Perceptiveness is the ability to appreciate something of good quality. It takes perceptiveness to tell the difference between a genuine Matisse oil painting and a well-done copy.
You use your perceptiveness to distinguish the flavor of a perfectly ripe peach from one that's not quite ready to be eaten, or to recognize a particularly well-written short story. You can also use the noun perceptiveness to mean a kind of understanding or comprehension — your perceptiveness can help you understand why a tired child is acting out. The Latin origin, also the root of perceive, is percipere, "obtain, gather, or seize," and also "to grasp with the mind."