{"title":"Syntactic Metalogic","authors":"","doi":"10.1017/9781316275603.006","DOIUrl":"https://doi.org/10.1017/9781316275603.006","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133247831","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}
{"title":"Semantic Metalogic","authors":"","doi":"10.1017/9781316275603.008","DOIUrl":"https://doi.org/10.1017/9781316275603.008","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125023389","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}
{"title":"Syntactic Metalogic Redux","authors":"","doi":"10.1017/9781316275603.007","DOIUrl":"https://doi.org/10.1017/9781316275603.007","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123383537","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}
{"title":"The Category of Propositional Theories","authors":"","doi":"10.1017/9781316275603.005","DOIUrl":"https://doi.org/10.1017/9781316275603.005","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"62 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128012892","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}
{"title":"Semantic Metalogic Redux","authors":"","doi":"10.1017/9781316275603.009","DOIUrl":"https://doi.org/10.1017/9781316275603.009","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123467100","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}
{"title":"Invitation to Metatheory","authors":"","doi":"10.1017/9781316275603.003","DOIUrl":"https://doi.org/10.1017/9781316275603.003","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"435 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123051842","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}
{"title":"Index","authors":"","doi":"10.1017/9781316275603.012","DOIUrl":"https://doi.org/10.1017/9781316275603.012","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"87 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126025200","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}
{"title":"From Metatheory to Philosophy","authors":"","doi":"10.1017/9781316275603.010","DOIUrl":"https://doi.org/10.1017/9781316275603.010","url":null,"abstract":"","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132431426","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}
{"title":"The Category of Sets","authors":"Hans Halvorson","doi":"10.1017/9781316275603.004","DOIUrl":"https://doi.org/10.1017/9781316275603.004","url":null,"abstract":"The aim of metatheory is to theorize about theories. For simplicity, let’s use M to denote this hypothetical theory about theories. Thus, M is not the object of our study, it is the tool we will use to study other other theories. And yet, it might be helpful to give you a sort of user’s manual for M . That’s the aim of this chapter. Let’s think about what we hope to do with M . We want to be able to talk about theories, which are supposed to be “collections of things,” or better, “structured collections of things.” In the first instance, we will think of theories as structured collections of sentences. What’s more, sentences themselves are structured collections of symbols. Fortunately, we won’t need to press the inquiry further into the question of the nature of symbols. It will suffice to assume that there are enough symbols, and that there is some primitive notion of identity of symbols. For example, I assume that you understand that “p” is the same symbol as “p”, and is different from “q”. Fortunately, much of the theory we need was worked out in previous generations. At the beginning of the 20th century, much effort was spent on formulating a theory of abstract collections (i.e. sets) that would be adequate to serve as a foundation for all of mathematics. Amazingly, the theory of sets can be formalized in predicate logic with only one symbol of non-logical vocabulary, a binary relation symbol “∈”. In the resulting first-order theory — usually called Zermelo-Frankel set theory — the quantifiers can be thought of as ranging over sets, and the relation symbol ∈ can be used to define further notions such as subset, Cartesian products of sets, functions from one set to another, etc..","PeriodicalId":427394,"journal":{"name":"The Logic in Philosophy of Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131207460","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}