Intuitions are more integrated across your personal accumulation of perceptions and preconceptions: strict reason or perception makes me doubt that this black thing is a swan, but it looks and floats around like a swan, even if I can't quantify how, so I guess it's a swan. Good enough for now until I encounter something that comes up against the boundary of my blurry intuition of what a swan is; at that point I'll think about it some more.
In a way, I perceive the black swan as a swan because of what my established intuitions about swan-ness are.