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There exists no evidence for god, therefore it is impossible to argue for or against his existence
Surely - it is always possible to argue. And.... besides some people would claim that there is evidence.
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If there were evidence for god, then faith would no longer be necessary. Therefore, god must exist without evidence.
If we could see the invisible man then he wouldnt't be invisible, therefore the invisible man must both exist and be invisible. : )
More seriously though, I think this indicates that statement is missing a linking component. Maybe the full argument is more like
God wants to see if we can show faith without evidence
There is no evidence
If there was evidence then that would contradict the first point
Therefore god exists.
ie the first line has to be assumed.
The second might or might not be correct - it seems plausible, but does not explain saints and other happennings which of the faithful see as proof. (Such as in the bible). Apparently a saint is proven... through a miracle yes?
The third point seems fine.
The fourth point rests on the earlier shakier points. And assumes that if god is plausible according to those - then he must exist (and be male and singular).
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You cannot disprove the existence of something that doesn't exist.
I think this wording is unclear. Perhaps you meant it the other way around? Or... do you mean that we cannot disprove the existence of something that is undetectable.
This may be the case. However generally speaking - those who believe in the undetectable are considered slightly insane. (I need to look up schizophrenia now).
Their beliefs are no longer matching their observed reality and that of those around them.
I cannot disprove the existence of the tooth fairy. However I can say that the tooth fairy seems implausible. Just as a violation of well established physical laws seems implausible. I expect the sun to rise tomorrow. I cannot prove that it will.
On the other hand... if one is inclined to believe that complete proof is required before believing in something, why believe in religion. And if religion, then which one....
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The burden of proof is on the party making the positive claim.
I'd argue that the burden rests on the people who knock on my door on weekends. Firstly because they've disturbed my peace - and second because they want me to read something or pay something or join something.
The burden rests on those who argue a particular change of behaviour or investment of time/money.