Thanks for this. Using your points I can refine my thesis as follows: if existence of an entity does not contradict the available body of observations that its non-existance is impossible to prove.
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I am only arguing in favor of the first half of the statement ( "god's non-existence is impossible to prove") but not the second half ("thus I, Martin Gardner, choose to believe in its existence")
>The belief of a deity amidst overwhelming evidence to the contrary is not an "educated guess," it's wishful thinking.
This has nothing to do with my post.
>He was of the idea that there is no way to prove the non-existence of god
This is, in fact, correct. In natural sciences it is only possible to show that something does exist. It is not possible to prove non-existatnce. (It is not the case in mathematics, but mathematics is not a natural science).
The easiest way to understand it is to realize that the body observations available to science was taken in a limited period of time and area of space. Thus the our current scientific view of the world is only formally valid in this limited domain. What exist outside of it is only our educated guess.