Followup to: You Provably Can't Trust Yourself

Yesterday I discussed the difference between:

A system that believes—is moved by—any specific chain of deductions from the axioms of Peano Arithmetic. (PA, Type 1 calculator)
A system that believes PA, plus explicitly asserts the general proposition that PA is sound. (PA+1, meta-1-calculator that calculates the output of Type 1 calculator)
A system that believes PA, plus explicitly asserts its own soundness. (Self-PA, Type 2 calculator)

These systems are formally distinct. PA+1 can prove things that PA cannot. Self-PA is inconsistent, and can prove anything via Löb's Theorem.

With these distinctions in mind, I hope my intent will be clearer, when I say that although I am human and have a human-ish moral framework, I do not think that the fact of acting in a human-ish way licenses anything.

I am a self-renormalizing moral system, but I do not think there is any general license to be a self-renormalizing moral system.

And while we're on the subject, I am an epistemologically incoherent creature, trying to modify his ways of thinking in accordance with his current conclusions; but I do not think that reflective coherence implies correctness.

Let me take these issues in reverse order, starting with the general unlicensure of epistemological reflective coherence.

If five different people go out and investigate a city, and draw five different street maps, we should expect the maps to be (mostly roughly) consistent with each other. Accurate maps are necessarily consistent among each other and among themselves, there being only one reality. But if I sit in my living room with my blinds closed, I can draw up one street map from my imagination and then make four copies: these five maps will be consistent among themselves, but not accurate. Accuracy implies consistency but not the other way around.

In Where Recursive Justification Hits Bottom, I talked about whether "I believe that induction will work on the next occasion, because it's usually worked before" is legitimate reasoning, or "I trust Occam's Razor because the simplest explanation for why Occam's Razor often works is that we live in a highly ordered universe". Though we actually formalized the idea of scientific induction, starting from an inductive instinct; we modified our intuitive underst...

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