X-Message-Number: 4121
Date: Sat, 1 Apr 1995 10:24:06 -0800
From: John K Clark <>
Subject: SCI.CRYONICS Godel

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 Wrote:

	   >as far as I can tell, old-fashioned dualists are rare these days. 
	     
Unfortunately that has not been my experience when consciousness
has been concerned, not even on this list. Some seem comfortable
with a mechanical explanation of consciousness PROVIDED the
mechanism is safely unknown and will always remain unknown. The
only reason I can see that uploading won't work is if the
duelists are correct and the soul won't fit inside a machine.
What I find puzzling is that advocates of Cryonics should have
faith in such things.
		 
	   >THE BARBER: We have all heard it: In a certain town, the barber 
	   >shaves everyone who doesn't shave himself; so who shaves the 
	   >barber? Paradox? Of course not--just an inadmissible premise; 
	   >there cannot be any such town or any such equivalent. 
	   
That's exactly what nearly all logicians and mathematicians
thought until 1931 when Kurt Godel published his paper " On
Formally Undecidable Propositions". In this paper, one of the
greatest intellectual accomplishments of all time, he showed
that the "barber" could ALWAYS be constructed and he showed exactly
how to do it. He proved that NO SYSTEM could represent all the
complexity of even a limited toy domain like whole numbers, much
less all true statements. Godel proved that ANY system has
undecidable propositions in it, 5 years after Godel, Turing
proved that for a random  proposition you can't even determine
if it's undecidable or not.  
	   
	   >2. "THIS SENTENCE IS FALSE." This is perhaps the purest form
	   >of the Liar "paradox." Supposedly the sentence as a whole can be 
	   >neither true nor false, although Aristotelian logic demands that 
	   >it be one or the other--IF IT IS A PROPOSITION." But obviously, 
	   >the sentence is NOT a proposition; it is not meaningful
			 
But exactly when is a sentence meaningful and when is it not?
What your talking about here is The Theory Of Types, it was
developed by Russell and Whitehead in 1910 in their enormous
Principia Mathematica and destroyed by Godel in 1931. They set
up a hierarchy to forbid self reference, at the bottom they had
a thing called "object language" that could only refer to things
in a limited domain , to refer to object language itself you
would have to use meta language, and so on. Godel rendered the
whole matter moot but at the time it seemed that The Theory Of Types 
could have some promise when dealing with formal statements in set theory, 
but in other areas it was a flop from day one. 

Even perfectly reasonable sentences like " In this post
I criticize the idea that an unfathomable soul is the source of
consciousness." would be branded as meaningless. According to 
Russell and Whitehead the sentence commits two sins first it
talks about "this post" and second it talks about me ("I") and
both things are forbidden. In fact, even a book explaining how
the theory of types works would be meaningless, according to the
theory of types, and that's just too high a price to pay for
getting rid of paradoxes.
	 

				   John K Clark          

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