However conclusive a mode of reasoning may be, and however accurately we may use it, it always remains possible that we shall fail to convince a man who disagrees with us. There may come a point in a moral dispute when it is wiser to agree to differ than to persist with fruitless efforts to convince an opponent. But this by itself is no more a reason for doubting the truth of our premises and the validity of our arguments than the teacher's failure to convince a pupil of the validity of a proof of Pythagoras's theorem is a reason for doubting the validity of the proof and the truth of the theorem. It is notorious that even an expert physicist may fail to convince a member of the Flat Earth Society that the earth is not flat, but we nevertheless know that the earth is not flat. Lewis Carroll's tortoise ingeniously resisted the best efforts of Achilles to convince him of the validity of a simple deductive argument, but of course the argument is valid.
(Renford Bambrough, "A Proof of the Objectivity of Morals," The American Journal of Jurisprudence 14 [1969]: 37-53, at 45 [italics in original])
Note from KBJ: This passage is riddled with confusions. First, it's often not clear whether a given proposition is true, or even whether it has a truth value. If I think that one of your premises is false, then your argument gets no grip on me. You may think your premises are true, but that does me no good. The burden of persuasion is on the arguer, whose job is to use premises that are already accepted by the interlocutor. If you use a premise that is not accepted, you fail. Second, there's a difference between structure (form) and content (substance). I may agree that your argument is valid, in the sense of truth-preserving, but deny that there is any truth to be preserved. This is not to say that reasonable people always agree about validity or invalidity, for they don't. You may think your argument valid while I think it's invalid. Why is this my fault? Why is it not your fault? You're the one making the argument. If you want to persuade me, you must use not only an argument the validity of which I accept, but premises the truth of which I accept. Argumentation, unlike reasoning, is interpersonal. Bambrough makes it seem as though the burden of rejection is on the interlocutor. No. The burden of persuasion is on the arguer. Third, why does Bambrough use the Flat Earth Society as his example? This rigs the game in his favor. Suppose I try to persuade the utilitarian Jeremy Bentham (1748-1832) that a given act of torture (call it X) is wrong. I argue as follows: (1) Torture is intrinsically and absolutely wrong (i.e., wrong in itself and with no exceptions); (2) X is a case of torture; therefore, (3) X is wrong. Bentham would accept the validity of my argument but reject the first premise. By Bambrough's logic, I, the arguer, should simply say that I know that torture is intrinsically and absolutely wrong, and therefore that I know that X is wrong. But that begs the question against Bentham, who rejects my major premise. My failure to convince Bentham of the wrongness of X is my failure, not his.
Keith Burgess-Jackson, J.D., Ph.D. 