Yesterday's NY Times magazine had an article about the British experimental novelist David Mitchell. Mitchell told a story to the author of the article about how, after an event in New Zealand a woman, a medievalist there asked him if knew about the humility topos. I imagine that Mitchell came across as very humble. At any rate she went on to say, and I quote because I am not certain how to parse it, "in the medieval era humility was seen as a great virtue. The humility topos was used for those abbots...who were actually monsters of arrogance, but were always banging on about how humble they were...". The woman said to him, "Watch out for the humility topos" and then disappeared. Aside from wanting to know what was meant here, should the first quote have put humility topos in quotes, for example, I would also like to know what is the subobject classifier of the humility topos. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Michael Barr wrote in part:
Aside from wanting to know what was meant here, should the first quote have put humility topos in quotes, for example, I would also like to know what is the subobject classifier of the humility topos.
As for what is meant, these links seem to be relevant: http://en.wikipedia.org/wiki/Inventio#Topoi http://web.cn.edu/kwheeler/lit_terms_h.html#humility_topos_anchor I don't think that "humility topos" should be in quotation marks, although it looks like "topos" is supposed to be italicised (as a foreign word, always with the foregin plural "topoi"). If anybody knows an eager literary theorist, see if you can get a response to the question "What classifies parts in the humility topos?" (using the term "part" instead of "subobject" to make it more accessible). The best answer that I could get from the Internet is the 1601 Elizabethan Poor Law. But I fear that this is in too restricted a context (the subobject classifier of some slice of the humility topos). http://books.google.com/books?id=f9_a4d0j9DQC&pg=PA262&dq=classify+part+"humility+topos"%3F&ots=entEEqom3l --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
In literary criticism a "topos" is a standard method of constructing an argument, or more generally, a commonplace: http://en.wikipedia.org/wiki/Literary_topos So, from what you wrote, I guessed that the medieval "humility topos" was the commonplace that religious figures were humble. But why guess? These days one can use Google! There are lots of discussions of the humility topos: http://www.google.com/search?q=humility+topos and I see that my guess was not quite right: http://web.cn.edu/kwheeler/lit_terms_h.html Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On 6/28/2010 4:49 PM, Michael Barr wrote:
Yesterday's NY Times magazine had an article about the British experimental novelist David Mitchell. Mitchell told a story to the author of the article about how, after an event in New Zealand a woman, a medievalist there asked him if knew about the humility topos. I imagine that Mitchell came across as very humble. At any rate she went on to say, and I quote because I am not certain how to parse it, "in the medieval era humility was seen as a great virtue. The humility topos was used for those abbots...who were actually monsters of arrogance, but were always banging on about how humble they were...". The woman said to him, "Watch out for the humility topos" and then disappeared.
Being but little learned, I looked this up. Wikipedia has (under "Inventio") Topoi are categories that help delineate the relationships among ideas. Specifically, the "humility topos" is the rhetorical strategy of pretending ignorance or naivete to entertain or disarm the listener. http://web.cn.edu/kwheeler/lit_terms_h.html Identifying the subobject classifier must be left to wiser heads than my own. -Robert Dawson [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
On Tue, 29 Jun 2010, Robert J. MacG. Dawson wrote:
Identifying the subobject classifier must be left to wiser heads than my own.
A good example of the humility topos! Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
It might be fair to remember that "Topoi" is the title of 6th book or Aristotle's Organon. "On Categories" is the title of the 1st book of Organon. Both concepts were very actively used by scolastic philosophers. Maybe we are their heirs of some sort ;) It would be interesting to know about the motivations of people who introduced these terms into mathematics. I think that MacLane said at one point that there was a terminological link through Rudolf Carnap, thus through neokantians. The notion of categories plays a prominent role in Kant's first Critique. But it is even more interesting if the term topos was introduced with an intentional reference to *dialectics*, which is what that part of Organon is about. -- dusko On Jun 28, 2010, at 12:49 PM, Michael Barr wrote:
Yesterday's NY Times magazine had an article about the British experimental novelist David Mitchell. Mitchell told a story to the author of the article about how, after an event in New Zealand a woman, a medievalist there asked him if knew about the humility topos. I imagine that Mitchell came across as very humble. At any rate she went on to say, and I quote because I am not certain how to parse it, "in the medieval era humility was seen as a great virtue. The humility topos was used for those abbots...who were actually monsters of arrogance, but were always banging on about how humble they were...". The woman said to him, "Watch out for the humility topos" and then disappeared.
Aside from wanting to know what was meant here, should the first quote have put humility topos in quotes, for example, I would also like to know what is the subobject classifier of the humility topos.
Michael
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
I've assumed (and told people) that "topos" was a back-formation from "topology" - that Grothendieck's intention was to imply that toposes were the structures of which topology was truly the study. (The argument falls into two parts: (a) to carry out topology you need sheaves and not just opens, and (b) there are suitable categories of sheaves that don't arise from ordinary spaces.) Certainly it is my own intention to stress the "generalized topological space" nature of toposes; but is my assumption about Grothendieck's intention actually correct? Steve. Dusko Pavlovic wrote:
It might be fair to remember that "Topoi" is the title of 6th book or Aristotle's Organon. "On Categories" is the title of the 1st book of Organon.
Both concepts were very actively used by scolastic philosophers. Maybe we are their heirs of some sort ;)
It would be interesting to know about the motivations of people who introduced these terms into mathematics. I think that MacLane said at one point that there was a terminological link through Rudolf Carnap, thus through neokantians. The notion of categories plays a prominent role in Kant's first Critique. But it is even more interesting if the term topos was introduced with an intentional reference to *dialectics*, which is what that part of Organon is about.
-- dusko
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Grothendieck introduced the term "topos" simply out of "topology" and "topological space". we should wonder who and why introduced "topology" and "topological space". Dusko Pavlovic wrote:
It might be fair to remember that "Topoi" is the title of 6th book or Aristotle's Organon. "On Categories" is the title of the 1st book of Organon.
Both concepts were very actively used by scolastic philosophers. Maybe we are their heirs of some sort ;)
It would be interesting to know about the motivations of people who introduced these terms into mathematics. I think that MacLane said at one point that there was a terminological link through Rudolf Carnap, thus through neokantians. The notion of categories plays a prominent role in Kant's first Critique. But it is even more interesting if the term topos was introduced with an intentional reference to *dialectics*, which is what that part of Organon is about.
-- dusko
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
One would suppose that the notions of literary topos and humility topos were of ancient origin. Certainly "topos" appears in Aristotle's Rhetoric in the original Greek. However its entry into the academic lexicon as an English word relevant to rhetoric and other literary forms would seem, as far as I've been able to tell, to have occurred at some point in the 20th century. 1. Volume Ti-Tz of the OED does not contain the word "topos," nor does it appear under the entries for "humility" or "literary." (Ordinarily the OED can relied on to record just about every English word that has appeared in print prior to the 20th century.) 2. Adams Sherman Hill, Boylston Professor of Rhetoric and Oratory in Harvard University from 1876 to 1904, wrote "The Foundations of Rhetoric" in 1892 with no mention of the concept of topos as a notion in rhetoric. The Wikipedia article on Ernst Robert Curtius at http://en.wikipedia.org/wiki/Ernest_Robert_Curtius says "He is best known for his 1948 work Europäische Literatur und Lateinisches Mittelalter. It was a major study of the Medieval Latin literature and its effect on subsequent writing in modern European languages. The book was largely responsible for introducing the literary topos concept as a scholarly and critical discussion of literary commonplaces." So unless someone comes up with an earlier use, it looks like 1948 may be the date, and German the language, of the first appearance of "topos" outside the original Greek of Aristotle. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
Yes, but Aristotle was not known in Europe in the original Greek. He was known in Latin until well after the Renaissance, and in vernacular languages taking their terms from Latin in recent centuries. The Online Etymolgical Dictionary gives for English: Topics: 1634, "argument suitable for debate," singular form of "Topics" (1568), the name of a work by Aristotle on logical and rhetorical generalities, from L. Topica, from Gk. Ta Topika, lit. "matters concerning topoi," from topoi "commonplaces," neut. pl. of topikos "commonplace, of a place," from topos "place." The meaning "matter treated in speech or writing, subject, theme" is first recorded 1720. Topical "of or pertaining to topics of the day" is recorded from 1873. Colin 2010/7/5 Vaughan Pratt <pratt@cs.stanford.edu>:
One would suppose that the notions of literary topos and humility topos were of ancient origin. Certainly "topos" appears in Aristotle's Rhetoric in the original Greek. However its entry into the academic lexicon as an English word relevant to rhetoric and other literary forms would seem, as far as I've been able to tell, to have occurred at some point in the 20th century.
1. Volume Ti-Tz of the OED does not contain the word "topos," nor does it appear under the entries for "humility" or "literary." (Ordinarily the OED can relied on to record just about every English word that has appeared in print prior to the 20th century.)
2. Adams Sherman Hill, Boylston Professor of Rhetoric and Oratory in Harvard University from 1876 to 1904, wrote "The Foundations of Rhetoric" in 1892 with no mention of the concept of topos as a notion in rhetoric.
The Wikipedia article on Ernst Robert Curtius at
http://en.wikipedia.org/wiki/Ernest_Robert_Curtius
says "He is best known for his 1948 work Europäische Literatur und Lateinisches Mittelalter. It was a major study of the Medieval Latin literature and its effect on subsequent writing in modern European languages. The book was largely responsible for introducing the literary topos concept as a scholarly and critical discussion of literary commonplaces."
So unless someone comes up with an earlier use, it looks like 1948 may be the date, and German the language, of the first appearance of "topos" outside the original Greek of Aristotle.
Vaughan Pratt
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
One would suppose that the notions of literary topos and humility topos were of ancient origin. Certainly "topos" appears in Aristotle's Rhetoric in the original Greek. However its entry into the academic lexicon as an English word relevant to rhetoric and other literary forms would seem, as far as I've been able to tell, to have occurred at some point in the 20th century.
The online OED confirms this; it does contain "topos", defining it as
"A traditional motif or theme (in a literary composition); a rhetorical commonplace, a literary convention or formula." and the earliest citation it gives is 1948, in Leo Spitzer's "Linguistics and literary history" (presumably referring to Curtius's work).
Interestingly, though, its earliest cited uses of "topic" (16th/17th century) are also as a translation of Aristotle's "topos", and with a similar meaning to Curtius's "topos". -Peter.
1. Volume Ti-Tz of the OED does not contain the word "topos," nor does it appear under the entries for "humility" or "literary." (Ordinarily the OED can relied on to record just about every English word that has appeared in print prior to the 20th century.)
2. Adams Sherman Hill, Boylston Professor of Rhetoric and Oratory in Harvard University from 1876 to 1904, wrote "The Foundations of Rhetoric" in 1892 with no mention of the concept of topos as a notion in rhetoric.
The Wikipedia article on Ernst Robert Curtius at
http://en.wikipedia.org/wiki/Ernest_Robert_Curtius
says "He is best known for his 1948 work Europäische Literatur und Lateinisches Mittelalter. It was a major study of the Medieval Latin literature and its effect on subsequent writing in modern European languages. The book was largely responsible for introducing the literary topos concept as a scholarly and critical discussion of literary commonplaces."
So unless someone comes up with an earlier use, it looks like 1948 may be the date, and German the language, of the first appearance of "topos" outside the original Greek of Aristotle.
-- Peter LeFanu Lumsdaine Carnegie Mellon University [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
1. Volume Ti-Tz of the OED does not contain the word "topos," nor does it appear under the entries for "humility" or "literary." (Ordinarily the OED can relied on to record just about every English word that has appeared in print prior to the 20th century.)
I have access to the full online version of the OED, which does contain the word topos. The earliest citation it has is to a 1948 work of Leo Spitzer, who was apparently a linguist and literary historian. Here is his Wikipedia page: http://en.wikipedia.org/wiki/Leo_Spitzer He was Austrian, and it seems quite possible that he could have read Curtius' treatise in the original German and begun to use the word "topos" himself in the same year. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
[Note, with humility, from moderator: this discussion has been allowed to continue off-topic too long already... let's end it, thanks.] Well, topos may not be a common English word until then, but "common place" is, and that is an English translation of topos, used for the same meaning, and derived from the rhetorical tradition. Melanchton's late sixteenth century textbook of theology, for example, was called Loci Communes (= common places in Latin). I think that the non-occurrence of topos in English probably says more about the relative infrequency of Greek terms and the greater frequency of their Latin equivalents (I haven't got an OED to hand, but it would be interesting to see if locus was ever used in that sense, and how early). Not only does the word topos occur in Aristotle's rhetoric, but he wrote a book on topoi, which is one of his logical works. One of the most interesting things about the term, at any rate in Greek, is that it thus has both logical and geometrical meanings, and that from very early. I can't help wondering whether Grothendieck had that in mind: he seems to have read widely enough for that to occur to him. Graham On Mon, 2010-07-05 at 13:20 -0700, Vaughan Pratt wrote:
One would suppose that the notions of literary topos and humility topos were of ancient origin. Certainly "topos" appears in Aristotle's Rhetoric in the original Greek. However its entry into the academic lexicon as an English word relevant to rhetoric and other literary forms would seem, as far as I've been able to tell, to have occurred at some point in the 20th century.
1. Volume Ti-Tz of the OED does not contain the word "topos," nor does it appear under the entries for "humility" or "literary." (Ordinarily the OED can relied on to record just about every English word that has appeared in print prior to the 20th century.)
2. Adams Sherman Hill, Boylston Professor of Rhetoric and Oratory in Harvard University from 1876 to 1904, wrote "The Foundations of Rhetoric" in 1892 with no mention of the concept of topos as a notion in rhetoric.
The Wikipedia article on Ernst Robert Curtius at
http://en.wikipedia.org/wiki/Ernest_Robert_Curtius
says "He is best known for his 1948 work Europäische Literatur und Lateinisches Mittelalter. It was a major study of the Medieval Latin literature and its effect on subsequent writing in modern European languages. The book was largely responsible for introducing the literary topos concept as a scholarly and critical discussion of literary commonplaces."
So unless someone comes up with an earlier use, it looks like 1948 may be the date, and German the language, of the first appearance of "topos" outside the original Greek of Aristotle.
Vaughan Pratt
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
2010/7/6 Graham White <graham@eecs.qmul.ac.uk>: Raises a very on-point question about Grothendieck's choice of the word "topos":
One of the most interesting things about the term, at any rate in Greek, is that it thus has both logical and geometrical meanings, and that from very early. I can't help wondering whether Grothendieck had that in mind: he seems to have read widely enough for that to occur to him.
It is not likely that Grothendieck was thinking much of Aristotle. He probably was thinking of the common French phrase "tu vois le topo." In crude translation "you see the topos." It actually means "you see the point" or " you know what I am talking about." Grothendieck's goal for topos theory was to explicate, and systematize, and vastly generalize a lot of routine arguments, that had become "commonplaces" in many different uses of cohomology -- so that as soon as you "see the topos" you know the outline of the situation. Then you only need to occupy yourself with a few relevant particulars to solve a particular problem. best, Colin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
participants (13)
-
Colin McLarty -
Dusko Pavlovic -
Eduardo J. Dubuc -
Graham White -
Jamie Vicary -
John Baez -
Michael Barr -
Peter LeFanu Lumsdaine -
Prof. Peter Johnstone -
Robert J. MacG. Dawson -
Steve Vickers -
Toby Bartels -
Vaughan Pratt