Absolute Logic: an alternative framework for formal logic

Abstract

This paper introduces an alternative framework for formal logic, termed "Absolute Logic", designed to overcome the intrinsic limitations and structural relativity of standard First-Order Logic (FOL). While FOL relies on external Tarskian structures to assign meaning and restricts quantification to a single, predetermined domain, the proposed system establishes an invariant, self-contained semantics where every symbol possesses an intrinsic meaning. By unifying the traditional syntactic dichotomy between terms and formulas into a single concept of "expression" and evaluating them relative to formalized variable-expression contexts, the system closely mirrors the natural, cumulative nature of human mathematical deduction. Furthermore, we address the critical balance between expressive power and constructive utility by integrating recursion-theoretic constraints, demonstrating how computability theory acts as a necessary bound to preserve foundational validity. The consistency and structural properties of the resulting language are formally established, providing a novel perspective on non-hierarchical, absolute logical systems.