Peacocke’s recent The Primacy of Metaphysics covers a wide range of topics. This critical discussion focuses on the book’s novel account of extensive magnitudes and numbers. First, I further develop and defend Peacocke’s argument against nominalistic approaches to magnitudes and numbers. Then, I argue that his view is more Aristotelian than Platonist because reified magnitudes and numbers are accounted for via corresponding properties and these properties’ application conditions, and because the mentioned objects have a “shallow nature” relative to the corresponding properties. The result is an asymmetric conception of abstraction, which contrasts with the neo-Fregeans’ but has important tenets in common with an approach that I have recently developed.

Peacocke 最近的The Primacy of Metaphysics涵盖了广泛的主题。这一批判性讨论的重点是该书对广泛的量级和数字的新颖描述。首先，我进一步发展并捍卫 Peacocke 反对关于数量和数字的唯名论方法的论点。然后，我认为他的观点更像是亚里士多德的而不是柏拉图的，因为具体化的数量和数量是通过相应的属性和这些属性的应用条件来解释的，并且因为提到的对象相对于相应的属性具有“浅层性质”。结果是抽象的不对称概念，它与新弗雷格派形成对比，但与我最近开发的方法具有重要的共同点。