Logic

How do you convince a person that arguments should be logical and should not have logical fallacies when that person does not believe in being logical nor accept the need for arguments to be fallacy free?

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Even if they are not so inclined, people should avoid fallacies, roughly because it makes them less likely to acquire new beliefs that are false. But you are not asking what people ought to do, but rather what will in fact lead them to want to avoid fallacies. Maybe we just need to know more about these people to answer this question. Thus perhaps they are inclined to accept pretty much any claim if it is presented in the form of a song, to the tune of 'Happy Days are Here Again'. In that case, I suggest you sing them 'Avoid fallacies, if you can' to that tune.

The trouble is that if we try to imagine people who are completely unresponsive to logical force, then who knows what will move them? But actually it's not clear that such a supposition is coherent, because any creature that would count as thinking at all must at least be somewhat responsive to logical force, if their thoughts are to have content. (Of course they may still be prone to various fallacies, and not much bothered by them.) So if our people are in fact reasonably sensitive to logical force, for example if they are inclined to go on to accept B if they already accepts (A or B) and (not-A), then there may be some hope that you can use cogent arguments to convince them to start worrying more about fallacies, arguments that show that they will be more likely to believe truths and to get what they want in life if they takes a rather less cavalier attitude towards logic and argument.

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