The famous philosopher once made an argument that the burden of proof regarding God lay on theists by proposing a belief of his own. Suppose, he said, that I say there is a teapot orbiting the sun somewhere in between earth and mars, too small to be seen. (if you have ever heard me talk of dead rabbits floating in deep space, it's the same thing) This statement, like the idea of God, cannot be disproved. However, any normal person would disregard his statement.
Defense:
Russell cleverly placed a few normal emotional responses on his side (which is perfectly natural in thought experiments) First of all, the teapot ought to have no conceivable effect on our behavior, and so falls to Occam's razor without mercy. However, the question of God is slightly more serious - more like asking whether the gun pointed at your head is real or not, even if there is no way of telling.
Second, he is assuming that no evidence can be gained regarding God, that no tests can be run to falsify his existence. This seems to be true because the only evidence cited, and quite naturally so, is historical or is constantly occurring all around us (like the arguments for God from perception, like color).
Third, as a corollary to the lack of evidence for God, he assumes that God cannot be proven. I find it rather funny (nearly cried in laughter, actually) that Russell is complaining about his inability to disprove God. He's not actually doing that, of course. If he admitted (truly or as a thought experiment) that evidence could be gained, he would doubtless think of ways to disprove God.
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