sensibility

noun

1. 1

   The ability to sense, feel or perceive; responsiveness to sensory stimuli; sensitivity.

2. 2

   Emotional or artistic awareness; keen sensitivity to matters of feeling or creative expression.

3. 3

   Excessive emotional awareness; the fact or quality of being overemotional.

4. 4

   (in the plural) An acute awareness or feeling.

   “I apologize if I offended your sensibilities, but that's the truth of the matter.”

5. 5

   The capacity to be perceived by the senses.