XPost: comp.theory, sci.logic, sci.lang   
   XPost: sci.math   
   From: PointedEars@web.de   
      
   Richard Damon wrote:   
   > On 1/3/26 5:15 PM, olcott wrote:   
   >> All deciders essentially: Transform finite string   
   >> inputs by finite string transformation rules into   
   >> {Accept, Reject} values.   
   >>   
   >> Thus making   
   >> "true on the basis of meaning expressed in language"   
   >> inherently computable.   
   >   
   > Nope.   
   >   
   > How does that answer the question of the truth of the statement:   
   >   
   > All Even Number greater than 2 are the sum of two primes.   
      
   I think you mean "All even numbers greater than 2 _can be written_ as the   
   sum of two primes.", which means something else.   
      
   Otherwise it is easy to find a counter-example: 8 = 4 + 4 is even, but 4 is   
   not prime (it is divisible by 2).   
      
   But also 8 = 3 + 5, and 3 and 5 are primes, so 8 _can be written_ as the sum   
   of two primes.   
      
   > That statement, or its inverse MUST be true,   
      
   You do not mean its inverse, but its logical negative:   
      
   If a statement is true, then its inverse is also true, but its logical   
   negative is false.   
      
   If a statement is false, then its inverse is also false, but its logical   
   negative is true.   
      
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