THE MACHINE CERTAINTY THEOREM
                          Part 3, Content Form
 
                                MCT - 8
                            25 December 1993
 
                 Copyright (C) 1993 Homer Wilson Smith
       Redistribution rights granted for non commercial purposes
 
                               THE PROOF
 
               L    = Learning
               C    = Certainty
               LC   = Learning with Certainty
               LNC  = Learning with Not Certainty
               D    = Distance (in either space or time)
               LBLE = Learning by Looking at Effects
 
                         1.  L <--> LC or LNC
  Learning <--> Learning with Certainty or Learning with Not Certainty
                         2.  (D and L) -> LBLE
      Distance and Learning implies Learning by Looking at Effects
                         3.  LBLE -> ~LC
 Learning by Looking at Effects implies Not (Learning with Certainty).
                         4.  LC
                    Learning with Certainty exists.
 
              (2,3)[A]   5.  (D and L) -> ~LC
      Distance and Learning implies Not (Learning with Certainty).
            (5)[B];[C]   6.  LC -> ~(D and L) ; -> (~D or ~L)
   Learning with Certainty implies either No Distance or No Learning.
                (1)[D]   7.  LC -> L
               Learning with Certainty implies Learning.
          (6,7)[E];[F]   8.  LC -> (~D or ~L) and L ; -> ~D
              Learning with Certainty implies No Distance.
              (4,8)[G]   9.  ~D
                              No Distance.
 
                                 Q.E.D.
 
              (T.O.I.)   A.  ((A -> B) and (B -> C)) -> (A -> C)
                (M.T.)   B.  (A -> B) -> (~B -> ~A)
            (D.N.O.A.)   C.  ~(A and B) -> (~A or ~B)
                         D.  (A <--> (B or C)) -> (B -> A)
                 (ADD)   E.  ((A -> B) and (A -> C)) -> (A -> (B and C))
                         F.  ((A or B) and ~B) -> A
                (M.P.)   G.  (A and (A -> B)) -> B
 
                                                          12/14/78
 
                                                      Homer Wilson Smith