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3 AM Philosophy

Is not having sufficient evidence sufficient justification?

Assuming principle of rationality, if an atheist says that they are an atheist because they have not heard any convincing arguments for God. Does this really give one sufficient justification to either hold to atheism in the strong case (B~p) or even in the weak case (~Bp)?
 
Given:

MT: p>q,~q, :.~p
MT: p>q,~q, :.~p
 
p>q If S has heard any convincing arguments for God, S would be a theist.
~q it is not the case S would be a theist.
:.p S has not heard any convincing arguments for God.

It seems to me that it tells me no new information that I can not deductive infer merely by S not being a theist. So is someone actually justified to either affrm God does not exist or even to justify withholding affirmation merely by saying that they have not ever heard any convincing arguments for God. In other words, can saying that you have not heard any convincing arguments for God be sufficient justification to deny the existence of God or even to sufficiently warrant withholding affirmation of the proposition of God existing?

To me it is a vacuous throw away statement that gives no actual justificatory reason which one not simple just deductively infer if someone is not a theist, and as such has, no justificatory power.

 
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