What if I told you that the entire universe was created last Thursday. All of our memories of everything past last Thursday were also created last Thursday.
There’s no way to disprove this. Someone can point out how we have observed scientific data like supernovae, coupled with what we know about the speed of light, which shows that these stars’ explosions took place both a long time ago and far away.
Nope. Those were created in media res last Thursday as well.
As I’ve presented it, there’s no observation possible that can be inconsistent with Last Thursdayism. This is what it means to be “not falsifiable”.
The concept of falsifiability was put forth by philosopher of science Karl Popper. But falsifiability is not just a philosophical defense of science. The drawbacks of having a non falsifiable model can be described mathematically.
This is Bayes Theorem:
P(H | E) means “the probability of H given E”. Let’s say H means “hypothesis” (or “model”) and E means “evidence” (or “data/observation”).
Bayes shows you how much more or less probable a hypothesis is given some evidence.
Instead of Last Thursdayism, let’s take on a real-world unfalsifiable hypothesis: Creationism / Intelligent Design. Creationists say that everything in the biological world was created by the Christian god. The Christian god is all powerful, so nothing is beyond His capabilities, right?
Let’s say our hypothesis H is Creationism, and our evidence E is “dolphins having a whole hand in their flippers”. Let’s also assume a position of agnosticism about Creationism, or P(H) = 50%.
Creationists says, dolphin skeletons showing a friggin’ HAND in their flippers fits perfectly with the hypothesis, right? In other words, assuming Creationism is true there’s nothing inconsistent with God giving dolphins hands in their flippers; meaning a 100% likelihood of dolphins having fingers and thumbs in their flippers. Or P(E | H) is 100%.
Now we get to the tricky part, so bear with me.
P(E) in the denominator is the probability of the evidence. It’s also called the Total Probability, and also has a formula:
Assume that A is actually E, and B is H for consistency. This reads, P(E) is a sum of various probabilities; with E staying the same but with alternative hypotheses (H). Which means we should be taking hypotheses other than Creationism into account when evaluating Creationism.
Let’s go with a simple alternative hypothesis: dolphins and humans have a common ancestor, which explains why the appendages have similar bone structures. Since related probabilities have to add up to 100%, and we’ve already assumed P(H) is 50%, this means that P(~H) — the theory of evolution — is also 50%.
This means we’re working with the long form of Bayes Theorem:
P(E | ~H), or the probability of dolphins having what looks like the skeleton of a human hand in their flippers, given that the theory of evolution is correct, is some value. Let’s say we are a die-hard Creationist and just assert that there is only a 1% chance of this being true.
Here’s the part where we start explaining why a non-falsifiable hypothesis is bad, beyond the arguments and assertions of philosophers of science.
I explained that P(H) and P(~H) together has to add up to 100%, which is why if P(H) is 50%, P(~H) is also 50%. But there are other terms in Bayes Theorem that have to exhaust the hypothesis space like P(H) + P(~H) have to.
P(E) plus P(~E) equals 100%
P(E | ~H) plus P(~E | ~H) equals 100%
P(E | H) plus P(~E | H) equals 100%
It’s this last one we want to pay attention to: The probability of not having the evidence given that the hypothesis is true.
For Creationism, what would that be? Assuming for Creationism the evidence we have — dolphins having the bone structure for grabbing things in their flippers even though they absolutely cannot grab things with their flippers — is expected. P(E | H), or P(Dolphins With Five Fingers | Creationism), is 100%.
But remember that P(E | H) plus P(~E | H) equals 100%. Which means if we assert that P(Dolphins With Five Fingers | Creationism) is 100% we are also asserting by inference that P(Dolphin With Some Other Skeletal Form In Their Flippers | Creationism), is 0%.
Would Creationism really concede that, if we had discovered dolphins with a bone structure that looks like a single flipper instead of a hand, this disproves Creationism? That there’s a zero percent chance of this happening? That this is beyond God’s abilities?
Of course not.
So instead of that concession, we have to concede — based on the rules of basic math — that P(Dolphins With Five Fingers | Creationism) is not 100%. It’s some number less than 100%. What this number is, is besides the point. The actual point is… what type of flipper structure is inconsistent with an all powerful god?
I’ve only introduced two hypothetical datapoints: P(Dolphins With Five Finger Bones | Creationism) and P(Dolphins With One Flipper Bone | Creationism) = 100%. Or, written in shorthand, P(E1 | Creationism) + P(E2 | Creationism) = 100%. What’s stopping God from other hypothetical evidence? P(E3 | Creationism), P(E4 | Creationism), P(E5 | Creationism), P(E100 | Creationism)? Is there any P(En | Creationism) that is so beyond God’s capabilities that it shouldn’t be included? Isn’t the limit really no limit at all? With God, all things are possible!
And that’s the problem. If P(E1 | Creationism) + P(E2 | Creationism) + P(E3 | Creationism) + … P(En | Creationism) = 100%, the probability of any one of those possible observations — with no other way to differentiate them — is n / 100. if n is infinity, what does this say about P(Dolphins With Five Finger Bones | Creationism) or P(Dolphins With One Flipper Bone | Creationism)? They are evidence out of an infinite sea of God’s possibilities; their individual likelihoods are vanishingly (infinitely…) small.
On the other hand (lol), P(Dolphins With One Flipper Bone | Theory of Evolution) should be zero, since dolphins that have a single flipper bone instead of a hand would be, rightly so, evidence against common descent.
As a somewhat off topic note, notice that Bayes Theorem doesn’t say anything about “scientific” in and of itself. Even though it’s not explicit, a lot of other problem-solving endeavors take a Bayesian approach to creating solutions. Your plumber, when diagnosing what’s causing your plumbing problems, does not bother with unfalsifiable explanations (e.g., invisible gremlins from the 5th dimension are responsible for your plumbing problems). Almost everything, from astrophysics to finding where you left your keys, are inferences to the best explanations.
Falsifiability might have been introduced as a defining element of science, but falsifiability is actually Bayesian, and science is just a special case of strong Bayesian evidence.
Other elements of good science — like extraordinary claims requiring extraordinary evidence, Occam’s Razor, absence of evidence is evidence of absence, the provisional nature of science — are also Bayesian and able to be expressed mathematically. Meaning that all of those things that are elements of good science are also elements of good troubleshooting in more mundane, everyday areas. Even and especially things that don’t claim to be science but are attempting to model the world.