Let's go back to my original example and say we want to know if A is true. We have the choice to run an experiment whose positive result E would give support to A. The linked video would say that before we run any experiment, we have no additional evidence for A. Essentially that P(A) = P(A). This is true.
The way this should be used in the real world is: I look even the slightest bit for A and don't find it. As long as my search for A had the smallest positive chance of finding it were it to exist, then my lack of ability to find A gave me information about the world, and we get that P(~A | ~E) > P(~A).
Edit: To be precise the maxim should be something like: "Absence of evidence after looking for evidence is evidence of absence".
Again, what is being said is, 'no evidence is no evidence'. If you have the absence of evidence then you have no evidence of absence.
We are--kind of--using the word absence in two senses. First as a synonym for none, a number less than one, zero; the second as a synonym for non-presence, non-existence, the lack of an extant sample.
Having zero [absent] evidence is not evidence that there is no extant sample [absence]. I hope that helps.
You where. What you are describing is, 'we constructed a hypothetical experiment and arrived at a null result'; that is, in fact, evidence.
No one is saying, 'a null result is not evidence of absence'.
Please stop conflating the presence of something with the absence of something.
Yes, the statement is a tautological statement. We are repeating the same assertion twice using different phrasing. And as such, the proposition as stated is logically irrefutable.
'No evidence is no evidence', is a correct—but diminished—restatement.
Have you watched the video?