Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail From: Julio Di Egidio 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 Organization: A noiseless patient Spider Lines: 49 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Thu, 03 Apr 2025 13:34:51 +0200 (CEST) Injection-Info: dont-email.me; posting-host="435e7dcc327492c4c74bebdda770ee53"; logging-data="329901"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/NvPvNlAYzf/LZvVW3/Rk65zPD52GHLeU=" User-Agent: Mozilla Thunderbird Cancel-Lock: sha1:jbOMD852SREHRypbaz4hzD7QI1w= In-Reply-To: Content-Language: en-GB, it 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