In an intellectual argument there are three factors to consider: logic, intuition, and motivation. The logic is the actual reasoning employed in the argument itself. The intuition is the deeper understanding of the principles involved in the argument, beyond the flow of the logic itself and the motivation is the reason for making the argument in the first place.
For example, in Bruce Charlton's article Reconceptualizing the metaphysical basis of biology, he writes:
"If Natural Selection is regarded as the bottom-line explanation - the fundamental metaphysical reality (as it is for biology, and often is with respect to the human condition) then this has radically nihilistic consequences. And this is a paradox - if natural selection was the only mechanism by which consciousness and intelligene arose then we could have no confidenec that the human discovery of natural selection was anything more than a (currently, but contingently) fitness-enhancing delusion.
...
In sum - Without teleology, there can be no possibility of knowledge.
(This is not some kind of a clever paradox - it is an unavoidable rational conclusion.)"
In this argument, the logic is the first paragraph, pointing out that if we believe natural selection is the rock-bottom reality of the human mind, then we have no guarantee that our reasoning is accurate, only that it has been useful for survival and reproduction. But then, the theory of natural selection itself, which was developed by the human mind, is also a product of natural selection. Hence, we have no guarantee that the theory of natural selection is true.
As Charlton points out, this reasoning can seem to be just a clever trick, rather than a serious argument. Partly this is the self-referential nature of the argument, but the other reason is that this paradox, taken by itself, leads us to a certain conclusion, but says no more about it once we arrive. So, we now move to the intition.
The intuition is that the theory of natural selection only refers to traits which aid survival and reproduction, it says nothing about ensuring that beliefs are true. It may be that true beliefs also aid in survival and reproduction or it may be that some false beliefs are better, but to make these kinds of considerations, we have to go outside of the theory of natural selection. And in a broader sense, the intuition behind other paradoxes is similar. By showing that a theory cannot account for itself, it is shown to be incomplete; it may be valid within a certain domain, but it is not a complete description outside of it.
As for the motivation, there are different motivations one could have. One possibility is that the argument is one prong of a strategy to discredit natural selection altogether. Another is to better understand natural selection by understanding its limitations. A third is to show that naturalism, the belief that physical nature is all that exists, is false.
C.S. Lewis used this argument for the third motivation in his book Miracles. Victor Reppert writes more about this in his book C.S. Lewis's Dangerous idea. Interestingly enough, on his blog, Reppert quotes Charles Darwin himself, who wrote in a letter:
"the horrid doubt always arises whether the convictions of man's mind, which has been developed from the mind of the lower animals, are of any value or at all trustworthy. Would any one trust in the convictions of a monkey's mind, if there are any convictions in such a mind?"
I find this framework helpful in understanding not just intellectual arguments, but writing and indeed communication of all kinds.
The three each have their own benefits and drawbacks.
For instance, analyzing writing from a logical perspective allows one to temporarily ignore the motivations and just focus on the arguments themselves. The difficulty is that the logic itself may not be spelled out or may take certain assumptions for granted, or may be satisfactory, but leave out the bigger picture. Motivations are in a sense the quickest. If one can determine that a communication is sent out with bad motivation, like mass media for example, then it can be ignored with no further thought. But the difficulty is that for less obvious examples, the specific motivation may take some time to infer and since people think differently, motivations may be unusual.
For example, there are people who are atheists because they believe the evidence in favor of the existence of God is uncertain, but choose the possibility that they least favor. They want to put forward the most powerful argument they can, so they can be proven wrong. This usually goes along with a fairly pessimistic personality. In fact, I think that Thomas the Apostle was this kind of person. He watned to believe that Jesus had been raised, but would rather be disappointed once than have his hopes raised and then destroyed. In his case, the fault was giving into disappointment rather than accepting the testimony of his fellow Apostles whom he had reason to trust.
The point is that this is a rare motivation, but it is real and so could be misunderstood if people do not take the time to think over it. And there are many other examples of motivations being misunderstood.
Intuition is the best in terms of understanding because when one has the intuition, one understands without needing to memorize the logic of an argument. In fact, having the inuition makes the argument easier to remember. But intutition can sometimes be difficult to commuicate.
In thinking about writing or speaking persuasively, it also helps to consider these elements and how an audience responds to each of them. Arguing against a belief according to its own logic or showing that it contradicts itself is in one sense the strongest possible refutation. But in practice, one finds that although it works well at shoring up the beliefs of those who already disbelieve or leading to doubts for those who are netural, this method is often unsuccessful in persuading those who already believe.
One reason is that refuting any particular statement is viewed as merely a fluke. Yes, that one is wrong, but what about everything else? Another reason is that it doesn't get to the underlying assumptions and understanding behind the belief.
By talking about the intuition, one can address these issues. Bruce Charlton does this well in his posts on climate change. When I first read some of these posts, I didn't "get it" right away. But what Charlton is doing is, rather than addressing any particular study at a methodological level, addressing the assumptions underlying the whole climate change framework. These assumptions are that we can not only predict what the climate is going to do, but control it, to an extraordinary degree of pecision. And once one thinks about it, it becomes apparent that we can't do this.
If intuition doesn't work, then one has to consider the moviations of one's audience and address those motivations. But there is no general method for this.
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