When faced with a paradox, there are several common responses:
1. Agnosticism/Skepticism - Simply throw up your hands declaring that nothing can truly be known and then go do whatever you like. Leads to a life of depravity and godlessness. This is not an option for Christians, since God has given us clear teaching and expects us to take it to heart.
2. Imbalance - Choose one side of the paradox and emphasize it until the other side is forgotten or overlooked. Leads to extreme dogmatism. This is not an option for Christians, since it requires us to ignore or explain away portions of God's Word.
3. Rationalism - Attempt to explain and solve the paradox by using complicated reasoning and relentless logic. Leads to pride (and possibly insanity!). This is not an option for Christians, since God opposes the proud.
4. Faith - Embrace both sides of the paradox. Accept that you are a finite being with a limited intellect. Believe that God has given both sides of the paradox for His glory and your good. Don't wait until you understand everything, but fall down adoring before the ONE Who does understand. Leads to humility and worship. This is the only real option for Christians who are faced with Biblical paradoxes.
This is not to say that we should never attempt to understand how things work or develop theories of how paradoxes might be solved. When approached humbly, such reasoning can be of great value. However, it is foolish for anyone to think he can FULLY explain the Trinity, the two natures of Christ, the virgin birth, or the relationship between God's sovereign election and human choice. These issues have been debated by great minds thoughout history - and they're still not fully explained.
Here's what we need to remember:
The moment we stop worshipping God, we begin to go off course. Do not trust the reasoning of your mind when you are not humbly aware of your finiteness and focused worshipfully on God's greatness. Come back to Him and be captivated by His wondrous grace again, then begin to think deeply. This is the safe course of theological reflection.