resolutely
From LSJ
ὃ γὰρ βούλεται, τοῦθ' ἕκαστος καὶ οἴεται → what he wishes to be true, each person also believes to be true | what he wishes, each person also believes
obstinately: Ar. and P. αὐθάδως; see also boldly.
zealously: P. and V. προθύμως.
