"
So if there are no criterion in other fields, how can I ever prove something to be sensical or nonsensical? "

You can't(as far as I can tell), but you seem to speak as if such an act is neccessary; why?

"But that's a poorly defined metaphysical concept, the idea of "existence". It's nonsensical that "existence" can imply itself."

It's more like:

Objects===Properties