What is the principle of contradiction? In a nutshell, it’s this: a thing cannot be and not be at the same time. Saint Thomas Aquinas shows that not even God can deny the principle of contradiction, the absolute law of the order of being, because it is impossible for God to will the absolutely impossible (Summa Contra Gentiles, Book 1, chap. 84).
Father Garrigou-Lagrange gives us eight principal reasons, based on Aristotle, for defending the necessity and real validity of the principle of contradiction. They are briefly:
1. To deny this necessity and this validity would be to deprive words of their fixed meaning and to render speech useless;
2. All idea of the reality of an essence, or thing or substance as such, would have to be abandoned; there would be only a becoming without anything which is on the way of becoming; it would be like saying that there can be a flux without a fluid, a flight without a bird, a dream without a dreamer;
3. There would no longer be any distinction between things, between a galley, a wall, and man;
4. It would mean the destruction of all truth, for truth follows being;
5. It would destroy all thought, even all opinion; for its very affirmation would be a negation.
6. It would mean the destruction of all desire and all hatred; there would be only absolute indifference, for there would be no distinction between good and evil; there would be no reason why we should act;
7. It would no longer be possible to distinguish degrees of error; everything would be equally false and true at the same time;
8. It would put an end to the very notion of becoming; between the beginning and the end of a movement; the first would already be the second, and any transition from one state to another would be impossible. Moreover, “becoming” could not be explained by any of the four causes. There would be no subject of becoming; the process would be without any efficient or final cause, and without specification, and it would be both attraction and repulsion, concretion as well as fusion.
(Rev. R. Garrigou-Lagrange, God: His Existence and His Nature, B. Herder Book Co., St. Louis, 1934, vol. 1, p. 1680)