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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 (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.
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.
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