OBJ-001: “Axioms aren’t proof”

Target claim(s)

Foundational axioms in T0-T1 (and any downstream lemma that treats them as “proven facts”).

The objection (steelman)

“You can’t prove axioms, so your framework is arbitrary. If you can choose any axioms, you can ‘prove’ anything. Therefore none of this compels assent.”

Why it seems compelling

People often expect one ultimate proof that stands on nothing. Axioms feel like “made up rules”.

Reply (logic-first)

• All reasoning systems bottom out in starting commitments (logic, math, and even empirical science presuppose existence, intelligibility, identity, and inference rules).
• The honest criterion for axioms is not “proved from nothing” but: indispensability, self-consistency, non-self-refutation, parsimony, and downstream explanatory power.
• The framework must never claim axioms are “empirically proven”; it must keep type discipline.

What would change my mind

• If an alternative axiom set yields equal or better explanatory power with fewer commitments and avoids self-refutation traps, the current axioms should be revised.