"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."
"But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves that You exist, and so therefore, by Your own arguments, You don't. Q.E.D."
"Oh dear," says God, "I hadn't thought of that," and promptly vanishes in a puff of logic.
Ah, the snares of logic. Even the divine fall prey to them. There are plenty more paradoxes in logic and our physical universe, particular in the fuzzy area of time-travel. The grandfather paradox, where you travel back in time and kill your own grandfather, is a famous example. These sort of paradoxes are usually ignored in Hollywood films or downright butchered in episodes of Red Dwarf.
Time-travel paradoxes have had physicists and philosophers alike muddled for years. Recently, one of my old lecturers, Prof David Pegg, wrote an article shedding some light on this area. Pegg, who did his PhD at Oxford in formalising a system to represent the direction of time, proves for simple systems (the travel of light particles) that quantum mechanics only allows retro time-travel with self-consistent loops.
What's a self-consistent loop? Pegg's example: you travel back in time to shoot yourself as a baby. You lift up the gun to shoot your infant self in the heart, but your weak arm drops and you shoot your infant self in the arm causing a life-long injury. Get it? Read the introduction of Pegg's paper a couple of times like I did. So you can only travel back if the loop is self-consistent hence, it causes no paradoxes.
Phew. A couple more paradoxes gone. But there's plenty more. For instance, why did the Big G leave a plethora of physical evidence suggesting that the Earth is 6 billion years old when it's allegedly only 6 thousand*. If you ask me, the Earth was probably made sometime before breakfast this morning and everything else we've simply conjured up to pass the time.
*OK, technically I guess this isn't really a paradox per se but I don't really care.