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Syntactic theory of mathematical expressions
Daiki Matsumoto1, Tomoya Nakai2
1Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan; Department of Humanities, Kanazawa Seiryo University, Kanazawa, Japan.
Cognitive Psychology
|September 25, 2023
Summary
This study applies theoretical linguistics to analyze mathematical expressions, proposing a new "Applicative" syntactic category to unify binary and ternary structures in mathematics.
Area of Science:
- Linguistics
- Cognitive Science
- Mathematics
Background:
- Theoretical linguists suggest natural language syntax underpins mathematical structures.
- Previous research lacked rigorous linguistic analysis of mathematical expressions.
- Existing studies show inconsistencies between linguistic theories and mathematical syntax.
Approach:
- Utilized a theoretical linguistics methodology to analyze mathematical expression syntax.
- Reviewed behavioral and neuroimaging studies on mathematical syntax.
- Proposed a novel syntactic category, 'Applicative', to reconcile observed structures.
Key Points:
- Identified inconsistencies with theoretical linguistics, particularly regarding ternary structures.
- The proposed 'Applicative' category unifies seemingly ternary structures using binary combinations.
- The framework encompasses basic arithmetic, algebraic equations, and calculus expressions.
Conclusions:
- This research provides the first comprehensive linguistic framework for analyzing mathematical expression syntax.
- The 'Applicative' category offers a new perspective on the cognitive underpinnings of mathematical reasoning.
- The findings bridge the gap between linguistic theory and the formal structures of mathematics.
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