# mct8.memo

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Mon Jul 27 00:06:02 EDT 2020

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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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