{"title":"In Defense of the Implicit Commitment Thesis","authors":"Ethan Brauer","doi":"10.3998/ergo.3114","DOIUrl":null,"url":null,"abstract":"The implicit commitment thesis is the claim that believing in a mathematical theory S carries an implicit commitment to further sentences not deductively entailed by the theory, such as the consistency sentence Con(S). I provide a new argument for this thesis based on the notion of mathematical certainty. I also reply to a recent argument by Walter Dean against the implicit commitment thesis, showing that my formulation of the thesis avoids the difficulties he raises.","PeriodicalId":51882,"journal":{"name":"Ergo-An Open Access Journal of Philosophy","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ergo-An Open Access Journal of Philosophy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3998/ergo.3114","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
引用次数: 0
Abstract
The implicit commitment thesis is the claim that believing in a mathematical theory S carries an implicit commitment to further sentences not deductively entailed by the theory, such as the consistency sentence Con(S). I provide a new argument for this thesis based on the notion of mathematical certainty. I also reply to a recent argument by Walter Dean against the implicit commitment thesis, showing that my formulation of the thesis avoids the difficulties he raises.