- Is Eve irrational?
- Can believing an unfalsifyable believe be rational?
- Can this argument be extended to believe in God?
I understand what you are trying to say, but I am struggling to see if it is true.
It's a straightforward corollary of Bayes theorem: if P(A) = 1 (or P(A) = 0), no amount of later updating can change this value. No matter what strong contrary evidence is presented.
This is indeed a simple model of a hardcore theist: he has already set P(god(s)) to true, so he is willing to dig himself a hole of unlimited depth to account for the evidence that oppose the existence of a divinity.
As for some example, Russel's teapot is a good choice: a teapot orbiting a distant sun in other galaxy. Is it falsifiable? With our current and future technology, probably not.
Is it logically falsifiable: yes! Even if you assign a very low probability to its existence, an alien species could just transport us there and show us that there's such a teapot.
On the other hand, as I mentioned earlier, if we had put P(teapot) = 0, then we will never accept the teapot existence, even in the face of space travelling aliens that show us that the thing is actually there.
I see... I have been using unfalsifiability and lack of evidence as a synonym. The title should have read: a rational believe without evidence
Thank You.