Log24

Sunday, December 17, 2017

Concrete Universals

Filed under: General — Tags: — m759 @ 6:45 PM

The remarks on universals in the previous post linked to the following
note by James Hillman:

James Hillman, Re-Visioning Psychology
Harper Collins, 1977, p. 155 —

"Myths also make concrete particulars into universals,
so that each image, name, thing in my life when
experienced mythically takes on universal sense,
and all abstract universals, the grand ideas of
human fate, are presented as concrete actions." 
[See note 48.]

Note 48:  Cf. P. Wheelwright's discussion of concrete universality
in The Burning Fountain  (Bloomington, Ind.: Indiana University
Press, 1968), pp. 52-54.

For Wheelwright's discussion, see the following excerpts from his book:

Pages 50-5152-5354-55.

Thursday, July 7, 2016

The Curious Case of the Concrete Universal

Filed under: General — Tags: , — m759 @ 3:35 AM

(Continued)

Erica Goode in the online New York Times  tonight

"Irving Gottesman, a pioneer in the field of behavioral genetics
whose work on the role of heredity in schizophrenia helped
transform the way people thought about the origins of serious
mental illness, died on June 29 at his home in Edina, Minn., a
suburb of Minneapolis. He was 85.

His wife, Carol, said he died while taking an afternoon nap.
Although Dr. Gottesman had some health problems, she said,
his death was unexpected, and several of his colleagues said
they received emails from him earlier that day."

A note from noon (EDT) on that day, June 29, for the Church of Synchronology

A detail from the page mentioned in the June 29 post above —

A passage related to the word "soul" discussed by Sullivan —

See as well a related biblical passage, better known at the time of Royce (ca. 1892)
than today, that would probably mean nothing to the late Dr. Gottesman.

Tuesday, September 23, 2014

Both Hands and an Ass Map

Filed under: General — Tags: — m759 @ 9:48 AM

Remarks by University Diaries  this morning suggested a search for
Rutgers in this journal. That search yields a post from Dec. 30, 2005,
that is closely related to both this morning's previous post and to recent
Log24 remarks on entities and concrete universals .

Sunday, September 21, 2014

Saturday-Morning Concept

Filed under: General,Geometry — m759 @ 7:59 PM

Why Is Our Sci-Fi So Glum About A.I.?,”
by Jayson Greene, NY Times Sunday Magazine  today —

“You come to pity these advanced beings, bumping against
the dunderheaded constraints that their less-advanced
creators have placed on them. Johansson’s Lucy grows so
powerful as her cerebral capacity multiplies that she is able
to manipulate her cellular structure. And yet, when pursued
by an entire planet’s worth of law enforcement, she settles
on a disguise straight out of Saturday-morning cartoons —
really big sunglasses and a hairdo change.”

See also this  journal on Saturday morning for a definition, and
Geometry of the I Ching for examples, of

changeable, instantiable entities, i.e., concrete universals.

Above the entrance to Plato's Academy: AGEOMETRETOS MEDEIS EISITO

Saturday, September 20, 2014

The Metaphysics of Entities

Filed under: General — Tags: — m759 @ 11:00 AM

Anthony Lane in The New Yorker , issue dated Sept. 22, 2014:

"The hero of 'The Zero Theorem' is a computer genius called Qohen Leth
(Christoph Waltz)…. He is the sole resident of a derelict church, where,
on a crucifix in front of the altar, the head of Christ has been replaced by
a security camera. No prayers are ever said, and none are answered.

In short, the place is deconsecrated, but to claim that it lacks any spark of
sacred yearning would be wrong, because Qohen devotes his days to seeking
the Zero Theorem, which—whatever it may be—lies at the fuzzy limit of
human powers. We crunch entities,” he says, as if that explained anything.
His employer is Mancom, a large corporation that, in Orwellian fashion,
oversees ordinary lives, although it betrays more frantic desperation than
glowering threat."

One approach to the metaphysics of entities was indicated in the previous
post, 'Metaphysics for Gilliam." A different approach:

"Categories, Sets, and the Nature of Mathematical Entities,"
by Jean-Pierre Marquis, Ch. 13, pp. 181-192, in the 2006 book
The Age of Alternative Logics , ed. by van Benthem et al.
(Springer, Netherlands).

From pages 182-183 —

13.2 The nature of mathematical entities

Let us start with the nature of mathematical entities in general and with a
rough and classical distinction that will simply set the stage for the picture we
want to develop. We essentially follow Lowe 1998* for the basic distinctions. We
need to distinguish between abstract and concrete entities, on the one hand, and
universals and particulars on the other hand. For our purpose, it is not necessary
to specify a criterion of demarcation between abstract and concrete entities. We
simply assume that such a distinction can be made, e.g. concrete entities can
change whereas abstract entities cannot. We assume that a universal is an entity
that can be instantiated by entities which themselves are not instantiable, the
latter being of course particulars. Given these distinctions, an entity can be a
concrete particular, a concrete universal, an abstract particular or an abstract
universal.

Our focus here is between the last two possibilities. For we claim that the
current conception of sets makes them abstract particulars whereas for objects
defined within categories, mathematical entities are abstract universals. This,
we claim, is true of category theory as it is.

* Lowe, E.J., 1998, The Possibility of Metaphysics , Oxford: Clarendon Press.

Sunday, June 30, 2013

Book Award

Filed under: General,Geometry — m759 @ 5:01 PM
 

"What on earth is
a 'concrete universal'?
"

— Said to be an annotation
(undated) by Robert M. Pirsig
of A History of Philosophy ,
by Frederick Copleston,
Society of Jesus.

In the spirit of the late Thomas Guinzburg

See also "Concrete Universal" in this journal.

Related material— From a Bloomsday reply
to a Diamond Theory  reader's comment, an excerpt—

The reader's comment suggests the following passages from
the book by Stirling quoted above—

 

Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow  in 1974.

Saturday, January 8, 2011

True Grid (continued)

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

"Rosetta Stone" as a Metaphor
  in Mathematical Narratives

For some backgound, see Mathematics and Narrative from 2005.

Yesterday's posts on mathematics and narrative discussed some properties
of the 3×3 grid (also known as the ninefold square ).

For some other properties, see (at the college-undergraduate, or MAA, level)–
Ezra Brown, 2001, "Magic Squares, Finite Planes, and Points of Inflection on Elliptic Curves."

His conclusion:

When you are done, you will be able to arrange the points into [a] 3×3 magic square,
which resembles the one in the book [5] I was reading on elliptic curves….

This result ties together threads from finite geometry, recreational mathematics,
combinatorics, calculus, algebra, and number theory. Quite a feat!

5. Viktor Prasolov and Yuri Solvyev, Elliptic Functions and Elliptic Integrals ,
    American Mathematical Society, 1997.

Brown fails to give an important clue to the historical background of this topic —
the word Hessian . (See, however, this word in the book on elliptic functions that he cites.)

Investigation of this word yields a related essay at the graduate-student, or AMS, level–
Igor Dolgachev and Michela Artebani, 2009, "The Hesse Pencil of Plane Cubic Curves ."

From the Dolgachev-Artebani introduction–

In this paper we discuss some old and new results about the widely known Hesse
configuration
  of 9 points and 12 lines in the projective plane P2(k ): each point lies
on 4 lines and each line contains 3 points, giving an abstract configuration (123, 94).

PlanetMath.org on the Hesse configuration

http://www.log24.com/log/pix11/110108-PlanetMath.jpg

A picture of the Hesse configuration–

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

(See Visualizing GL(2,p), a note from 1985).

Related notes from this journal —

From last November —

Saturday, November 13, 2010

Story

m759 @ 10:12 PM

From the December 2010 American Mathematical Society Notices

http://www.log24.com/log/pix10B/101113-Ono.gif

Related material from this  journal—

Mathematics and Narrative and

Consolation Prize (August 19, 2010)

From 2006 —

Sunday December 10, 2006

 

 m759 @ 9:00 PM

A Miniature Rosetta Stone:

The image “http://www.log24.com/log/pix05B/grid3x3med.bmp” cannot be displayed, because it contains errors.

“Function defined form, expressed in a pure geometry
that the eye could easily grasp in its entirety.”

– J. G. Ballard on Modernism
(The Guardian , March 20, 2006)

“The greatest obstacle to discovery is not ignorance –
it is the illusion of knowledge.”

— Daniel J. Boorstin,
Librarian of Congress, quoted in Beyond Geometry

Also from 2006 —

Sunday November 26, 2006

 

m759 @ 7:26 AM

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art  or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at the nine engravings and at the circle,
checking strange correspondences between them."
The Club Dumas ,1993

"And it's whispered that soon if we all call the tune
Then the piper will lead us to reason."
Robert Plant ,1971

The nine engravings of The Club Dumas
(filmed as "The Ninth Gate") are perhaps more
an example of the concrete than of the universal.

An example of the universal*– or, according to Krauss,
a "staircase" to the universal– is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo, the field of Reason…."
John Outram, architect    

For more on the field of reason, see
Log24, Oct. 9, 2006.

A reasonable set of "strange correspondences"
in the garden of Apollo has been provided by
Ezra Brown in a mathematical essay (pdf).

Unreason is, of course, more popular.

* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:

"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."

– Hegel, Lectures on the History of Philosophy ,
   "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
– Thomas Pynchon   

And from last October —

Friday, October 8, 2010

 

m759 @ 12:00 PM
 

Starting Out in the Evening
… and Finishing Up at Noon

This post was suggested by last evening's post on mathematics and narrative and by Michiko Kakutani on Vargas Llosa in this morning's New York Times .

http://www.log24.com/log/pix10B/101008-StartingOut.jpg

 

Above: Frank Langella in
"Starting Out in the Evening"

Right: Johnny Depp in
"The Ninth Gate"

http://www.log24.com/log/pix10B/101008-NinthGate.jpg

"One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage."

– "Is Fiction the Art of Lying?"* by Mario Vargas Llosa,
    New York Times  essay of October 7, 1984

* The Web version's title has a misprint—
   "living" instead of "lying."

"You've got to pick up every stitch…"

Monday, January 3, 2011

Shining

Filed under: General — m759 @ 11:07 AM

For the authors of the new book All Things Shining

See the discussions of "concrete universals" in James Hillman's Re-Visioning Psychology  and in Donald Phillip Verene's Vico and Joyce

IMAGE- The imaginative universal in Vico and Joyce

The index to All Things Shining  contains no entries for Hillman (or his mentor Jung), Verene, Joyce, Vico, or the word "universal."

It does, however, contain four references to an example  of a universal —

whiteness, 161, 169-173, 175, 178

See also "whiteness" in this  journal.

Sunday, June 13, 2010

Sunday School

Filed under: General — m759 @ 9:00 AM

What on earth is a 'concrete universal'?"
Said to be an annotation (undated)
by Robert M. Pirsig of A History of Philosophy,
by Frederick Copleston, Society of Jesus.

From Aaron Urbanczyk's 2005 review of Christ and Apollo  by William Lynch, S.J., a book first published in 1960—

"Lynch's use of analogy vis-a-vis literature provides, in a sense, a philosophical basis to the theoretical paradox popularized by W. K. Wimsatt (1907-1975), which contends that literature is a sort of 'concrete universal.'"

The following figure has often been
offered in this journal as a symbol of Apollo

Image-- 3x3 array of white squares

Arguments that it is, rather, a symbol of Christ
may be left to the Society of Jesus.

One possible approach—
Urbanczyk's review says that
"Christianity offers the critic
   a privileged ontological window…."

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

Delmore Schwartz

Tuesday, July 21, 2009

Tuesday July 21, 2009

Filed under: General — Tags: — m759 @ 9:00 AM

Today's Readings:

Thursday, July 16, 2009

Thursday July 16, 2009

Filed under: General — m759 @ 4:00 PM

The White Itself

David Ellerman has written that

"The notion of a concrete universal occurred in Plato's Theory of Forms [Malcolm 1991]."

A check shows that Malcolm indeed discussed this notion ("the Form as an Ideal Individual"), but not under the name "concrete universal."

See Plato on the Self-Predication of Forms, by John Malcolm, Oxford U. Press, 1991.

From the publisher's summary:

"Malcolm…. shows that the middle dialogues do indeed take Forms to be both universals and paradigms…. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual."

Ellerman also cites another discussion of Plato published by Oxford:

Kneale and Kneale on Plato's theory of forms and 'the white itself'

For a literary context, see W. K. Wimsatt, Jr., "The Structure of the Concrete Universal," Ch. 6 in Literary Theory: An Anthology, edited by Julie Rivkin and Michael Ryan, Wiley-Blackwell, 2004.

Other uses of the phrase "concrete universal"– Hegelian and/or theological– seem rather distant from the concerns of Plato and Wimsatt, and are best left to debates between Marxists and Catholics. (My own sympathies are with the Catholics.)

Two views of "the white itself" —

 "So did God cause the big bang?
 Overcome by metaphysical lassitude,
 I finally reach over to my bookshelf
 for The Devil's Bible.
 Turning to Genesis I read:
 'In the beginning
 there was nothing.
 And God said,
 'Let there be light!'
 And there was still nothing,
 but now you could see it.'"
 
 -- Jim Holt, Big-Bang Theology,
    Slate's "High Concept" department 
 
   Fiat Lux, and After

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."

-- Delmore Schwartz

Wednesday, August 22, 2007

Wednesday August 22, 2007

Filed under: General — m759 @ 10:31 AM
The Enchanted Twilight

The Associated Press
Tuesday, August 21, 2007

GENEVA: British-born author Magdalen Nabb, whose crime novels about a quirky Italian investigator were acclaimed by her idol Georges Simenon, has died, her Swiss publishing house said Tuesday. She was 60.

Nabb, who also wrote stories for children and young adults, died of a stroke on Saturday [August 18, 2007] in Florence, Italy, where she had lived and worked since 1975, said Diogenes Verlag AG of Zurich….

Nabb published 13 books for children and young adults, including “The Enchanted Horse,” “Twilight Ghost” and the “Josie Smith” series about a “girl who always has plenty of ideas.”

See also, from the
date of Nabb’s death,

Happy Birthday,
Robert Redford:
 A Concrete Universal
.

No matter how it’s done,
you won’t like it.

— Robert Redford to     
  Robert M. Pirsig in Lila 

Material related to
Twilight Ghost:

Logos and Epiphany
and
Fire Chaplain.

“A twilight ghost doesn’t come to
frighten people, though it might
want to tell them something.
A twilight ghost is just
     a kind of long lost memory….”

Magdalen Nabb

Saturday, August 18, 2007

Saturday August 18, 2007

Filed under: General — m759 @ 7:20 PM
A Concrete Universal

What on earth is
a ‘concrete universal’?

Said to be an annotation
(undated) by Robert M. Pirsig
of A History of Philosophy,
by Frederick Copleston,
Society of Jesus.

No matter how it’s done,
you won’t like it.

— Robert Redford to     
  Robert M. Pirsig in Lila    


“In chapters 19 and 20 of LILA there is a discussion about the possibility of making Zen and the Art into a movie. It opens with a scene where Robert Redford, who ‘really would like to have the film rights,’ comes to meet and negotiate with Phaedrus in his New York City hotel room. Phaedrus tells the famous actor that he can have the rights to the book, but maybe that’s just because he’s star-struck and doesn’t like to haggle. Under his excitement, Phaedrus has a bad feeling about it. He tells us that he’s been warned by several different people not to allow such a film to be made. Even Redford warned him not to do it. So what’s the problem? As it’s put at the end of that discussion, ‘Films are social media; his book was largely intellectual. That was the center of the problem.'”

David Buchanan at robertpirsig.org

“The insight is constituted precisely by ‘seeing’ the idea in the image, the intelligible in the sensible, the universal in the particular, the abstract in the concrete.”

— Fr. Brian Cronin‘s Foundations of Philosophy, Ch. 2, “Identifying Direct Insights,” quoted in Ideas and Art

See also Smiles of a Summer Evening, the current issue of TIME, the time of this entry (7:20:11 PM ET), and Plato, Pegasus, and the Evening Star.

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: General — Tags: — m759 @ 12:00 PM
For Balanchine's Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze

most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…


Balanchine,  George… (75 of 1212 words)

"What on earth is
a concrete universal?"
— Robert M. Pirsig

Review:

From Wikipedia's
"Upper Ontology"
and
Epiphany 2007:

"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."

There is, however,
"the field of reason"–

the 3×3 grid:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as

"a staircase to
  the Universal."

Other artists regard
Epiphany itself as an
approach to
the Universal:

"Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.
"

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:

 

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

 

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Wednesday, January 3, 2007

Wednesday January 3, 2007

Filed under: General — m759 @ 11:32 AM
The Wanderer:
 
11:32:56

“What on earth is
a concrete universal?”
Robert M. Pirsig  

Hexagram 56

“James Joyce meant Finnegans Wake to become a universal book. His universe was primarily Dublin, but Joyce believed that the universal can be found in the particular. ‘I always write about Dublin,’ he said to Arthur Power, ‘because if I can get to the heart of Dublin I can get to the heart of all the cities of the world’ (Ellmann 505). He achieved that goal in Ulysses by making Bloom a universal wanderer, the everyman trying to find his way in the labyrinth of the world.” —The Joyce of Science

Related material:

From A Shot at Redemption

The Past as Prologue:
Grand Rapids Revisited

Constantine (cartoon) and Donald Knuth

John Constantine,
cartoon character, and
Donald E. Knuth,
Lutheran mathematician

“…. recent books testify
further to Calvin College’s
unparalleled leadership
in the field of
Christian historiography….”

“I need a photo opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
In a cartoon graveyard.”

A photo opportunity —

Photo op for Gerald Ford

and a recent cartoon:

Cartoon of Gerald Ford with halo

History, said Stephen….

From Calvin College,
today’s meditation:

Monday, November 27, 2006

Monday November 27, 2006

Filed under: General — m759 @ 2:45 AM
The Poetry
of Philosophy

“What on earth is
   a ‘concrete universal’?”

Said to be an annotation
(undated)
by Robert M. Pirsig of
A History of Philosophy,
by Frederick Copleston,
Society of Jesus
.

For an answer, see
The Structure of the
Concrete Universal
in Literature
,”
by W. K. Wimsatt, Jr.,
PMLA, Vol. 62, No. 1
(March, 1947), pp. 262-280.

This is reprinted in Wimsatt’s
The Verbal Icon:
Studies in the
Meaning of Poetry
.

The final chapter of
The Verbal Icon
is titled
“Poetry and Christian Thinking.”
For more on Wimsatt
and this topic, see
Reclaiming the Bible
as Literature,”
by Louis A. Markos.

Sunday, November 26, 2006

Sunday November 26, 2006

Filed under: General — m759 @ 7:26 AM

Rosalind Krauss
in "Grids," 1979:

"If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World, for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter.  They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.

Or, to take a more up-to-date example…."

"He was looking at
the nine engravings
and at the circle,
checking strange
correspondences
between them."
The Club Dumas,1993

"And it's whispered that soon
if we all call the tune
Then the piper will lead us
to reason."
Robert Plant,1971

The nine engravings of
The Club Dumas
(filmed as "The Ninth Gate")
are perhaps more an example
of the concrete than of the
universal.

An example of the universal*–
or, according to Krauss, a
"staircase" to the universal–
is the ninefold square:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

"This is the garden of Apollo,
the field of Reason…."
John Outram, architect    

For more on the field
of reason, see
Log24, Oct. 9, 2006.

A reasonable set of
"strange correspondences"
in the garden of Apollo
has been provided by Ezra Brown
in a mathematical essay (pdf).

Unreason is, of course,
more popular.

* The ninefold square is perhaps a "concrete universal" in the sense of Hegel:

"Two determinations found in all philosophy are the concretion of the Idea and the presence of the spirit in the same; my content must at the same time be something concrete, present. This concrete was termed Reason, and for it the more noble of those men contended with the greatest enthusiasm and warmth. Thought was raised like a standard among the nations, liberty of conviction and of conscience in me. They said to mankind, 'In this sign thou shalt conquer,' for they had before their eyes what had been done in the name of the cross alone, what had been made a matter of faith and law and religion– they saw how the sign of the cross had been degraded."

— Hegel, Lectures on the History of Philosophy, "Idea of a Concrete Universal Unity"

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon   
 

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