*There is only one God*. Whatever exists is *ipso facto* individual; to be one it needs no extra property and calling it one merely denies that it is divided. Simple things are neither divided nor divisible; composite things do not exist when their parts are divided. So existence stands or falls with individuality, and things guard their unity as they do their existence. But what is simply speaking one can yet in certain respects be many: an individual thing, essentially undivided, can have many non-essential properties; and a single whole, actually undivided, can have potentially many parts.Only when one is used to count with does it presuppose in what it counts some extra property over and above existence, namely, quantity. The one we count with contrasts with the many it counts in the way a unity of measurement contrasts with what it measures; but the individual unity common to everything that exists contrasts with plurality simply by lacking it, as undividedness does division. A plurality is however *a* plurality: though simply speaking many, inasmuch as it exists, it is, incidentally, one. A continuum is homogeneous: its parts share the form of the whole (every bit of water is water); but a plurality is heterogeneous: its parts lack the form of the whole (no part of the house is a house). The parts of a plurality are unities and non-plural, though they compose the plurality not as non-plural but as existing; just as the parts of a house compose the house as material, not as not houses. Whereas we define plurality in terms of unity (many things are divided things to each of which is ascribed unity), we define unity in terms of division. For division precedes unity in our minds even if it doesn’t really do so, since we conceive simple things by denying compositeness of them, defining a point, for example, as lacking dimension. Division arises in the mind simply by negating existence. So the first thing we conceive is the existent, then―seeing that this existent is not that existent―we conceive division, thirdly unity, and fourthly plurality.There is only one God. Firstly, God and his nature are identical: to be God is to be this individual God. In the same way, if to be a man was to be Socrates there would only be one man, just as there was only one Socrates. Moreover, God’s perfection is unlimited, so what could differentiate one God from another? Any extra perfection in one would be lacking in the other and that would make him imperfect. And finally, the world is one, and plurality can only produce unity incidentally insofar as it too is somehow one: the primary and non-incidental source of unity in the universe must himself be one. The one we count with measures only material things, not God: like all objects of mathematics, though defined without reference to matter, it can exist only in matter. But the unity of individuality common to everything that exists is a metaphysical property applying both to non-material things and to God. But what in God is a perfection has to be conceived by us, with our way of understanding things, as a lack: that is why we talk of God as lacking a body, lacking limits and lacking division.
Thomas Aquinas, Summa Theologiae: A Concise Translation
logic, mereology, philosophy, theology