A witless person is a numskull. To be witless is not to lack the "funny" kind of "wit," but to lack the "brains" kind of "wit." If you're witless, you don't have your wits about you.

I wouldn't call you stupid, exactly. After all, anyone who can calculate pi to the 20th decimal point without even using a pencil is anything but dumb. But I would call you witless for not knowing that when a woman asks you "Does this dress make me look fat?," the answer should always be "No." You may have heard someone say "Keep your wits about you," which means "Stay alert!" Well, if you're behaving in a witless fashion, then you're not being alert or showing proper judgment. Even smart people can be witless from time to time.

Definitions of witless
  1. adjective
    (of especially persons) lacking sense or understanding or judgment
    synonyms: nitwitted, senseless, soft-witted
    lacking or marked by lack of intellectual acuity
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