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.ce ((Editor's comments in double parenthesis - Homer))
.ce ADR - 394
.ce Copyright (C) Homer Wilson Smith
.ce Redistribution rights granted for non commercial purposes
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Date:         Thu, 20 Jul 89 13:17:21 EDT
From:         Homer 
Subject:      Re: double think
To:           Adore-l list 
In-Reply-To:  Message of Mon, 17 Jul 89 14:39:52 EDT from 

>I am fully versed in the first and second order predicate and
>propositional logics.

     I should have known.  Now I am in deeeeeep trouble.

     I should point out that I am NOT well versed in second order
predicate and propositional logics, in fact I can hardly pronounce
the words.

>Your premise is ~p [nothing can be proven]
>Given:  ~p
>        ~p -> p
>         p

     Let     p mean 'Something can be proven.'
     Let not-p mean 'Nothing can be proven.' (its not true something can...)
     Let     r mean 'not-p is proven'.

     Norman claims my arguement states that not-p implies p.

     In English that reads,

     If 'nothing can be proven' then 'something can be proven'.

     Clearly this is neither a tautology nor is it obviously true.

     And I never made the statement and I never used it in any proof
on this subject.

     The state I made was

     If not-p is PROVEN then p.    (If r then p.)

     This is very different from

     If not-p is TRUE then p.

     not-p might very well be true, this does not give rise
to a contradiction in itself.

     All I have said is that

     If not-p is true then not-p can not be PROVEN.
     If not-p is proven, then p.

     And THAT CAN be proven.

     Thus not-p is false. (Because of the one counter example.)

     For sure.

     I await Norman's rapier analysis, except he is sulking licking
his wounds off the list.

     My condolences.

 Homer               Adore-l list         7/20/89*double think