算术多元化与句法的客观性

Noûs Pub Date : 2024-07-02 DOI:10.1111/nous.12510
Lavinia Picollo, Daniel Waxman
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引用次数: 0

摘要

算术多元论认为,并不存在一种真正的算术,而是存在许多表面上相互冲突的算术理论,每种理论都有自己的语言。多元论近来引起了相当大的兴趣,但也遭到了不少批评。帕森斯(2008 年)提出了一个强有力的反对意见,呼吁用分类结果来反驳看似相互冲突的真正算术的可能性。普特南(Putnam,1994 年)和科尔纳(Koellner,2009 年)提出的另一个突出的反对意见则以句法的算术化为基础,认为算术多元论与句法的客观性不一致。首先,我们回顾了这些论点,并解释了它们最终失败的原因。然后,我们提出了一个新颖、更复杂的论证,避免了这两种论证的缺陷。我们的论证结合了这两种反对意见的策略,以证明关于算术的多元论包含关于句法的多元论。最后,我们根据我们的论证探讨了多元论的可行性,并得出结论:稳定的多元论立场是一致的。只要算术理论和句法理论系统地共同变化,这种立场就允许存在相互对立的一揽子理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Arithmetical pluralism and the objectivity of syntax
Arithmetical pluralism is the view that there is not one true arithmetic but rather many apparently conflicting arithmetical theories, each true in its own language. While pluralism has recently attracted considerable interest, it has also faced significant criticism. One powerful objection, which can be extracted from Parsons (2008), appeals to a categoricity result to argue against the possibility of seemingly conflicting true arithmetics. Another salient objection raised by Putnam (1994) and Koellner (2009) draws upon the arithmetization of syntax to argue that arithmetical pluralism is inconsistent with the objectivity of syntax. First, we review these arguments and explain why they ultimately fail. We then offer a novel, more sophisticated argument that avoids the pitfalls of both. Our argument combines strategies from both objections to show that pluralism about arithmetic entails pluralism about syntax. Finally, we explore the viability of pluralism in light of our argument and conclude that a stable pluralist position is coherent. This position allows for the possibility of rival packages of arithmetic and syntax theories, provided that they systematically co‐vary with one another.
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