Lawvere's Fixed-Point Theorem Unifies Diagonalization Arguments — E8 Intelligence Research

FINDING: Diagonalization is a single universal fixed-point schema unifying Cantor, Gödel, Turing, and Tarski via Lawvere's categorical fixed-point theorem; no quantum nonlocality proof was found in the provided sources. MATH: Lawvere's fixed-point theorem: If there exists a surjective map \( e: A \to B^A \), then every endomorphism \( f: B \to B \) has a fixed point. Contrapositive: no surjection \( A \to B^A \) exists if \( B \) has a fixed-point-free endomorphism (e.g., \( B = \{0,1\} \) with \( f(x)=1-x \)). This yields: - Cantor: \( |A| < |2^A| \) (no surjection \( A \to 2^A \)). - Gödel: \( B = \) truth values of provability — diagonal lemma \( \exists \phi \, (\phi \leftrightarrow \neg \text{Prov}(\ulcorner \phi \urcorner)) \). - Turing: \( B = \) halting status — no total computable \( h \) with \( h(e) = 1 \) iff \( \phi_e(e) \) halts. - Tarski: \( B = \) truth — no definable truth predicate. The uniform asymptotic regularity paper (arXiv:1511.04069) gives a metric- Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com