XPost: sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 20/01/2026 21:39, olcott wrote:   
      
   > a meta‑level system is required to stand above PA and   
   > filter expressions before PA ever evaluates them. The   
   > meta‑system performs the structural work PA cannot do:   
   > it detects cycles, blocks diagonalization, rejects   
   > non‑truth‑bearers, and prevents PA from entering   
   > infinite loops.   
      
      
   Then the truth predicate is a restricted truth predicate.   
      
   I think Tarski's findings don't directly apply to what Olcott is doing   
   as they are stated for systems with negation (of statements) carrying   
   the semantics of contradiction. PA doesn't seem to have that in its   
   axioms; then there's the matter of universal generality: is that a   
   predicate, connective, or an operation? Some of those take the truth   
   "predicate" away from Elementary Theorems, some of them don't but   
   negation must lose its naivety as it becomes an operation.   
      
   How does one characterise PA among:   
      
   - syntactical system   
   - schematic system   
   - abstract formal system   
   - concrete formal system   
   etc...   
      
   understanding that there is some overlap.   
      
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   Tristan Wibberley   
      
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