I am looking for examples of theories that we now know to be correct, but that would have have been unfalsifiable in a slightly different context --- e.g., in the past, or in hypothetical scenarios. (Unsurprisingly, this is motivated by the unfalsifiability of some claims around AI X-risk. For more context, see my sequence on Formalising Catastrophic Goodhart's Law.)

My best example so far is Newton's theory of gravity and the hypothetical scenario where we live in an underground bunker with no knowledge of the outside world: We would probably first come up with the theory that "things just fall down". If we look around, no objects seem to be attracting each other, like Newton would have us believe. Moreover, Newton's theory is arguably weirder and more complex. And Newton's theory doesn't make any experimental predictions that we could realistically verify.

Specifically, I am looking for examples of phenomena with the following properties (examples in footnotes):

1. The phenomenon is something unambiguous and where, in the present day, virtually nobody^[1] has any doubt about it being true.^[2] Bonus points if the phenomenon is something that happens very robustly, rather than merely something that can happen.^[3]
2. There is some historical or hypothetical scenario S such that the phenomenon obviously never occurs in S or its past. Bonus points for plausibility.^[4]
3. In the scenario S, it is, obviously, practically impossible to exhibit the phenomenon empirically.^[5]
4. In the scenario S, it is, obviously, practically impossible to gain evidence on the phenomenon through formal analysis (which includes mathematical modelling and the use of computers). Bonus points if the reason for this is that we know some "first principles" from which the phenomenon might be derived, but doing the actual derivation is obviously too complex (as opposed to requiring a clever idea).^[6]

1. ^{^}

   Sure, there are always crazy people, creationists, the Lizardman constant, etc. But hopefully the examples make it clear enough what I am after.

2. ^{^}

   Examples of "unambiguous and widely agreed-upon" phenomena are: "The Earth orbits the sun", "physics and chemistry can give rise to complex life", or "eating lots of sweets is not good for your health". But not "communism is bad", which is too vague, or "faster-than-light travel is impossible", which is not obvious to everybody.

3. ^{^}

   An example of phenomena that happen very robustly are "sufficiently dense things form black holes", "stars go out", and "the law of large numbers". In contrast, things that merely can happen are "physics and chemistry giving rise to complex life", "sun eclipse", and "twin primes".

4. ^{^}

   Examples of phenomena that would obviously not happen in particular scenarios or their history are: "Eating lots of sweets is not good for your health" before 1000 BCE, "sufficiently powerful AI would cause human extinction" today, or "any two particles attract each other via gravity" if you live in a bunker and don't know about the outside world. But not "heavier-than-air is impossible" in 1000 BCE, because birds can fly. And not "eating lots of sweets is not good for your health" in 1000 CE, because it's not obvious enough that there weren't problems with sugar before then.

5. ^{^}

   Examples of phenomena that are, obviously, practically impossible to observe experimentally are: "Humans can harness nuclear energy" in 1700, or "physics and chemistry can give rise to complex life" if you can't rely on materials from Earth. But not "eating lots of sweets is not good for your health" once you have sugar, or "smoking isn't healthy" anytime; at least not unless you ban unethical experiments.

6. ^{^}

   Examples of phenomena on which it is, obviously, practically impossible to gain evidence by formal analysis, are: "Physics and chemistry can give rise to complex life" or "eating lots of sweets is not good for your health"; both of these get the bonus points. "Riemann hypothesis" and "P vs NP" are debatable, but definitely don't get the bonus points. Phenomena like "if you don't eat, you will die" , "if you aim a rocket straight at the Moon, it will fail to land there" if you only know high-school math, "CO2 causes global warming", and "nukes could cause nuclear winter" do not count, since we can demonstrate these phenomena in models that are simplified, but for which many people would agree that the model is at least somewhat accurate and informative of the real thing.