sensibility

noun

1. The ability to sense, feel or perceive; responsiveness to sensory stimuli; sensitivity.
2. Emotional or artistic awareness; keen sensitivity to matters of feeling or creative expression.
3. Excessive emotional awareness; the fact or quality of being overemotional.
4. (in the plural) An acute awareness or feeling.“I apologize if I offended your sensibilities, but that's the truth of the matter.”