XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/15/2026 9:27 PM, Richard Damon wrote:   
   > On 1/15/26 7:24 PM, olcott wrote:   
   >> On 1/15/2026 5:10 PM, Tristan Wibberley wrote:   
   >>> I understand a schematic system is one whose deduction rules or,   
   >>> perhaps, inference rules (if there's a difference) are specified as   
   >>> axioms of the same system.   
   >>>   
   >>> 1. Can that be a syntactical system or a formal system just as well and   
   >>> still be called a schematic system?   
   >>>   
   >>> 2. Suppose it's a positive intuitionist system, what are the most   
   >>> notable things to consider vis-a-vis extensions?   
   >>>   
   >>   
   >> A formal system anchored in proof-theoretic semantics   
   >> with PA as its axioms expresses all of PA and is not   
   >> incomplete.   
   >>   
   >>   
   >   
   > Put you can't do that.   
   >   
   > The problem is that the axiom of induction isn't compatible with proof-   
   > theoretics as I understand it.   
   >   
      
   As you fail to understand it. Look deeper.   
   G can be expressed in my system yet is   
   rejected as semantically non-well-founded.   
      
   > That, or you end up with issues that the existance or non-existance of a   
   > number that meets a property might not be a truth-bearing statement, and   
   > you can't tell if it is, until you find the answer.   
   >   
   > This makes "Truth" not a fixed quantity, which isn't very satisfying for   
   > a logic system. Knowledge might change, but truth shouldn't.   
      
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)