French fluency is neither necessary nor sufficient for understanding EGA.
There’s a certain sense in which understanding a particular French “dialect” (the collection of words + localized grammar + shared mental context required to make sense of EGA, the one which forms the basis for modern French algebraic geometry (?)) is a sufficient condition for understanding EGA.
There’s also a sense in which understanding this French algebro-geometric dialect is an almost necessary condition for understanding EGA past a certain point (happy to consider disputations, and perhaps the understanding one receives from the necessity condition is less directed at the concepts which the literature built off of but rather the peculiarities of Grothendieck et. al.’s mental states & historical context).
Packaging “shared mental context” with a “dialect” and subsequently claiming that understanding the “dialect” is necessary and sufficient for understanding the embedded concepts is begging the question.
It seems like there is this restricted language associated with a set of concepts, the concepts themselves can are understood in the context of the restricted language, the concepts are mostly divorced from the embedded grammar of the parent language, and we don’t have a very good way of drawing a boundary around this “restricted language.”
In a general sense, this kind of “conceptual binding” is not rigid. Strong Sapir-Whorf is incorrect, the Ghananian can learn English, I can just read Hartshorne or solely Anglophonic literature to learn algebraic geometry.
However, canonical boundaries make sense even when the the boundaries are leaky. A species is not completely closed under reproduction, however it makes sense to think of species as effectually reproductively closed. A cell wall separates a cell from its environment, even if osmosis or active transport allows for various molecules to be transported in and out.
One might expect this binding to be “stronger” when the inferential distance between the typical concepts of some reference class of language-speaker and the concepts discussed in the “dialect” to be larger.
A general description of a language used by a group of communicators is the tuple (alphabet, shared conception of grammatical rules, shared semantic conception of language atoms & combinator outputs).
However, there are natural attractors in this space. Ex. traditional dialects, modern languages. Shared conception diffs between language-speakers are significantly smaller than shared conception diffs between two different language speakers (this is by default unresolvable unless there’s some shared conception of translation, at which point they’re sort of speaking the same conceptual language?)
When talking about algebraic geometry, it feels like an English geometer and a French geometer are speaking more similar languages than a French geometer and a French cafe owner.
I want to say: “an idiolect is a natural attractor in the space of languages for a group of communicators discussing a certain set of concepts, the idioms of the idiolect are identified with the concepts discussed, and the idiolect is quasi-closed under idiomatic composition.”
Identifying shared languages as emergent coordination structures between a group of communicators feels satisfying.
However, returning to the case of algebraic geometry, it feels like I can “grok” the definitions of the structures described without understanding the embedded French grammar in EGA. Maybe the correct decomposition of a shared language is (shared idiomatic conception) + (translation interface), and we should just care about the “pre-idiolect.”
This is just a world model? Describable without reference to other communicators? Loses some aspect of “coordination”?
Maybe the pre-idiolect is s.t. n communicators can communicate idioms & their compositions with minimal description of a translation interface.
The idiom <-> concept correspondence feels correct. Like, on some level, one of the primary purposes of a grammatical structure is to take the concepts which are primarily bound to words & make sense of their composition, and lexicogenesis is a large part of language-making. But it feels like restricting to wordly atoms is too constraining and there are structural atoms that carry semantic meaning, and idiom can encompass these.
How do you reify concept-space enough to chunk it into non-overlapping parts?
I am trying to point at a superstructure and say “here is a superstructure.” I am trying to identify the superstructure by a closure criterion, and I am trying to understand what the closure criterion is. Something language-like should be identifiable this way? And the appropriate notion of closure will then let us chunk correctly?
Maybe superstructures are not generally identifiable via closure?
“Shared understanding” feels better? The point of a language is a mechanism by which communicators communicate, and it so happens that languages happen to be characterizable by some general formal propeties.
idiolects?
French fluency is neither necessary nor sufficient for understanding EGA.
There’s a certain sense in which understanding a particular French “dialect” (the collection of words + localized grammar + shared mental context required to make sense of EGA, the one which forms the basis for modern French algebraic geometry (?)) is a sufficient condition for understanding EGA.
There’s also a sense in which understanding this French algebro-geometric dialect is an almost necessary condition for understanding EGA past a certain point (happy to consider disputations, and perhaps the understanding one receives from the necessity condition is less directed at the concepts which the literature built off of but rather the peculiarities of Grothendieck et. al.’s mental states & historical context).
Packaging “shared mental context” with a “dialect” and subsequently claiming that understanding the “dialect” is necessary and sufficient for understanding the embedded concepts is begging the question.
It seems like there is this restricted language associated with a set of concepts, the concepts themselves can are understood in the context of the restricted language, the concepts are mostly divorced from the embedded grammar of the parent language, and we don’t have a very good way of drawing a boundary around this “restricted language.”
In a general sense, this kind of “conceptual binding” is not rigid. Strong Sapir-Whorf is incorrect, the Ghananian can learn English, I can just read Hartshorne or solely Anglophonic literature to learn algebraic geometry.
However, canonical boundaries make sense even when the the boundaries are leaky. A species is not completely closed under reproduction, however it makes sense to think of species as effectually reproductively closed. A cell wall separates a cell from its environment, even if osmosis or active transport allows for various molecules to be transported in and out.
One might expect this binding to be “stronger” when the inferential distance between the typical concepts of some reference class of language-speaker and the concepts discussed in the “dialect” to be larger.
A general description of a language used by a group of communicators is the tuple (alphabet, shared conception of grammatical rules, shared semantic conception of language atoms & combinator outputs).
Outside of purely formal settings, the shared conceptions of grammar & semantics will be leaky. How much can be purely recovered from shared words?
However, there are natural attractors in this space. Ex. traditional dialects, modern languages. Shared conception diffs between language-speakers are significantly smaller than shared conception diffs between two different language speakers (this is by default unresolvable unless there’s some shared conception of translation, at which point they’re sort of speaking the same conceptual language?)
When talking about algebraic geometry, it feels like an English geometer and a French geometer are speaking more similar languages than a French geometer and a French cafe owner.
I want to say: “an idiolect is a natural attractor in the space of languages for a group of communicators discussing a certain set of concepts, the idioms of the idiolect are identified with the concepts discussed, and the idiolect is quasi-closed under idiomatic composition.”
Identifying shared languages as emergent coordination structures between a group of communicators feels satisfying.
However, returning to the case of algebraic geometry, it feels like I can “grok” the definitions of the structures described without understanding the embedded French grammar in EGA. Maybe the correct decomposition of a shared language is (shared idiomatic conception) + (translation interface), and we should just care about the “pre-idiolect.”
This is just a world model? Describable without reference to other communicators? Loses some aspect of “coordination”?
Maybe the pre-idiolect is s.t. n communicators can communicate idioms & their compositions with minimal description of a translation interface.
The idiom <-> concept correspondence feels correct. Like, on some level, one of the primary purposes of a grammatical structure is to take the concepts which are primarily bound to words & make sense of their composition, and lexicogenesis is a large part of language-making. But it feels like restricting to wordly atoms is too constraining and there are structural atoms that carry semantic meaning, and idiom can encompass these.
How do you reify concept-space enough to chunk it into non-overlapping parts?
I am trying to point at a superstructure and say “here is a superstructure.” I am trying to identify the superstructure by a closure criterion, and I am trying to understand what the closure criterion is. Something language-like should be identifiable this way? And the appropriate notion of closure will then let us chunk correctly?
Maybe superstructures are not generally identifiable via closure?
The load-bearing constraint for considering species as superorganisms is a closure property. They’re not particularly well-describable by Dennett’s intentional stance.
I want to say “idiolect:species :: communicator:member-organism :: idiom:gene.”
I don’t want to identify lexemes as the atoms of a language-like-structure. Chomsky et. al.’s new mathematical merge formalism is cool but construed, and I have not seen a clean way to differentiate meaningful lexeme composition from non-meaningful lexeme composition.
“Shared understanding” feels better? The point of a language is a mechanism by which communicators communicate, and it so happens that languages happen to be characterizable by some general formal propeties.