The Logical Structure of Physical Laws: A Fixed Point Reconstruction

📝 Original Info

• Title: The Logical Structure of Physical Laws: A Fixed Point Reconstruction
• ArXiv ID: 2512.25057
• Date: 2025-12-31
• Authors: Eren Volkan Küçük

📝 Abstract

We formalise the self-referential idea of physical lawhood ("self-subsumption") as the requirement that a theory contains exactly those candidate laws that are admissible relative to the theory itself. We show that a naive extensional formulation collapses into a Russell-style type confusion (and, if forced, a selfmembership pathology). The repair is to distinguish the type of law-candidates from the type of law-packages and to encode admissibility as an operator F on a lattice of packages; self-subsumption then becomes the fixed-point equation S = F(S). Under standard assumptions (packages forming a complete lattice and F monotone), Tarski's fixed point theorem yields a canonical least fixed point µF , interpreted as a minimal stable theory under the chosen admissibility constraints. We construct broad classes of such monotone admissibility operators from invariance principles via Galois connections, and we illustrate the schema with toy instantiations inspired by quantum electrodynamics and general relativity that capture symmetry and locality constraints. We do not propose a procedure that derives the laws of nature from first principles; rather, we provide a general fixed-point architecture for reconstructing stable theory-packages from explicit admissibility criteria.

📄 Full Content

...(본문 내용이 길어 생략되었습니다. 사이트에서 전문을 확인해 주세요.)