1 Objection 1: It would seem that the intellect understands the indivisible before the divisible. For the Philosopher says Phys. i, 1) that we understand and know from the knowledge of principles and elements. But principles are indivisible, and elements are of divisible things. Therefore the indivisible is known to us before the divisible.
1 Ad octavum sic proceditur. Videtur quod intellectus noster per prius cognoscat indivisibile quam divisibile. Dicit enim philosophus, in I Physic., quod intelligimus et scimus ex principiorum et elementorum cognitione. Sed indivisibilia sunt principia et elementa divisibilium. Ergo per prius sunt nobis nota indivisibilia quam divisibilia.
2 Objection 2: Further, the definition of a thing contains what is known previously, for a definition proceeds from the first and more known, as is said Topic. vi, 4. But the indivisible is part of the definition of the divisible; as a point comes into the definition of a line; for as Euclid says, a line is length without breadth, the extremities of which are points; also unity comes into the definition of number, for number is multitude measured by one, as is said Metaph. x, Did. ix, 6. Therefore our intellect understands the indivisible before the divisible.
2 Praeterea, id quod ponitur in definitione alicuius, per prius cognoscitur a nobis, quia definitio est ex prioribus et notioribus, ut dicitur in VI Topic. Sed indivisibile ponitur in definitione divisibilis, sicut linea enim, ut Euclides dicit, est longitudo sine latitudine, cuius extremitates sunt duo puncta. Et unitas ponitur in definitione numeri, quia numerus est multitudo mensurata per unum, ut dicitur in X Metaphys. Ergo intellectus noster per prius intelligit indivisibile quam divisibile.
3 Objection 3: Further, Like is known by like. But the indivisible is more like to the intellect than is the divisible; because the intellect is simple De Anima iii, 4). Therefore our intellect first knows the indivisible.
3 Praeterea, simile simili cognoscitur. Sed indivisibile est magis simile intellectui quam divisibile, quia intellectus est simplex, ut dicitur in III de anima. Ergo intellectus noster prius cognoscit indivisibile.
4 On the contrary, It is said De Anima iii, 6) that the indivisible is expressed as a privation. But privation is known secondarily. Therefore likewise is the indivisible.
4 Sed contra est quod dicitur in III de anima, quod indivisibile monstratur sicut privatio. Sed privatio per posterius cognoscitur. Ergo et indivisibile.
5 I answer that, The object of our intellect in its present state is the quiddity of a material thing, which it abstracts from the phantasms, as above stated Question 84, Article 7). And since that which is known first and of itself by our cognitive power is its proper object, we must consider its relationship to that quiddity in order to discover in what order the indivisible is known. Now the indivisible is threefold, as is said De Anima iii, 6.
First, the continuous is indivisible, since actually it is undivided, although potentially divisible: and this indivisible is known to us before its division, which is a division into parts: because confused knowledge is prior to distinct knowledge, as we have said above Article 3). Secondly, the indivisible is so called in relation to species, as man's reason is something indivisible. This way, also, the indivisible is understood before its division into logical parts, as we have said above De Anima iii, 6); and again before the intellect disposes and divides by affirmation and negation.
The reason of this is that both these kinds of indivisible are understood by the intellect of itself, as being its proper object. The third kind of indivisible is what is altogether indivisible, as a point and unity, which cannot be divided either actually or potentially. And this indivisible is known secondarily, through the privation of divisibility. Wherefore a point is defined by way of privation as that which has no parts; and in like manner the notion of one is that is indivisible, as stated in Metaph.
x, Did. ix, 1. And the reason of this is that this indivisible has a certain opposition to a corporeal being, the quiddity of which is the primary and proper object of the intellect. But if our intellect understood by participation of certain separate indivisible forms), as the Platonists maintained, it would follow that a like indivisible is understood primarily; for according to the Platonists what is first is first participated by things.
5 Respondeo dicendum quod obiectum intellectus nostri, secundum praesentem statum, est quidditas rei materialis, quam a phantasmatibus abstrahit, ut ex praemissis patet. Et quia id quod est primo et per se cognitum a virtute cognoscitiva, est proprium eius obiectum, considerari potest quo ordine indivisibile intelligatur a nobis, ex eius habitudine ad huiusmodi quidditatem. Dicitur autem indivisibile tripliciter, ut dicitur in III de anima. Uno modo, sicut continuum est indivisibile, quia est indivisum in actu, licet sit divisibile in potentia. Et huiusmodi indivisibile prius est intellectum a nobis quam eius divisio, quae est in partes, quia cognitio confusa est prior quam distincta, ut dictum est.
Alio modo dicitur indivisibile secundum speciem, sicut ratio hominis est quoddam indivisibile. Et hoc etiam modo indivisibile est prius intellectum quam divisio eius in partes rationis, ut supra dictum est, et iterum prius quam intellectus componat et dividat, affirmando vel negando. Et huius ratio est, quia huiusmodi duplex indivisibile intellectus secundum se intelligit, sicut proprium obiectum. Tertio modo dicitur indivisibile quod est omnino indivisibile, ut punctus et unitas, quae nec actu nec potentia dividuntur. Et huiusmodi indivisibile per posterius cognoscitur, per privationem divisibilis.
Unde punctum privative definitur, punctum est cuius pars non est, et similiter ratio unius est quod sit indivisibile, ut dicitur in X Metaphys. Et huius ratio est, quia tale indivisibile habet quandam oppositionem ad rem corporalem, cuius quidditatem primo et per se intellectus accipit. Si autem intellectus noster intelligeret per participationem indivisibilium separatorum, ut Platonici posuerunt, sequeretur quod indivisibile huiusmodi esset primo intellectum, quia secundum Platonicos, priora prius participantur a rebus.
6 Reply to Objection 1: In the acquisition of knowledge, principles and elements are not always known) first: for sometimes from sensible effects we arrive at the knowledge of principles and intelligible causes. But in perfect knowledge, the knowledge of effects always depends on the knowledge of principles and elements: for as the Philosopher says in the same passage: Then do we consider that we know, when we can resolve principles into their causes.
6 Ad primum ergo dicendum quod in accipiendo scientiam, non semper principia et elementa sunt priora, quia quandoque ex effectibus sensibilibus devenimus in cognitionem principiorum et causarum intelligibilium. Sed in complemento scientiae, semper scientia effectuum dependet ex cognitione principiorum et elementorum, quia, ut ibidem dicit philosophus, tunc opinamur nos scire, cum principiata possumus in causas resolvere.
7 Reply to Objection 2: A point is not included in the definition of a line in general: for it is manifest that in a line of indefinite length, and in a circular line, there is no point, save potentially. Euclid defines a finite straight line: and therefore he mentions a point in the definition, as the limit in the definition of that which is limited. Unity is the measure of number: wherefore it is included in the definition of a measured number. But it is not included in the definition of the divisible, but rather conversely.
7 Ad secundum dicendum quod punctum non ponitur in definitione lineae communiter sumptae, manifestum est enim quod in linea infinita, et etiam in circulari, non est punctum nisi in potentia. Sed Euclides definit lineam finitam rectam, et ideo posuit punctum in definitione lineae, sicut terminum in definitione terminati. Unitas vero est mensura numeri, et ideo ponitur in definitione numeri mensurati. Non autem ponitur in definitione divisibilis, sed magis e converso.
8 Reply to Objection 3: The likeness through which we understand is the species of the known in the knower; therefore a thing is known first, not on account of its natural likeness to the cognitive power, but on account of the power's aptitude for the object: otherwise sight would perceive hearing rather than color.
8 Ad tertium dicendum quod similitudo per quam intelligimus, est species cogniti in cognoscente. Et ideo non secundum similitudinem naturae ad potentiam cognoscitivam est aliquid prius cognitum, sed per convenientiam ad obiectum, alioquin magis visus cognosceret auditum quam colorem.