Whether the intellect understands the indivisible before the divisible?

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.

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.

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.

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.

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 (Q[84], A[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 (A[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.

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."

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.

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.