A genuine logical contradiction requires that affirming and denying the same proposition simultaneously be unintelligible, but atheism is historically intelligible and coherently statable.
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Able to be understood or known through reason and thought, rather than through our five senses.
proposition(Used in the context of a semantic theory sensitive to differences in subject matter.)
The content expressed by a sentence, individuated at least in part by the subject matter of the sentence and the contents of its subsentential expressions.
unintelligible(as describing what would happen to Baumgarten's theory without this distinction)
Impossible to understand or make sense of; completely unclear or contradictory.