This is a short quote from St. Augustine talking about the nature of logic (i.e. deductive valid logic, not irrational induction). Ultimately, he says, it’s origin is with God. I would say that Logic is man pointing out particular common or rudimentary structures of God’s thinking, and then giving them names. Some of these structures are so foundational to God’s own thoughts, such as the law of contradiction, that if man does not follow them, man ceases to think at all. The Logos doctrine in John 1 includes this doctrine of logic, so that to translate “Logos” as “Logic” is as good a translation as “Word.”
Also, Augustine focuses on the fact that Logic is observed, not made up by man. Logic is what makes math work. Thus, think about this from the perspective of math. Man does not make up the idea that 1 plus 1 equals 2; rather, man discovers a truth of God and can be smart by affirming this or be dumb and wicked by denying it. I have 1 and 1 arms; and so do most people. There is a reason why you do not find shirts at the store with 170 sleeves stitched in. The reason is that 1 and 1 equals 2 sleeves, and not 170.
Valid Logical Sequence is Not Devised But Only Observed by Man.
50. And yet the validity of logical sequences is not a thing devised by men, but is observed and noted by them that they may be able to learn and teach it; for it exists eternally in the reason of things, and has its origin with God. For as the man who narrates the order of events does not himself create that order; and as he who describes the situations of places, or the natures of animals, or roots, or minerals, does not describe arrangements of man; and as he who points out the stars and their movements does not point out anything that he himself or any other man has ordained;—in the same way, he who says, “When the consequent is false, the antecedent must also be false,” says what is most true; but he does not himself make it so, he only points out that it is so. And it is upon this rule that the reasoning I have quoted from the Apostle Paul proceeds. For the antecedent is, “There is no resurrection of the dead,”—the position taken up by those whose error the apostle wished to overthrow. Next, from this antecedent, the assertion, namely that, there is no resurrection of the dead, the necessary consequence is, “Then Christ is not risen.” But this consequence is false, for Christ has risen; therefore the antecedent is also false. But the antecedent is, that there is no resurrection of the dead. We conclude, therefore, that there is a resurrection of the dead. Now all this is briefly expressed thus: If there is no resurrection of the dead, then is Christ not risen; but Christ is risen, therefore there is a resurrection of the dead. This rule, then, that when the consequent is removed, the antecedent must also be removed, is not made by man, but only pointed out by him. And this rule has reference to the validity of the reasoning, not to the truth of the statements.” [St. Augustine, Christian Doctrine. ch.32]