Priggishness is the quality — the habit, the air — of being priggish. Not the person, but the way of being: that mix of moral pride and looking down on others. You might talk about the priggishness of a remark, or someone’s priggishness about money, food, or “correct” behaviour. It is a long, formal noun and you will mostly meet it in writing. Though actually, English speakers reach for this word when pride is too kind and snobbery is not quite right: a snob looks down from class or taste; priggishness looks down from morals. It always carries disapproval. Nobody boasts of their priggishness.