the ambiguous meaning of ambiguity

From http://academicearth.org/courses/the-unanswered-question-1973--leonard-bernsteins-masterful-lectures-on-music/

"ambi" has two meanings:

• "bothness", on both sides at once, implying duality, such as used in ambidextrous, ambivalence
• "aroundness", such as used in ambience, ambit, all referring to the general surround