An archaic or variant form of atheistic; relating to or characteristic of atheism or atheists.
From 'atheistic' + the suffix '-al,' which doubles the final adjective form. This older variant was more common in Early Modern English but is now largely replaced by 'atheistic.'
In 17th-century religious debates, calling someone 'atheistical' was one of the most serious insults—worse than blasphemy in some contexts—because it suggested they had rejected reason itself!
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