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Source: p 44-45, Introducing Philosophy for Canadians: A Text with Integrated Readings (2011 1 ed.)

Preface: If the following is too long to read, read only 1 and 2.

Question: Suppose 1 impossible. Then what can and should an ethical, rational philosopher do? One can politely tell this opponent that he/she is only unreasonably stubborn, self-serving, and defensive, but then what?

  Although it might seem to you as if arguments are conclusive, one way or the other, this is almost never the case. An argument can be convincing and persuasive, but there is always room for further argument if someone is stubborn or persistent enough. A good counter- example can always be explained away, and even a large number of counterexamples might be explained away if one is willing to adjust other aspects of the theory, by refining definitions, for example. What ultimately sinks a bad hypothesis or general claim is the weight of the extra explanations it needs. For example, someone argues that there are Martians currently living on earth. You point out that no one on earth has ever seen a Martian. Your opponent explains this away by suggesting that the Martians are invisible to the human eye. You argue that the atmosphere on earth would not support Martian life. Your opponent argues that they are a different form of life, different from any that we can understand. You ask your opponent what these Martians do and how we might come to test his or her view Your opponent says that the Martians don't want us to know that they are here, so they are careful not to do anything that would let us discover their presence. [1.] At this point, you will probably walk away in disgust. [End of 1.] [2.] You have not silenced your opponent. In fact, he or she might go on inventing new ways out of your arguments forever. But, at a certain point, your opponent's explanations will have become so obviously self-serving and defensive that you and everyone else will be completely justified in ignoring them. The point of argument, remember, is to persuade. Absolute proof is impossible. But this means too that persuading some people is also impossible. There are limits to argument—at least, practical limits. [End of 2.]

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    This doesn't seem fundamentally answerable in terms of philosophy. Precisely, because the question is how do you respond to an irrational response at which point we're not doing philosophy. – virmaior Jun 14 '16 at 4:37
  • @virmaior I generally agree, but I took a shot at asking it, because it can be applied reflectively. Meditation on one's own arguments are widely addressed as foundational to Philosophy. – PV22 Jun 14 '16 at 5:08
  • i guess i agree. why are you arguing with this person, and what would it mean to "win" against them ? – user6917 Jun 14 '16 at 7:32
  • I agree with mathematician: how are you defining success? There are valid definitions of success for which you can always succeed , and there are definitions for which the ability to suceed is provably not in your power – Cort Ammon Jun 14 '16 at 17:05
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The proverbial example of what your asking, is illustrated in Socrates's trial and death as described in Plato's "Dialogues". In the story Socrates choices to stay in Athens and stand trial based on his "convictions to the truth and knowledge". And despite being given several opportunities to escape with his life into exile, he chose to argue against his opponent and be executed for it.

If you believe that Socrates was a nobel martyr, then proceed to employ the Socratic method towards the opponents credit. In his case, he won the argument at the cost of his life (it should be noted that 400 BC Greek society had different moral, spiritual and social norms).

If you can respect Socrates's story but see a cautionary tale of Pride getting best of someone, then you may wish to reflect on one of your initial premises; "your opponent must submit to your belief". Though this is more literary than philosophical, I believe its an apt allusion to the question your asking. I would posit that respecting another includes respecting that the other person may not agree with what your position.

Not to be holistic, but perhaps also reflect on the fact that it is an opportunity to test your position in "the natural light" (Rene Descartes, "Meditations on First Philosophy")

If when I don’t perceive the truth clearly and distinctly enough I simply suspend judgment, I am behaving correctly and avoiding error. It is a misuse of my free will to have an opinion in such cases: if I choose the wrong side I shall be in error; and even if I choose the right side, I shall be at fault because I'll have come to the truth by sheer chance and not through a perception of my intellect. The latter, as the natural light shows me clearly, should be what influences my will when I affirm things. I have said that error is essentially a privation – a lack of something that I should have – and now I know what this privation consists in. It doesn’t lie in the will that God has given me, or even in the mode of operation that God has built into it; rather it consists in my misuse of my will. Specifically, it consists in my lack of restraint in the exercise of my will, when I form opinions on matters that I don’t clearly understand.

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