Foolish or not thinking clearly; characterized by incomplete or muddled thinking.
From 'half' + 'headed' (as in 'blockheaded' or 'hothead'). The compound formation suggests someone whose head is only half-engaged in thinking.
This insult is actually pretty logical—if someone has 'only half a head' for thinking, they're operating at half capacity, which is why Medieval and Early Modern English had so many creative 'half-' insults!
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