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The establishment of such an isochronic relationship
with a discoverer's original discovery, spanning a distance
in calendar time of decades, centuries, and sometimes
millennia, is the means for transforming the mental
act of reliving such a discovery into an intelligible object
of conscious reflection. There is thus the sharing of this
experience, not only between the individual student and
the original discoverer, but among all those who, from
all centuries, have shared such reliving of that same
original experience in this isochronic way.
This is what Francesco Zorzi prohibited,204 what
Paolo Sarpi's asset Francis Bacon forbade,205 what Newton
implicitly banned with his "hypotheses non fingol ,,206
and what Immanuel Kant abhorred in Leibniz's Monadololfy.
207 That prohibition and abhorrence are directed
explicitly against the practice of apprehending as intelligible
objects of conscious reflection the provably creative
proesses of mentation.
All these Aristotelians, whether as materialists, empiricists,
or modernist logical positivists, demand that the
subjects of conscious reflection be delimited to two classes
of experience: sense-perceptions and the emotions which'
are more or less mysteriously attached to those senseperceptions.208
From this is derived the empiricism of
Zorzi, Bacon, Hobbes, Locke, and the radical empiricism
of Ortes, Adam Smith, Jeremy Bentham, Thomas Malthus,
James Mill, John Stuart Mill, and Bertrand Russell,
the "information theory" of Norbert Wiener, and the
pseudo-scientific economics of John Von Neumann.
204. Zorzi (Giorgi), loc. cit.
205. Bacon asserts in the New Organon: "There are and can be only
two ways of searching into and discovering truth. The one flies
from the senses and particulars to the most general axioms . ...
[Tlhis is now in fashion. The other derives axioms from the
senses and particulars, rising by a gradual and unbroken ascent,
so that it arrives at the most general axioms last of all. This is
the true way, but as yet untried." Aphorism XIX, in The New
\ Organon and Related Writings, ed. by Fulton H. Anderson (Indianapolis:
Bobbs-Merrill Company, 1960), p. 43.
206. See Sir Isaac Newton's Mathematical Principles of Natural Philosophy
and His System of the World, revised trans. by Florian Cajori
(Berkeley: University of California Press, 1960), General Scholium,
p. 547.
207. Kant, loc. cit., passim.
208. Among "New Age" varieties of psychologists and sociologists,
Sigmund Freud popularized the term "cathexis" for this. The
U.N.O.'s mind-destroying "educational reform" sometimes promoted
under the rubric of "Outcome-Based Education," is based
upon virtually banning all cognitive thought. Out of racists
such as the Harvard University circles of Jensen and Shockley
comes the dogma that certain "races" are not naturally inclined
to cognitive thought, but only to conditioning of their associative-emotional
behavior. The New Ager cult-lunacy of "right
brain, left brain" originates in the same pseudo-scientific gobbledygook
as these referenced U.N.O. and Harvard developments.
In defiance of such Venetian and kindred pI:ohibitions,
continue with our subject of this momnt, the
indicated humanist method of education. Continue to
focus upon a constructive geometry as the model topic
for such a method. Through the method indicated, the
secondary school pupil 'is becoming acquainted personally
with the experience of two types of discovery indicated:
those which extend a theorem-lattice, and those
which are true Platonic hypotheses, which overturn a
lattice of reference;.
Most of today's relatively better formal education209
functions somewhat well on the lower level: extending
the lattice. This is good, of course. The pupil is taking
the historical examples as a model of a method for
elaborating propositions which are hewed, if possible,
into consistency with a recognized set of underlying
axiomatic assumptions. As long as the propositions are
rooted in the notion of actual or anticipated measurement
of actually occurring processes, this is an indispensable
part of the educational process.210
Henceforth, the reader should continue to read what
is written here, on this subject of humanist methods of
education, with the presumption that we are referencing
as "humanist" an emphasis upon the use of primary
sources as a guide to reliving the original experience of
a specific discovery. The essential connection between
the two classes of discovery in all uses of this method,
is that the pupil is rendering the quality of those mental
processes which generate (and regenerate) that discovery an
intelligible subject of comcious reflection. The difference,
is between the species of mental activity which are taken
as the subject of conscious reflection. This is the kernel
of Nicolaus of Cusa's method of learned ignorance (De
Docta Ignorantia), upon which the emergence of modern
science was founded.211
209. If itself tending increasingly to the exceptional.
210. It is sufficient to note, as a word of caution, that without that
mooring in an orientation toward measurement, examining
formal theorem-lattices merely from the standpoint of Aristotelian
logic can lead into insanity. This is a notorious problem
among specialists in mathematics from a logical positivist or
related standpoint: they do not go mad despite being "good
mathematicians"; they go mad because they are all too devoutly
trained in that variety of "mathematical thinking"; the more
academic honors they accrete, the greater the danger, the rarer
the survivor of that lately increasing mental disorder: "Kronecker's
Disease."
211. This is perhaps the place to note, specifically, that the same
method is key to Classical fine arts. The failure of many otherwise
gifted and learned musicians to grasp the rudiments of
Beethoven's method of composition, as employed in most exemplary
fashion in his late quartets, can be represented as the same
fo rm of mental disorder which impedes comprehension of Georg
Cantor's work on the transfinite, or Riemann's famous Hypa-
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