The Knowable and the Unknowable: A Carlo‑Formal Taxonomy of Epistemic Behaviour in the Carlo Field

This document presents the formal Carlo‑epistemic taxonomy that distinguishes the knowable from the unknowable based solely on recursion behaviour, collapse dynamics, and structural stability. Building on the unknowable‑first epistemic principle, the paper defines knowability and unknowability not as semantic or truth‑based categories, but as behavioural classes determined entirely by the Carlo Field’s operators. A statement S is knowable in Carlo terms if its recursive expansion stabilises under collapse: \[Knowable(S) C(R(S)) = S\] A statement S is unknowable if its recursion does not stabilise, but collapse forces stability: \[Unknowable(S) C(R(S)) ≠ S but K(R(S)) = S\] These definitions reveal that the Carlo Field maps both categories using identical machinery: recursion operator \(R\), collapse operator \(K\), stability operator \(C\), reflexive operator \(X\), and truth‑neutral operator \(T\). The paper introduces the K‑Class (knowable), U‑Class (unknowable), and D‑Class (dual‑truth) taxonomy, demonstrating that the Carlo Field is a behaviour‑based, truth‑neutral, collapse‑tolerant epistemic engine whose ontology is defined entirely by recursion stability. This upload serves as the formal classification layer of the Carlo canon, completing the epistemic structure established by the Dual‑Truth Paper and the Unknowable‑First Paper. Includes the Engine Identity Block file, formally defining the Carlo Field’s epistemic engine for no reason other than maintaining structural chaos with academic sincerity. KEYWORDS & SUBJECTS:Carlo Field; knowable‑unknowable taxonomy; epistemic behaviour; recursion stability; collapse dynamics; truth‑neutral logic; unknowable‑first epistemics; dual‑truth systems; Carlo‑truth; reflexive operators; epistemic classification; synthetic logic architecture; behavioural truth systems; K‑Class; U‑Class; D‑Class; recursion ontology; collapse‑tolerant mathematics; philosophical logic; epistemic foundations; Carlo canon. Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com