Avon, Mauro (2025) An "Absolute" Type of Logic. [Preprint]

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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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Avon, Mauro avonma@gmail.com 0000-0003-4368-4759
Keywords:	logic; foundations of mathematics
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics
Depositing User:	Dr. Mauro Avon
Date Deposited:	13 Aug 2025 20:32
Last Modified:	13 Aug 2025 20:32
Item ID:	26198
Subjects:	Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Mathematics
Date:	10 August 2025
URI:	https://philsci-archive.pitt.edu/id/eprint/26198

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