“Can hardly wait” versus “can't hardly wait”
These two seem to be opposites of each other because of the additional "not" in one of them. However, they seem to be interchangeable. Are they? What's the difference?
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The correct version here in "can hardly". This is what anyone who uses either phrase likely means, at least.
While "cannot hardly" is grammatically correct, it is effectively a double negative, and thus its meaning is confusing at best, plain wrong at worst. Translate it as "I am nearly unable to do ..." and you should see why its meaning is not the same. Sure, it could be used correctly in some contexts (the exact opposite of "can hardly"), but I'd posit that almost all of its colloquial usage is wrong; a bit like "I don't want nothing".
While people use them in the same way, this is not correct.
Can Hardly is the correct way.. as in "I can hardly wait to get there."
Saying "I can't hardly wait to get there." is effectively saying I can wait. It is a double negative and "not" and "hardly" cancel one another out.