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From: Julio Di Egidio <julio@diegidio.name>
Newsgroups: sci.logic
Subject: There is no logic here either: meaning is not compositional! (Was:
 Chicken and egg, with curry?)
Date: Thu, 3 Apr 2025 13:34:51 +0200
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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