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Across
  1. 1. having or showing a perceptive understanding or insight; shrewd
  2. 6. a fundamental truth or proposition that serves as the foundation for a system of belief or behaviour or for a chain of reasoning
  3. 8. extreme tiredness resulting from mental or physical exertion or illness
  4. 9. the amount by which something, especially a sum of money, is too small
Down
  1. 1. to publicly support or suggest an idea, development, or way of doing something
  2. 2. (of an argument or point) having a sound basis in logic or fact; reasonable or cogent
  3. 3. a situation in which a difficult choice has to be made between two or more alternatives, especially ones that are equally undesirable
  4. 4. an individual's conception or impression of something known, experienced, or imagined
  5. 5. a traditional story, especially one concerning the early history of a people or explaining a natural or social phenomenon, and typically involving supernatural beings or events
  6. 7. produce and discharge (something, especially gas or radiation)