Sets, Properties, and Unrestricted Quantification
Sets, Properties, and Unrestricted Quantification
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集合、属性和无限制定量
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发表时间：
2006
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通讯作者：
Øystein Linnebo
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作者：
Øystein Linnebo
称一个量词为无限制的，如果它涵盖了绝对所有的事物：不仅仅是所有的物理事物或与某些特定话语或话语相关的所有事物，而是绝对涵盖了所有存在的事物。乍一看，无限制的量化似乎是完全一致的。因为这种量化似乎涉及到各种各样的主张，即所有正常的人都有能力理解。例如，一些基本的逻辑和数学真理似乎涉及不受限制的量化，如绝对一切都是自同一性的真理和绝对没有成员的空集的真理。各种形而上学的观点似乎也涉及无限制的量化，例如物理主义的观点认为绝对一切都是物理的。然而，集合论和语义悖论已经被用来挑战无限制量化的一致性。有人认为，每当我们形成一个定量范围的概念时，这个概念就可以用来定义不在这个范围内的进一步的对象，从而确立了定量毕竟不是无限制的本文有两个主要目标。我的第一个目标是指出迄今为止对无限制量化最有希望的辩护存在的一些问题。我的第二个目标是发展更好的防守。迄今为止，对无限制量化最有希望的防御是使用类型层次结构（第3节）。我指出，有一些重要的语义见解是类型理论家无法完全概括地表达的（第4节）。我认为，这个问题类似于哲学家们所面临的问题，他们否认无限制量化的一致性。我对无限制量化的另一种辩护是基于集合和属性之间的明显区别（第5节）。集合是组合实体，通过对其元素的引用而个性化。属性是有内涵的个体
Call a quantifier unrestricted if it ranges over absolutely all things: not just over all physical things or all things relevant to some particular utterance or discourse but over absolutely everything there is. Prima facie, unrestricted quantification seems to be perfectly coherent. For such quantification appears to be involved in a variety of claims that all normal human beings are capable of understanding. For instance, some basic logical and mathematical truths appear to involve unrestricted quantification, such as the truth that absolutely everything is self-identical and the truth that the empty set has absolutely no members. Various metaphysical views too appear to involve unrestricted quantification, such as the physicalist view that absolutely everything is physical. However, the set-theoretic and semantic paradoxes have been used to challenge the coherence of unrestricted quantification. It has been argued that, whenever we form a conception of a certain range of quantification, this conception can be used to define further objects not in this range, thus establishing that the quantification wasn’t unrestricted after all.1 This paper has two main goals. My first goal is to point out some problems with the most promising defense of unrestricted quantification developed to date. My second goal is to develop a better defense. The most promising defense of unrestricted quantification developed to date makes use of a hierarchy of types (Section 3). I show that there are some important semantic insights that type-theorists cannot express in full generality (Section 4). I argue that this problem is analogous to those faced by philosophers who deny the coherence of unrestricted quantification. My alternative defense of unrestricted quantification is based on a sharp distinction between sets and properties (Section 5). Sets are combinatorial entities, individuated by reference to their elements. Properties are intensional entities, individuated