The Diamond Theory Of Truth Part 2


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
Quotations added after
the death of W. V.
Quine on Christmas
Day, 2000:
“Contrary to John Keats’s
First and Second Laws of
Aesthetics (‘Beauty is truth,
truth beauty’) truth and
beauty are poles apart.
Keats’s ode itself, while
denying this by precept,
bears it out by example.
Truth occupies the alethic
pole of the intellectual
sphere and beauty the
aesthetic pole. Each is
admirable in its way. The
alethic pole exerts the main
pull on science, in the
broad sense: Wissenschaft,
comprising mathematics,
history, and all the hard
and soft sciences in
between. The aesthetic pole
is the focus of belles
lettres, music, art for art’s
sake.”
— W. V. Quine in
Quiddities, Harvard
University Press, 1987
“It’s a thing that
nonmathematicians don’t
realize. Mathematics is
actually an aesthetic
subject almost entirely.”
— John H. Conway, quoted
on page 165, Notices of the
American Mathematical
Society, February 2001.
“There are almost as many
different constructions of
M
as there have been24
mathematicians interested
in that
most remarkable
of all finite groups.”
— John H. Conway in
Sphere Packings, Lattices,
and Groups, third edition,
Springer-Verlag, 1999
“The miraculous
enters…. When we
investigate these problems,
some fantastic things
happen…. At one point while
working on this book we
even considered adopting a
special abbreviation for ‘It
is a remarkable fact that,’
since this phrase seemed
to occur so often. But in
fact we have tried to avoid
such phrases and to
maintain a scholarly
decorum of language.”
— John H. Conway and N. J.
A. Sloane, Sphere
Packings…, preface to first
edition (1988)
Many actions of the Mathieu
group M
may best be24
understood by splitting the
24-element set on which it
acts into a “trio” of three
interchangeable 8-element
sets — “octads,” as in the
“Miracle Octad Generator”
of R. T. Curtis. (See
chapters 10 and 11 of the
above book by Conway and
Sloane.) It is a remarkable
fact that the characteristics
of such a
trio are not
wholly unlike those of the
more famous structure
described below by Saint
Bonaventure.
— S. H. Cullinane, March 1,
2001
“Beware lest you believe
that you can comprehend
the Incomprehensible, for
there are six
characteristics (of
the
Trinity) which will lead the
eye of the mind to
dumbstruck admiration.
Thus, there is
supreme communicability
coupled with the
individuality of persons;
supreme
consubstantiality with the
plurality of hypostases;
total likeness with
separate personalities;
complete equality with
order;
coeternity with
emanations;
complete intimacy with
emission.
Who would not be rapt by
the thought of such
marvels?….
All of this is prefigured by
the Cherubim….”
— Saint Bonaventure, The
Mind’s Journey to God
(1259)
(translated by Lawrence S.
Cunningham, Franciscan
Herald Press, Chicago,
1979),
Chapter Six, “On the
Contemplation of the Most
Blessed Trinity under its
Name: Goodness”
“Was there really a
cherubim waiting at the
star-watching rock…?
Was he real?
What is real?”
— Madeleine L’Engle, A
Wind in the Door, Farrar,
Straus and Giroux, 1973,
conclusion of Chapter
Three, “The Man in the
Night”
“Oh, Euclid, I suppose.”
— Madeleine L’Engle, A
Wrinkle in Time, Farrar,
Straus and Giroux, 1962,
conclusion of Chapter Five,
“The
Tesseract”

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