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charset="utf-8" Content-Transfer-Encoding: quoted-printable Another snippet. Reading up in German literature on Carnap e.g. [1,2] suggests that Carnap may have chosen the word "Funktor" to rhyme with "Junktor". Both rhyme with "Operator": a sign which allows us to derive an expression = from another expression: a Junktor (logical connective in propositional calculus) derives a proposit= ion from propositions, and a Funktor (placeholder for a function) derives a terms from terms. Kuno Lorenz, Funktor, in: J=C3=BCrgen Mittelstra=C3=9F (ed.) Enzyklop=C3=A4= die Philosophie und Wissenschaftstheorie Band 2 C=E2=80=93F-J.B. Metzler (2= 005) ibid., Operator, in: J=C3=BCrgen Mittelstra=C3=9F (ed.) Enzyklop=C3=A4die P= hilosophie und Wissenschaftstheorie Band 6 O=E2=80=93Ra-J.B. Metzler (2016) This is consistent with Haskell Curry's "Foundations of Mathematical Logic"= : "There are three main classes of phrases, viz., nouns, sentences, and funct= ors. A noun names some object (real or imaginary); a sentence expresses a statement; and a functor is a means of combining phrases to form other phrases." (p. 32) Generally, the movement from (Opera-)tion to (Opera-)tor is one towards hig= her-order-(opera-)tions, in linguistics, logic and mathematics. A hidden issue is whether higher order means logical/analytic or not =E2=80= =93 this might relate to the argument MacLane makes about Carnap. It is worth quoting the full footnote by Ralf Kro=CC=88mer in Tool and Obje= ct (p.59) that you refer to writes that Mac Lane "purloined" the word ("It = seemed in order to take over that word for a better and less philosophical = purpose.", Mac Lane, The Development and Prospects for Category Theory, p. = 131) "It was Mac Lane who reviewed the English translation of Carnap=E2=80=99s L= ogische Syntax der Sprache in the Bulletin of the AMS (1938); he mentions t= here that (and how) Carnap employs the term. In [1996, 131], Mac Lane write= s: =E2=80=9CCarnap [=E2=80=A6] had talked of functors in a different sense = and made some corresponding mistakes. It seemed in order to take over that = word for a better and less philosophical purpose=E2=80=9D. This somewhat ar= rogant account obscures the fact that Carnap=E2=80=99s terminology has alwa= ys since been widely employed in logical analysis of language. Steve Awodey= at a 2005 Paris meeting on history of category theory (entitled =E2=80=9CI= mpact des categories. 60 ans de the=CC=81orie des cate=CC=81gories: aspects= historiques et philosophiques=E2=80=9D, October 10=E2=80=9314, ENS, Paris)= delivered an interesting talk about the relationship between Carnap and Ma= c Lane, especially on the role of Mac Lane in Quine=E2=80=99s reception of = Carnap." Here is a link to the talk by Steve Awodey: https://youtu.be/alLgEf0uVkg?fe= ature=3Dshared&t=3D1194 As much as I can tell, the (great) talk is about Mac Lane's critique of Car= nap's analyticity (preceding Quine). For reference, the Mac Lane review of Carnap is available here: https://www= .semanticscholar.org/paper/Carnap-on-Logical-Syntax-Maclane/a5b00cabfce7c99= 8ba830a68019014bcab252baa > On 19. Feb 2024, at 16:49, Johannes Huebschmann wrote: > > Perhaps I misremember something. > I will try to check this. > Frege extensively uses the term "function". > > Originally > "functio" is a classical Latin word, derived from > the verbe " fungor, fungi" (be engaged in, perform). > > > Best > > Johannes > > > > De: "Steve Awodey" > =C3=80: "Johannes Huebschmann" > Envoy=C3=A9: Lundi 19 F=C3=A9vrier 2024 15:06:47 > Objet: Re: On the etymology of the word "functor" > > > > On Feb 19, 2024, at 05:22, Johannes Huebschmann wrote: > > Frege used the term "functor". > > Do you have a reference for this? > > 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 w= ord "functor" imported by Mac Lane in category theory from philosophy. I wo= nder if someone more experienced than me can find a better answer to this m= ystery. > > - As it is well-known, Mac Lane says in the historical notes of Chapter 1= in CWM, that the name "functor" is borrowed from Carnap's "Logische Syntax= der Sprache"; Carnap writes the book in 1934. > > In his book "Tool and object", Ralf Kr=C2=A8omer partially rectifies this= claim in that he says: " The somewhat arrogant account [of Mac Lane's revi= ew of Carnap's LSS] obscures the fact that Carnap=E2=80=99s terminology has= always since been widely employed in logical analysis of language". > > So, whence did Carnap borrow the term? Was it also a "current informal pa= rlance" [CWM, p. 30] in the logical analysis of language, as much as "natur= al transformation" was in Mathematics? (cf. again Kr=C2=A8omer, where he ma= kes 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 = structures", attributes the term to Tadeusz Kotarbi=C5=84ski, where it was = introduced in his 1929's Elementy teorji poznania -in a somewhat clumsy tra= nslation, edited in English as "Gnosiology" by O. Wojtasiewicz, and only in= 1966. It seems then reasonable that Mac Lane, not knowing Polish (or did h= e?) just wasn't aware of this much older occurrence. Curry's paper is behin= d a paywall for me, but in his 1979's book "Foundations of Mathematical Log= ic" Curry summarized some ideas from his "Logical 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 "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 "Gnosiology" (t= he original in Polish seems quite difficult to recover, but I'd happy to se= e it), they will notice that yes, the term "functor" is explained to some e= xtent in the text, but it is not introduced in proper detail, as if the con= cept was already there and Kotarbi=C5=84ski just borrowed it from someone e= lse. (Kotarbi=C5=84ski speaks of a functor as an abstract "sentential conne= ctive" at page 259, at the very start of his second chapter "The deductive = method". > "Gnosiology" comes with an appendix containing the review that Adjukiewic= z wrote on Kotarbi=C5=84ski's book; Adjukiewicz uses the word functor quite= liberally (see for example: "if that of which mathematics speaks is the ob= jective correlates of some functors occurring in mathematical theorems, cor= relates which in turn have no arguments, then mathematics speaks of numbers= , as, for example, in the arithmetical statement <<3 + 2 =3D 5>> such ultim= ate arguments are numbers, and nothing else"). There is no mention about Ko= tarbi=C5=84ski being the first to use the word, be it as formalization of 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 "func= tor" to =C5=81ukasiewicz or Le=C5=9Bniewski, but never explicitly links any= of the two to the term (I quote: p 244, "Lukasiewicz, in his system of the= sentential calculus, places the functors directly before the functions to = which they pertain" and p 403 "other logical types can be formed by sentenc= e-forming or term-forming functors of the various kinds (Lesniewski)"). I f= ind 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 ver= y beginning of "the implication and negation functors of =C5=81ukasiewicz" = referring to Rosser and Turquette's book "Many-valued logics". Unfortunatel= y, the only edition of the book I could find has zero occurrences of the wo= rd "functor". From what I can find on the internet, Le=C5=9Bniewski seems t= o widely employ the _concept_ of a functor, and he is taken as the most anc= ient philosopher doing 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 > You're receiving this message because you're a member of the Categories m= ailing list group from Macquarie University. To take part in this conversat= ion, 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 --MCBoundary=_12402200846393391 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=UTF-8 Another snippet.

Reading up in German literature on Carnap e.g. [1,2] suggests that
Carnap may have chosen the word "Funktor" to rhyme with "Jun= ktor".
Both rhyme with "Operator": a sign which allows us to derive an e= xpression from another expression:
a Junktor (logical connective in propositional calculus) derives a proposit= ion from propositions, and
a Funktor (placeholder for a function) derives a terms from terms.

Kuno Lorenz, Funktor, in: J=C3=BCrgen Mittelstra=C3=9F (ed.) Enzyklop=C3=A4= die Philosophie und Wissenschaftstheorie Band 2 C=E2=80=93F-J.B. Metzler (2= 005)
ibid., Operator, in: J=C3=BCrgen Mittelstra=C3=9F (ed.) Enzyklop=C3=A4die P= hilosophie und Wissenschaftstheorie Band 6 O=E2=80=93Ra-J.B. Metzler (2016)=

This is consistent with Haskell Curry's "Foundations of Mathematical L= ogic":

"There are three main classes of phrases, viz., nouns, sentences, and = functors.
A noun names some object (real or imaginary); a sentence expresses
a statement; and a functor is a means of combining phrases to form other phrases." (p. 32)

Generally, the movement from (Opera-)tion to (Opera-)tor is one towards hig= her-order-(opera-)tions, in linguistics, logic and mathematics.
A hidden issue is whether higher order means logical/analytic or not =E2=80= =93 this might relate to the argument MacLane makes about Carnap.

It is worth quoting the full footnote by Ralf Kro=CC=88mer in Tool and Obje= ct (p.59) that you refer to writes that Mac Lane "purloined" the = word ("It seemed in order to take over that word for a better and less= philosophical purpose.", Mac Lane, The Development and Prospects for Category Theory, p. 131)

"It was Mac Lane who reviewed the English translation of Carnap=E2=80= =99s Logische Syntax der Sprache in the Bulletin of the AMS (1938); he ment= ions there that (and how) Carnap employs the term. In [1996, 131], Mac Lane= writes: =E2=80=9CCarnap [=E2=80=A6] had talked of functors in a different sense and made some corresponding mistakes. It seemed in order= to take over that word for a better and less philosophical purpose=E2=80= =9D. This somewhat arrogant account obscures the fact that Carnap=E2=80=99s= terminology has always since been widely employed in logical analysis of language. Steve Awodey at a 2005 Paris meeting on h= istory of category theory (entitled =E2=80=9CImpact des categories. 60 ans = de the=CC=81orie des cate=CC=81gories: aspects historiques et philosophique= s=E2=80=9D, October 10=E2=80=9314, ENS, Paris) delivered an interesting talk about the relationship between Carnap and Mac Lane, especially on the= role of Mac Lane in Quine=E2=80=99s reception of Carnap."


Here is a link to the talk by Steve Awodey: https://youtu.be/alLgEf0uVkg?feature=3Dshared&t=3D1194
As much as I can tell, the (great) talk is about Mac Lane's critique of Car= nap's analyticity (preceding Quine).
For reference, the Mac Lane review of Carnap is available here: https://www.semanticscholar.org/paper/Carnap-on-Logical-Syntax-Maclane/a5b0= 0cabfce7c998ba830a68019014bcab252baa


> On 19. Feb 2024, at 16:49, Johannes Huebschmann <johannes.huebschma= nn@univ-lille.fr> wrote:
>
> Perhaps I misremember something.
> I will try to check this.
> Frege extensively uses the term "function".
>
> Originally
> "functio" is a classical Latin word, derived from
> the verbe " fungor, fungi" (be engaged in, perform).
>
>
> Best
>
> Johannes
>
>
>
> De: "Steve Awodey" <awodey@cmu.edu>
> =C3=80: "Johannes Huebschmann" <johannes.huebschmann@univ= -lille.fr>
> Envoy=C3=A9: Lundi 19 F=C3=A9vrier 2024 15:06:47
> Objet: Re: On the etymology of the word "functor"
>
>
>
> On Feb 19, 2024, at 05:22, Johannes Huebschmann <johannes.huebschma= nn@univ-lille.fr> wrote:
>
> Frege used the term "functor".
>
> Do you have a reference for this?
>
> 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 th= e word "functor" imported by Mac Lane in category theory from phi= losophy. I wonder if someone more experienced than me can find a better ans= wer 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 language".
>
> 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 somewh= at clumsy translation, edited in English as "Gnosiology" by O. Wojtasiewicz, and only in 1966. It seems then reasonable that Mac La= ne, not knowing Polish (or did he?) just wasn't aware of this much older oc= currence. 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 where Curry introduces the toy language of sz=C3=A1m, tet=C3=A9l and= tant=C3=A9t), and the word "functor" itself occurs multiple time= s 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 Kotar= bi=C5=84ski just borrowed it from someone else. (Kotarbi=C5=84ski speaks of= a functor as an abstract "sentential connective" 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 mathematic= s speaks is the objective correlates of some functors occurring in mathematical theorems, correlates which in turn have no arguments, then= mathematics speaks of numbers, as, for example, in the arithmetical statem= ent <<3 + 2 =3D 5>> such ultimate arguments are numbers, and no= thing else"). There is no mention about Kotarbi=C5=84ski being the first to use the word, be it as formalization of 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 m= ore.
>
> 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 explici= tly links any of the two to the term (I quote: p 244, "Lukasiewicz, 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 ver= y beginning of "the implication and negation functors of =C5=81ukasiew= icz" referring 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 ancient philosopher doing 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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