Objection 1. It seems that true and false are not contraries. For true and false are opposed, as that which is to that which is not; for "truth," as Augustine says (Soliloq. ii, 5), "is that which is." But that which is and that which is not are not opposed as contraries. Therefore true and false are not contrary things.
Objection 2. Further, one of two contraries is not in the other. But falsity is in truth, because, as Augustine says, (Soliloq. ii, 10), "A tragedian would not be a false Hector, if he were not a true tragedian." Therefore true and false are not contraries.
Objection 3. Further, in God there is no contrariety, for "nothing is contrary to the Divine Substance," as Augustine says (De Civ. Dei xii, 2). But falsity is opposed to God, for an idol is called in Scripture a lie, "They have laid hold on lying" (Jeremiah 8:5), that is to say, "an idol," as a gloss says. Therefore false and true are not contraries.
On the contrary, The Philosopher says (Peri Herm. ii), that a false opinion is contrary to a true one.
I answer that, True and false are opposed as contraries, and not, as some have said, as affirmation and negation. In proof of which it must be considered that negation neither asserts anything nor determines any subject, and can therefore be said of being as of not-being, for instance not-seeing or not-sitting. But privation asserts nothing, whereas it determines its subject, for it is "negation in a subject," as stated in Metaph. iv, 4: v. 27; for blindness is not said except of one whose nature it is to see. Contraries, however, both assert something and determine the subject, for blackness is a species of color. Falsity asserts something, for a thing is false, as the Philosopher says (Metaph. iv, 27), inasmuch as something is said or seems to be something that it is not, or not to be what it really is. For as truth implies an adequate apprehension of a thing, so falsity implies the contrary. Hence it is clear that true and false are contraries.
Reply to Objection 1. What is in things is the truth of the thing; but what is apprehended, is the truth of the intellect, wherein truth primarily resides. Hence the false is that which is not as apprehended. To apprehend being, and not-being, implies contrariety; for, as the Philosopher proves (Peri Herm. ii), the contrary of this statement "God is good," is, "God is not good."
Reply to Objection 2. Falsity is not founded in the truth which is contrary to it, just as evil is not founded in the good which is contrary to it, but in that which is its proper subject. This happens in either, because true and good are universals, and convertible with being. Hence, as every privation is founded in a subject, that is a being, so every evil is founded in some good, and every falsity in some truth.
Reply to Objection 3. Because contraries, and opposites by way of privation, are by nature about one and the same thing, therefore there is nothing contrary to God, considered in Himself, either with respect to His goodness or His truth, for in His intellect there can be nothing false. But in our apprehension of Him contraries exist, for the false opinion concerning Him is contrary to the true. So idols are called lies, opposed to the divine truth, inasmuch as the false opinion concerning them is contrary to the true opinion of the divine unity.
Source: Summa Theologica (New Advent)