What to convince me of something like the dangers of GMOs, why I should vote for your favorite political candidate, that intelligent alien life is out there somewhere or had an important role in shaping human history, that you have seen Bigfoot, or even the existence of your preferred god(s)? I'll let you in a secret: I have a big weakness when it comes to matters of persuasion. It makes me fairly easy to persuade.
I change my mind about all sorts of things all the time, and it is easy to persuade me to do so. You see, I am highly susceptible to evidence. Provide me with good evidence in support of what you want me to believe, evidence that is sufficient to support whatever it is that you'd like to persuade me of, and I'll probably come around to your point of view.
Suppose an acquaintance from high school I hadn't heard from in over 20 years were to contact me out of the blue on Facebook. While catching up, he informs me that he just bought a new Corvette. Given what I remember of him, I find this difficult to believe. He was always a bit of an anti-materialist and far too worried about the environment to buy such a thirsty car. He was also the boring sort of individual who never seemed to have any interest in risk-taking or recklessness, even as an adolescent. The possibility that he, of all people, would buy such a car would strike me as implausible even though I realize people can change a great deal in 20 years. I'd be open to the possibility that he was telling the truth but more than a bit skeptical.
And yet, when he shares a photo of himself standing next to his new car and tells me about how much fun he has been having with it, my doubts would melt away. He has persuaded me. Sure, maybe it is an odd hoax and I'm being fooled for some reason. But here's the important thing: the nature of his claim, while initially striking me as implausible based on my distant memories of him, is not so far-fetched as to require all that much evidence. Barring some reason for suspicion (e.g., maybe he was a chronic liar), I accept his evidence as sufficient to support his claim.
Now suppose that another acquaintance from college contacted me one day (also on Facebook) to inform me that a mutual friend has a serious illness and that she is worried about him. It isn't that I'd immediately disbelieve her, but I'd find this news difficult to accept because I've been in touch with our mutual friend and heard nothing about any sort of illness. Why wouldn't he have told me he was sick? And why wouldn't any of our other mutual friends who would know both of us better than this woman have said anything? It doesn't add up.
This particular acquaintance cannot provide anything in the way of evidence, and I'm not sure what sort of evidence it is fair to expect her to provide. She explains how she came to learn of the illness, and her explanation certainly sounds plausible. But in this case, I need more. I reached out to someone who knows all of us and would be in a far better position to have this sort of information. She confirmed everything and provided new information. Our friend was diagnosed recently but responded well to treatment and is now in remission. He has always been a fairly private person and wanted to keep this to himself until he knew the outcome of the initial round of treatment. She said that she thought it would now be okay with him for others to know and suggested that I contact him. I did so, and he confirmed her entire account.
Now consider an entirely different sort of scenario where evidence is even harder to come by. Someone I have never met offline but have come to know reasonably well online asks me who I plan to vote for in the 2016 presidential election. Upon hearing that I am undecided, she takes it upon herself to try to persuade me to vote for her preferred candidate. This is a case where evidence, at least what we would typically consider evidence, may be a bit trickier. Her claim is that her preferred candidate is the best option and the one I should support. Her best bet in persuading me is probably a combination of reasoned argument with evidence brought in to support particular points as necessary (e.g., evidence of how her candidate has voted on specific issues or that her candidate has demonstrated good judgment in other areas).
Despite how resistant I might initially be to her choice of candidate, I will change my mind if her argument is good enough and supported with sufficient evidence. I am persuadable, and I will listen to reason. What she needs to do is make an effective case for why her choice is better than the other options. Explaining why this choice is better for her may help, but the key will by why this choice is also better for me.
The amount and type of evidence and reasoned argument I require will vary across these and other scenarios. The more outlandish, implausible, far-fetched, or important the claim, the more evidence and the better argument will be necessary. If you want to convince me that you have a interesting car in your garage, the bar is fairly low; if you want to convince me that you have a dragon in your garage, the bar is quite a bit higher. Why? I already have plenty of evidence that cars exist. In contrast, I am unaware of any evidence that dragons exist.
What about claims of the supernatural (e.g., demons, angels, ghosts, souls, or gods)? Can I be persuaded that any of these things are real? Absolutely. Of course, the evidence one would need would be considerable. I'd need evidence sufficient to support these important but extremely implausible claims. Anything less would probably not have much of an impact. It is not that I am any less persuadable in such cases, only that I recognize that such claims will require far more in the way of support.
It is also worth nothing that virtually none of the Christians I've encountered actually seem to give a damn whether I believe in a god; they want me to believe in their specific idea of god. And not only that, but they want me to believe a long list of specific claims about their god. I mention this because even if a Christian could persuade me that there was some sort of god, this would not necessarily mean that I'd believe it had to be theirs or that I'd believe any of the other things they seem to want me to believe about it.
