How about we go back to the beginning. Plato's Cave Simile has been mentioned and it's important in the history of Western philosophy because it articulates an intuitive distinction between "things as they are in themselves", and things as we take them to be. It represents the beginning of transcendentalism - the belief that behind this veil of illusion there is a transcendental reality, which, if we are lucky and we use the right practices, we might get a glimpse of, but even if we get no insight into the nature of this ultimate reality, we still, at some deep level, believe in it's existence. Kant called it a necessary category of thought. In a sense then we are all intuitive Platonists.
But what if the world isn't like that - check out
this link at the Stanford Encyclopedia on process philosophy for an interesting summary of an alternative - non-religious - view.