An "Absolute" Type of Logic

TL;DR

This paper introduces an alternative logic system that enhances naturalness and generality by removing traditional restrictions, unifying expressions, and simplifying the deductive framework, aiming for a more faithful model of human reasoning.

Contribution

It presents a novel logic framework that eliminates type hierarchies and external structures, unifies terms and formulas, and offers a minimal, intuitive deductive system.

Findings

Soundness and consistency are established.

Completeness is examined.

The system offers a unified foundation for formal reasoning.

Abstract

This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external structures, making the meaning of expressions depend solely on their constituent symbols. Terms and formulas are unified into a single notion of expression, with set-builder notation integrated as a primitive construct. Connectives and quantifiers are treated as operators among others rather than as privileged primitives. The deductive framework is minimal and intuitive, with soundness and consistency established and completeness examined. While computability requirements may limit universality, the system offers a unified and potentially more faithful model of human mathematical deduction, providing an alternative foundation for formal reasoning.