Thursday, March 16, 2017

Iacta Est

Filed under: Uncategorized — m759 @ 2:30 PM

"Though realism is excellent rhetoric, maybe the best,
in a purely technical or instrumental sense,
that cannot be an adequate reason to accept it
as a serious intellectual position. In its tropes of
Death and Furniture we see a rhetoric  that refuses
to acknowledge its own existence; a politics  that
can claim a critical-radical credibility only by
the selective use of its opponents' analytic tools;
and a theology  which is deeply conservative and
seeks nothing less than the death of disruptive,
disturbing inquiry. While tedium, good taste, political
and moral sensibility will properly determine what
sorts of given realities are thought worthy of inquiry,
those considerations are no grounds for promoting
a realist ontology for social science, nor any other
science, nor for rejecting relativism. On the contrary,
relativism is social science par excellence . . . ."

Loughborough University

— Edwards, D., Ashmore, M., and Potter, J. (1995),
"Death and furniture: The rhetoric, politics and theology
of bottom line arguments against relativism," 
History of the Human Sciences , 8, 25-49.

Related material:

Platonic  realism in this journal, yesterday's post Ripples, and

Gravity's Shadow , 2004 —

Gravity's Ghost , 2010 —

See also an "Inception"-related object —

Saturday, November 30, 2013

For Sean Connery

Filed under: Uncategorized — m759 @ 7:00 PM

On St. Andrew's Day.

A Connery adventure in Kuala Lumpur—

For another Kuala Lumpur adventure, see today's update
to "In Defense of Plato's Realism"—

The July 5, 2007, post linked to
"Plato, Pegasus, and the Evening Star."
For related drama from Kuala Lumpur, see
"Occam's Razor, Plato's Beard."

Sunday, December 2, 2012


Filed under: Uncategorized — Tags: — m759 @ 4:30 PM

From the Los Angeles Times  yesterday

"Chess player Elena Akhmilovskaya Donaldson sits
in deep concentration at the U.S. chess championship
in Seattle in 2002. (Greg Gilbert / Seattle Times / 
January 5, 2002)"

Linda Shaw, Seattle Times :

"Elena Akhmilovskaya Donaldson, who was once the world's
second-ranked women's chess player and eloped in 1988
with the captain of the U.S. chess team when they were both
playing at a tournament in Greece, has died. She was 55.

Donaldson, who earned the title of international women's
grandmaster, died Nov. 18 in her adopted hometown of Seattle…."

more »

From the Log24 post "Sermon" on the date of Donaldson's death,
Sunday, Nov. 18, 2012—

"You must allow us to play every conceivable combination of chess."
— Marie-Louise von Franz in Number and Time

An October 2011 post titled  Realism in Plato's Cave displays
the following image:

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil,
by Albrecht Dürer

George Steiner and myself  in Closing the Circle, a Log24 post
of Sept. 4, 2009: 

“Allegoric associations of death with chess are perennial….”

"Yes, they are."

For related remarks on knight moves and the devil, see
today's previous two posts, Knight's Labyrinth and The Rite.

Wednesday, October 5, 2011


Filed under: Uncategorized — m759 @ 10:30 PM

University Diaries  today

"Educated people— with some exceptions, like Nader— like to explore the senses, and indeed many of your humanities courses (like the one UD ‘s teaching right now about beauty, in which we just read Susan Sontag’s “Against Interpretation,” with its famous concluding lines: In place of a hermeneutics, we need an erotics of art ) feature artworks and ideas that celebrate sensuality."

This suggests a review lecture on the unorthodox concept of lottery hermeneutics .

Today's New York Lottery—


A quote suggested by the UD  post

"Sainte-Beuve's Volupté  (1834) introduced the idea of idler as hero (and seeking pleasurable new sensations as the highest good), so Baudelaire indulged himself in sex and drugs."

Article on Baudelaire by Joshua Glenn in the journal Hermenaut

Some reflections suggested by Hermenaut  and by the NY evening numbers, 674 and 1834—

(Click images to enlarge.)




Cool Mystery:


Detective Cruz enters Planck's Constant Café in "The Big Bang."

As for the midday numbers—

For 412, see 4/12, and for 1030, see 10/30, Devil's Night (2005).

For further background, consult Monday's Realism in Plato's Cave.

Monday, October 3, 2011

Realism in Plato’s Cave

Filed under: Uncategorized — m759 @ 8:08 PM

In memory of the late combinatorialist-philosopher Gian-Carlo Rota

Excerpts from the introduction to Allan Casebier's

Film and Phenomenology: Towards a Realist Theory of Cinematic Representation
(Cambridge Studies in Film, Cambridge University Press, 1991) —

Pages 1-2,  pages 3-4,  pages 5-6.

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil, by Albrecht Dürer

Wednesday, August 10, 2011


Filed under: Uncategorized — m759 @ 12:25 PM

From math16.com

Quotations on Realism
and the Problem of Universals:

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."
— Simon Blackburn, Think, Oxford University Press, 1999, page 268

"You will all know that in the Middle Ages there were supposed to be various classes of angels…. these hierarchized celsitudes are but the last traces in a less philosophical age of the ideas which Plato taught his disciples existed in the spiritual world."
— Charles Williams, page 31, Chapter Two, "The Eidola and the Angeli," in The Place of the Lion (1933), reprinted in 1991 by Eerdmans Publishing

For Williams's discussion of Divine Universals (i.e., angels), see Chapter Eight of The Place of the Lion.

"People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only 'truths' strictly worthy of the name. Such truths I will call 'diamonds'; they are highly desirable but hard to find….The happy metaphor is Morris Kline's in Mathematics in Western Culture (Oxford, 1953), p. 430."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 114 and 117

"A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the 'Story Theory' of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.' The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory…. I concluded long ago that each enterprise contains only stories (which the scientists call 'models of reality'). I had started by hunting diamonds; I did find dazzlingly beautiful jewels, but always of human manufacture."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 256 and 259

Trudeau's confusion seems to stem from the nominalism of W. V. Quine, which in turn stems from Quine's appalling ignorance of the nature of geometry. Quine thinks that the geometry of Euclid dealt with "an emphatically empirical subject matter" — "surfaces, curves, and points in real space." Quine says that Euclidean geometry lost "its old status of mathematics with a subject matter" when Einstein established that space itself, as defined by the paths of light, is non-Euclidean. Having totally misunderstood the nature of the subject, Quine concludes that after Einstein, geometry has become "uninterpreted mathematics," which is "devoid not only of empirical content but of all question of truth and falsity." (From Stimulus to Science, Harvard University Press, 1995, page 55)
— S. H. Cullinane, December 12, 2000

The correct statement of the relation between geometry and the physical universe is as follows:

"The contrast between pure and applied mathematics stands out most clearly, perhaps, in geometry. There is the science of pure geometry, in which there are many geometries: projective geometry, Euclidean geometry, non-Euclidean geometry, and so forth. Each of these geometries is a model, a pattern of ideas, and is to be judged by the interest and beauty of its particular pattern. It is a map or picture, the joint product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But the point which is important to us now is this, that there is one thing at any rate of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. It is obvious, surely, that they cannot be, since earthquakes and eclipses are not mathematical concepts."
— G. H. Hardy, section 23, A Mathematician's Apology, Cambridge University Press, 1940

The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)— 

From The Search for Invariants (June 20, 2011):

The conclusion of Maja Lovrenov's 
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—

"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."

— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241


Related material from Sunday's New York Times  travel section—

"Exhibit A is certainly Ljubljana…."

Monday, August 8, 2011

Diamond Theory vs. Story Theory (continued)

Filed under: Uncategorized — m759 @ 5:01 PM

Some background

Richard J. Trudeau, a mathematics professor and Unitarian minister, published in 1987 a book, The Non-Euclidean Revolution , that opposes what he calls the Story Theory of truth [i.e., Quine, nominalism, postmodernism] to what he calls the traditional Diamond Theory of truth [i.e., Plato, realism, the Roman Catholic Church]. This opposition goes back to the medieval "problem of universals" debated by scholastic philosophers.

(Trudeau may never have heard of, and at any rate did not mention, an earlier 1976 monograph on geometry, "Diamond Theory," whose subject and title are relevant.)

From yesterday's Sunday morning New York Times

"Stories were the primary way our ancestors transmitted knowledge and values. Today we seek movies, novels and 'news stories' that put the events of the day in a form that our brains evolved to find compelling and memorable. Children crave bedtime stories…."

Drew Westen, professor at Emory University

From May 22, 2009

Poster for 'Diamonds' miniseries on ABC starting May 24, 2009

The above ad is by
  Diane Robertson Design—

Credit for 'Diamonds' miniseries poster: Diane Robertson Design, London

Diamond from last night’s
Log24 entry, with
four colored pencils from
Diane Robertson Design:

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design
See also
A Four-Color Theorem.

For further details, see Saturday's correspondences
and a diamond-related story from this afternoon's
online New York Times.

Sunday, October 3, 2010

Search for the Basic Picture

Filed under: Uncategorized — m759 @ 5:01 PM

(Click to enlarge.)


The above is the result of a (fruitless) image search today for a current version of Giovanni Sambin's "Basic Picture: A Structure for Topology."

That search was suggested by the title of today's New York Times  op-ed essay "Found in Translation" and an occurrence of that phrase in this journal on January 5, 2007.

Further information on one of the images above—


A search in this journal on the publication date of Giaquinto's Visual Thinking in Mathematics  yields the following—

Thursday July 5, 2007

m759 @ 7:11 PM

In defense of Plato’s realism

(vs. sophists’ nominalism– see recent entries.)

Plato cited geometry, notably in the Meno , in defense of his realism.
Consideration of the Meno 's diamond figure leads to the following:

The Eightfold Cube and its Inner Structure

For the Meno 's diamond figure in Giaquinto, see a review—


— Review by Jeremy Avigad (preprint)

Finite geometry supplies a rather different context for Plato's  "basic picture."

In that context, the Klein four-group often cited by art theorist Rosalind Krauss appears as a group of translations in the mathematical sense. (See Kernel of Eternity and Sacerdotal Jargon at Harvard.)

The Times  op-ed essay today notes that linguistic  translation "… is not merely a job assigned to a translator expert in a foreign language, but a long, complex and even profound series of transformations that involve the writer and reader as well."

The list of four-group transformations in the mathematical  sense is neither long nor complex, but is apparently profound enough to enjoy the close attention of thinkers like Krauss.

Saturday, July 21, 2007

Saturday July 21, 2007

Filed under: Uncategorized — m759 @ 9:45 AM

Death of a Nominalist

“All our words from loose using have lost their edge.” –Ernest Hemingway

(The Hemingway quotation is from the AP’s “Today in History” on July 21, 2007; for the context, see Death in the Afternoon.)

Today seems as good a day as any for noting the death of an author previously discussed in Log24 on January 29, 2007, and January 31, 2007.

Joseph Goguen
died on July 3, 2006. (I learned of his death only after the entries of January 2007 were written. They still hold.)

Goguen’s death may be viewed in the context of the ongoing war between the realism of Plato and the nominalism of the sophists. (See, for instance, Log24 on August 10-15, 2004, and on July 3-5, 2007.)

Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf):

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.’ Similarly, the ‘situations’ in the situation semantics of Barwise and Perry, which resemble conceptual spaces (but are more sophisticated– perhaps too sophisticated), are considered to be actually existing, real entities [23], even though they may include what are normally considered judgements.5 The classical semiotics of Charles Sanders Peirce [24] also tends towards a Platonist view of signs. The viewpoint of this paper is that all formalisms are constructed in the course of some task, such as scientific study or engineering design, for the heuristic purpose of facilitating consideration of certain issues in that task. Under this view, all theories are situated social entities, mathematical theories no less than others; of course, this does not mean that they are not useful.”

5 The “types” of situation theory are even further removed from concrete reality.

[23] Jon Barwise and John Perry. Situations and Attitudes. MIT (Bradford), 1983.
[24] Charles Sanders Peirce. Collected Papers. Harvard, 1965. In 6 volumes; see especially Volume 2: Elements of Logic.

From Log24 on the date of Goguen’s death:

Requiem for a clown:

“At times, bullshit can only be
countered with superior bullshit.”

Norman Mailer

This same Mailer aphorism was quoted, along with an excerpt from the Goguen passage above, in Log24 this year on the date of Norman Mailer’s birth.  Also quoted on that date:

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God….

Whether the above excerpt– from Hans Christian Oersted‘s The Soul in Nature (1852)– is superior to the similar remark of Goguen, the reader may decide.

Thursday, July 5, 2007

Thursday July 5, 2007

Filed under: Uncategorized — m759 @ 7:11 PM

In Defense of
Plato’s Realism

(vs. sophists’ nominalism–
see recent entries.)

Plato cited geometry,
notably in the Meno,
in defense of his realism.
Consideration of the
Meno’s diamond figure
leads to the following:

The Eightfold Cube and its Inner Structure

Click on image for details.

As noted in an entry,
Plato, Pegasus, and
the Evening Star,

linked to
at the end of today’s
previous entry,
the “universals”
of Platonic realism
are exemplified by
the hexagrams of
the I Ching,
which in turn are
based on the seven
trigrams above and
on the eighth trigram,
of all yin lines,
not shown above:

Trigram of K'un, the Receptive

The Receptive


Update of Nov. 30, 2013:

From  a little-known website in Kuala Lumpur:
(Click to enlarge.)

The remarks on Platonic realism are from Wikipedia.
The eightfold cube is apparently from this post.

Thursday July 5, 2007

Filed under: Uncategorized — m759 @ 12:48 PM
Their Name is Legion

“Although it may not at first be obvious,
the substitution for real religions
 of a religion drained of particulars
is of a piece with the desire to
exorcise postmodernism.”

Stanley Fish, July 2002

The previous entry linked to an entry of June 2002 that attacked the nominalism of Stanley Fish.  Here is another such attack:

From “Stanley Fish: The Critic as Sophist,” by R.V. Young, in Modern Age, June 22, 2003:

In one of the definitive works of conservatism in the twentieth century, Richard Weaver designates the rise of nominalism as a critical turn in the emergence of the intellectual and cultural disintegration associated with liberalism, which it is the business of a reviving conservatism to contest: “The defeat of logical realism in the great medieval debate was the crucial event in the history of Western culture; from this flowed those acts which issue now in modern decadence.” It is nominalism that provides the intellectual foundation– if a paradox may be hazarded– for the attack by Fish and numerous others (their name is Legion) on the very idea of intellectual foundations:  

It was William of Occam who propounded the fateful doctrine of nominalism, which denies that universals have real existence. His triumph tended to leave universal terms mere names serving our  convenience. The issue ultimately involved is whether there is a  source of truth higher than, and independent of, man; and the answer to the question is decisive for one’s view of the nature and destiny of humankind. The practical result of nominalist philosophy is to banish the reality which is perceived by the intellect and to posit as reality that which is perceived by the senses. (4)

(4). Ideas Have Consequences (Chicago and London, 1948), 3.

R.V. YOUNG is Professor of English at North Carolina State University and author of At War With the Word and Doctrine and Devotion in Seventeenth-Century Poetry (2000).

Related material:

Simon Blackburn on
Plato and sophists,
realism and nominalism
(previous entry)


Plato, Pegasus, and

the Evening Star

Friday, July 7, 2006

Friday July 7, 2006

Filed under: Uncategorized — m759 @ 7:00 PM

ART WARS continued

To the “Endgame Art” review
in today’s New York Times,
a magic-realism response:


In memory of
Roderick MacLeish:

Now, we are seven.
— Yul Brynner

Related material:

Log24 for 6/6/6

Plato, Pegasus, and
the Evening Star.

Monday, June 26, 2006

Monday June 26, 2006

Filed under: Uncategorized — Tags: — m759 @ 9:29 AM

A Little Extra Reading

In memory of
Mary Martin McLaughlin,
a scholar of Heloise and Abelard.
McLaughlin died on June 8, 2006.

"Following the parade, a speech is given by Charles Williams, based on his book The Place of the Lion. Williams explains the true meaning of the word 'realism' in both philosophy and theology. His guard of honor, bayonets gleaming, is led by William of Ockham."

Midsummer Eve's Dream

A review by John D. Burlinson of Charles Williams's novel The Place of the Lion:

"… a little extra reading regarding Abelard's take on 'universals' might add a little extra spice– since Abelard is the subject of the heroine's … doctoral dissertation. I'd suggest the article 'The Medieval Problem of Universals' in the online Stanford Encyclopedia of Philosophy."

Michael L. Czapkay, a student of philosophical theology at Oxford:

"The development of logic in the schools and universities of western Europe between the eleventh and fifteenth centuries constituted a significant contribution to the history of philosophy. But no less significant was the influence of this development of logic on medieval theology. It provided the necessary conceptual apparatus for the systematization of theology. Abelard, Ockham, and Thomas Aquinas are paradigm cases of the extent to which logic played an active role in the systematic formulation of Christian theology. In fact, at certain points, for instance in modal logic, logical concepts were intimately related to theological problems, such as God's knowledge of future contingent truths."

The Medieval Problem of Universals, by Fordham's Gyula Klima, 2004:

"… for Abelard, a status is an object of the divine mind, whereby God preconceives the state of his creation from eternity."

Status Symbol

(based on Weyl's Symmetry):

The image “http://www.log24.com/log/pix06A/060604-Roots.jpg” cannot be displayed, because it contains errors.

"… for then we would know

the mind of God"
Stephen Hawking, 1988

For further details,
click on the picture.

Wednesday, November 30, 2005

Wednesday November 30, 2005

Filed under: Uncategorized — m759 @ 8:20 PM


Brian Davies is a professor of mathematics at King’s College London.  In the December Notices of the American Mathematical Society, he claims that arithmetic may, for all we know, be inconsistent:

“Gödel taught us that it is not possible to prove that Peano arithmetic is consistent, but everyone has taken it for granted that in fact it is indeed consistent.
    Platonistically-inclined mathematicians would deny the possibility that Peano arithmetic could be flawed.  From Kronecker onwards many consider that they have a direct insight into the natural numbers, which guarantees their existence. If the natural numbers exist and Peano’s axioms describe properties that they possess then, since the axioms can be instantiated, they must be consistent.”

“It is not possible to prove that Peano arithmetic is consistent”…?!

Where did Gödel say this?  Gödel proved, in fact, according to a well-known mathematician at Princeton, that (letting PA stand for Peano Arithmetic),

“If PA is consistent, the formula expressing ‘PA is consistent’ is unprovable in PA.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Remarkably, even after he has stated correctly Gödel’s result, Nelson, like Davies, concludes that

“The consistency of PA cannot be concretely demonstrated.”

I prefer the argument that the existence of a model ensures the consistency of a theory.

For instance, the Toronto philosopher William Seager writes that

“Our judgement as to the consistency of some system is not dependent upon that system’s being able to prove its own consistency (i.e. generate a formula that states, e.g. ‘0=1’ is not provable). For if that was the sole basis, how could we trust it? If the system was inconsistent, it could generate this formula as well (see Smullyan, Gödel’s Incompleteness Theorems, (Oxford, 1992, p. 109)). Furthermore, [George] Boolos allows that we do know that certain systems, such as Peano Arithmetic, are consistent even though they cannot prove their own consistency. Presumably, we know this because we can see that a certain model satisfies the axioms of the system at issue, hence that they are true in that model and so must be consistent.”

Yesterday’s Algorithm:
    Penrose and the Gödel Argument

The relationship between consistency and the existence of a model is brought home by the following weblog entry that neatly summarizes a fallacious argument offered in the AMS Notices by Davies:

The following is an interesting example that I came across in the article “Whither Mathematics?” by Brian Davies in the December issue of Notices of the American Mathematical Society.

Consider the following list A1 of axioms.

(1) There is a natural number 0.
(2) Every natural number a has a successor, denoted by S(a).
(3) There is no natural number whose successor is 0.
(4) Distinct natural numbers have distinct successors: a = b if and only if S(a) = S(b).
(5) If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all the natural numbers.

Now consider the following list A2 of axioms.

(1) G is a set of elements and these elements obey the group axioms.
(2) G is finite but not isomorphic to any known list of finite simple groups.
(3) G is simple, in other words, if N is a subset of G satisfying certain properties then N=G.

We can roughly compare A2 with A1. The second axiom in A2 can be thought of as analogous to the third axiom of A1. Also the third axiom of A2 is analogous to the fifth axiom of A1, insofar as it refers to an unspecified set with cetain properties and concludes that it is equal to G.

Now, as is generally believed by most group theorists, the system A2 is internally inconsistent and the proof its inconsistency runs for more than 10000 pages.

So who is to deny that the system A1 is also probably internally inconsistent! Particularly since Godel proved that you can not prove it is consistent (staying inside the system). May be the shortest proof of its inconsistency is one hundred million pages long!

— Posted by Krishna,
   11/29/2005 11:46:00 PM,
   at his weblog,
  “Quasi-Coherent Ruminations”

An important difference between A1 (the set of axioms of Peano arithmetic) and A2 (a set of axioms that describe a new, unknown, finite simple group) is that A1 is known to have a model (the nonnegative integers) and A2 is not known to have a model.

Therefore, according to Seager’s argument, A1 is consistent and A2 may or may not be consistent.

The degree to which Seager’s argument invokes Platonic realism is debatable.  Less debatable is the quasireligious faith in nominalism proclaimed by Davies and Nelson.  Nelson’s own account of a religious experience in 1976 at Toronto is instructive.

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

— Edward Nelson,
   Mathematics and Faith (pdf)

Nelson’s “Mathematics and Faith” was written for the Jubilee for Men and Women from the World of Learning held at the Vatican, 23-24 May 2000.  It concludes with an invocation of St. Paul:

During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his Pellegrino di Roma.  “For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Belief in the consistency of arithmetic may or may not be foolish, and therefore an Emersonian hobgoblin of little minds, but bullshit is bullshit, whether in London, in Princeton, in Toronto, or in Rome.

Thursday, November 3, 2005

Thursday November 3, 2005

Filed under: Uncategorized — m759 @ 11:07 AM


USA Today on last night’s White House dinner:

“In his toast, Bush said the royal visit was ‘a reminder of the unique and enduring bond’ between the two countries.”

From Log24, July 18, 2003:

The use of the word “idea” in my entries’ headlines yesterday was not accidental.  It is related to an occurrence of the word in Understanding: On Death and Truth, a set of journal entries from May 9-12.  The relevant passage on “ideas” is quoted there, within commentary by an Oberlin professor:

“That the truth we understand must be a truth we stand under is brought out nicely in C. S. Lewis’ That Hideous Strength when Mark Studdock gradually learns what an ‘Idea’ is. While Frost attempts to give Mark a ‘training in objectivity’ that will destroy in him any natural moral sense, and while Mark tries desperately to find a way out of the moral void into which he is being drawn, he discovers what it means to under-stand.

‘He had never before known what an Idea meant: he had always thought till now that they were things inside one’s own head. But now, when his head was continually attacked and often completely filled with the clinging corruption of the training, this Idea towered up above him-something which obviously existed quite independently of himself and had hard rock surfaces which would not give, surfaces he could cling to.’

This too, I fear, is seldom communicated in the classroom, where opinion reigns supreme. But it has important implications for the way we understand argument.”

— “On Bringing One’s Life to a Point,” by Gilbert Meilaender, First Things, November 1994

The old philosophical conflict between realism and nominalism can, it seems, have life-and-death consequences.  I prefer Plato’s realism, with its “ideas,” such as the idea of seven-ness.  A reductio ad absurdum of nominalism may be found in the Stanford Encyclopedia of Philosophy under Realism:

“A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false….”

The claim that 7 is not prime is, regardless of its motives, dangerously stupid.

The New York Lottery evening number
for All Souls’ Day, Nov. 2, 2005, was


Related material:

Entries for Nov. 1, 2005 and
the song Planned Obsolescence
by the 10,000 Maniacs

(Hope Chest:
The Fredonia Recordings)

Tuesday, November 1, 2005

Tuesday November 1, 2005

Filed under: Uncategorized — Tags: , — m759 @ 12:00 PM

Antidote to Atiyah

In a recent talk, "The Nature of Space," Sir Michael Atiyah gave a misleading description of Plato's doctrine of "ideas," or "idealism."  Atiyah said that according to Plato, ideas reside in  "an imaginary world–  the world of the mind," and that what we see in the external world is "some pale reflection" of ideas in the mind.

An antidote to Atiyah's nonsense may be found in the Catholic Encyclopedia:

"So it came to pass that the word idea in various languages took on more and more the meaning of 'representation,' 'mental image,' and the like. Hence too, there was gradually introduced the terminology which we find in the writings of Berkeley, and according to which idealism is the doctrine that ascribes reality to our ideas, i.e. our representations, but denies the reality of the physical world. This sort of idealism is just the reverse of that which was held by the philosophers of antiquity and their Christian successors; it does away with the reality of ideal principles by confining them exclusively to the thinking subject; it is a spurious idealism…."

Atiyah contrasts his mistaken view of Plato with what he calls the "realism" of Hume.  He does not mention that Plato's doctrine of ideas is also known as "realism."  For details, see, again, the Catholic Encyclopedia:

"The conciliation of the one and the many, the changing and the permanent, was a favourite problem with the Greeks; it leads to the problem of universals. The typical affirmation of Exaggerated Realism, the most outspoken ever made, appears in Plato's philosophy; the real must possess the attributes of necessity, universality, unity, and immutability which are found in our intellectual representations. And as the sensible world contains only the contingent, the particular, the unstable, it follows that the real exists outside and above the sensible world. Plato calls it eîdos, idea. The idea is absolutely stable and exists by itself (ontos on; auta kath' auta), isolated from the phenomenal world, distinct from the Divine and human intellect…. The exaggerated Realism of Plato… is the principal doctrine of his metaphysics."
Atiyah's misleading remarks may appeal to believers in the contemptible religion of Scientism, but they have little to do with either historical reality or authentic philosophy.

Thursday, April 7, 2005

Thursday April 7, 2005

Filed under: Uncategorized — m759 @ 9:00 AM
Nine is a Vine

“Heaven is a state,
a sort of metaphysical state.”
— John O’Hara, Hope of Heaven, 1938

The image “http://www.log24.com/log/pix05/HopeOfHeaven1938.jpg” cannot be displayed, because it contains errors.

 “Mathematical realism holds that mathematical entities exist independently of the human mind.  Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. The term Platonism is used because such a view is seen to parallel Plato’s belief in a “heaven of ideas”, an unchanging ultimate reality that the everyday world can only imperfectly approximate. Plato’s view probably derives from Pythagoras, and his followers the Pythagoreans, who believed that the world was, quite literally, built up by the numbers. This idea may have even older origins that are unknown to us.” — Wikipedia


Related material:

In memory of Jesus of Nazareth,
the “true vine,”
who, some historians believe,
died on this date:

The Crucifixion of John O’Hara.

In memory of the Anti-Vine:

The image “http://www.log24.com/log/pix05/DayOfTheLocust.jpg” cannot be displayed, because it contains errors.

See Dogma and
Heaven, Hell,
and Hollywood.
Related material:

The Usual Suspects


Thursday, December 26, 2002:

Holly for Miss Quinn 

Tonight’s site music is for Stephen Dedalus
and Miss Quinn, courtesy of Eithne Ní Bhraonáin. 

Miss Quinn



Monday, January 10, 2005

Monday January 10, 2005

Filed under: Uncategorized — m759 @ 11:00 AM


In memory of Humphrey Carpenter:

“Aslan’s last words come at the end of The Last Battle: ‘There was a real railway accident […] Your father and mother and all of you are–as you used to call it in the Shadow-Lands–dead. The term is over: the holidays have begun. The dream is ended: this is the morning.’ The final paragraph of the novel, which follows these words, functions as a coda; it is full of the conventions which signal the wrapping up of a story. This direct speech is the true climax of the Chronicles. Aslan is given the last word in these quiet but emphatic lines. He is the ultimate arbiter of reality: ‘There was a real railway accident.’ Plato, in addition to the Christian tradition, lies behind the closing chapters of The Last Battle….

‘It’s all in Plato, all in Plato: bless me, what do they teach them at these schools!’ “

Joy Alexander, Aslan’s Speech

See also From Tate to Plato (Nov. 19, 2004), Habeas Corpus (Nov. 24, 2004), and the Log24 entries of last Friday through Sunday.

There was a real railway accident.

Friday, July 25, 2003

Friday July 25, 2003

Filed under: Uncategorized — m759 @ 11:59 PM

Realism in Literature:
Under the Volcano

Mexican Volcano Blast
Scares Residents


Filed at 11:13 p.m. EDT Friday, July 25, 2003

PUEBLA, Mexico (AP) — Mexico’s Popocatepetl volcano shot glowing rock and ash high into the air Friday night, triggering a thunderous explosion that panicked some residents in nearby communities.

Here are 3 webcam views of the volcano.   Nothing to see at the moment.

Literary background:

Malcolm Lowry’s Under the Volcano,

Plato, Pegasus, and the Evening Star,

A Mass for Lucero,

Shining Forth,

and, as background for today’s earlier entry on Platonism and Derrida,

The Shining of May 29.


For more on Plato and Christian theology, consult the highly emotional site

Further Into the Depths of Satan:

“…in The Last Battle on page 170 [C. S.] Lewis has Digory saying, ‘It’s all in Plato, all in Plato.’ Now, Lewis calls Plato ‘an overwhelming theological genius’ (Reflections on the Psalms, p. 80)….”

The title “Further Into the Depths of Satan,” along with the volcano readings above, suggests a reading from a related site:

Gollum and the Mystery of Evil:

“Gollum here clearly represents Frodo’s hidden self. It is ‘as if we are witnessing the darkest night of the soul and one side attempting to master the other’ (Jane Chance 102). Then Frodo, whose finger has been bitten off, cries out, and Gollum holds the Ring aloft, shrieking: ‘Precious, precious, precious! My Precious! O my Precious!’ (RK, VI, 249). At this point, stepping too near the edge, he falls into the volcano, taking the Ring with him. With this, the mountain shakes.’ “

In the above two-step vignette, the part of Gollum is played by the author of “Further Into the Depths of Satan,” who called  C. S. Lewis a fool “that was and is extremely useful to his father the devil.”

See Matthew 5:22: “…whosoever shall say, Thou fool, shall be in danger of hell fire.” 

Friday, July 18, 2003

Friday July 18, 2003

Filed under: Uncategorized — m759 @ 4:09 PM

Hideous Strength

On a Report from London:

Assuming rather prematurely that the body found in Oxfordshire today is that of David Kelly, Ministry of Defence germ-warfare expert and alleged leaker of information to the press, the Financial Times has the following:

“Mr Kelly’s death has stunned all the players involved in this drama, resembling as it does a fictitious political thriller.”

Financial Times, July 18,
   2003, 19:06 London time

I feel it resembles rather a fictitious religious thriller… Namely, That Hideous Strength, by C. S. Lewis.  The use of the word “idea” in my entries’ headlines yesterday was not accidental.  It is related to an occurrence of the word in Understanding: On Death and Truth, a set of journal entries from May 9-12.  The relevant passage on “ideas” is quoted there, within commentary by an Oberlin professor:

“That the truth we understand must be a truth we stand under is brought out nicely in C. S. Lewis’ That Hideous Strength when Mark Studdock gradually learns what an ‘Idea’ is. While Frost attempts to give Mark a ‘training in objectivity’ that will destroy in him any natural moral sense, and while Mark tries desperately to find a way out of the moral void into which he is being drawn, he discovers what it means to under-stand.

‘He had never before known what an Idea meant: he had always thought till now that they were things inside one’s own head. But now, when his head was continually attacked and often completely filled with the clinging corruption of the training, this Idea towered up above him-something which obviously existed quite independently of himself and had hard rock surfaces which would not give, surfaces he could cling to.’

This too, I fear, is seldom communicated in the classroom, where opinion reigns supreme. But it has important implications for the way we understand argument.”

— “On Bringing One’s Life to a Point,” by Gilbert Meilaender, First Things,  November 1994

The old philosophical conflict between realism and nominalism can, it seems, have life-and-death consequences.  I prefer Plato’s realism, with its “ideas,” such as the idea of seven-ness.  A reductio ad absurdum of nominalism may be found in the Stanford Encyclopedia of Philosophy under Realism:

“A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false….”

The claim that 7 is not prime is, regardless of its motives, dangerously stupid… A quality shared, it seems, by many in power these days.

Monday, December 16, 2002

Monday December 16, 2002

Filed under: Uncategorized — m759 @ 10:00 PM

Rebecca Goldstein
at Heaven’s Gate

This entry is in gratitude for Rebecca Goldstein’s
excellent essay
in The New York Times of December 16, 2002.

She talks about the perennial conflict between two theories of truth that Richard Trudeau called the “story theory” and the “diamond theory.” My entry of December 13, 2002, “Rhyme Scheme,” links the word “real” to an article in the Stanford Encyclopedia of Philosophy that contains the following:

“According to a platonist about arithmetic, the truth of the sentence ‘7 is prime’ entails the existence of an abstract object, the number 7. This object is abstract because it has no spatial or temporal location, and is causally inert. A platonic realist about arithmetic will say that the number 7 exists and instantiates the property of being prime independently of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false…”

This discussion of “sevenness,” along with the discussion of “eightness” in my December 14, 2002, note on Bach, suggest that I supply a transcription of a note in my paper journal from 2001 that deals with these matters.

From a paper journal note of October 5, 2001:

The 2001 Silver Cup Award
for Realism in Mathematics
goes to…
Glynis Johns, star of
The Sword and the Rose,
Shake Hands with the Devil, and
No Highway in the Sky.

Glynis Johns is 78 today.

“Seven is heaven,
Eight is a gate.”
— from
Dealing with Memory Changes
as You Grow Older
by Kathleen Gose and Gloria Levi

“There is no highway in the sky.”
— Quotation attributed to Albert Einstein.
Gotthard Günther’s website
“Achilles and the Tortoise, Part 2”.)

“Don’t give up until you
Drink from the silver cup
And ride that highway in the sky.”
America, 1974

See also page 78 of
Realism in Mathematics
(on Gödel’s Platonism)
by Penelope Maddy,
Clarendon Press, Oxford, 1990
(reprinted, 2000).

Added 12/17/02: See also
the portrait of Rebecca Goldstein in
Hadassah Magazine
Number 10
(June/July 1997).

For more on the Jewish propensity to
assign mystical significance to numbers, see
Rabbi Zwerin’s Kol Nidre Sermon.

For the significance of “seven” in Judaism, see
Zayin: The Woman of Valor.
For the significance of “eight” in Judaism, see
Chet: The Life Dynamic.

For the cabalistic significance of
“Seven is heaven, Eight is a gate,”
note that Zayin, Seven, signifies
“seven chambers of Paradise”
and that Chet, Eight, signifies
the “gateway to infinity.”

For the significance of the date 12.17, see
Tet: The Concealed Good.

Friday, December 13, 2002

Friday December 13, 2002

Filed under: Uncategorized — m759 @ 2:27 PM

Rhyme Scheme

"The introduction of Charge-Coupled Devices (CCDs)
has dramatically changed the methods
astronomers use to view objects."
— Santa Barbara Instrument Group, Inc.

"They should have sent a poet." 
— Jodie Foster in the film version
of Carl Sagan's Contact

star cluster

M16 Nebulous Star Cluster.
300 second Model ST-7
CCD image
taken through a
7", f/7 Astrophysics refractor
utilizing the self-guiding mode.

"Say 'Abba,'
Jesus told
his followers. 
'Our Father.'"



— Rhyme

On the question of what reality is:
"Under what circumstances do we think things are
real? ….

This question speaks to a small, manageable problem
having to do with the camera and not
what it is the camera takes pictures of."

Erving Goffman,    
Frame Analysis, An Essay on
the Organization of Experience
Harper & Row, 1974, p. 2

Friday, August 30, 2002

Friday August 30, 2002

Filed under: Uncategorized — Tags: , — m759 @ 2:30 AM

For Mary Shelley, on her birthday: A Chain of Links The creator of Frankenstein might appreciate the following chain of thought. Lucifer.com Lucifer Media Corporation Lucifer Media Sites The Extropy Institute: International Transhumanist Solutions Why Super-Human Intelligence Would Be Equivalent To Precognition, by Marc Geddes:

"Consider the geometry of multiple dimensions as an analogy for mental abilities… …if there is a 4th dimension of intelligence, to us ordinary humans stuck with 3 dimensional reasoning, this 4th dimension would be indistinguishable from precognition. Post-humans would appear to us ordinary humans as beings which could predict the future in ways which would be inexplicable to us. We should label post-humans as 'Pre-Cogs.'

In the Steven Speilberg [sic]  film Minority Report, we encounter genetically engineered humans with precisely the abilities described above."

Internet Movie Database page on "Minority Report"

IMDb page on "Minority Report" author Philip K. Dick

IMDb biography of Philip K. Dick, where our chain of links ends.  Here Dick says that

"The basic tool for the manipulation of reality is the manipulation of words. If you can control the meaning of words, you can control the people who must use the words."

On the other hand, Dick also says here that

"Reality is that which, when you stop believing in it, doesn't go away."

These two quotations summarize, on the one hand, the cynical, relativistic nominalism of the postmodernists and, on the other hand, the hard-nosed realism of the Platonists.

What does all this have to do with "the geometry of multiple dimensions"?

Consider the famous story for adolescents, A Wrinkle in Time, by Madeleine L'Engle.   The author, a well-meaning Christian, tries, like all storytellers,  to control her readers by controlling the meaning of words.   The key word in this book is "tesseract," a term from multi-dimensional geometry.   She insists that a tesseract has mystic properties and cannot be visualized.  She is wrong (at least about the visualizing).

See The Tesseract: A look into 4-dimensional space, by Harry J. Smith.

See also the many revealing comments in Harry J. Smith's Guestbook.

One of Smith's guests remarks, apropos of Smith's comments on St. Joseph, that he has his own connection with St. Augustine.

For a adult-level discussion of Augustine, time, eternity, and Platonism, see the website Time as a Psalm in St. Augustine, by A. M. Johnston.

See also the remark headlining Maureen Dowd's New York Times column of August 28, 2002, Saint Augustine's Day:

"I'm with Dick."

Whether the realist Dick or the nominalist Dick, she does not say.

As for precognition, see my series of journal notes below, which leads up to two intriguing errors in an Amazon.com site on the "Forbidden Planet" soundtrack.   The first two audio samples from this soundtrack are (wrongly) entitled "Birdland" and "Flamingo."  See also the West Wing episode rebroadcast on Wednesday, August 28, 2002,

The Black Vera Wang

C. J. Cregg (Allison Janney), who models a black Vera Wang dress in that episode, has the Secret Service codename Flamingo.

"…that woman in black She's a mystery She's everything a woman should be Woman in black got a hold on me"

(Foreigner 4 in my August 28 note below)

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