Book II

The text of Gemistus Plethon Georgius Gemistus Plethon (c. 1355–1452) was a late Byzantine philosopher who sought to revive Platonism. His name here suggests this manuscript version was annotated or preserved through his school of thought.

If we say that mathematical objects subsist from sensory things—the soul painting or shaping the circular or triangular form within herself based on the triangles or circles found in matter—from where does the precision original: akribeia; the exactitude and mathematical rigour that allows for absolute proof. and the immutability of these principles arise?

For it is necessary that they come either from sensory things or from the soul. Yet, it is impossible for them to come from sensory things, for these partake of far less precision. Therefore, they must come from the soul, which adds the perfect to the imperfect and the precise to the imprecise.

For where among sensory things is the partless original: ameres; the definition of a mathematical point as that which has no parts or magnitude., or the widthless original: aplatēs; the definition of a line as "breadthless length.", or the depthless original: abathes; the definition of a surface which has only length and width.?

Where is the equality of those straight lines, or the truthful accuracy of the sides as they ought to be, or the rectitude of the angles? Do we not see how all sensory things are mixed together? Nothing is pure, but everything is in a state of becoming original: genesis; in Platonic thought, the physical world is "becoming" (changing), while the world of forms is "being" (eternal).. Even the heavens, to the extent that they are physical, divide and move everything in a state of extension.

How, then, shall we grant a permanent essence to immovable principles original: akinitois logois; the stable laws of geometry that never change, unlike physical objects. if they are derived from things that are moving and shifting from one state to another? For everything that subsists from moving essences must itself have a changeable explanation derived from them.

How shall we attach precision to that which is accurate and unassailable if it comes from things that are not precise? How can the sensory realm be the cause of immovable knowledge, when knowledge requires causes greater than what the senses provide? We must assume, then, that the soul is the productive source of mathematical forms and principles. She contains the paradigms within herself essentially; they are her very substance, and from this, her acts of knowledge are projections original: probolai; the Neoplatonic idea that the soul "throws forward" or unfolds its innate, hidden knowledge into conscious mathematical thought..