Not based on logic; lacking logical reasoning or rational basis; irrational or contrary to logic.
From the prefix 'a-' (meaning 'not' or 'without') plus 'logical,' following a common English pattern of negation seen in words like 'amoral,' 'atypical,' and 'asexual.'
The 'a-' prefix meaning 'not' or 'without' comes from Greek and Latin and is super productive in English—you can stick it in front of almost any word to negate it!
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