XPost: comp.theory, comp.lang.c++, comp.lang.c   
   From: flexibeast@gmail.com   
      
   Kaz Kylheku <643-408-1753@kylheku.com> writes:   
      
   > A contradiction is a piece of foreign material in a formal system.  It   
   > is nonsensical to bring it in, and assert it as a truth; it makes no   
   > sense to do so. Once you do, it creates contagion.   
      
   As an aside, the field of paraconsistent logic, which excludes the PoE,   
   tries to study and develop 'inconsistency-tolerant' formal systems:   
      
     https://en.wikipedia.org/wiki/Paraconsistent_logic   
      
   > The entailment relations of paraconsistent logics are propositionally   
   > weaker than classical logic; that is, they deem fewer propositional   
   > inferences valid. The point is that a paraconsistent logic can never   
   > be a propositional extension of classical logic, that is,   
   > propositionally validate every entailment that classical logic   
   > does. In some sense, then, paraconsistent logic is more conservative   
   > or cautious than classical logic. It is due to such conservativeness   
   > that paraconsistent languages can be more expressive than their   
   > classical counterparts including the hierarchy of metalanguages due to   
   > Alfred Tarski and others.   
      
      
   Alexis.   
      
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