On the logic of "it" - Sparse (hopefully-)not-so-metaphysical thoughts
The idea of a Characteristica Universalis, i.e. an encyclopedic compendium of acquired knowledge in terms of a universal formal language that is potentially able to express all understanding, becomes in our times the inverse idea that language encapsulates all there is to understanding (whence in particular the idea/hope that so called Large Language Models are "a solution to problems").
But the simplest formalization exercise indicates that between language and understanding (or, language and "reality") there is an essential gap that only imagination can fill.
What does this expression mean: `fun x y => x + y` ?
What does this expression mean: `a^${h} <>~ T` ?
What does this expression mean: `2` ?
Sure, we might explain each of those, but, as long as the explanation is itself formal, we'd still need to find the bottom of it (what does "it" mean?). Eventually, the problem of meaning remains at the level of our formal primitives.
And that is properly our symbolic level, the one that simply "cannot and will not be explained". I.e. not any more than its own shape is its own diagram (or that "(its) nature is its own explanation"): ultimately, the idea/hope being, we cannot explain it but we can understand it to the point of naming it.
Incidentally, a principle is "let code speak for itself", which entails that our formal language should be as readable as natural language, just without the ambiguities, as the formal aspect exactly takes care that code cannot lie about itself (about its assumptions as well as derivations).
That much for a concrete convergence of formal and symbolic logic. Indeed, I'd propose Leibniz's formal-encyclopedic project is by now feasible, with applications potentially up to the legal context.
However, and precisely for concreteness, I think we cannot get away with it unless under a (trustless, surely) contract, where "it" takes the form of a (collaborative, hopefully) game-theoretic protocol, for "the acquisition, revision, consolidation and exercise of mutually informed and formally verified knowledge".
