modeller (again) // We can never prove, by definition , that something imaginary exists .//
You might, (though I doubt it), accept the existence of human experiences from which you may, for reasons I have no wish to enter, be excluded by your own dependence on what you perceive as rationalism.
One glaring example being the 'Argument from Religious Experience'.
The argument from religious experience stems from the experience of God to the existence of God. In its strong form, this argument asserts that it is only possible to experience that which exists, and so that the phenomenon of religious experience demonstrates the existence of God. People experience God, therefore there must be a God; case closed.
No matter how much this infuriates you, for some, it is a life-enhancing fact requiring no proof whatsoever.