Objection 1. It seems that this name "God" is applied to God univocally by nature, by participation, and according to opinion. For where a diverse signification exists, there is no contradiction of affirmation and negation; for equivocation prevents contradiction. But a Catholic who says: "An idol is not God," contradicts a pagan who says: "An idol is God." Therefore GOD in both senses is spoken of univocally.
Objection 2. Further, as an idol is God in opinion, and not in truth, so the enjoyment of carnal pleasures is called happiness in opinion, and not in truth. But this name "beatitude" is applied univocally to this supposed happiness, and also to true happiness. Therefore also this name "God" is applied univocally to the true God, and to God also in opinion.
Objection 3. Further, names are called univocal because they contain one idea. Now when a Catholic says: "There is one God," he understands by the name God an omnipotent being, and one venerated above all; while the heathen understands the same when he says: "An idol is God." Therefore this name "God" is applied univocally to both.
On the contrary, The idea in the intellect is the likeness of what is in the thing as is said in Peri Herm. i. But the word "animal" applied to a true animal, and to a picture of one, is equivocal. Therefore this name "God" applied to the true God and to God in opinion is applied equivocally.
Further, No one can signify what he does not know. But the heathen does not know the divine nature. So when he says an idol is God, he does not signify the true Deity. On the other hand, A Catholic signifies the true Deity when he says that there is one God. Therefore this name "God" is not applied univocally, but equivocally to the true God, and to God according to opinion.
I answer that, This name "God" in the three aforesaid significations is taken neither univocally nor equivocally, but analogically. This is apparent from this reason: Univocal terms mean absolutely the same thing, but equivocal terms absolutely different; whereas in analogical terms a word taken in one signification must be placed in the definition of the same word taken in other senses; as, for instance, "being" which is applied to "substance" is placed in the definition of being as applied to "accident"; and "healthy" applied to animal is placed in the definition of healthy as applied to urine and medicine. For urine is the sign of health in the animal, and medicine is the cause of health.
The same applies to the question at issue. For this name "God," as signifying the true God, includes the idea of God when it is used to denote God in opinion, or participation. For when we name anyone god by participation, we understand by the name of god some likeness of the true God. Likewise, when we call an idol god, by this name god we understand and signify something which men think is God; thus it is manifest that the name has different meanings, but that one of them is comprised in the other significations. Hence it is manifestly said analogically.
Reply to Objection 1. The multiplication of names does not depend on the predication of the name, but on the signification: for this name "man," of whomsoever it is predicated, whether truly or falsely, is predicated in one sense. But it would be multiplied if by the name "man" we meant to signify different things; for instance, if one meant to signify by this name "man" what man really is, and another meant to signify by the same name a stone, or something else. Hence it is evident that a Catholic saying that an idol is not God contradicts the pagan asserting that it is God; because each of them uses this name GOD to signify the true God. For when the pagan says an idol is God, he does not use this name as meaning God in opinion, for he would then speak the truth, as also Catholics sometimes use the name in the sense, as in the Psalm, "All the gods of the Gentiles are demons" (Psalm 95:5).
The same remark applies to the Second and Third Objections. For these reasons proceed from the different predication of the name, and not from its various significations.
Reply to Objection 4. The term "animal" applied to a true and a pictured animal is not purely equivocal; for the Philosopher takes equivocal names in a large sense, including analogous names; because also being, which is predicated analogically, is sometimes said to be predicated equivocally of different predicaments.
Reply to Objection 5. Neither a Catholic nor a pagan knows the very nature of God as it is in itself; but each one knows it according to some idea of causality, or excellence, or remotion (12, 12). So a pagan can take this name "God" in the same way when he says an idol is God, as the Catholic does in saying an idol is not God. But if anyone should be quite ignorant of God altogether, he could not even name Him, unless, perhaps, as we use names the meaning of which we know not.
Source: Summa Theologica (New Advent)