Despite dissatisfaction with certain standard definitions others are quite sufficient.
Perception or perceive, for example, not only commonly concerns sensory experience but also mental apprehension:
Perception (noun)
- the act or faculty of apprehending by means of the senses or the mind; cognition; awareness
(Random House Kernerman Webster’s College Dictionary Perception - definition of perception by The Free Dictionary )
Perceive (verb)
- to become aware of (something) through the senses, esp the sight; recognize or observe
- to come to comprehend; grasp
(Collins English Dictionary Complete and Unabridged, 12th Edition Perceive - definition of perceive by The Free Dictionary)
Previous draft for reference: