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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeAug 15th 2015

    I added a hatnote to syntactic category remarking on an alternative usage of the phrase.

  1. I added a link to categorial grammar since that is related to the usage you are talking about.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeAug 19th 2015

    It doesn’t look related…

  2. The “categorial” in categorial grammar refers to grouping of syntactic expressions into “syntactic categories”, with the primary example in that context being the classification of natural language expressions into noun phrases, verb phrases, etc. I think this falls under the usage you were referring to [if I am not misinterpreting?]

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeAug 20th 2015

    I thought it referred to category theory; there is a lot of mention of lambda-calculus and Lambek used to speak at category theory conferences. Are you sure?

  3. I also understand the term “categorial grammar” in the way Colin describes, as a formalism for organizing different syntactic categories in natural language (and a very interesting one which, by the way, is very much in the spirit of logical frameworks). The Wikipedia article is not exhaustive on history, but it does mention that categorial grammar predates Lambek’s introduction of the “syntactic calculus”, going back to Ajdukiewicz (1935) and Bar-Hillel (1953). Ajdukiewicz’s article is here in the original German and here in translation. I think there is some lucky overloading going on: Adjukiewicz even mentions “functor categories”!

  4. “Functor” has a standard (if perhaps archaic) meaning in linguistics and philosophy of language, essentially a linguistic expression which must combine with further linguistic expressions. E.g. An intransitive verb is a functor which must combine with a noun. In the context of Ajdukiewicz “functor category” would mean function type.

    • CommentRowNumber8.
    • CommentAuthorColin Zwanziger
    • CommentTimeAug 21st 2015
    • (edited Aug 21st 2015)

    It seems that usage for “functor” originates with Polish school logicians and the word was borrowed from there into category theory via Carnap:

    Now the discovery of ideas as general as these is chiefly the willingness to make a brash or speculative abstraction, in this case supported by the pleasure of purloining words from the philosophers: “Category” from Aristotle and Kant, “Functor” from Carnap (Logische Syntax der Sprache), and “natural transformation” from then current informal parlance. (Saunders Mac Lane, Categories for the Working Mathematician, 29–30).

    • CommentRowNumber9.
    • CommentAuthorMike Shulman
    • CommentTimeAug 21st 2015


    • CommentRowNumber10.
    • CommentAuthorColin Zwanziger
    • CommentTimeAug 21st 2015
    • (edited Aug 21st 2015)

    As Noam points out, the use of “category” to mean a type of syntactic expressions in the context of something recognizable as categorial grammar dates at least to Ajdukiewicz in the 1930’s.

    You can make a syntactic category in the sense of the nlab from a categorial grammar, however. E.g. A Lambek categorial grammar generates a biclosed monoidal category.

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