It is significant for this reason.
There are those who enter the process of discussion seeking the truth, and then there are those who simply wish to have their egos gratified by "winning" the argument, and the truth be darned. (*) If we were to take all that everyone said at face value, then those of the latter inclination would bring the process to a screeching halt, merely by offering insincere judgements as to the persuasiveness of particular arguments.
The way past this is to note that some of their actions, or firmly held attitudes or positions, while inexplicable if these people truly believe as they say they do, are easily understood if they hold a contrary position. If no other plausible candidate for what their hidden beliefs are, which these positions or actions would be a natural expression of, present themselves, then we may say that regardless of what the other person pretends to believe, they have expressed support for what they pretend to deny, through their actions. If there are multiple possibilities, then those actions have indicated that one of these is what they actually believe.
Either way, at that point one may rightly take what they have acknowledged through their actions, to be a given, and proceed. If your opponent refuses to admit the truth, at that point, then he is either persisting in lying to you, and those listening, or he has lied to himself so long, that he has forgotten that he is lying. Either way, he is to be ignored until he decides that sincerity is of greater value that the search for a false sense of victory, as he seeks to triumph over the truth. There is nothing that one may learn from talking to a liar, and the liar himself knows the truth that you would waste your time and breath trying to convince him of.
Question : "Yes, but what of those listening in ?"
.. Answer : Explain your position, and invite them to
..................... join you in supporting it.
In this spirit, you should explain to others why you ignore him when he argues his insincere point, and ask them to check out what you have said, for themselves, and decide whether or not this topic is a fruitful one to discuss with the man. In the case of a truly outrageous point like this one, one may proceed with confidence that what one has said, will be confirmed.
When a reasonable length of time has passed, and they've had a chance to see the blindingly obvious, ask them if they would not agree that there is little point to taking the man seriously, when he makes that assertion, going on to suggest that they simply continue the source, henceforth. At this point, you will find yourself with an opportunity to gauge your companions' judgment.
Some out of rigid adherence to foolish custom, will refuse this reasonable suggestion. Politely agree to disagree, and walk away from them, in whichever sense seems practical, speaking no more of this subject to them, or of their stance on this subject to others, unless it should come up, and then only to the extent necessary to defend one's own position. Focus your attention on those who can be reasoned with. Why waste one's words on those who will refuse to hear them? Or seek to recruit fools in the effort to spread the recognition of a truth? A fool brings disrepute upon his cause, through his poor representation of it.
Question : "Isn't that a little unfriendly?"
.. Answer : Life is a little unfriendly. Learn to deal with it.
Have we named any specific individual here, and mocked him? As popular a reaction as the above question reflects, it has no rational component. The only way to get through a day without making judgements as to the reliability of the judgement and character of others, is either by being utterly credulous, or by wasting vast amounts of one's time, checking the arguments of those others have the sense to avoid. There are only so many hours in a day, and fools are so abundant, and so desperate to be heard, that if one was to honestly listen to all, without exercising any fundamental discretion in one's choice of company, one would have no time to do anything else. That comes at the expense of others, and one's self as well.
Better you should invest your effort in those who, in listening to reason, show themselves to be capable of it. They will argue the case for your position to others far better. The one who craves the company of the foolish may find more supporters, briefly, but fools are a fickle lot.
Lacking any basis for real conviction, they are lost when the reality that they have become objects of ridicule finally begins to penetrate their thick skulls. Your smaller, but rock hard base of support, will wear away at the soft opposition. A fool, briefly outnumbered by the wiser in his immediate vicinity from time to time, is lost to his cause, little by little, because whenever he longer feels the comfortable sense of validation he gets out of being in the majority, he has loses a little more of the self confidence and sense of security he gained from speaking up.
A sensible individual, surrounded by the foolish, is merely annoyed by their company. Lacking the herd instinct, and finding his view of reality from a rational understanding of what he has seen and heard, he realises that what is foolish when spoken by one, does not become reasonable merely through its repetition by many. Your base of support, though it grows more slowly, will be more enduring if it sticks together, and knows where it is sensible to invest its effort.
Question :
"Wouldn't some say that this would be an ad hominem argument?"
Yes, some will object to our raising the sincerity of our opponent as an issue, saying that we attack the man instead of the argument. But when the man's entire argument consists of the offering of a gut reaction (an unsubstantiated instinct), then what argument has he offered that we are to respond to?
To do as we do, and persuade others to do likewise, is not to offer an "ad hominem" argument as some would try to claim. If someone's entire 'argument' consists of the words "I disagree", offering the contrary 'evidence' of his report as what his instincts tell him about the matter under discussion, then "the man", and the validity of those instincts and his testimony about them isn't a side issue that draws us away from his argument, they ARE his argument, in its entirety. To demand that we not criticise him, is to demand that we not rebut his 'argument'.
Is there unpleasantness involved? Yes, but it is unpleasantness for a purpose we can scarcely put aside. It is unpleasantness in the service of honesty, a virtue which if discarded, renders all others meaningless. Let us note that if the other side is sincere, and in the right, our technique here will not work. So, by adopting it, the only thing lost, is the effectiveness of insincerity, and the impact of poor judgment on the popular consensus. Good things to lose.
Let's return to preceding discussion.
(*) Or some other applicable word.