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.

中文翻译：

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算术多元论和句法客观性


算术多元主义认为，不存在一种真正的算术，而是存在许多明显相互冲突的算术理论，每种理论都有自己的语言。尽管多元化最近引起了人们的极大兴趣，但它也面临着严厉的批评。帕森斯（Parsons，2008）提出了一个强有力的反对意见，它诉诸绝对性结果来反对看似相互冲突的真实算术的可能性。 Putnam (1994) 和 Koellner (2009) 提出的另一个突出反对意见利用句法的算术化来论证算术多元主义与句法的客观性不一致。首先，我们回顾这些论点并解释它们最终失败的原因。然后，我们提出了一个新颖的、更复杂的论点，避免了两者的陷阱。我们的论点结合了两种反对意见的策略，表明算术的多元化必然带来语法的多元化。最后，我们根据我们的论点探讨了多元化的可行性，并得出结论：稳定的多元化立场是连贯的。这一立场允许算术和句法理论相互竞争的可能性，只要它们系统地相互变化。