I can’t be sure of the exact example but adding Bayesian to my search I am certain this is what was being discussed. My gripe here is, as I think you pointed out, not with formal logic or even the validity of Bayesianism.
Strictly speaking, comparing the sentences ‘absence of evidence is evidence of absence’ and ‘absence of evidence is not evidence of absence’ it would seem to me the former is true and the latter is false. I have not encountered any instance of this being left as a simple semantic argument.
I don’t take the ‘is not’ phrase as necessarily true compared to the ‘is’ phrase. Rather, I take it to be obviously true in regards to the intent of the person saying it. I think your elephant example gets to the heart of the difference. That being proof and evidence. An elephant not being in a specified place and time is proof of an elephant not being in a specified place and time. If I say an elephant was in a specified place at some prior time and we observed elephant footprints and feces that doesn’t prove an elephant was there but it is certainly evidence of an elephant. This, I think, is the problem with the celestial teapot argument. I don’t need to observe the teapot to think it exists but I do need some evidence. Perhaps a celestial tea spill.
I hope that clarifies where I am coming from. It seems that the ‘is’ sentence is not adequate to disprove the ‘is not’ sentence because they are not saying the same things. What’s more troubling, if I am understanding this Bayesian thing correctly, it is saying the longer something goes without evidence the less likely it will be true. I don’t see how one could get there from absence of evidence is evidence of absence. How can any probability, greater than zero, be assigned when you have already concluded that there is no evidence?
I think there is another angle that I am overlooking but this is making my head hurt, I hope reading this doesn’t have the same effect on you.