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.
Obj. 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.
Obj. 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 Obj. 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 Obj. 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 Obj. 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.
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