Elements of Mathematics: A Problem-Centered Approach to History and Foundations
Элементы математики: проблемно-ориентированный подход к истории и основаниям
2022-02-14
SCID: 54.1/entgxca4
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inconsistencymathematical foundationsmathematical rigornaive mathematical theorynatural language
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Abstract (AI)
In general, naïve theory in mathematics is a term referring to a mathematical\ntheory that employs natural language to describe its objects of study. Many terms in\na naïve theory are not defined with mathematical rigor, and thus the theory is prone\nto “excesses,” possibly leading to inconsistencies.
Key Findings
1
Because many terms in naïve theories lack mathematical rigor, these theories are vulnerable to conceptual excesses.
2
Naïve mathematical theories describe their objects using natural language rather than fully formal definitions.
3
Such excesses can potentially lead naïve mathematical theories to inconsistency.
4
The paper frames mathematics through a problem-centered approach connected to questions of history and foundations.
Research Object
naïve mathematical theory
Research Subject
the use of natural language and lack of rigorous definitions, including the resulting susceptibility to excesses and inconsistencies
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2022-02-14
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