knowing full well; fully aware; with full knowledge
Used when someone does something while being fully aware of the situation, risks, or consequences. Often followed by で or に.
See also: 承知の上で
Knowing full well the danger, he went to the rescue.
Did you say that with full knowledge of the facts?
Phrase composed of 承知 (understanding, consent) + の (possessive particle) + 上 (on top of, after). Literally 'on top of understanding', meaning 'with full knowledge'.