mct8.memo

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                     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

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================== http://www.lightlink.com/theproof ===================
Learning implies Learning with Certainty or Learning without Certainty.
Learning across a Distance implies Learning by Being an Effect.
Learning by Being an Effect implies Learning without Certainty.
Therefore, Learning with Certainty implies Learning, but 
not by Being an Effect, and not across a Distance.