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I am posing this question because I have encountered so many christians who rely on the fact that you cannot disprove god's existence as some indication that he does exist.

So I wonder what they will make of this question?

My view is that for all practical purposes it is reasonable to behave as though FX does not exist. There is very little evidence that he does (though there is more than there is of god's existence) and there is an extremely low probability that one individual could visit, via the somewhat extreme route that involves millions of chimneys, every child in the world in one night.

So it is perfectly reasonable to say, in  normal parlance, that FX does not exist.

And the same applies to god. It is just that at this point christians suddenly stop using normal parlance and demand that we start talking like mathematicians with aboslute precision so that they can cling to the impossibility of proving a negative as somehow indcating that the negative is therefore a positive.