Objection 1. It would seem that the exclusive word "alone" [solus] is not to be added to an essential term in God. For, according to the Philosopher (Elench. ii, 3), "He is alone who is not with another." But God is with the angels and the souls of the saints. Therefore we cannot say that God is alone.
Objection 2. Further, whatever is joined to the essential term in God can be predicated of every person "per se," and of all the persons together; for, as we can properly say that God is wise, we can say the Father is a wise God; and the Trinity is a wise God. But Augustine says (De Trin. vi, 9): "We must consider the opinion that the Father is not true God alone." Therefore God cannot be said to be alone.
Objection 3. Further if this expression "alone" is joined to an essential term, it would be so joined as regards either the personal predicate or the essential predicate. But it cannot be the former, as it is false to say, "God alone is Father," since man also is a father; nor, again, can it be applied as regards the latter, for, if this saying were true, "God alone creates," it would follow that the "Father alone creates," as whatever is said of God can be said of the Father; and it would be false, as the Son also creates. Therefore this expression "alone" cannot be joined to an essential term in God.
On the contrary, It is said, "To the King of ages, immortal, invisible, the only God" (1 Timothy 1:17).
I answer that, This term "alone" can be taken as a categorematical term, or as a syncategorematical term. A categorematical term is one which ascribes absolutely its meaning to a given "suppositum"; as, for instance, "white" to man, as when we say a "white man." If the term "alone" is taken in this sense, it cannot in any way be joined to any term in God; for it would mean solitude in the term to which it is joined; and it would follow that God was solitary, against what is above stated (2). A syncategorematical term imports the order of the predicate to the subject; as this expression "every one" or "no one"; and likewise the term "alone," as excluding every other "suppositum" from the predicate. Thus, when we say, "Socrates alone writes," we do not mean that Socrates is solitary, but that he has no companion in writing, though many others may be with him. In this way nothing prevents the term "alone" being joined to any essential term in God, as excluding the predicate from all things but God; as if we said "God alone is eternal," because nothing but God is eternal.
Reply to Objection 1. Although the angels and the souls of the saints are always with God, nevertheless, if plurality of persons did not exist in God, He would be alone or solitary. For solitude is not removed by association with anything that is extraneous in nature; thus anyone is said to be alone in a garden, though many plants and animals are with him in the garden. Likewise, God would be alone or solitary, though angels and men were with Him, supposing that several persons were not within Him. Therefore the society of angels and of souls does not take away absolute solitude from God; much less does it remove respective solitude, in reference to a predicate.
Reply to Objection 2. This expression "alone," properly speaking, does not affect the predicate, which is taken formally, for it refers to the "suppositum," as excluding any other suppositum from the one which it qualifies. But the adverb "only," being exclusive, can be applied either to subject or predicate. For we can say, "Only Socrates"--that is, no one else--"runs: and Socrates runs only"--that is, he does nothing else. Hence it is not properly said that the Father is God alone, or the Trinity is God alone, unless some implied meaning be assumed in the predicate, as, for instance, "The Trinity is God Who alone is God." In that sense it can be true to say that the Father is that God Who alone is God, if the relative be referred to the predicate, and not to the "suppositum." So, when Augustine says that the Father is not God alone, but that the Trinity is God alone, he speaks expositively, as he might explain the words, "To the King of ages, invisible, the only God," as applying not to the Father, but to the Trinity alone.
Reply to Objection 3. In both ways can the term "alone" be joined to an essential term. For this proposition, "God alone is Father," can mean two things, because the word "Father" can signify the person of the Father; and then it is true; for no man is that person: or it can signify that relation only; and thus it is false, because the relation of paternity is found also in others, though not in a univocal sense. Likewise it is true to say God alone creates; nor, does it follow, "therefore the Father alone creates," because, as logicians say, an exclusive diction so fixes the term to which it is joined that what is said exclusively of that term cannot be said exclusively of an individual contained in that term: for instance, from the premiss, "Man alone is a mortal rational animal," we cannot conclude, "therefore Socrates alone is such."
Source: Summa Theologica (New Advent)