An Argument Against Brute Facts

/ Mark Shaw
  1. If there are brute facts, then there is at least one fact x that is brute (i.e. unexplained and inexplicable).
  2. Fact x is brute only if there is no sufficient condition for it obtaining.
  3. There being no sufficient condition for the obtaining of x is a sufficient condition for the obtaining of x.
  4. Therefore, x is both brute and not brute. [from 2 and 3]
  5. Contradictory facts do not exist.
  6. Therefore, there are no brute facts. [conclusion, from 1-5]