{"title":"论Peirce β图的三个抽象性层次","authors":"R. Atkins","doi":"10.1080/01445340.2022.2056781","DOIUrl":null,"url":null,"abstract":"Peirce’s beta graphs are roughly equivalent to our first-order predicate logic. However, Bellucci and Pietarinen have recently argued that the beta graphs are not well-equipped to handle asymmetric relative terms. I survey four proposed solutions to the problem and find them all wanting. I offer a fifth solution according to which Peirce’s beta graphs function at three different levels of abstractness from natural language. I diagnose the problem of asymmetric relative terms as arising when we transition from the first to the second level of abstractness. Making grammatical information encoded in natural language explicit at the first level of abstractness and interpreting graphs at the second level of abstractness as shorn of grammatical information resolves the problem. The solution is both well-motivated by Peirce’s own commitments and increases the expressiveness of the beta graphs.","PeriodicalId":55053,"journal":{"name":"History and Philosophy of Logic","volume":"44 1","pages":"16 - 32"},"PeriodicalIF":0.5000,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Three Levels of Abstractness in Peirce’s Beta Graphs\",\"authors\":\"R. Atkins\",\"doi\":\"10.1080/01445340.2022.2056781\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Peirce’s beta graphs are roughly equivalent to our first-order predicate logic. However, Bellucci and Pietarinen have recently argued that the beta graphs are not well-equipped to handle asymmetric relative terms. I survey four proposed solutions to the problem and find them all wanting. I offer a fifth solution according to which Peirce’s beta graphs function at three different levels of abstractness from natural language. I diagnose the problem of asymmetric relative terms as arising when we transition from the first to the second level of abstractness. Making grammatical information encoded in natural language explicit at the first level of abstractness and interpreting graphs at the second level of abstractness as shorn of grammatical information resolves the problem. The solution is both well-motivated by Peirce’s own commitments and increases the expressiveness of the beta graphs.\",\"PeriodicalId\":55053,\"journal\":{\"name\":\"History and Philosophy of Logic\",\"volume\":\"44 1\",\"pages\":\"16 - 32\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-01-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"History and Philosophy of Logic\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://doi.org/10.1080/01445340.2022.2056781\",\"RegionNum\":3,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"HISTORY & PHILOSOPHY OF SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"History and Philosophy of Logic","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1080/01445340.2022.2056781","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
On Three Levels of Abstractness in Peirce’s Beta Graphs
Peirce’s beta graphs are roughly equivalent to our first-order predicate logic. However, Bellucci and Pietarinen have recently argued that the beta graphs are not well-equipped to handle asymmetric relative terms. I survey four proposed solutions to the problem and find them all wanting. I offer a fifth solution according to which Peirce’s beta graphs function at three different levels of abstractness from natural language. I diagnose the problem of asymmetric relative terms as arising when we transition from the first to the second level of abstractness. Making grammatical information encoded in natural language explicit at the first level of abstractness and interpreting graphs at the second level of abstractness as shorn of grammatical information resolves the problem. The solution is both well-motivated by Peirce’s own commitments and increases the expressiveness of the beta graphs.
期刊介绍:
History and Philosophy of Logic contains articles, notes and book reviews dealing with the history and philosophy of logic. ’Logic’ is understood to be any volume of knowledge which was regarded as logic at the time in question. ’History’ refers back to ancient times and also to work in this century; however, the Editor will not accept articles, including review articles, on very recent work on a topic. ’Philosophy’ refers to broad and general questions: specialist articles which are now classed as ’philosophical logic’ will not be published.
The Editor will consider articles on the relationship between logic and other branches of knowledge, but the component of logic must be substantial. Topics with no temporal specification are to be interpreted both historically and philosophically. Each topic includes its own metalogic where appropriate.