There is no logic here either: meaning is not compositional! (Was: Chicken and egg, with curry?)

On 03/01/2025 21:04, Julio Di Egidio wrote:

Partial and tentative:
 ```
   Functional = Closures/applications, Reduction/canonicity
     /    |
Logical  |   = Predicates/queries, Resolution/subsumption
     \    |
   Imperative = Procedures/invocations, Execution/...
```
 And there are two views of that triangle: Logical is the top of the *ideal* such triangle, along the lines of a universe with Prop on top, which we can reason with; Imperative is the bottom of a *concrete* such triangle, the bootstrap as well as the final point of application of any concrete system.
 And Logical is the constructive (structural) type-theory founding the Functional, where Functional exists for expressivity and modularity (what else?), plus can be compiled back/down to machine language...
 Right?

No: and I won't repeat the whole Aristotle-up-to-1994 story, but once
upon a time we had vocabularies vs dictionaries (we kids were simply
explained that the latter are "sort of" a simplification of the former):
today we only have dictionaries...  The point here being:
A word is not a locution (not an idiom), and a dictionary is not an
encyclopedia: that is, *meaning is not compositional*!  Contrast with
the by now ubiquitous paradigm of compositionality from a foundation,
i.e. bottom-up from some fixed ground, with closure in category theory,
the other side of the same coin: and in spite of decades of warnings
from actual linguists, not to even mention the philosophers: indeed,
from that point of view, what I am saying is pretty basic.
But, preparing for my Nobel article, I have spent a week now looking for
"something else" in the mathematical and mathematico-logical literature,
namely, a genuine mathematisation, if not formalisation, of some notion
of "encyclopedic compendium" ("floating co-definitions"?), and I just
cannot yet find or see any of it... can you?
Ah, the good old Leibniz and what a Monad actually is, or a
Characteristica Universalis.  Or, a seed and the plant...
"It's a long way, back to where we were."
-Julio