This is a little complicated, but it is critically important in all of human thought. Bishop Fulton Sheen translated a passage of Aquinas referring to the effects of abandoning the first principle of reason as committing "mental suicide" after stressing the fact that the first principle of reason is the strongest and clearest thing "the Angelic Doctor" wrote about. G. K. Chesterton called forgetting or ignoring the first principle of reason "the assassination of Thomism."
The first principle of reason is stated two ways, one "negative" and one "positive." Negatively, it is called the principle or law of (non) contradiction, and is stated simply as, "Nothing can both 'be' and 'not be' at the same time and under the same conditions." The folk aphorism puts it this way: "You can't have your cake and eat it, too." Most simply put, reason is not and cannot be contradictory.
This, by the way, is the answer to the silly argument used to "prove" that God doesn't exist: "If God can do anything, then He can make a weight so heavy He can't lift it." The statement contains an internal contradiction, and is therefore nonsense as it violates the principle of contradiction. Another example is, "Everything I say is a lie." The statement is contradictory, and therefore nonsense.
The first principle of reason is also stated positively as the principle of identity. This is more complicated: "That which is true is as true, and is true in the same way, as everything else that is true." Another way of putting this is that you can't change things simply by changing definitions or "re-editing the dictionary."
Once you have agreed on the definition of a thing, you can't go changing it unless 1) the new definition reflects reality (not just opinion) and 2) everyone in the debate or argument agrees on and accepts the new definition. You cannot simply assert a new definition and call everyone who does not accept your new definition a liar, a lunatic, or a criminal. As Chesterton explained in his biographical sketch of Aquinas,
"If there is one phrase that stands before history as typical of Thomas Aquinas, it is that phrase about his own argument: “It is not based on documents of faith, but on the reasons and statements of the philosophers themselves.” Would that all Orthodox doctors in deliberation were as reasonable as Aquinas in anger! Would that all Christian apologists would remember that maxim; and write it up in large letters on the wall, before they nail any theses there. At the top of his fury, Thomas Aquinas understands, what so many defenders of orthodoxy will not understand. It is no good to tell an atheist that he is an atheist; or to charge a denier of immortality with the infamy of denying it; or to imagine that one can force an opponent to admit he is wrong, by proving that he is wrong on somebody else’s principles, but not on his own. After the great example of St. Thomas, the principle stands, or ought always to have stood established; that we must either not argue with a man at all, or we must argue on his grounds and not ours. We may do other things instead of arguing, according to our views of what actions are morally permissible; but if we argue we must argue “on the reasons and statements of the philosophers themselves.”
Once you understand the first principle of reason you will win every argument you get into — assuming, of course, that you also keep in mind Mortimer Adler's remarks about the difference between knowledge which is based on empirical evidence and logic — reason or the intellect — and is thus always true, and opinion, which is based on applying faith — the will — where faith doesn't belong and may or may not be true. (And, as a general rule, the louder someone shrieks his or her opinion and the more insulting he or she gets the less likely it is to be true.)
By following these rules, last semester I received 434 out of 435 in a business law course, the highest grade ever recorded in that class. I missed the one point because I forgot a computer acronym on one of the tests. My mind completely blanked out. I received about a dozen points on other tests because even though the professor still disagreed with my answers, I presented a good argument based on evidence and logic, and her goal was to teach us to think, not simply parrot back what the book said.