Hare-brained, or Hair-brained.
Mad as a March hare, giddy, foolhardy.
“Let’s leave this town; for they [the English] are hair-brained slaves,
And hunger will enforce them to be mere eager.”
Shakespeare: 1 Henry VI., i. 2.
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Entry taken from Dictionary of Phrase and Fable, edited by the Rev. E. Cobham Brewer, LL.D. and revised in 1895.