I've had the experience of exchanging conversations recently with an apologetic or a troll (I can't tell which one is) after he came to respond a post from my blog and I have to be honest with you, I don't know how you deal with them because no matter how much evidence I provide, how much definitions I try establish, how much scriptures I try to write about their nasty stuff, how much logic and reason I try to give them, they will not care about it. It doesn't matter how nice I try to be and focused on the key points depending on the subject, it's impossible to get them understand. In fact, they will ignore it all and instead they give you shit with a bunch of fallacies, deflections and empty insults because of "hurt feelings" or "muh faith."
In the end, I had to block the person because he wouldn't stop harassing me.
Seriously, kudos to you for knowing how to handle it because I just learned that it takes a lot of energy and time to write important points depending on the subject and you must have a lot of apologetics and trolls coming in your asks or reblogging in your posts.
Honestly, after a hundred or so of them, you start to pick up on a pattern, and can even predict the beats before they happen.
When you hear that everything "has a beginning" or something created it" you know they're doing the argument from first cause, unmoved mover, Kalam or similar.
When they ask about atheist morality or the existence of objective morality, they're going to do the argument from morality and likely to bring out the Atheist Atrocities Fallacy, usually with Hitler misrepresented as an atheist. Because non-believers decide for themselves what's okay and don't have to answer to anyone, since, you know, society and conscience don't exist and nobody could empathize with not wanting to be killed.
When they ask about the meaning of life, they're going to admit that in the entire infinite universe, they can't find meaning and need it dictated from above.
When they ask about death, they're going to tell you that you send yourself to hell, graze the edge of Pascal's Wager and insist that you'll find out when you're dead.
When they tell you that there's "proof," they're going to give you a passage from their scripture. mischaracterize a scientific principle as coinciding with their doctrine, insist that their thing is historically proven, lie some more, and then tell you that you can't prove that it doesn't exist.
When claims of scientific and historical proof go nowhere, they'll resort to personal testimony as "proof". Of some time when their god saved them during a bad time in their life (usually drugs), spoke to them, some unexplained experience occurred, or someone they knew had a near-death experience and that's all the proof they need - that is, argument from anecdote. They'll tell you how their god answers their petty prayers, then when you ask why their god helped them get the job but won't help the victims of famine or the victims of pedophile priests, it will be "free will" and the failings of humans.
When they tell you that you have "faith" a god doesn't exist, faith in science, they're going to equivocate on the word "faith" and refuse to accept or understand the concept of atheism as a "Not Guilty" verdict versus an "Innocent" verdict (that we don't have to believe a god doesn't exist to reject the claim that a god does exist).
When you point out terrible things in their scripture, they'll insist that it wasn't god doing or saying that, that they deserved it anyway, that it was okay at that time, that's taken "out of context", a metaphor, that the scripture also says something else - which is irrelevant to whether it says what you've described - even when theirs is taken out of context or isn't even there at all, and that you have to believe it to understand it, meaning that you can't understand it to then believe it.
When you ask how we can get truth from faith, they'll fluff around for a while about how they know the Truth from faith, use a No True Scotsman, refuse to answer, then deflect onto another beat (above).
They'll accuse you of not being open-minded, dogmatic in your atheism and insist that you must have been hurt by religion - they might even throw in a No True Scotsman, that you were hurt by people who weren't "true" Xians or whatever - to reject (their) god.
Eventually they're insist that they just have faith, and that it gives them warm gooeys, say they pity you for having nothing in your life, say it makes them sad that you've chosen to reject (their) god, and that they'll pray for you.
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These don't necessarily happen in this order or occur linearly. You may bounce around back and forth between any of them, even revisit one or more, particularly if the believer is doing a lot of deflection.
They say that experienced martial artists can tell what their opponent is going to do before they do it. I'm not going to pretend that I'm an "expert" or on the same level as a martial arts artist, but after a few bouts, you realize they're using the same playbook.
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The problem is that you and the believer want different things. You want to understand what's true, and they want to feel good with the Truth™ that they already Know™.
You're thinking about how this stuff is self-contradictory, inconsistent and even outright immoral, but they're thinking about singing in church, church picnics, and the time that god made sure that grandma survived her hip replacement surgery.
You want to talk about the (il)logic and (un)reason embedded within their beliefs, citations and all, and they want to save the heathen from pissing off Magical Space Daddy and ending up at the eternal Weenie Roast.
All of these beliefs are attached to feelings of safety, protection and control - both that everything isn't just subject to complete, random chaos because (their) god is control, and that they can derive some control themselves through prayer.
With any interaction with a believer, you need to consider why you're doing so, what you look to get from it. Are you practicing counter-apologetics and fallacy detection/rebuttal? Are you hoping to convince them of anything? Are you looking to see if there's an argument you haven't heard yet so you can upskill? This isn't a one-time consideration either; it's something you need to keep evaluating during the course of it. And at some point you might have to just pull the ripcord and be done with it, and save yourself and the other person the wasted time and effort.
One-on-one engagements I don't find so useful. They want to proselytize at me, I know the most I can do is take a small chip out of their armor that might result in a Fridge Logic moment down the track, and it's been ages since I've heard a new argument. I find reblogs that let other people see the claims believers make and how to rebut them to be more useful.
I haven't actually had one-on-one in a while; the last one was someone who wanted to continue reblogs to private. When I declined, since I didn't see much point as they were entirely about faith which I don't value, they persisted anyway, so I smashed two PM windows worth of the usual beats on faith and got rid of them.
Which is to say, pick your battles. You don't have to be drawn into an argument with every random who believes something stupid just because they show up in your PMs or Asks.
Even when you do, don't expect much more than a mix-tape of the greatest hits.