From: ram@zedat.fu-berlin.de   
      
   Richard Heathfield  writes:   
   >To argue for a mathematical model (such as a Turing machine) that   
   >never halts necessarily and /obviously/ entails the claim that a   
   >mathematical model can exist in perpetuity, for if the model   
   >ceases to exist, so does the Turung machine.   
      
     In mathematics, words have meanings given to them   
     by definitions of a /theory/.   
      
     For example, this is a simple mathematical theory:   
      
   |Theory A   
   |   
   |This theory is based on set theory, so it takes   
   |the notions from set theory for granted.   
   |   
   |Definition 1:   
   |In this theory, any set is also called a /Turing   
   |machine/.   
   |   
   |Definition 2:   
   |We say that a Turing machine /never halts/ if it's   
   |not finite.   
   |   
   |Theorem 1:   
   |The Turing machine N (the set of all natural numbers)   
   |never halts. (The proof is obvious from the definitions.)   
      
     In theory A, N is a Turing machine that never halts.   
      
     The mathematical model of the theory A does not have   
     a physical existence in time. So it never started to   
     exist in this sence nor can it ever cease to exist.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)