Cathédrale de Chartres; Civilization, Medieval; Mont-Saint-Michel (Abbey : France)
"One step more, Mr. Abelard, if I do not weary you! Let me take
three of these metres which do not exist, and place them so that the
ends of one shall touch the ends of the others. May I ask what is
that figure?"
"I presume you mean it to be a triangle."
"Precisely! and what sort of a triangle?"
"An equilateral triangle, the sides of which measure one metre
each."
"Now let me take three more of these metres which do not exist, and
construct another triangle which does not exist;--are these two
triangles or one triangle?"
"They are most certainly one--a single concept of the only possible
equilateral triangle measuring one metre on each face."
"You told us a moment ago that a universal could not exist wholly
and exclusively in two individuals at once. Does not the universal
by definition--THE equilateral triangle measuring one metre on each
face--does it not exist wholly, in its integrity of essence, in each
of the two triangles we have conceived?"
"It does--as a conception."
"I thank you! Now, although I fear wearying you, perhaps you will
consent to let me add matter to mind. I have here on my desk an
object not uncommon in nature, which I will ask you to describe."
"It appears to be a crystal."
"May I ask its shape?"
"I should call it a regular octahedron."
"That is, two pyramids, set base to base? making eight plane
surfaces, each a perfect equilateral triangle?"
"Concedo triangula (I grant the triangles)."
"Do you know, perchance, what is this material which seems to give
substantial existence to these eight triangles?"
"I do not."
"Nor I! nor does it matter, unless you conceive it to be the work of
man?"
"I do not claim it as man's work."
"Whose, then?"
"We believe all actual creation of matter, united with form, to be
the work of God."
"Surely not the substance of God himself? Perhaps you mean that this
form--this octahedron--is a divine concept."
"I understand such to be the doctrine of the Church."
"Then it seems that God uses this concept habitually to create this
very common crystal. One question more, and only one, if you will
permit me to come to the point. Does the matter--the material--of
which this crystal is made affect in any way the form--the nature,
the soul--of the universal equilateral triangle as you see it
bounding these eight plane surfaces?"
"That I do not know, and do not think essential to decide. As far as
these triangles are individual, they are made so by the will of God,
and not by the substance you call triangle. The universal--the
abstract right angle, or any other abstract form--is only an idea, a
concept, to which reality, individuality, or what we might call
energy is wanting. The only true energy, except man's free will, is
God."
Public-domain text, read in full here on John Shaqi.
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