{"title":"卡尔纳普的数学哲学","authors":"Benjamin Marschall","doi":"10.1111/phc3.12884","DOIUrl":null,"url":null,"abstract":"For several decades Carnap’s philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that apparently decisive objections to his position target a straw man. This raises two questions. First, how exactly should we characterise Carnap’s actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these by looking at Carnap’s response to the incompleteness theorems. Drawing on objections put forward by Gödel and Beth, I argue that some crucial aspects of Carnap’s positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap’s position requires are made.","PeriodicalId":40011,"journal":{"name":"Philosophy Compass","volume":" ","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Carnap's philosophy of mathematics\",\"authors\":\"Benjamin Marschall\",\"doi\":\"10.1111/phc3.12884\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For several decades Carnap’s philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that apparently decisive objections to his position target a straw man. This raises two questions. First, how exactly should we characterise Carnap’s actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these by looking at Carnap’s response to the incompleteness theorems. Drawing on objections put forward by Gödel and Beth, I argue that some crucial aspects of Carnap’s positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap’s position requires are made.\",\"PeriodicalId\":40011,\"journal\":{\"name\":\"Philosophy Compass\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2022-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Philosophy Compass\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1111/phc3.12884\",\"RegionNum\":1,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"0\",\"JCRName\":\"PHILOSOPHY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Philosophy Compass","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1111/phc3.12884","RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"0","JCRName":"PHILOSOPHY","Score":null,"Total":0}
For several decades Carnap’s philosophy of mathematics used to be either dismissed or ignored. It was perceived as a form of linguistic conventionalism and thus taken to rely on the bankrupt notion of truth by convention. However, recent scholarship has revealed a more subtle picture. It has been forcefully argued that Carnap is not a linguistic conventionalist in any straightforward sense, and that apparently decisive objections to his position target a straw man. This raises two questions. First, how exactly should we characterise Carnap’s actual philosophy of mathematics? Secondly, is his position an attractive alternative to established views? I will tackle these by looking at Carnap’s response to the incompleteness theorems. Drawing on objections put forward by Gödel and Beth, I argue that some crucial aspects of Carnap’s positive account have remained underdeveloped. Suggestions on what a full evaluation of Carnap’s position requires are made.