It is commonly accepted that the lack of evidence for a particular proposition makes belief in said proposition irrational.
However, imagine the following proposition,
P: An object exists for which evidence can never be comprehended nor even acquired by humanity.
This seems a certainly reasonable proposition, and in fact, belief in this proposition seems to be completely rational. After all, the universe is vast and perhaps infinite, and due to said vastness, the probability that such a thing exists which we can never reach, and, even if we did, would never be able to grasp due to our limited intelligence and perception, seems, to me at least, rather high.
And yet, by its design, this object has no evidence.
So, is this an example of a proposition which has no evidence but which it is still rational to believe in, and hence the premise that "each belief in something which has no evidence is irrational" ... is false?
One may counter-argue that the knowledge that our intelligence and perception is limited, coupled with the vastness of the universe, is itself evidence that such an object must exist. However, now I feel we are moving the goalposts and changing our definition of the word "evidence" into something less tangible and moving into the territory of probability, and it is well-known that probability is ridiculously hard to define and almost always subjective. If that is how we then wish to play the game, then "I believe in God because the probability that all of this came of nothing is so low according to my subjective probability distribution" must be considered an acceptable piece of evidence, which I don't feel it is.