Objection 1. It would seem that the angels are not in great numbers. For number is a species of quantity, and follows the division of a continuous body. But this cannot be in the angels, since they are incorporeal, as was shown above (Article 1). Therefore the angels cannot exist in any great number.
Objection 2. Further, the more a thing approaches to unity, so much the less is it multiplied, as is evident in numbers. But among other created natures the angelic nature approaches nearest to God. Therefore since God is supremely one, it seems that there is the least possible number in the angelic nature.
Objection 3. Further, the proper effect of the separate substances seems to be the movements of the heavenly bodies. But the movements of the heavenly bodies fall within some small determined number, which we can apprehend. Therefore the angels are not in greater number than the movements of the heavenly bodies.
Objection 4. Dionysius says (Div. Nom. iv) that "all intelligible and intellectual substances subsist because of the rays of the divine goodness." But a ray is only multiplied according to the different things that receive it. Now it cannot be said that their matter is receptive of an intelligible ray, since intellectual substances are immaterial, as was shown above (Article 2). Therefore it seems that the multiplication of intellectual substances can only be according to the requirements of the first bodies--that is, of the heavenly ones, so that in some way the shedding form of the aforesaid rays may be terminated in them; and hence the same conclusion is to be drawn as before.
On the contrary, It is said (Daniel 7:10): "Thousands of thousands ministered to Him, and ten thousands times a hundred thousand stood before Him."
I answer that, There have been various opinions with regard to the number of the separate substances. Plato contended that the separate substances are the species of sensible things; as if we were to maintain that human nature is a separate substance of itself: and according to this view it would have to be maintained that the number of the separate substances is the number of the species of sensible things. Aristotle, however, rejects this view (Metaph. i, text 31) because matter is of the very nature of the species of sensible things. Consequently the separate substances cannot be the exemplar species of these sensible things; but have their own fixed natures, which are higher than the natures of sensible things. Nevertheless Aristotle held (Metaph. xi, text 43) that those more perfect natures bear relation to these sensible things, as that of mover and end; and therefore he strove to find out the number of the separate substances according to the number of the first movements.
But since this appears to militate against the teachings of Sacred Scripture, Rabbi Moses the Jew, wishing to bring both into harmony, held that the angels, in so far as they are styled immaterial substances, are multiplied according to the number of heavenly movements or bodies, as Aristotle held (Metaph. xi, text 43); while he contended that in the Scriptures even men bearing a divine message are styled angels; and again, even the powers of natural things, which manifest God's almighty power. It is, however, quite foreign to the custom of the Scriptures for the powers of irrational things to be designated as angels.
Hence it must be said that the angels, even inasmuch as they are immaterial substances, exist in exceeding great number, far beyond all material multitude. This is what Dionysius says (Coel. Hier. xiv): "There are many blessed armies of the heavenly intelligences, surpassing the weak and limited reckoning of our material numbers." The reason whereof is this, because, since it is the perfection of the universe that God chiefly intends in the creation of things, the more perfect some things are, in so much greater an excess are they created by God. Now, as in bodies such excess is observed in regard to their magnitude, so in things incorporeal is it observed in regard to their multitude. We see, in fact, that incorruptible bodies, exceed corruptible bodies almost incomparably in magnitude; for the entire sphere of things active and passive is something very small in comparison with the heavenly bodies. Hence it is reasonable to conclude that the immaterial substances as it were incomparably exceed material substances as to multitude.
Reply to Objection 1. In the angels number is not that of discrete quantity, brought about by division of what is continuous, but that which is caused by distinction of forms; according as multitude is reckoned among the transcendentals, as was said above (30, 3; 11).
Reply to Objection 2. From the angelic nature being the nighest unto God, it must needs have least of multitude in its composition, but not so as to be found in few subjects.
Reply to Objection 3. This is Aristotle's argument (Metaph. xii, text 44), and it would conclude necessarily if the separate substances were made for corporeal substances. For thus the immaterial substances would exist to no purpose, unless some movement from them were to appear in corporeal things. But it is not true that the immaterial substances exist on account of the corporeal, because the end is nobler than the means to the end. Hence Aristotle says (Metaph. xii, text 44) that this is not a necessary argument, but a probable one. He was forced to make use of this argument, since only through sensible things can we come to know intelligible ones.
Reply to Objection 4. This argument comes from the opinion of such as hold that matter is the cause of the distinction of things; but this was refuted above (Question 47, Article 1). Accordingly, the multiplication of the angels is not to be taken according to matter, nor according to bodies, but according to the divine wisdom devising the various orders of immaterial substances.
Source: Summa Theologica (New Advent)