Reading through it now. It was unsatisfying until I found “Multiple range” theory.
It’s compatible with my computational-thinking and can encompass any of the other theories within it, if needed.
I can work it on an Excel spreadsheet, which I once finally discovered can be accurately described as:
“Step-indexed Kripke models over recursive worlds.”
“non-monotonic dataflow programming, concurrent logic programming”.
So while it may not be “satisfying” (pun) for many, it’s effective.
You’re welcome. It was a good challenge. My bias is this:
I believe every paradox has a solution. It may not be fully satisfying to the “game of logic” as it were, but it will work and work effectively and repeatedly.
Absolutely. We already do. I see Incompleteness as a necessary part of the way of things. I think the flaw in logic goes back to the problem of proper categories for proper things and such.
Ah – Umbrella Problem of Consciousness. What’s the problem of consciousness?
Ah – qualia and phenomina Nature of experience. Limitations of Set theory and also wishing to avoid excessive generalizing from specifics.
Humans have the ability to modify language in many ways that aren’t always written down. I think in our quests for simplification (looking for elegant theories), we can accidentally scrap what turns out to be important.
Common example is “tone of voice”. If you don’t factor that in during a communication session, you can end up with erroneous conclusions; that is, what you _believe_ is vague turns out to be quite specific _but only if_ you took into account enough social cues.
Language expressiveness is complex but I don’t think it’s infinitely complex.
Michael Halliday’s Systemic Functional Grammar can be indispensable here. It is not a mathematical solution but rather is based upon the logic built-in to language itself.
Searching for a mathematical solution or philosophical solution to a grammatical problem (not semantics, as grammar is prior to the semantics stage and is fundamental to the functioning of language) may be part of this difficulty.
“For Halliday, grammar is described as systems not as rules, on the basis that every grammatical structure involves a choice from a describable set of options. Language is thus a meaning potential. Grammarians in SF tradition use system networks to map the available options in a language. In relation to English, for instance, Halliday has described systems such as mood, agency, theme, etc. Halliday describes grammatical systems as closed, i.e. as having a finite set of options. By contrast, lexical sets are open systems, since new words come into a language all the time”
That can be tricky. Increasing Expressiveness can be Stem Cells. But without differentiation, which decreases expressiveness, what do you have?
You have the double-edged statement made to me by teachers as a child:
“He has such great potential”.