{"title":"No Easy Road to Impredicative Definabilism","authors":"Øystein Linnebo, Sam Roberts","doi":"10.1093/philmat/nkad013","DOIUrl":null,"url":null,"abstract":"Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that it fails to characterize the domain uniquely. Thus, we conclude, there is no easy road to impredicative definabilism.","PeriodicalId":49004,"journal":{"name":"Philosophia Mathematica","volume":"5 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1093/philmat/nkad013","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that it fails to characterize the domain uniquely. Thus, we conclude, there is no easy road to impredicative definabilism.
Bob Hale为一种新的财产概念进行了辩护,这种概念在两个关键方面都是Fregean的。首先,像弗雷格一样,黑尔坚持认为每个性质都可以用一个开放公式来定义。第二,像弗雷格一样,但与后来的定义主义者不同,黑尔试图证明完全的不确定性理解是合理的。我们认为,他的辩护中最具创新性的部分是“可定义性约束”,它可以作为属性域的隐含定义。我们使这个约束形式上精确,并证明它不能唯一地刻画域。因此,我们得出的结论是,没有一条通往不可定义性的简单道路。
期刊介绍:
Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.