perceptiveness

(noun) a feeling of understanding. Synonyms: insight, perceptivity.

(noun) delicate discrimination (especially of aesthetic values). Synonyms: taste, appreciation, discernment. Examples: "Arrogance and lack of taste contributed to his rapid success." "To ask at that particular time was the ultimate in bad taste."

(noun) perception of that which is obscure. Synonyms: discernment.

(noun) the quality of insight and sympathetic understanding.