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charset="utf-8" Content-Transfer-Encoding: quoted-printable Interesting, do you have a reference for Frege's usage of the word (and his= definition, if any)? "Perhaps it then was lingua franca in philosophy circles." I am starting to believe that, yes. Il giorno lun 19 feb 2024 alle ore 10:32 Johannes Huebschmann > ha scrit= to: Frege used the term "functor". Perhaps it then was lingua franca in philosophy circles. Also we should be aware of the notion of function being a recent idea (Euler ...). Best Johannes ________________________________ De: "Fosco Loregian" > =C3=80: "categories" > Envoy=C3=A9: Samedi 17 F=C3=A9vrier 2024 13:09:21 Objet: On the etymology of the word "functor" It seems surprisingly difficult to trace back the precise origin of the wor= d "functor" imported by Mac Lane in category theory from philosophy. I wond= er if someone more experienced than me can find a better answer to this mys= tery. - As it is well-known, Mac Lane says in the historical notes of Chapter 1 i= n CWM, that the name "functor" is borrowed from Carnap's "Logische Syntax d= er Sprache"; Carnap writes the book in 1934. In his book "Tool and object", Ralf Kr=C2=A8omer partially rectifies this c= laim in that he says: " The somewhat arrogant account [of Mac Lane's review= of Carnap's LSS] obscures the fact that Carnap=E2=80=99s terminology has a= lways since been widely employed in logical analysis of language". So, whence did Carnap borrow the term? Was it also a "current informal parl= ance" [CWM, p. 30] in the logical analysis of language, as much as "natural= transformation" was in Mathematics? (cf. again Kr=C2=A8omer, where he make= s a good point of how the term was employed by Lefschetz and Hurewicz). It seems that Haskell Curry, in his "Some logical aspects of grammatical st= ructures", attributes the term to Tadeusz Kotarbi=C5=84ski, where it was in= troduced in his 1929's Elementy teorji poznania -in a somewhat clumsy trans= lation, edited in English as "Gnosiology" by O. Wojtasiewicz, and only in 1= 966. It seems then reasonable that Mac Lane, not knowing Polish (or did he?= ) just wasn't aware of this much older occurrence. Curry's paper is behind = a paywall for me, but in his 1979's book "Foundations of Mathematical Logic= " Curry summarized some ideas from his "Logical aspects" (it's the paper wh= ere Curry introduces the toy language of sz=C3=A1m, tet=C3=A9l and tant=C3= =A9t), and the word "functor" itself occurs multiple times in the latter bo= ok, with no particular introduction -reasonable, in 1979. Too bad that, if one is stubborn enough to find a copy of "Gnosiology" (the= original in Polish seems quite difficult to recover, but I'd happy to see = it), they will notice that yes, the term "functor" is explained to some ext= ent in the text, but it is not introduced in proper detail, as if the conce= pt was already there and Kotarbi=C5=84ski just borrowed it from someone els= e. (Kotarbi=C5=84ski speaks of a functor as an abstract "sentential connect= ive" at page 259, at the very start of his second chapter "The deductive me= thod". "Gnosiology" comes with an appendix containing the review that Adjukiewicz = wrote on Kotarbi=C5=84ski's book; Adjukiewicz uses the word functor quite l= iberally (see for example: "if that of which mathematics speaks is the obje= ctive correlates of some functors occurring in mathematical theorems, corre= lates which in turn have no arguments, then mathematics speaks of numbers, = as, for example, in the arithmetical statement <<3 + 2 =3D 5>> such ultimat= e arguments are numbers, and nothing else"). There is no mention about Kota= rbi=C5=84ski being the first to use the word, be it as formalization of a c= oncept from common parlance, or as a word coined for the first time. This is where I start getting lost, and my skills are not enough any more. Kotarbi=C5=84ski seems in fact to attribute the coinage of the word "functo= r" to =C5=81ukasiewicz or Le=C5=9Bniewski, but never explicitly links any o= f the two to the term (I quote: p 244, "Lukasiewicz, in his system of the s= entential calculus, places the functors directly before the functions to wh= ich they pertain" and p 403 "other logical types can be formed by sentence-= forming or term-forming functors of the various kinds (Lesniewski)"). I fin= d very little evidence that this attribution can be confirmed; this paper h= ttp://www.numdam.org/article/CM_1968__20__153_0.pdf talks from the very = beginning of "the implication and negation functors of =C5=81ukasiewicz" re= ferring to Rosser and Turquette's book "Many-valued logics". Unfortunately,= the only edition of the book I could find has zero occurrences of the word= "functor". From what I can find on the internet, Le=C5=9Bniewski seems to = widely employ the _concept_ of a functor, and he is taken as the most ancie= nt philosopher doing so (Le=C5=9Bniewski dies a few years after Carnap's bo= ok is published!) but there seems to be no proof that he was the first to e= mploy the _name_. I'd like to get to the end of this. Any help? Fosco You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | Learn = more about Microsoft 365 Groups You're receiving this message because you're a member of the Categories mai= ling list group from Macquarie University. To take part in this conversatio= n, reply all to this message. View group files | Leave group | = Learn more about Microsoft 365 Groups --000000000000739f720611b99316 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Interesting, do you have a reference for Frege's usage of = the word (and his definition, if any)?

"Perhaps it then was
lingua franca in philosophy circles."

I am starting to believe that, yes.



Il giorno lun 19 feb 2024 alle ore 10= :32 Johannes Huebschmann <johannes.huebschmann@univ-lille.fr> ha scritto:
Frege used the term "functor". Perhaps it then was
lingua franca in philosophy circles.
Also we should be aware of the notion of function
being a recent idea (Euler ...).

Best

Johannes



De: "Fosco Loregian" <fosco.loregian@gmail.com>
=C3=80: "categories" <categories@mq.edu.au>
Envoy=C3=A9: Samedi 17 F=C3=A9vrier 2024 13:09:21
Objet: On the etymology of the word "functor"

It seems surprisingly difficult to trace back the precise = origin of the word "functor" imported by Mac Lane in categor= y theory from philosophy. I wonder if someone more experienced than me can = find a better answer to this mystery.

- As it is well-known, Mac Lane says in the historical notes of Chapte= r 1 in CWM, that the name "functor" is borrowed from Carnap's &qu= ot;Logische Syntax der Sprache"; Carnap writes the book in 1934.

In his book "Tool and object", Ralf Kr=C2=A8omer partially r= ectifies this claim in that he says: " The somewhat arrogant account [= of Mac Lane's review of Carnap's LSS] obscures the fact that Carnap=E2=80= =99s terminology has always since been widely employed in logical analysis of languag= e". 

So, whence did Carnap borrow the term? Was it also a "current inf= ormal parlance" [CWM, p. 30] in the logical analysis of language, as m= uch as "natural transformation" was in Mathematics? (cf. again Kr= =C2=A8omer, where he makes a good point of how the term was employed by Lefschetz and Hurewicz).

It seems that Haskell Curry, in his "Some logical aspects of gram= matical structures", attributes the term to Tadeusz Kotarbi=C5=84ski, = where it was introduced in his 1929's Elementy teorji poznania -in a somewhat clumsy translation, edited in English as "Gnosiology" by O. Wojtasiewicz, and only in 1966. It se= ems then reasonable that Mac Lane, not knowing Polish (or did he?) just was= n't aware of this much older occurrence. Curry's paper is behind a paywall = for me, but in his 1979's book "Foundations of Mathematical Logic" Curry summarized some ideas from his "Logica= l aspects" (it's the paper where Curry introduces the toy language of sz=C3=A1m, tet=C3=A9l and tant=C3=A9t), and the word &= quot;functor" itself occurs multiple times in the latter book, with no= particular introduction -reasonable, in 1979.

Too bad that, if one is stubborn enough to find a copy of "Gnosio= logy" (the original in Polish seems quite difficult to recover, but I'= d happy to see it), they will notice that yes, the term "functor"= is explained to some extent in the text, but it is not introduced in proper detail, as if the concept was already= there and Kotarbi=C5=84ski just borrowed it from someone else. (Kotar= bi=C5=84ski speaks of a functor as an abstract "sentential connective&= quot; at page 259, at the very start of his second chapter "The deductive method".
"Gnosiology" comes with an appendix containing the review th= at Adjukiewicz wrote on Kotarbi=C5=84ski's book; Adjukiewicz uses the = word functor quite liberally (see for example: "if that of which mathe= matics speaks is the objective correlates of some functors occurring in mathematical theorems, correlates which in turn have no argum= ents, then mathematics speaks of numbers, as, for example, in the arithmeti= cal statement <<3 + 2 =3D 5>> such ultimate arguments are numbe= rs, and nothing else"). There is no mention about Kotarbi=C5=84ski being the first to use the word, be it as formalization o= f a concept from common parlance, or as a word coined for the first time.

This is where I start getting lost, and my skills are not enough = any more. 

Kotarbi=C5=84ski seems in fact to attribute the coinage of the word &q= uot;functor" to =C5=81ukasiewicz or Le=C5=9Bniewski, but never ex= plicitly links any of the two to the term (I quote: p 244, "Lukasiewic= z, in his system of the sentential calculus, places the functors directly before the functions to which they pertain" and p 403 "other log= ical types can be formed by sentence-forming or term-forming functors of th= e various kinds (Lesniewski)"). I find very little evidence that this = attribution can be confirmed; this paper http://www.numdam.org/article/CM_1968__20__153_0.pdf talks from the very beginning of "the implication and negation functo= rs of =C5=81ukasiewicz" referring to Rosser and Turquette's book "= ;Many-valued logics". Unfortunately, the only edition of the book I co= uld find has zero occurrences of the word "functor". From what I can find on the internet, Le=C5=9Bniewski seems to widely employ th= e _concept_ of a functor, and he is taken as the most ancient philosopher d= oing so (Le=C5=9Bniewski dies a few years after Carnap's book is published!= ) but there seems to be no proof that he was the first to employ the _name_.

I'd like to get to the end of this. Any help?



Fosco
 
 
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