A cumulative case has "power in numbers" on its side. If a conclusion has 100 pieces of evidence and lines of reasoning that support it, one piece or line that goes against it may not necessarily bring the whole thing down. That single piece or line may need to be verified or reinterpreted, but cannot be ignored. If someone is aware of the large cumulative case for their worldview, one discovery is not likely to bring their belief of their worldview down.
I was recently asked about challenges to a worldview. It was proposed that sometimes a person who is being challenged may simply not have the understanding of the challenge to recognize that the implications pose a problem to his cumulative case. I think that this happens all the time. If someone continues to say that there is not an error, without providing reasons, they are living in denial (one of the psychological defense mechanisms). This could be due to being afraid that they may actually be wrong. It could also be the result that someone thinks so highly of their own abilities that they can't possible be wrong. The former further leads to rationalization (another defense mechanism)- reasoning that doesn't actually target the challenge (but sounds "smart" enough to appease the challenged or his/her audience or even him/herself). The latter leads to simply ignoring the challenge. Both are emotionally charged and the result of not having a powerful cumulative case. We do not know a person's psyche precisely (no credible psychologist, psychiatrist, or neurologist can say that we even that the ability to), but we can reduce the possible options. Either direction a person chooses to go, they are exhibiting at least one defense mechanism and either employing a second (in the case of the former) or suffering from a form of narcissism (in the case of the latter).
Simply "knowing of something" (a challenge in this case) allows for easy emotional dismissal of it. "Understanding why and how something is" makes the emotional dismissal a little bit more difficult, but more powerful and dangerous. If you just "know of" a something, you can easily change your mind about your acceptance of it. However, if you "understand" something and still choose to dismiss it, you will rationalize a stronger case against it, making it more difficult to ever accept it.
Likewise the possession of a cumulative case distinguishes between those who simply know of a view and those who truly understand a view. Here is what I mean: Simply "knowing of something" (a worldview in this case) allows for easy emotional dismissal or acceptance of it. "Understanding why and how" the worldview is true (false) makes the emotional acceptance (dismissal) much easier, and the cumulative case more powerful if accomplished. On the flip side (watch closely), "understanding why and how" the worldview is true (false) makes the emotional dismissal (acceptance) of it much more difficult, but the cumulative case more dangerous if accomplished.
The dangerous cumulative case is what leads people into deep delusions about reality. These false beliefs (no matter how strong the cumulative case) are still against reality and reality is always ready to remind us that it is still where we live. The majority of these reminders come in the form of pain and confusion (both emotional and logical). I'm not saying that we will ever be able to have no pain or confusion; that would require omniscience (a perfectly, precisely, accurate worldview). We are still human with limited knowledge and understanding of everything. A cumulative case-based worldview will just help reduce the pain and confusion.
Of course, simply experiencing less pain and confusion does not necessarily mean that you have a cumulative case for the correct worldview. It could also mean that you are just deeper in your delusion, as I hinted towards above. I have said for a long time that pain is not necessarily bad. It will paralyze our logic and reason while we deal with the emotional side of a situation. When dealing with worldviews, pain is partly caused by not having a complete understanding of reality. That pain (whether imposed by a person in the form of a challenge or imposed by experience with reality) provides us with an opportunity. After our emotions are done paralyzing our logic and reason (differing amounts of time based on the situation and the person), we have the chance to seize the opportunity provided to build a stronger cumulative case for our worldview.
People, who are challenged, should investigate the challenge- especially if they are challenged on a ground that they are unfamiliar with (interdisciplinary consistency is vital to a cumulative case for a worldview- see my blog post on it). This provides an opportunity to change, adjust, or nuance an argument; all those will lead to a stronger cumulative case for one's worldview. Careful thinkers and investigators will realize that true humility (as difficult as it is to sustain for long periods of time) provides an avenue for creating robust and accurate worldviews. At that point, they may be confident enough that a challenge can be accepted. Even if that challenge turns out to be not only valid, but correct, only one piece of the many pieces have been destroyed. Time to adjust for benefit.
As we discover more that we don't understand and work through it, our understanding of our worldview will become more complete. More complete understanding allows us to possess and present an extremely powerful cumulative case to anyone who asks for the reason for the hope we have.
I have one more round of thoughts on cumulative cases that will be offered next week.