TL;DR
This paper advocates for mathematical conceptualism as a rigorous and practical foundation for mathematics, arguing it is more suitable for ordinary mathematical practice than other foundational approaches.
Contribution
It provides a comprehensive explanation and defense of mathematical conceptualism, positioning it as a superior foundational stance for mathematics.
Findings
Mathematical conceptualism is cogent and rigorous.
It is better suited to ordinary mathematical practice.
The paper defends conceptualism against alternative foundations.
Abstract
This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all other foundational stances.
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Taxonomy
TopicsHistory and Theory of Mathematics · Mathematical and Theoretical Analysis