Plutarch's Platonic questions (3.1)

In the Republic,[*] he supposes the universe, as one line, to be cut into two unequal sections; again he cuts each of these sections in two after the same proportion, and supposes the two sections first made to constitute the two genera of things sensible and things intelligible in the universe. The first represents the genus of intelligibles, comprehending in the first subdivision the primitive forms or ideas, in the second the mathematics. Of sensibles, the first subdivision comprehends solid bodies, the second comprehends the images and representations of them. Moreover, to every one of these four he has assigned its proper judicatory faculty;—to the first, reason; to the mathematics, the understanding; to sensibles, belief; to images and likenesses, conjecture.

BUT WHAT DOES HE MEAN BY DIVIDING THE UNIVERSE INTO UN EQUAL PARTS? AND WHICH OF THE SECTIONS, THE INTELLIGIBLE OR THE SENSIBLE, IS THE GREATER? FOR IN THIS HE HAS NOT EXPLAINED HIMSELF.

At first sight it will appear that the sensible is the greater portion. For the essence of intelligibles being indivisible, and in the same respect ever the same, is contracted into a little, and pure; but an essence divisible and pervading bodies constitutes the sensible part. Now what

is immaterial is limited; but body in respect of matter is infinite and unlimited, and it becomes sensible only when it is defined by partaking of the intelligible. Besides, as every sensible has many images, shadows, and representations, and from one and the same original several copies may be taken both by nature and art; so the latter must needs exceed the former in number, according to Plato, who makes things intelligible to be patterns or ideas of things sensible, like the originals of images and reflections. Further, Plato derives the knowledge of ideas from body by abstraction and cutting away, leading us by various steps in mathematical discipline from arithmetic to geometry, thence to astronomy, and setting harmony above them all. For things become geometrical by the accession of magnitude to quantity; solid, by the accession of profundity to magnitude; astronomical, by the accession of motion to solidity; harmonical, by the accession of sound to motion. Abstract then sound from moving bodies, motion from solids, profundity from superficies, magnitude from quantity, we are then come to pure intelligible ideas, which have no distinction among themselves in respect of the one single intelligible essence. For unity makes no number, unless joined by the infinite binary; then it makes a number. And thence we proceed to points, thence to lines, from them to superficies, and profundities, and bodies, and to the qualities of the bodies so and so qualified. Now the reason is the only judicatory faculty of intelligibles; and the understanding is the reason in the mathematics, where intelligibles appear as by reflection in mirrors. But as to the knowledge of bodies, because of their multitude, Nature has given us five powers or distinctions of senses; nor are all bodies discerned by them, many escaping sense by reason of their smallness. And though every one of us consists of a body and soul, yet the hegemonic and intellectual faculty is small, being hid in the huge mass of flesh. And the case is the same in the universe, as to sensible and intelligible. For intelligibles are the principles of bodily things, but every thing is greater than the principle whence it came.