1.
having said that; even so; that said; but still
A conjunctive expression used to acknowledge what was just stated and then introduce a qualification or opposing point. It softens a shift to a contrary view, like English "that said" or "even so."
Literally "even if (one) says so," used to grant a previous point before pushing back against it. Typically stands at the head of a sentence, followed by the speaker's reservation.