On mathematical instrumentalism*
On mathematical instrumentalism*
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论数学工具主义*
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Ignjatović
中科院分区：
文献类型：
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作者：
Patrick Caldon;A. Ignjatović
摘要 在本文中，我们设计了一些技术工具来处理与通常称为数学工具主义的哲学观点相关的问题。这些工具本身就很有趣，与其哲学后果无关。例如，我们证明，尽管被称为 IΣ1 的皮亚诺斯算术片段是原始递归算术 (PRA) 方程理论的保守扩展。 IΣ1 比 PRA 具有超指数加速。另一方面，逆向数学计划中研究的理论将强大的数学原理形式化，仅比 IΣ1 具有多项式加速。
Abstract In this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peanos Arithmetic known as IΣ1 is a conservative extension of the equational theory of Primitive Recursive Arithmetic (PRA). IΣ1 has a super-exponential speed-up over PRA. On the other hand, theories studied in the Program of Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over IΣ1.