X-Message-Number: 5852
From: 
Date: Wed, 28 Feb 1996 13:27:42 -0500
Subject: Penrose & Russell

Joe Strout (#5841) makes fun of Penrose's search for mysterious quantum
phenomena to explain the alleged ability of people to do thinking of a type
inaccessible to ordinary programmed computers--thinking that is
"non-algorithmic." 

Penrose (and others) base their surmises, at least in part, on Goedel's
theorems, which purport to show that, in any logical or mathematical system
(of sufficient complexity), there are true statements which cannot be proven
within the system. Mr. Strout's point was that this peculiarity does not
depend on one thinker being organic and another inorganic; it merely depends
on the self-referential quality of the proposition.

However, if we look just at English-language versions or supposed analogs of
Goedel-like theorems, the premise is wrong in the first place, so the problem
does not arise. There are NOT any such true statements unprovable within the
system. In Mr. Strout's example--

"Roger Penrose cannot consistently believe this proposition."

--just as in some of the Russell "paradoxes," the key is to recognize that
"this proposition" is without real content, without any root referent, and
therefore is not properly a "proposition" at all. It is just another tiresome
example of the ease with which the mind can be confused by language. 

Mathematicians stoutly maintain that there is a fundamental difference
between the Goedel theorems and their apparent English-language analogs, and
that the theroems are unassailable. We'll see.

Robert Ettinger  


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