Objection 1. It would seem that our intellect does not understand by composition and division. For composition and division are only of many; whereas the intellect cannot understand many things at the same time. Therefore it cannot understand by composition and division.
Objection 2. Further, every composition and division implies past, present, or future time. But the intellect abstracts from time, as also from other individual conditions. Therefore the intellect does not understand by composition and division.
Objection 3. Further, the intellect understands things by a process of assimilation to them. But composition and division are not in things, for nothing is in things but what is signified by the predicate and the subject, and which is one and the same, provided that the composition be true, for "man" is truly what "animal" is. Therefore the intellect does not act by composition and division.
On the contrary, Words signify the conceptions of the intellect, as the Philosopher says (Peri Herm. i). But in words we find composition and division, as appears in affirmative and negative propositions. Therefore the intellect acts by composition and division.
I answer that, The human intellect must of necessity understand by composition and division. For since the intellect passes from potentiality to act, it has a likeness to things which are generated, which do not attain to perfection all at once but acquire it by degrees: so likewise the human intellect does not acquire perfect knowledge by the first act of apprehension; but it first apprehends something about its object, such as its quiddity, and this is its first and proper object; and then it understands the properties, accidents, and the various relations of the essence. Thus it necessarily compares one thing with another by composition or division; and from one composition and division it proceeds to another, which is the process of reasoning.
But the angelic and the Divine intellect, like all incorruptible things, have their perfection at once from the beginning. Hence the angelic and the Divine intellect have the entire knowledge of a thing at once and perfectly; and hence also in knowing the quiddity of a thing they know at once whatever we can know by composition, division, and reasoning. Therefore the human intellect knows by composition, division and reasoning. But the Divine intellect and the angelic intellect know, indeed, composition, division, and reasoning, not by the process itself, but by understanding the simple essence.
Reply to Objection 1. Composition and division of the intellect are made by differentiating and comparing. Hence the intellect knows many things by composition and division, as by knowing the difference and comparison of things.
Reply to Objection 2. Although the intellect abstracts from the phantasms, it does not understand actually without turning to the phantasms, as we have said (1; 84, 7). And forasmuch as it turns to the phantasms, composition and division of the intellect involve time.
Reply to Objection 3. The likeness of a thing is received into the intellect according to the mode of the intellect, not according to the mode of the thing. Wherefore something on the part of the thing corresponds to the composition and division of the intellect; but it does not exist in the same way in the intellect and in the thing. For the proper object of the human intellect is the quiddity of a material thing, which comes under the action of the senses and the imagination. Now in a material thing there is a twofold composition.
First, there is the composition of form with matter; and to this corresponds that composition of the intellect whereby the universal whole is predicated of its part: for the genus is derived from common matter, while the difference that completes the species is derived from the form, and the particular from individual matter. The second comparison is of accident with subject: and to this real composition corresponds that composition of the intellect, whereby accident is predicated of subject, as when we say "the man is white." Nevertheless composition of the intellect differs from composition of things; for in the latter the things are diverse, whereas composition of the intellect is a sign of the identity of the components. For the above composition of the intellect does not imply that "man" and "whiteness" are identical, but the assertion, "the man is white," means that "the man is something having whiteness": and the subject, which is a man, is identified with a subject having whiteness. It is the same with the composition of form and matter: for animal signifies that which has a sensitive nature; rational, that which has an intellectual nature; man, that which has both; and Socrates that which has all these things together with individual matter; and according to this kind of identity our intellect predicates the composition of one thing with another.
Source: Summa Theologica (New Advent)