
Linguistics Using Category Theory (2018) - jesuslop
https://golem.ph.utexas.edu/category/2018/02/linguistics_using_category_the.html
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willis936
Even if a mathematical definition of a sandwich is presented, it is very
unlikely to have majority support in localities of any size (down to two
individuals).

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rgoulter
In your particular example, I like the cube rule (e.g. to answer 'is a hotdog
a sandwich?')

EDIT: [http://cuberule.com/](http://cuberule.com/)

~~~
willis936
Then subs are tacos and not sandwiches? I would disagree.

The definition I like for sandwich is “A set of materials in the configuration
ABA, mated along their longest side”. It holds up in contexts outside of food,
that the word “sandwich” is sometimes used in, and is valid in
dimensionalities other than 3.

The sub issue remains though. Semantically, it could be argued that subs are
sandwiches that have not had their end fully cut.

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crimsonalucard
I'm starting to study category theory and I'm realizing if there exists a
formal theory around 'design' and 'abstraction' category theory is it.

I could be wrong though. What do you guys think?

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codekilla
Jean-Pierre Marquis, in his contribution to the volume "What is Category
Theory", wrote: 'Category theory is the Architectronic of Concepts'.

I think this is the best way I have heard it put.

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notfashion
Here's the quote:

"Once category _theory_ was developed and used, in particular when the central
theoretical role played by adjoint functors was understood, a fascinating
process of reversal of perspective, a gestalt switch, took place: what was
seem as a useful tool in organizing and guiding mathematical thought became a
theoretical framework that revealed the basic or fundamental principles
underlying mathematical concepts, theories and theorems. Thus, the Stone
duality theorem is indeed more perspicuously presented in the context of
categories and functors—it is organized nearly and the basic consequences of
the result are transparent—but once it is seen as a special case of a very
general adjoint situation, a _theoretical_ understanding of the phenomenon
becomes available. Category theory is not _applied_ to Stone's theorem, it is
the latter that becomes a specific instance of a general, universal conceptual
situation.

Although it might in the end be more obscure than what I have said so far, I
dare at this stage put forward a slogan that, I believe, sums up the core of
what I have been presenting: _category theory is the architectonic of
mathematics_. Category theory is, indeed, as in the philosophical sense of the
expression "architectonic", the systematization of mathematical knowledge.
Mathematical knowledge _is_ systematic. Mathematics _is_ a conceptual system.
That much is indubitable."

Note that it's -tectonic (from the Greek for carpenter) not -ectronic (from
electron). And it's just "the architectonic of mathematics", not concepts in
general. There are obviously architectonics of other things as well, like
(spatial) architecture itself, or music, or cooking. So while perhaps CT is
the ultimate theory of algebraic abstractions, but it's not the only kind of
design system that exists. It represents the mathematical aspect of design.

~~~
codekilla
No, in the article I'm referencing he goes further, to concepts. It's here:
[https://www.amazon.com/What-Category-Theory-Giandomenico-
Sic...](https://www.amazon.com/What-Category-Theory-Giandomenico-
Sica/dp/8876990313)

I had confused in my mind -tectonic with a phrase from another book I admire:
[https://www.amazon.com/Between-Two-Ages-Americas-
Technetroni...](https://www.amazon.com/Between-Two-Ages-Americas-
Technetronic/dp/0313234981). I guess that's what I get for not double-
checking; and you get a random book link :)

~~~
notfashion
Yes, I did (later on) see his "stretch" version of the slogan at the end of
the article, but I don't buy it. Everyone knows there are operations that
can't be encoded in category theoretic terms, for example a lot of things in
analysis. It's silly to claim that it subsumes all concepts.

He also alludes in that final paragraph to Kant (who used the term
architectonic in his philosophy) so that's a hint that he has a Kantian
perspective in mind. IMO that makes that final paragraph too speculative and
frankly just out of scope if we're trying to talk about the design of
software. I know a bit about Kant, and it seems to me that he doesn't really
have anything to say about what a theory of the design of abstractions would
look like. It's all too much of a stretch. Combining philosophers and category
theory (take Zalamea for example) seems to produce "architecture astronauts,".

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WaxProlix
Chris Barker of NYU does a lot of category theory and linguistics work. I
remember a colloquium or two which did good work in talking about modeling
certain semantic structures in monad terms.

I remember it because at the time I liked the idea of keeping a monadically
updated 'context' node (at or above C) in an otherwise fairly orthodox
Chomskyan x-bar framework to start modeling the syntax-semantics interface,
but never really pursued linguistics as the money was just so bad.

Good times, formal linguistics could use some of the rigor and computational
methods that computer science has offered for a few decades.

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jesuslop
That colloquium looked nice, I assume no slides are available? Barker is
anouncing another seminar on deep learning and semantics, that looks
intriguing from the attached public materials. I think that compsci furnishes
ideas from formal language parsing that can be toy models of fragments of
natural languages, Montague made a case in favour of formalizability. Wadler
investigated monadic parsing and this can be an entry point for what is
happening in linguistics. I have as reference arXiv:cs/0205026v1

added: on Barker seminar day 4 I see CCG derivations that are a close
formalism of pregroup grammars used in the original post, nice to see this
concurrently with nnets talk.

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haxterstockman
A post on Category Theory from UT that doesn't mention Steedman or Baldridge?!

