Further Analysis of Olcott's Category Error
From
Mr Flibble@21:1/5 to
All on Sat May 31 19:44:56 2025
Flibble's Argument: Execution vs Simulation in SHDs ====================================================
In the context of Simulating Halt Deciders (SHDs), the distinction between execution and simulation is fundamental.
Correct: External Simulation
----------------------------
int main() {
HHH(DDD); // SHD simulates/analyzes DDD from the outside.
}
- In this model, DDD is not being executed — it's being passed as data to HHH, which is analyzing it.
- Even if DDD() (the function definition) contains a recursive call to HHH(DDD), this is just part of the code being simulated, not something
that is actively executing.
- Thus, the simulation can detect infinite recursion structurally, without running DDD.
Incorrect: Active Execution
---------------------------
int main() {
DDD(); // Directly executes DDD, which calls HHH(DDD) during runtime.
}
- In this scenario, you’re actually running DDD, not simulating it.
- If DDD() calls HHH(DDD) at runtime, you're now mixing execution and
analysis in the same layer, violating the stratified model.
- This results in self-referential execution that undermines decidability
— a category error akin to the original halting paradox.
Key Insight
-----------
As long as DDD is not executing and is only being simulated by HHH, it doesn’t matter that DDD would call HHH(DDD) — because that call is never actually made. It exists in the simulated model, not in the runtime environment. Thus, structural recursion can be detected safely and treated
as non-halting without triggering a paradox.
This stratification (meta → base) is what keeps the model coherent.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)