To say a proposition is false is to say its negation is true, so that another way to state this dilemma is that both sides believe they are arguing for the sake of truth.
One of two things can happen. The first, one side capitulates and comes to believe what he thought was true is indeed false, a happy ending. The second, and far more common situation, is that an impasse is reached. This is the truest test of personality.
I once had an argument with a full-grown, well educated, degree-holding woman about the numerical result of dividing any real number by one. I stated that the result is always the original number. She agreed, except in the case of 1 divided by 1, the result of which, she vehemently insisted, was 0. Why? Well, “You divide one into one and you have nothing left.” And nothing is zero.
No mathematical trick, example, demonstration, or appeal could shake this woman’s conviction. She patiently listened, at first anyway, to whatever I had to say, but always returned to the certain sure “fact” that if you divide one into one you have nothing left. She eventually gave up on me, dismissing my bizarre opinion as the result of an eccentric mind addled by overexposure to arcane books.
We parted on friendly terms. We had contact a few times afterwards where it became clear she was not going to write any op-eds about my recalcitrance, nor was she going to organize any protest, nor indeed was she going to plead for the government to restrain my speech so that I might not spread my error to the young. She decided to let me be, doubtless reasoning to herself that not everybody can know everything, that some inaccuracy is inevitable.
Some disagreements must necessarily lead to a parting of the ways. Murderer Kermit Gosnell and his counsel disagreed with the State of Pennsylvania over several propositions, and still disagree. Now the State will use force, not to impel Gosnell to believe what he does not, but to restrain and punish him for his actions. The distinction is important. Gosnell is not facing grief because of his belief, but his behavior.
Convincing adults that what they believe is false is always hard labor and often impossible. Many people, particularly those in positions of power, cannot abide dissension, so they use their power to squelch opposition. They create speech codes, restrict the press, implement “fairness” doctrines, or mute opponents physically. This happens on a smaller scale in homes or offices run by bullies.
It’s not the action of others which grates, but it’s that they won’t see reason. Why can’t he just understand! What is wrong with him! Some people are tenacious and will not let a point drop until his opponent lies about agreeing, or his opponent runs away to avoid harassment. Others are so passionate that they will not countenance the company of those with fail to march in step with them. Friendships are ruined over political disagreements neither party has much chance of influencing.
These days it seems the civilized standby “Let’s agree to disagree” is used less frequently, replaced by estrangements. The absence of the polite “out” is a predictor of tumultuous times. Camps are being drawn, sides taken. These things happen.
And now it strikes me that there is one more possibility than the two sides ultimately agreeing or disagreeing. Many years ago, I had to break up a bedtime fight between my two sons because one claimed, “Davy Crockett is too King of the wild frontier!” while the second took the opposite position. A détente was reached when I convinced them that if they didn’t shut up and go to sleep it wouldn’t matter what Davy Crockett was. Thus a proposition can be seen as uninteresting, too.