clairvoyance — the alleged power of perceiving things beyond the natural range of the senses
insight — an instance of apprehending the true nature of a thing, especially through intuitive understanding: an insight into 18th-century life.
lucidity — the quality of being easily understood, completely intelligible, or comprehensible: She makes her argument with pointed logic and exemplary lucidity.
precognition — knowledge of a future event or situation, especially through extrasensory means.
prescience — knowledge of things before they exist or happen; foreknowledge; foresight.
sixth sense — a power of perception beyond the five senses; intuition: His sixth sense warned him to be cautious.