bottom now. I disagree with your goals / points / claims, and here is why.
1. Main idea of the "paper" is to guess right Basic Terms and then Initial axioms
It’s good to lead with something foundational: I think your foundation is wrong. First, the goal is never to “guess”, it is to conclude, based on what? Logic and that which is undeniable, the facts. What things are properly “axiomatic”? Contrary to much theoretical reasoning of the modern world, axioms are not arbitrary stipulated statements, they are statements (or statement-like things) that cannot reasonably be denied. Your experience of seeing a cat on the table is axiomatic. Basically, low-level perception is axiomatic. Based on perceptions, you can derive valid conclusions.
However, theorists do tend to jump the gun and just make statements that we like for some reason, without bothering with a rigorous program of logical reduction. In my opinion, the most sensible approach to dealing with the superfluous plethora of technical concepts and the serious lack of logical analysis of how concepts relate to each other is, simply, to try to identify the empirically best-motivated linguistic concepts, and then engage in the enterprise of organizing them into a self-contained hierarchical system. For example, “case” seems to be a valid linguistic concept. But how is “case” different from certain other concept that are somewhat similar (for example “preposition” or “plural”)? “Plural” might have in common that it is realized as an affix on a noun, but then so is “definite” (not in English, but in many languages). Eventually, you will find that “case” is not a “basic term”, instead “affix” is more basis. Or, you can focus on the semantic properties of case and (hmmmm… I am less sanguine about the prospects for a non-vacuous semantic definition of case). I think the concept is not directly about semantics, it’s about syntax, which then has some connection to semantics.
I suggest disposing of unfounded speculations, and replacing them with considered evaluations of facts. Let’s pick on case. Assemble basic reference material on “case” in as many languages as you can. At the minimum, you should look at something Slavic, at least two Finno-Ugric languages, Mongolian, Quechuan, Japanese, Mandarin, Inuit, Nez Perce, something Algonkian, a couple of Austronesian languages, a couple of Niger-Congo languages, something Nilotic and a Dravidian language. Do you find a “diminutive” case, or a “possessive” case? If not, why not? What other facts about case seem to be true, and what distinguishes case from other similar things?
