Cusa: On informed ignorance

Thus wise men have been right in taking examples of things which can be investigated with the mind from the field of mathematics, and not one of the Ancients who is considered of real importance approached a difficult problem except by way of the mathematical analogy. That is why Boethius, the greatest scholar among the Romans, said that for a man entirely unversed in mathematics, knowledge of the Divine was unattainable. ...
The finite mind can therefore not attain to the full truth about things through similarity. For the truth is neither more nor less, but rather indivisible. What is itself not true can no more measure the truth than what is not a circle can measure a circle; whose being is indivisible. Hence reason, which is not the truth, can never grasp the truth so exactly that it could not be grasped infinitely more accurately. Reason stands in the same relation to truth as the polygon to the circle; the more vertices a polygon has, the more it resembles a circle, yet even when the number of vertices grows infinite, the polygon never becomes equal to a circle, unless it becomes a circle in its true nature.
The real nature of what exists, which constitutes its truth, is therefore never entirely attainable. It has been sought by all the philosophers, but never really found. The further we penetrate into informed ignorance, the closer we come to the truth itself. ...

Those who hold firmly to the first view [that the circle can be squared] seem to be satisfied with the fact that given a circle, there exists a square which is neither larger nor smaller than the circle. ... If, however, this square is neither smaller nor larger than the circle, by even the smallest assignable fraction, they call it equal. For this is how they understand equality  one thing is equal to another if it neither exceeds it nor falls short of it by any rational fraction, even the smallest. If one understands the notion of equality in this way, then, I believe, one can correctly say that, given the circumference of a certain polygon, there exists a circle with the same circumference. If, however, one interprets the idea of equality, insofar as it applies to a quantity, absolutely and without regard to rational fractions, then the statement of the others is right: there is no noncircular area which is precisely equal to a circular area.

JOC/EFR August 2007
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