{"title":"A PROBLEM AND A SOLUTION FOR NEO-FREGEANISM","authors":"M. Gabbay","doi":"10.1515/9783110328875.289","DOIUrl":null,"url":null,"abstract":"I argue that Benacerraf’s famous objection to mathematical realism in his paper “What numbers could not be” can be adapted to present severe difficulties for the Neo-Fregean programme. I formulate an alternative abstraction principle and argue that there is no reason for the natural numbers to be generated by one abstraction principle rather than the other. Independently of this conclusion, the formal comparison of the two abstraction principles involves a result of interest to Neo-Fregeans: I offer a solution to the bad company objection.","PeriodicalId":317292,"journal":{"name":"From ontos verlag: Publications of the Austrian Ludwig Wittgenstein Society - New Series","volume":"21 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"From ontos verlag: Publications of the Austrian Ludwig Wittgenstein Society - New Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/9783110328875.289","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
I argue that Benacerraf’s famous objection to mathematical realism in his paper “What numbers could not be” can be adapted to present severe difficulties for the Neo-Fregean programme. I formulate an alternative abstraction principle and argue that there is no reason for the natural numbers to be generated by one abstraction principle rather than the other. Independently of this conclusion, the formal comparison of the two abstraction principles involves a result of interest to Neo-Fregeans: I offer a solution to the bad company objection.
我认为，贝纳塞拉夫在他的论文《数字不可能是什么》(What numbers could not be)中对数学实在论的著名反对，可以用来给新fregean纲领提出严峻的困难。我提出了另一种抽象原则，并认为自然数没有理由由一种抽象原则产生，而不是由另一种抽象原则产生。独立于这个结论之外，这两个抽象原则的正式比较涉及到新弗雷格主义者感兴趣的结果:我提供了一个解决坏公司反对意见的解决方案。
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