XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 04/01/2026 18:55, Mike Terry wrote:   
   > Gödel's concerns there being a statement G such that neither G nor ¬G   
   > has a derivation in the system.  There is no reference to "truth" in   
   > that and I'd say his proof is essentially syntactical in nature.   
      
   From Curry and Feys very brief mention of the distinction I think   
   Gödel's system P is a semantical system (it has numbers as objects   
   distinct from their presentation - which allows him to just make it all   
   the more complicated). Does that mean his proof must be semantical?   
      
   Also he relies on a meta-system which means embedding, does that force   
   the proof to be semantical even if derivations in P are syntactical?   
      
   I haven't got a handle on semantical vs syntactical.   
      
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