# 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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Mon Jul 27 00:06:02 EDT 2020
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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.

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