On the Soul (De Anima) with Simplicius Commentary

It is owing, likewise, to the illuminations of a separate intellect infused into the soul that all men have common conceptions, which are certain vestiges and resemblances of intellect. The knowledge of these conceptions is indemonstrable, or rather, it is superior to demonstration. Examples include: that things equal to the same thing are equal to each other; that if equals are taken from equal things, the remainders are equal; that in everything there is either affirmation or negation; that all things desire the good; and the like. We require no proof to believe these; we know them immediately, and our knowledge of them is superior to that of demonstration.

These common conceptions, therefore, which all men possess, are evidently resemblances of intellect. Hence, intellect is said to be the principle of science, by which we obtain knowledge of intelligibles.

Socrates, in the Phædrus, describes three characters who are elevated from a sensible to an intellectual life—who, according to him, complete the primary life of the soul: the philosopher, the lover, and the musician. The principle and path of elevation for the lover is through apparent beauty, employing the middle forms of beautiful objects as steps in the ascent. For the musician, who is allotted the third rank, the transition is from sensible harmony to unapparent harmony and the reasons it contains. To the one, sight is the instrument of reminiscence; to the other, hearing. But for him who is naturally a philosopher, whence and by what means is the reminiscence of intellectual knowledge effected, and the excitation to real being and truth? This character, on account of its imperfection, also requires a proper principle. It must be excited from within itself; and he who is naturally such is astonished by the contemplation of real being.

And again, page 9, Proclus observes: "Plato clearly evinces that the mathematical sciences have a power of purifying and elevating the soul, removing, like the Homeric Minerva, the darkness of sense from the intellectual light of the dianoetic power, which is better worth saving than ten thousand eyes; so that these disciplines not only partake of Mercurial gifts, but also of those of Minerva."