{"title":"A Two-Part Defense of Intuitionistic Mathematics","authors":"Samuel Elliott","doi":"10.33043/S.14.1.27-39","DOIUrl":null,"url":null,"abstract":"The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.","PeriodicalId":375047,"journal":{"name":"Stance: an international undergraduate philosophy journal","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stance: an international undergraduate philosophy journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33043/S.14.1.27-39","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
The classical interpretation of mathematical statements can be seen as comprising two separate but related aspects: a domain and a truth-schema. L. E. J. Brouwer’s intuitionistic project lays the groundwork for an alternative conception of the objects in this domain, as well as an accompanying intuitionistic truth-schema. Drawing on the work of Arend Heyting and Michael Dummett, I present two objections to classical mathematical semantics, with the aim of creating an opening for an alternative interpretation. With this accomplished, I then make the case for intuitionism as a suitable candidate to fill this void.
数学陈述的经典解释可以被看作是由两个独立但相关的方面组成:一个领域和一个真理模式。L. E. J. browwer的直觉主义项目为这一领域中对象的另一种概念以及伴随的直觉主义真理图式奠定了基础。根据阿伦德·海廷和迈克尔·达米特的工作，我提出了对经典数学语义学的两个反对意见，目的是为另一种解释创造一个开放的空间。完成了这一点后，我认为直觉主义是填补这一空白的合适人选。
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