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One understanding of what it is  to conceive the existence/nonexistence 
of something is that it is to imagine experiencing its presence/ absence.  But if 
this is, indeed, what it means to conceive the  existence/nonexistence of 
something, it seems  clear that the nonexistence of God is  inconceivable. 
Consider the following reasoning. 
One understanding of what it is to conceive the existence/nonexistence of something is that it is to imagine experiencing its presence/ absence. But if this is, indeed, what it means to conceive the existence/nonexistence of something, it seems clear that the nonexistence of God is inconceivable. 

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To experience the absence of a  thing x is to experience the presence of some other thing y, whose presence is incompatible with that of x.  But it is a contradiction of the very concept of God to suppose that the presence of anything could be incompatible with the (omni-)presence of God. Therefore, there is no way of imagining experiencing God's  absence, because one cannot imagine experiencing the presence of anything that would be incompatible with God's presence. 

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