Reviewed by:

• Quine, New Foundations, and the Philosophy of Set Theory by Sean Morris
• Gregory Lavers

This book has two main goals: first, to show that Quine's New Foundations (NF) set theory is better motivated than often assumed; and second, to defend Quine's philosophy of set theory. It is divided into three parts. The first concerns the history of set theory and argues against readings that see the iterative conception of set being the dominant notion of set from the very beginning. The second part concerns Quine's philosophy of set theory. Part 3 is a contemporary assessment of the philosophical status of NF. Here one of the central targets is Boolos's defense of the iterative conception of set and his dismissal of NF as completely unnatural.

As this is a very short review, I will avoid specific points and focus on what I see as a tension between Morris's two goals. I will also focus on how this tension relates to a feature of Morris's interpretation of Quine. Morris considers Quine's account of explication and takes Quine's position on set theory to be that the various set theories are explications of what we mean by 'sets.' Quine's most detailed discussion of explication is in §53 of Word and Object. The ordered pair, Quine claims here, is a paradigm of philosophical analysis [End Page 342] because we can identify the central feature of an ordered pair that any explication must preserve: <x, y> = <w, z> only if x = w and y = z. Whether we explicate ordered pairs as Wiener recommends or as Kuratowski recommends is of no importance. The explications may be inconsistent with one another, but they diverge only over what Quine calls "don'tcares" (Word and Object [Cambridge, MA: MIT, 1960], 259). Both are acceptable because they both preserve the central feature of the intuitive notion.

After mentioning the absence of objects for sets to be explicated in terms of, Morris writes, "Still, I think explication is the right way to describe Quine's approach to set theory" (124). There is, however, another reason, beyond sets' being ontologically fundamental, for why the various set theories fall short of explicating the notion of set. For Quine, as we saw, an explication begins by identifying the central feature of the concept that ought to be preserved (for more on this, see my "On the Quinean-Analyticity of Mathematical Propositions," Philosophical Studies 159 [2012]: 299–319). We cannot identify the central defining feature of our ordinary conception of set, in Quine's words, "because the natural scheme is the unrestricted one that the antinomies discredit" (The Ways of Paradox and Other Essays [Cambridge, MA: Harvard University Press, 1976], 16). It is simply not the case that the various set theories agree on a common core that underlies our intuitive understanding of sets, and disagree only over "don't-cares." In many places, Quine claims that the intuitive notion of set is the inconsistent one, and that the various set theories are not guided by intuition: "Intuition here is bankrupt" (Set Theory and Its Logic, rev. ed. [Cambridge, MA: Harvard University Press, 1969], x).

The question of whether any of the various set theories are an explication of the/a notion of set becomes important when the discussion turns to Boolos and the iterative conception of set. The problem with Boolos's view, as Morris sees things, is not the argument that ZF (Zermelo-Fraenkel set theory) is well motivated, but that ZF alone is a well-motivated set theory. Boolos writes, "ZF alone (together with its extensions and subsystems) is … an independently motivated theory of sets: there is so to speak, a 'thought behind it' about the nature of sets which might have been put forth even if, impossibly, naïve set theory had been consistent" (Logic, Logic, and Logic [Cambridge, MA: Harvard University Press, 1998], 17). Morris seeks to defend Quine by arguing that other set theories, including NF, are also well motivated. Quine, as Morris shows, displayed a pluralistic...

审核人：

• 肖恩·莫里斯（Sean Morris）的《Quine，新基础和集合论哲学》
• 格雷戈里·莱弗斯

本书有两个主要目标：首先，表明奎因的新基础（NF）集合理论比通常假设的动机更好。第二，捍卫奎因的集合论哲学。它分为三个部分。第一个涉及集合论的历史，并反对从一开始就将集合的迭代概念视为集合的主要概念的读物。第二部分涉及奎因的集合论哲学。第三部分是对NF哲学地位的当代评估。这里的主要目标之一是Boolos对集合的迭代概念的辩护，以及他对NF的完全不自然的否决。

因为这是一篇简短的评论，所以我将避免具体点，而是着眼于我认为是莫里斯的两个目标之间的紧张关系。我还将重点讨论这种紧张关系如何与莫里斯对奎因的解释的一个特征相关联。莫里斯认为奎因对解释的解释，并认为奎因在集合论上的立场是，各种集合论都是对我们所谓的“集合”的解释。奎因（Quine）对释义的最详细讨论是在Word and Object的§53中。奎因（Quine）在这里宣称，这对有序对是哲学分析的范式[End Page 342]因为我们可以识别任何对必须保留的有序对的中心特征：<x，y> = <w，z>仅当x = w和y = z时。我们是否按照Wiener的建议或Kuratowski的建议来复制有序对并不重要。这些解释可能彼此不一致，但是它们仅在Quine所说的“不在乎”上有所分歧（Word和Object [Cambridge，MA：MIT，1960]，259）。两者都是可以接受的，因为它们都保留了直观概念的中心特征。

莫里斯在提到没有对象时，莫里斯写道：“不过，我认为，表达是描述奎因的集合论方法的正确方法”（124）。但是，除了集合在本体论上的基础之外，还有另一个原因，就是为什么各种集合理论都未能阐明集合的概念。正如我们所看到的，对于Quine来说，首先从确定应该保留的概念的中心特征开始进行说明（有关此内容的更多信息，请参见我的“论数学命题的奎尼分析”，哲学研究159 [2012]：299 –319）。用奎因的话来说，我们无法确定我们普通的集合概念的中心定义特征，“因为自然方案是对立论抹黑的不受限制的方案”（悖论和其他散文的方式[剑桥，马萨诸塞州：哈佛大学出版社，1976年]，第16页。并非所有的集合论都在一个共同的核心上达成共识，这是我们对集合的直觉理解的基础，而仅在“无关紧要”上存在分歧。Quine在许多地方声称，集合的直观概念是前后矛盾的，而且各种集合理论都不是凭直觉进行指导的：“这里的直觉是破产的”（《集合论及其逻辑》，修订版，[剑桥，MA ：哈佛大学出版社，1969]，x）。

当讨论转向Boolos和集合的迭代概念时，各种集合论中的任何一个是否都是集合论的一个问题就变得很重要。正如莫里斯所看到的那样，Boolos观点的问题并不是ZF（Zermelo-Fraenkel集合论）动机良好的论据，而是ZF本身就是动机良好的集合论。Boolos写道：“仅ZF（及其扩展和子系统）是……一种独立动机的集合理论：可以这么说，关于集合性质的“思考”，即使不可能，也可能提出，天真的集合论是一致的”（逻辑，逻辑和逻辑[马萨诸塞州剑桥市：哈佛大学出版社，1998年]，第17页。莫里斯（Morris）通过辩称包括NF在内的其他既定理论也有很好的动机来捍卫Quine。正如莫里斯（Morris）所展示的，奎因展示了多元化的...