Fundamental Arrogance in Christianity

[Mister Agenda]

I question the utility of logic as way of proving something exists without reference to evidence for that thing existing.

I have a rock on my desk. We know that rocks and real are that they do exist and that their existence is easily demonstrated. Yet there is no logic that can prove my claim is true, the only way for other people to know my rock is there with any reasonable certainty is for someone do something to demonstrate that I have it.

If pure logic doesn't work for things that we know can be real, how can it work for things that can't be demonstrated to exist?