Four philosophical concerns about higher-order logic in general and the specific demands placed on it by the neo-logicist project are distinguished. The paper critically reviews recent responses to these concerns by, respectively, the late Bob Hale, Richard Kimberly Heck, and myself. It is argued that these score some successes. The main aim of the paper, however, is to argue that the most serious objection to the applications of higher-order logic required by the neo-logicist project has not been properly understood. The paper concludes by outlining a strategy, prefigured in recent work of Øystein Linnebo, for meeting this objection.

中文翻译：

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盘点：Hale、Heck 和 Wright 谈新逻辑主义和高阶逻辑

区分了关于一般高阶逻辑的四个哲学关注点以及新逻辑主义项目对其提出的具体要求。本文批判性地回顾了已故的鲍勃·黑尔、理查德·金伯利·赫克和我本人最近对这些担忧的回应。有人认为，这些取得了一些成功。然而，这篇论文的主要目的是论证对新逻辑主义项目所要求的高阶逻辑应用最严重的反对意见尚未得到正确理解。本文最后概述了一种策略，该策略在 Øystein Linnebo 最近的工作中进行了预想，以应对这一反对意见。