Update: Zvi wrote his own post.
Law of No Evidence: Any claim that there is “no evidence” of something is evidence of bullshit.
―Covid 5/13: Moving On by Zvi
But in probability theory, absence of evidence is always evidence of absence
―Absence of Evidence Is Evidence of Absence by Eliezer Yudkowsky
This is not a contradiction. Zvi and Yudkowsky are both correct.
"No evidence" is a vague term. Consider the phrase "There is no evidence of Bigfoot". It could mean one of two things.
- Explorers looked for Bigfoot and didn't find him. This is evidence Bigfoot doesn't exist.
- Nobody looked for Bigfoot and nobody found him. This is not evidence Bigfoot doesn't exist.
It is true "no evidence" is evidence of absence insofar as "no evidence" means "we ran good experiments and they failed to produce evidence for the hypothesis". But in this case you shouldn't say "no evidence". You should say "evidence of absence".
Inference starts with priors and are then updates them according to evidence. If there is no evidence related to a hypothesis then your beliefs reflect your original priors. If "no evidence" refers to true "absence of evidence" then everyone needs to retreat to their Bayesian priors. But this not what anyone means when they say "no evidence" because your Bayesian priors for one context are informed by transfer learning of evidence from other contexts e.g. I have a computer programmer friend who thinks about everything in terms of software metaphors.
If someone deliberately uses vague language instead of precise language then it is because they are trying to conflate two ideas which should not be conflated. If someone says there is "no evidence" of something then it is because they are trying to pass off "nobody looked for Bigfoot and nobody found him" as "explorers looked for Bigfoot and nobody found him".
Saying "there is no evidence of UFOs" communicates nothing useful. You must explain why absence of evidence constitutes evidence of absence.
If you want to prove that red light doesn't cause cancer you don't say there is "no evidence". You should explain the frequency dependence of the photoelectric effect.
If someone deliberately uses general language instead of precise language then that is good because general language is easier to falsify than precise language. Vague language is bullshit because it is hard to falsify. ↩︎