Well, we all have experienced it before. It's that feeling we get in our gut when we've experienced something one way and then are told it's actually another way. This doesn't sit right, it's hard to move on from (at least for me). Inevitably, these situations are labelled a contradiction. I would be lying if I told you I only find contradictions in others' belief systems, but unfortunately that's part of the path God is bringing me through now. How can a good and just God control every single thing that happens on the Earth for the purpose of His will, and at the same time hold us solely responsible for our sin? I have experienced God as good and just in my life and I have an innate understanding of what justice looks like so I reject this idea as a contradiction. Contradiction always stems from how we experience the "facts" in question.
Paradox occurs in my mind when I experience two seemingly contradictory facts, ideas, propositions (etc) as equally valid. How can Christ be fully man and fully God? I rely on the experience of the New Testament authors to attest to Christ's humanity while I rely on my experience of Him as God in my life to attest to His divinity. I cannot attribute paradox to the contradictions of other faith traditions because I either experience only one of the facts in question or none at all. For example, Buddhists believe that desire and ignorance are at the root of all suffering and that Nirvana is achieved only by eliminating desire. While I agree that desire can be a form and a cause of sin and suffering, I have never ever met anyone who has been able to successfully rid themselves of desire, nor do I think it possible. Even the desire to rid oneself of desire would ultimately cause you suffering. This then is a contradiction and an impossibility to me.
Now I'm aware that I've pretty much built a house of cards with nothing but experience and feeling as the foundation, which vary wildly from person to person. This is not to say there is not an ultimate Truth out there, just that we differ in how we relate to it. Experience and feeling are two separate things but they tend to go hand in hand. I was lucky enough to grow up in a stable home in a stable country with a (relatively) stable childhood. My understanding of justice is defined by my experience of it due to the circumstances I was born into. Conversely, a girl my age can be born into an unstable family, in an unstable country, with a horrific childhood marked by abuse and degradation and her experience of justice will be decidedly different than mine.
I bring all of these things up not only to justify why I might label apparent inconsistencies in my own faith as paradox rather than contradiction but to justify why someone of another faith might do the same thing. The longer I sit here staring at the blinking cursor, the longer I realize this topic brings up more question than it answers (surprise, surprise), questions I'm definitely not qualified to address. For example, if paradox always stems from how we experience a fact or proposition, then how can we ever know if anything is true? Then there's the very obvious explanation that we (myself included) are willing to call something a paradox because it sounds nicer than contradiction and is a little easier to live with. So here we are, and I fear I dug a hole that will be hard to get out of.
What about you? Can you think of times when you're willing to call something a paradox just to avoid the fear of it being a contradiction?