Re: The humility topos

Re: The humility topos

[Toby Bartels]

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


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Re: The humility topos

[Colin McLarty]

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



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Re: The humility topos

[Graham White]

[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



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Re: The humility topos

[Jamie Vicary]

> 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.


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Re: The humility topos

[Peter LeFanu Lumsdaine]

> 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



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Re: The humility topos

[Colin McLarty]

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
>

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Re: The humility topos

[Vaughan Pratt]

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


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Re: The humility topos

[Jean-Pierre Marquis]

Yes,

according to Pont, the name "topologie" comes from Johann Benedikt  
Listing, a student of Gauss, who introduced it for the first time in  
1836. He referred to analysis situs and geometry but decided that a  
new name was required and suggested "topology".

Best,

Jean-Pierre
Le 10-07-02 à 11:41, Michael Barr a écrit :

> The older name for topology was "analysis situs", analysis of  
> place.  Why that was changed is unknown to me, but the topo- root is  
> just Greek for place and it would be a stretch to assume anything  
> else without good evidence.
>
> A French mathematician named, IIRC, Jean Pont wrote a book called,  
> "L'Histoire de la topologie algébrique avant Poincaré" that traces  
> topology, at least algebraic topologie to Euler's solution to the  
> bridges of Königsberg problem.  I think V-F+E = 2 came next.
>
> Michael

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Re: The humility topos

[Colin McLarty]

Yes, this is Grothendieck's stated intention, in the article "Topos"
written with Verdier in SGA 4 (p. 301).

But at the same time he and his friends knew well that topo, with
plural topos, is ordinary French for a little speech, and is common
slang for a school essay.  This comes from the long-time use of
"topos" as a term in rhetoric taken from Aristotle.

I have not found older uses of the specific term "humility topos," but
"topos" in this rhetorical sense is not postmodern.  It is one of the
oldest scholarly terms.

Colin



2010/7/2 Steve Vickers <s.j.vickers@cs.bham.ac.uk>:
> 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.

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Re: The humility topos

[Michael Barr]

The older name for topology was "analysis situs", analysis of place.  Why 
that was changed is unknown to me, but the topo- root is just Greek for 
place and it would be a stretch to assume anything else without good 
evidence.

A French mathematician named, IIRC, Jean Pont wrote a book called, 
"L'Histoire de la topologie algébrique avant Poincaré" that traces 
topology, at least algebraic topologie to Euler's solution to the bridges 
of Königsberg problem.  I think V-F+E = 2 came next.

Michael

On Fri, 2 Jul 2010, Eduardo J. Dubuc wrote:

> 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

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Re: The humility topos

[Eduardo J. Dubuc]

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

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Re: The humility topos

[Robert J. MacG. Dawson]

On 6/30/2010 11:07 PM, Chris Mortensen wrote:
> Dear Categories/Robert Dawson,
> What was called the humility topos (below) was called Socratic Irony for a
> couple of millennia. Postmodernism has made an industry of re-badging old ideas
> and representing them as new discoveries.

 	My superficial (and this is an admission not an example) research
suggests that they are not quite the same thing.  In particular,
Socratic irony is transparent;  "humility topos" was used (for instance)
to describe the practice in mediaeval theological writings of assuming
an attitude of humility that was, if not always genuine, at least
intended to appear so (though the phrase can be used in other ways as
well).  "Perhaps I'm being very stupid, but isn't that term meant to be
negative?" is probably Socratic irony; when the Pope styles himself
"servant of the servants of God" or a Victorian gentleman signed a
letter begging to remain "your humble and obedient servant", that is
humility topos. (Or, for a more subtle modern example, when a conference
speaker cites others' papers by name and his own under an initial.)

 	Traditional rhetorical terms tend to have (unnecessarily?) subtle
distinctions - perhaps in the Aristotelian tradition. One could get by
very nicely using the same word for "simile" and "metaphor" provided
everybody else understood this.

 	Robert


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Re: The humility topos

[Steve Vickers]

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


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Re: The humility topos

[Dusko Pavlovic]

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


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Re: The humility topos

[Prof. Peter Johnstone]

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


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Re: The humility topos

[Robert J. MacG. Dawson]

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


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The humility topos

[John Baez]

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


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The humility topos

[Michael Barr]

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

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