properness

noun

1. (uncountable, usually)The state or condition of being proper; propriety.

   “The kind of women who put papers on shelves and had little towels like that instinctively distrusted and disliked Mack and the boys. Such women knew that they were the worst threats to a home, for they offered ease and thought and companionship as opposed to neatness, order, and properness.”

2. (uncountable, usually)The state or condition of being proper (of a proper fraction, proper subset, etc.).
3. (obsolete, uncountable, usually)Excellence, quality.

   “Ignatius Loyola, the founder of the Jesuits […] betook himself to his beads, and by those means got more honour than ever he should have done with the use of his limbs and properness of person […]”