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