.ll 72
.fo off
.co on
.ce ((Editor's comments in double parenthesis - Homer))
.ce ADR - 390
.ce
.ce Copyright (C) Homer Wilson Smith
.ce Redistribution rights granted for non commercial purposes
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Date: Mon, 17 Jul 89 17:11:47 EDT
From: Homer
Subject: double think
To: adore-l@ualtavm
I will keep Norman's long answer to the logic problem and
take it to a logician at Cornell, maybe I will find out what
quantifying over non particulars means.
It is a common practice in logic to disprove a statement by showing
that it leads to a contradiction. A good example of this
is the proof that the square root of 2 is trancendental. You assume
it is rational, and you come up with a contradiction, therefore
it cant be rational, and being transcendental is all thats left.
Just so, if you can show that p leads to not p, then p must be false.
If p means 'nothing can be proven', then proving this true, would
make it false. This in itself does not make p false, it only makes it
impossible to prove. Its perfectly possible that 'nothing can be proven'
but you just would not be able to prove it. But THAT CAN be proven, that
if it were true, you would not be able to prove it. Thus something can be
proven. Thus 'nothing can be proven' is clearly false.
It is true that this example is not the same as the square root
of 2 problem. Merely assuming p to be true does not in itself lead
to a contraction the way it does with the square root of 2.
However it is none the less true that you cant prove 'nothing
can be proven' with out contradicting yourself and THAT CAN be proven.
So it is possible that the self referencing nature of this particuar
problem makes it not suitable to the normal forms of logic.
But it should also be obvious that people who walk around saying
that 'nothing can be proven' and 'certainty is impossible' are not suitable
to the normal forms of logic either.
Which was the whole point of my posting.
Homer adore-l@ualtavm 7/17/89 double think