X-Message-Number: 23848
From: 
Date: Sat, 10 Apr 2004 09:51:09 EDT
Subject: Liar and Goedel

Thomas Donaldson wrote in part:
The Cretan problem ["paradox" of The Liar or Epimenides] ultimately led to 
the conclusion that there could be unprovable math theorems. 
Ostensibly. It is true that Goedel likened his undecidability theorem to The 
Liar, but that was inaccurate, because provability and truth are completely 
different. 

Furthermore, Goedel's conclusion was a mere language trick and of no 
mathematical significance. He only showed that it is possible to label certain 
sentences in such a way that they are undecidable. In a somewhat similar vein, 
Cantor's definition of "set" allowed nonsense sets.

Robert Ettinger


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