Augustine covers a lot of ground in this interesting quote from De Doctrina Christiana, Book 2, Chapters 31,32

There are also valid processes of reasoning which lead to false conclusions, by following out to its logical consequences the error of the man with whom one is arguing; and these conclusions are sometimes drawn by a good and learned man, with the object of making the person from whose error these consequences result, feel ashamed of them and of thus leading him to give up his error when he finds that if he wishes to retain his old opinion, he must of necessity also hold other opinions which he condemns. For example, the apostle did not draw true conclusions when he said, “Then is Christ not risen,” and again, “Then is our preaching vain, and your faith is also vain;” and further on drew other inferences which are all utterly false; for Christ has risen, the preaching of those who declared this fact was not in vain, nor was their faith in vain who had believed it.
But all these false inferences followed legitimately from the opinion of those who said that there is no resurrection of the dead. These inferences, then, being repudiated as false, it follows that since they would be true if the dead rise not, there will be a resurrection of the dead. As, then, valid conclusions may be drawn not only from true but from false propositions, the laws of valid reasoning may easily be learnt in the schools, outside the pale of the Church. But the truth of propositions must be inquired into in
the sacred books of the Church.

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