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WHAT STANDS BETWEEN GROUNDING RULES AND LOGICAL RULES IS THE EXCLUDED MIDDLE

Part of: Philosophical aspects of logic and foundations Proof theory and constructive mathematics

Published online by Cambridge University Press:  23 December 2024

FRANCESCO A. GENCO
FRANCESCO A. GENCO*
Affiliation:
LUCI GROUP, DEPARTMENT OF PHILOSOPHY “PIERO MARTINETTI” UNIVERSITÀ DEGLI STUDI DI MILANO VIA FESTA DEL PERDONO 7, 20122 MILAN, ITALY CENTER FOR LOGIC, LANGUAGE AND COGNITION (LLC) DEPARTMENT OF PHILOSOPHY AND EDUCATION SCIENCES UNIVERSITY OF TURIN VIA S. OTTAVIO, 20, 10124, TURIN, ITALY
*
E-mail: [email protected]
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Abstract

The distinction between the proofs that only certify the truth of their conclusion and those that also display the reasons why their conclusion holds has a long philosophical history. In the contemporary literature, the grounding relation—an objective, explanatory relation which is tightly connected with the notion of reason—is receiving considerable attention in several fields of philosophy. While much work is being devoted to characterising logical grounding in terms of deduction rules, no in-depth study focusing on the difference between grounding rules and logical rules exists. In this work, we analyse the relation between logical grounding and classical logic by focusing on the technical and conceptual differences that distinguish grounding rules and logical rules. The calculus employed to conduct the analysis provides moreover a strong confirmation of the fact that grounding derivations are logical derivations of a certain kind, without trivialising the distinction between grounding and logical rules, explanatory and non-explanatory parts of a derivation. By a further formal analysis, we negatively answer the question concerning the possible correspondence between grounding rules and intuitionistic logical rules.

Keywords

groundingclassical logicexcluded middle lawintuitionistic logicproof theory

MSC classification

Primary: 03A99: None of the above, but in this section
Secondary: 03F03: Proof theory, general
Type
Research Article
Information
The Review of Symbolic Logic , Volume 18 , Issue 1 , March 2025 , pp. 1 - 27
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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