From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 2.12.2025 klo 16.49:   
   > On 12/2/2025 3:15 AM, Mikko wrote:   
   >> olcott kirjoitti 1.12.2025 klo 14.27:   
   >>   
   >>> A prove is any sequence of steps that shows   
   >>> that its conclusion is necessarily true.   
   >> That depends on the exact meaning of "shows". The usual meaning of   
   >> "show" is to make something visible. But merely making some sequence   
   >> of some steps visible does not make it a proof.   
      
   > What I usually mean by proof is any kind of correct   
   > semantic logical entailment anchored in the basis   
   > of expressions of language that are certainly true.   
      
   That depends on the exact meanings you give to "correct" and "semantic   
   logical entailment". The usual meanings of the words permit correct   
   semantic logical entailments that are not proofs.   
      
   > This requires a formal system having a formal   
   > language such that semantics is fully integrated   
   > into syntax using something like Rudolf Carnap   
   > Meaning Postulates. It also requires something   
   > like Gödel's 1944 "theory of simple types".   
      
   Meaning Postulates do not integrate semantics into the syntax. THey   
   include parts of the meanings as postulates of a theory so that   
   they can be used in inferences. But they have no effect to the   
   syntactic validity of any expression.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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