De mathematica.
The Name and Nature of Mathematics
Hugh introduces mathematics as a discipline, distinguishing its superstitious misuse in divination from its true role as the study of abstract quantity through reason.
Mathematics, then, is the name given to this structured field of knowledge. The word mathesis, when written without the 'h' and the t is unaspirated, is interpreted as 'vanity' and points to the superstition of those who place human fates in the constellations. And this is also why people of this sort came to be called mathematicians. But when the t is aspirated, the word sounds like 'teaching.' And this is the discipline that considers abstract quantity. Abstract quantity is what we call it because, separating it in our minds from matter or from other accidents — such as even, odd, and the like — we handle it through reasoning alone, which is what teaching does, not nature.
Intellectible Substance and the Soul's Calling
Drawing on Boethius, Hugh describes how souls share in intellectible substance and are blessed in proportion to their return to pure intelligence.
Boethius calls this 'intelligible,' because through thought and intelligence it grasps the first, intellectible part of all the works of heaven and of the divine nature above, and whatever under the sphere of the moon holds power through a more blessed mind and a purer substance, and finally the souls of human beings, which, though they once shared in that earlier intellectible substance, degenerated through contact with bodies, falling from the intellectible to the intelligible, so that they are no more understood than they understand, and they become more blessed in purity of intelligence the more often they turn back toward the intellectible. For the nature of spirits and of souls, because it is incorporeal and simple, shares in the intellectible substance.
The Soul's Descent Through Sense and Imagination
Hugh traces how the soul, though simple and intellectible, becomes composite and degenerates when it reaches toward bodies through the senses and imagination.
But because it doesn't descend uniformly through the instruments of the senses to grasp sensible things, and because it draws their likeness to itself through imagination, in doing so it in a certain way abandons its own simplicity, by which it loses the rational principle of its composition. For what is like a composite can't be called entirely simple. Therefore the same thing is intellectible and intelligible at the same time, in different respects. It's intellectible in that its nature is incorporeal and can't be grasped by any sense. But it's intelligible because it is indeed a likeness of sensible things, and yet not itself sensible. For it's intellectible because it is neither sensible nor a likeness of the sensible. But the intelligible is perceived by intellect alone, and yet it doesn't perceive by intellect alone, because it has imagination or sense by which it grasps the things that lie within reach of the senses. So by touching bodies it degenerates, because while it reaches out through the passions of the senses toward the invisible forms of bodies and draws them, once touched, into itself through imagination, it is torn from its own simplicity as often as it is shaped by certain qualities of a contrary passion.
Ascent to Pure Understanding
The soul finds its happiness by gathering itself back into unity and ascending from distraction to participation in intellectible substance.
But when, ascending from this distraction toward pure understanding, it gathers itself into one, it becomes happier by participation in intellectible substance.1
Read the original Latin
Mathematica autem doctrinalis scientia dicitur. mathesis enim quando t habet sine aspiratione, interpretatur vanitas, et significat superstitionem illorum, qui fata hominum in constellationibus ponunt. unde et huiusmodi mathematici appellati sunt. quando autem t habet aspiratum, doctrinam sonat. haec autem est, quae abstractam considerat quantitatem. abstracta enim quantitas dicitur, quam intellectu a materia separantes, vel ab aliis accidentibus, ut est, par, impar, et huiuscemodi, in sola ratiocinatione tractamus, quod doctrina facit, non natura. hanc Boethius intelligibilem appellat, quae primam partem, intellectibilem, cogitatione atque intelligentia comprehendit, quae sunt omnium caelestium operum supernae divinitatis, et quidquid sub lunari globo beatiore animo atque puriore substantia valet, et postremo humanarum animarum, quae omnia cum prioris illius intellectibilis substantiae fuissent, corporum tactu ab intellectibilibus ad intelligibilia degenerarunt, ut non magis ipsa intelligantur, quam intelligant, et intelligentiae puritate tunc beatiora sint, quoties sese intellectibilibus applicarint. spirituum namque et animarum natura, quia incorporea et simplex est, intellectibilis substantiae particeps est.
sed quia per instrumenta sensuum non uniformiter ad sensibilia comprehendenda descendit, eorumque similitudinem per imaginationem ad se trahit, in eo quodammodo suam simplicitatem deserit, quo compositionis rationem amittit. neque enim omnimodo simplex dici potest, quod composito simile est. eadem igitur res diversis respectibus intellectibilis simul et intelligibilis est. intellectibilis eo quod incorporea sit natura, et nullo sensu comprehendi possit. intelligibilis vero ideo, quod similitudo quidem est sensibilium, nec tamen sensibilis. intellectibile est enim, quod nec sensibile est, nec similitudo sensibilis. intelligibile autem quod ipsum quidem solo percipitur intellectu, sed non solo intellectu percipit, quia imaginationem vel sensum habet, quo ea quae sensibus subiacent comprehendit. tangendo ergo corpora degenerat, quia, dum invisibiles corporum formas per sensuum passiones procurrit easque attactas per imaginationem in se trahit, toties a sua simplicitate scinditur, quoties aliquibus contrariae passionis qualitatibus informatur.
cum vero ab hac distractione ad puram intelligentiam conscendens in unum se colligit, fit beatior intellectibilis substantiae participatione.
Notes
- 1 ↩intellectibilis rendered as 'intellectible' (the object of pure intellect, incorporeal and beyond sense) to preserve Hugh of St. Victor's technical distinction from intelligibilis; paraphrase risks collapsing the contrast.
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