可行的建构主义

AI总结：

本文提出可行主义作为解决严格有限主义问题的替代方法，通过多项式时间问题的计算可行性来解释实践中的构造可能性。

摘要：

杜梅特为直觉主义提出的论点是众所周知的。存在一种担忧，即该论点证明了过多的内容，特别是它支持了极端且明显不一致的严格有限主义立场。核心问题是如何阐明在实践中构造一个算术术语或验证一个陈述的可能性。严格有限主义的答案受到 Sorites 矛盾的困扰。我们提出并发展了可行主义作为一种更具说服力的观点，其中计算可行性，如多项式时间问题的类别，提供了对

英文摘要：

Dummett's argument for intuitionism is well known. There is a concern that the argument proves too much, specifically, that it supports the extreme and apparently incoherent position of strict finitism. The central question is how to explicate the notion that it is possible in practice to construct an arithmetical term or verify a statement. The strict finitist answer is plagued by the sorites paradox. We propose and develop feasibilism as a more plausible view, where computational feasibility, as captured by the class of polynomial-time problems, yields a robust and expedient explication of "possible in practice". In this approach, the complexity is bounded by a polynomial function of the input size, rather than bounded by a constant (as in strict finitism), thus resolving the sorites issues. We show that a system of strictly bounded arithmetic, introduced by Sam Buss, precisely formalizes the feasibilist view so as to satisfy Dummett's requirements.

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