There is nothing that stipulates that a belief has to be rational or logical. A person is entitled to believe whatever they want, for whatever reason they find sufficient and no one has the right to tell them differently.
However, any being worthy of being call a God would be capable of providing the evidence needed to convince me.
If such a being exists and it has not provided the evidence then we can conclude the following:
1) The being doesn't care if I believe or not and will not judge me either way. In this case my lack of belief has no bearing what so ever.
or
2) The being doesn't care to provide the evidence and will judge me based on how I live my life. In this case my lack of belief has no bearing what so ever.
or
3) The being doesn't care to provide the evidence and will judge me based on if I believe or not. Such a being is not worthy of worship.
or
4) The being doesn't care to provide the evidence and will judge me based on an unknown criteria. This group consists on endless possible variations (I am noting going to list them all). Those that I have considered result in such a being not being worthy of worship and/or my lack of belief will not having no bearing what so ever.
I therefore conclude that the lack of evidence for any god or gods means the either that there are no beings worth of the title, or that my lack of belief has no bearing, or that any beings worthy of the title are not worthy of worship.
Points 1 - 3 cover most of the god claims I have heard. Point 4 is a blanket statement for all other possiblities I have been able to come up with.
If you find any faults in my logic I will be more than willing to discuss them. Also if anyone has a God claim that falls into the blanket category we could discuss that individually.
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He hoped and prayed that there wasn't an afterlife. Then he realized there was a contradiction involved here and merely hoped that there wasn't an afterlife.
- Douglas Adams, The Hitch Hiker's Guide to the Galaxy