相对范畴性与抽象原则
Relative Categoricity and Abstraction Principles
摘要：
最近许多数学哲学的作者都非常重视算术和集合论的基础理论的传统公理化的相对范畴性（\cite{Parsons1990a}，\cite{Parsons2008} §{49}，\cite{McGee1997aa}，\cite{Lavine1999aa}，\cite{Vaananen2014aa}）。当代数学哲学中的另一项伟大事业是赖特和黑尔在抽象原则上建立数学的计划（\cite{Hale2001}，\cite{Cook2007aa}）。在\cite{Walsh2012aa}中，人们注意到一个传统的抽象原则，即休谟的原则，具有一定的相对范畴属性，在这里我们称之为\emph{natural relative categoricity}。在本文中，我们表明，大多数其他的抽象原则是PDMATHAMV自然相对分类，因此，实际上有大量的不相容之间的这两个最近的趋势，在当代数学哲学。为了更好地理解在抽象原则的背景下相对范畴性的精确要求，我们将这些约束与（i）抽象原则上的稳定性类可接受性标准进行比较和对比。\cite{Hodes1984, Hodes1990aa, Hodes1991}（\cite{Cook2012aa}），Antonelli \cite{Antonelli2010aa}和Fine~ \cite{Fine2002}对抽象原理的Tarski-Sher逻辑性要求，Hodes \cite{Hodes1984, Hodes1990aa, Hodes1991}的超赋值思想。
英文摘要：
Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmetic and set theory (\cite{Parsons1990a}, \cite{Parsons2008} §{49}, \cite{McGee1997aa}, \cite{Lavine1999aa}, \cite{Vaananen2014aa}). Another great enterprise in contemporary philosophy of mathematics has been Wright's and Hale's project of founding mathematics on abstraction principles (\cite{Hale2001}, \cite{Cook2007aa}). In \cite{Walsh2012aa}, it was noted that one traditional abstraction principle, namely Hume's Principle, had a certain relative categoricity property, which here we term \emph{natural relative categoricity}. In this paper, we show that most other abstraction principles are \emph{not} naturally relatively categorical, so that there is in fact a large amount of incompatibility between these two recent trends in contemporary philosophy of mathematics. To better understand the precise demands of relative categoricity in the context of abstraction principles, we compare and contrast these constraints to (i) stability-like acceptability criteria on abstraction principles (cf. \cite{Cook2012aa}), (ii) the Tarski-Sher logicality requirements on abstraction principles studied by Antonelli \cite{Antonelli2010aa} and Fine~\cite{Fine2002}, and (iii) supervaluational ideas coming out of Hodes' work \cite{Hodes1984, Hodes1990aa, Hodes1991}.
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