Every time I turn around, I seem to run into another Christian or Muslim making a shifting the burden of proof fallacy (such as in the movie God's Not Dead), so I guess I have to explain it even though countless other people have already explained this.
First, let me refer you to some of the better explanations. There is the now-infamous celestial teapot, which comes from an essay by Bertrand Russel. If you're not in the mood for reading, QualiaSoup made an excellent 11-minute video essay that uses a skull-juggling psychic were-walrus as the example for the burden of proof, which I have to admit is even funnier than Russel's celestial teapot.
When I have this same discussion, I generally talk about fairies.
Reductio Ad Absurdum
If you are a theist, you may be confused about why you start out talking about the existence of God, and suddenly, the atheist you are talking to is changing the subject to fairies, celestial teapots, and skull-juggling psychic were-walruses. Often, I am accused of comparing God to a fairy. While I do think God has much in common with fairies, I think many theists miss what is going on.
Remember that arguments support or fail to support claims. A bad argument is an argument that fails to support its claim. Sometimes, if you are emotionally attached to the conclusion, it can be hard to honestly examine the supporting arguments or supporting evidence. Thus, in order to illustrate what is wrong with the logic of the supporting argument, I sometimes apply the same logic to a different conclusion. I choose fairies as the new conclusion simply because I assume that you have no particular emotional attachment to the claim of whether or not fairies exist.
This of course leads to special pleading fallacies. I assure you that what I am about to say applies to the vast majority of existence claims, and I will cover the cases where this argument doesn't apply.
Most Existence Claims are Non-Falsifiable
Yes, there really are people who believe that fairies are real, although the belief was much more common in the 1800s and before. No, it doesn't matter if people really believe in fairies. I don't know why so many Christians raise this objection. What I'm about to say applies regardless of how many or how few people actually think fairies are real.
There is an endless series of rhetorical games that a fairy believer can always claim leaves open the possibility that fairies are real despite my best efforts to disprove fairies. For example, the fairy-believer can claim that the fairies were hiding in the cupboard while I was searching for them in the shed. Thus, the only way I can conclusively disprove fairies is if I can simultaneously search every cubic centimeter of the universe, and we don't even know how far the universe extends beyond what we can observe in our own light cone. I would literally have to be omniscient in order to disprove fairies.
Since I am not omniscient, I cannot possibly disprove fairies, even if fairies do not in fact exist. Thus, the existence of fairies is non-falsifiable. Like most existence claims, fairies cannot be disproved even if they are not real, but they can be proved if real.
The fact that I cannot disprove fairies is not a valid reason to believe that fairies are real. The fact that I can't disprove fairies only means that this existence claim is just like most existence claims.
I also cannot disprove elves, Bigfoot, orcs, Chupacabra, vampires, goblins, werewolves, djinn, mermaids, shinigami, nor any of the thousands of gods of the thousands of religions that are or have ever been practiced by man. Heck, I can't even disprove any of the fictional gods because it is theoretically possible (however improbable) that the author was accidentally correct.
The Loch Ness Monster is Falsifiable
Existence claims can be falsified when the claim is sufficiently specific, or if the claim includes something that is logically impossible. For example, the Loch Ness Monster happens to be a falsifiable existence claim. In fact, it has already been falsified.
Ecologists have become pretty good at estimating the biomass of a given ecosystem. The estimate of the total biomass of Ness lake suggests that there simply isn't enough food to support anything bigger than 31 kg.
The same goes for gods. For people with very vague definitions of "god," then their god is as unfalsifiable as fairies. But many from Abrahamic religions insist that God exists and is omnipotent, omniscient, and omnibenevolent. Like the Loch Ness monster, this adds enough specificity to the existence claim to make it falsifiable. A being with all 3 properties is logically inconsistent and can be shown to not exist. Similarly, any two of those properties is logically inconsistent. Heck, omnipotence is logically incoherent all by itself as it creates all manner of paradoxes.
Of course, Jews, Christians, and Muslims claim that those properties are not self-refuting, but oddly they are the ones who insist on sticking to definitions of those terms that very much are. At any rate, this is not the time to go into detail about those arguments about omnipotence, omniscience, and omnibenevolence.
Elephants Are Non-Falsifiable
Do you know what else is a non-falsifiable existence claim? Elephants. The existence of elephants cannot be falsified even if elephants do not in fact exist, but can be proved if… well, will you look at that. We have evidence for the existence of elephants, therefore it is reasonable to believe that elephants are real.
The same goes for electrons, and traffic laws, and a whole bunch of other things. In fact, for things that exist, it is generally trivial to find proof for their existence, even if producing that proof yourself requires building something expensive in a laboratory (or a multibillion-dollar atom smasher as in the case of the Higgs boson). Even if you can't build the correct device or travel to some exotic location, you can generally find the evidence produced by those who did.
For most existence claims, we cannot falsify the claim even if the claim is false, but we can prove the claim if true. Lack of disproof is not a valid reason to think something is real. If it were, then there are an infinite number of things we would have to accept as real, including a large number of things I could simply make up in the future. Are you really prepared to believe that all the gods of all the religions are real just because you couldn't be bothered to accept the burden of proving the existence of your own god?
Because most gods from most religions are mutually exclusive. Most religions claim to represent the only real gods and that all the gods of all the other religions are not real. Thus, if the burden of proof is on the person who doesn't accept the claim, then that means that all the gods of all the religions are real, but if all the gods of all the religions are real, then that means the Bible and the Quran are definitely false because both books claim to represent the one and only true god. So while insisting on reversing the burden of proof might count as proof of the existence of your god, it would also disprove the religion you follow.
It's Not Just Theists
If you pay attention, you can see the same shifting the burden of proof fallacy all over the place. UFO believers are notorious for doing this. They will show grainy footage of whatever, then demand that someone prove that the item in the image is not an alien space ship. People who believe in Bigfoot will show that infamous film footage and ask people to prove that the image is not an image of the real thing. That nutbar on the History channel who believes in the ancient astronaut theory keeps asking everyone else to disprove his various claims.
When it comes to existence claims, lack of disproof is not a good reason to believe something is real. The only time it is reasonable to believe something is real is when you have some kind of valid evidence for it. I have to specify valid evidence, not just evidence. The Bigfoot believers, fairy believers, and UFO believers have lots and lots of evidence, they just don't have any good evidence.
By contrast, there are a wide variety of experiments you can do for yourself to prove that dark matter and dark energy exist. Granted, we have no idea what they are (including, possibly, a problem in how we calculate gravity), but we can definitely prove that it exists and in the case of dark matter, prove where it exists (or where our gravity calculations go wrong if that is the case).
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