Objective Truth in RAM-Bounded Machines: A Pragmatic Formal Framework

This paper proposes a novel framework for defining objective truth relative to finite-state machines with bounded RAM and no memory. Rather than treating truth as an absolute or idealized property, this approach defines truth operationally: as what can be verified in real-time by a constrained system. The paper introduces five postulates for objective sets and statements, formalizes a hierarchy of machine-verifiable truths, and reinterprets Gödel’s incompleteness theorems through the lens of computational finitude. It further contrasts this model with Turing completeness and explores implications for logic, epistemology, and machine intelligence.