Intuition and Geometry

Intuition is usually distinguished from Reason as non-discursive, and from Sensation as non-Empirical.  Usually, its Object is conceived as simple, and contact with it as immediate.  But, there have been a wide variety of concepts of that Object--for Platonists, a Form; for Spinoza, God; for Bergson, Motion; and, in ordinary parlance, an ulterior motive of another.  So, Euclidean Geometry, as a Deductive system, is clearly non-Intuitive.  And Pythagorean Numerology is likely Intuitive.  But, the classification of the Cognition of Pythagorean Geometry is less clear.  On the one hand, as a Form, a geometrical figure might be Intuited.  But, once an Angle is involved, the object becomes more complex.  For, as has been previously discussed, an Angle cannot be reduced to a mere Vertex, and, instead, must be derived from a concept of Circulinearity, to which mere Rectilinearity is inadequate, and, indeed, with which it is incommensurable.  So, plainly, the Pythagorean Theorem, which entails the measures of both Lines and Angles, is not simple, and, hence, cannot be Intuited, even at a moment of nascent inception.  Thus, even if not as formalized as Euclidean Geometry, Pythagorean Geometry is too complex for Intuition, and, so, must incorporate Reason at some moment.