论文标题
分类论证的哲学用途
Philosophical Uses of Categoricity Arguments
论文作者
论文摘要
数学家和哲学家在令人惊讶的各种环境中呼吁分类论点。一个熟悉的例子呼吁二阶分类性，以表明连续假设尽管正式独立性，但具有确定的真实价值，但即使在集合理论中，这也不会耗尽分类性的用途，更不用说其在讨论算术中的各种角色中出现。在这里，我们比较和对比对这些部署的取样，以了解这些论点何时成功以及何时失败。我们的故事始于两个历史地标，即Dedekind和Zermelo，分别涉及算术和设定理论，并以两位主要的当代作家查尔斯·帕森斯（Charles Parsons）和共同作者蒂姆·纽·巴顿（Tim Button）和肖恩·沃尔什（Sean Walsh）的形式结束，再次在算术和智慧理论上结尾。在这两者之间，我们停止了乔治·克雷塞尔（Georg Kreisel）的众所周知的贡献。在每种情况下，我们都会问：作者从哲学上开始做什么？他们实际上是在数学上做什么（或可以做什么）？是否已完成（或可以做）完成他们打算做的事情？我们发现这种关注的焦点是启发性的：这些作者具有质量不同的哲学目标，而对一个人有用的东西可能对他人不起作用。
Mathematicians and philosophers have appealed to categoricity arguments in a surprisingly varied range of contexts. One familiar example calls on second-order categoricity in an attempt to show that the Continuum Hypothesis, despite its formal independence, has a determinate truth value, but this does not exhaust the uses of categoricity even in set theory, not to mention its appearance in various roles in discussions of arithmetic. Here we compare and contrast a sampling of these deployments to get a sense of when these arguments tend to succeed and when they tend to fail. Our story begins with two historical landmarks, Dedekind and Zermelo, on arithmetic and set theory, respectively, and ends with two leading contemporary writers, Charles Parsons and the co-authors Tim Button and Sean Walsh, again on arithmetic and set theory, respectively. In between, we pause over the well-known contribution of Georg Kreisel. In each case we ask: what does the author set out to accomplish, philosophically?; what do they actually do (or what can be done), mathematically?; and does what is done (or can be done) accomplish what they set out to do? We find this focus on context illuminating: these authors have qualitatively different philosophical goals, and what works for one might not work for another.
