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A Logical Foundation for Potentialist Set Theory最新文献

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Inference Rules 推理规则
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.008
Hongfei Fu, J. Hopcroft
{"title":"Inference Rules","authors":"Hongfei Fu, J. Hopcroft","doi":"10.1017/9781108992756.008","DOIUrl":"https://doi.org/10.1017/9781108992756.008","url":null,"abstract":"A B –––––– A&B A&B –––––– A A&B –––––– B ~(A&B) =========== A → ~B vI vO ∼ ∼ ∼ ∼vI/O A –––––– A∨B B –––––– A∨B A∨B ∼A –––––– B A∨B ∼B –––––– A ~(A∨B) ∼A –––––– A→B B –––––– A→B A→B A –––––– B A→B ∼B –––––– ∼A ~(A→B) =========== A & ~B ↔ ↔ ↔ ↔I ↔ ↔ ↔ ↔O ∼ ∼ ∼ ∼↔ ↔ ↔ ↔I/O A→B B→A –––––– A↔B A↔B –––––– A→B A↔B –––––– B→A ~(A↔B) =========== ∼A↔B I O DN A ∼A –––– ––– A ~∼A ===== A Note: The ~O and ~I rules are combined, using a long equals sign '==='. Henceforth, any rule that is displayed with '===' is a bi-directional rule, which can be used both as an in-rule and as an out-rule.","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115328939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Anti-Objectivism About Set Theory 关于集合论的反客观主义
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.018
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引用次数: 0
Platonism or Nominalism? 柏拉图主义还是唯名论?
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.010
{"title":"Platonism or Nominalism?","authors":"","doi":"10.1017/9781108992756.010","DOIUrl":"https://doi.org/10.1017/9781108992756.010","url":null,"abstract":"","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128307415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Archimedean and Rich Instantiation 阿基米德和丰富实例化
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.023
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引用次数: 0
Actualist Set Theory 现实主义集合论
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.002
{"title":"Actualist Set Theory","authors":"","doi":"10.1017/9781108992756.002","DOIUrl":"https://doi.org/10.1017/9781108992756.002","url":null,"abstract":"","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127421367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Vindication of FOL Inference in Set Theory 集合论中FOL推理的证明
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.022
{"title":"Vindication of FOL Inference in Set Theory","authors":"","doi":"10.1017/9781108992756.022","DOIUrl":"https://doi.org/10.1017/9781108992756.022","url":null,"abstract":"","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"177 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126023472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explanatory Indispensability 解释的必要
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.013
{"title":"Explanatory Indispensability","authors":"","doi":"10.1017/9781108992756.013","DOIUrl":"https://doi.org/10.1017/9781108992756.013","url":null,"abstract":"","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"46 9-10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131519956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Putnamian Potentialism: Putnam and Hellman 普特南潜力论:普特南和赫尔曼
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.003
{"title":"Putnamian Potentialism: Putnam and Hellman","authors":"","doi":"10.1017/9781108992756.003","DOIUrl":"https://doi.org/10.1017/9781108992756.003","url":null,"abstract":"","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"183 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132924785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Indispensability 不可缺少
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.2307/j.ctvgs09k1.10
A. Paseau, Alan Baker
{"title":"Indispensability","authors":"A. Paseau, Alan Baker","doi":"10.2307/j.ctvgs09k1.10","DOIUrl":"https://doi.org/10.2307/j.ctvgs09k1.10","url":null,"abstract":"Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's first half traces the evolution of the Indispensability Argument from its origins in Quine and Putnam's works, taking in naturalism, confirmational holism, Field's program, and the use of idealisations in science along the way. Its second half examines the explanatory version of the Indispensability Argument, and focuses on several more recent versions of easy-road and hard-road fictionalism respectively.","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"170 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132436337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Physical Magnitude Statements and Sparsity 物理大小声明和稀疏性
A Logical Foundation for Potentialist Set Theory Pub Date : 2022-02-28 DOI: 10.1017/9781108992756.014
{"title":"Physical Magnitude Statements and Sparsity","authors":"","doi":"10.1017/9781108992756.014","DOIUrl":"https://doi.org/10.1017/9781108992756.014","url":null,"abstract":"","PeriodicalId":294618,"journal":{"name":"A Logical Foundation for Potentialist Set Theory","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121637752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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