The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0009
Salvatore Florio, Øystein Linnebo
{"title":"Superplurals","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0009","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0009","url":null,"abstract":"Can the step from the singular to the plural be iterated? The resulting superplurals would have many valuable applications but are often met with skepticism. This chapter clarifies what superplural reference would be and distinguishes four grades of superplural involvement, ranging from the possibility of a superplural logic to the existence of superplurals in natural language. While the lower grades are shown to be unproblematic, the chapter provides a careful analysis of arguments for and against the higher grades, concluding, in particular, that a strong case can be made for the existence of superplurals in natural language.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131068788","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0007
Salvatore Florio, Øystein Linnebo
{"title":"The Semantics of Plurals","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0007","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0007","url":null,"abstract":"Plural logic provides an appealing framework for the regimentation of natural language plurals. However, the choice of a regimenting language leaves wide open the semantic question of how this language should be interpreted. One option is to interpret a plural term as denoting a non-empty set. Another is to embrace plurals in the metalanguage and take a plural term to have plural reference. A detailed comparison of the options reveals that there is no simple solution to the problem of choosing among them.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122893886","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0004
Salvatore Florio, Øystein Linnebo
{"title":"Plurals and Set Theory","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0004","url":null,"abstract":"What is the relation between some things and their set? This chapter begins with a formal comparison of plural logic and set theory, which clarifies an important technical aspect of the question. The chapter then turns to more philosophical issues, investigating whether pluralities should be eliminated in favor of sets or vice versa. Both attempted eliminations are rejected in favor of a view, inspired by Cantor, that retains both pluralities and sets, using the former to provide a metaphysical account of the latter.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"332 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115869252","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0011
Salvatore Florio, Øystein Linnebo
{"title":"Absolute Generality and Singularization","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0011","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0011","url":null,"abstract":"Is it possible to assert something of absolutely everything there is? While such absolute generality appears possible, it faces serious theoretical challenges. This chapter examines one such challenge, based on the possibility of one-to-one mappings from pluralities to objects. The challenge gives rise to a trilemma. First, generality relativists deny the possibility of absolute generality, at the cost of being unable to express various important insights. Second, traditional generality absolutists deny the possibility of the mentioned mappings, but are pushed up a hierarchy of logics of higher and higher order, resulting in an expressibility deficit akin to that of the relativists. This motivates taking a closer look at the third option, which restricts traditional plural logic.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131340611","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0006
Salvatore Florio, Øystein Linnebo
{"title":"Plurals and Second-Order Logic","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0006","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0006","url":null,"abstract":"While plural logic can be interpreted in monadic second-order logic, the full system of second-order logic cannot be interpreted in plural logic. This means it is formally possible to eliminate plural logic in favor of monadic second-order logic. However, a number of philosophical considerations militate against such an elimination. The conclusion of this chapter echoes that of the preceding ones: although the two systems can occasionally be used for similar purposes, the notions they represent are different and must be kept apart.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125050285","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0003
Salvatore Florio, Øystein Linnebo
{"title":"The Refutation of Singularism?","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0003","url":null,"abstract":"Traditional analyses of plurals tended to eliminate plural expressions in favor of singular ones. These “singularist” analyses have recently faced many objections, which are intended to provide indirect support for the alternative analysis provided by plural logic. This chapter evaluates four such objections and concludes that they are less compelling than is often assumed. This conclusion is borne out by a close examination of various plural versions of Cantor’s theorem.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121989327","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0012
Salvatore Florio, Øystein Linnebo
{"title":"Critical Plural Logic","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0012","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0012","url":null,"abstract":"This chapter develops and motivates an alternative, more critical plural logic, thus exploring the third horn of the trilemma from the previous chapter. First, a liberal view of mathematical definitions is defended, according to which any objects can be used to define a set. This entails that the traditional plural comprehension scheme needs to be restricted. Some successor principles are then formulated on the basis of the idea that any plurality needs to be circumscribed. Finally, the resulting critical plural logic is shown to give rise to a natural and elegant approach to set theory.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124453910","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}
The Many and the OnePub Date : 2021-07-22DOI: 10.1093/oso/9780198791522.003.0002
Salvatore Florio, Øystein Linnebo
{"title":"Taking Plurals at Face Value","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1093/oso/9780198791522.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198791522.003.0002","url":null,"abstract":"Plural logic is a logical system in which plural terms and predicates figure as primitive expressions alongside the singular resources of ordinary first-order logic. The philosophical significance of this system depends on two of its alleged features: being pure logic and providing more expressive power than first-order logic. This chapter first introduces the language and axioms of plural logic and then analyzes this logic’s main philosophical applications in metaphysics, philosophy of mathematics, and semantics.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133413898","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":"On the Innocence and Determinacy of Plural Quantification","authors":"Salvatore Florio, Øystein Linnebo","doi":"10.1111/NOUS.12091","DOIUrl":"https://doi.org/10.1111/NOUS.12091","url":null,"abstract":"Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. Both assumptions are problematic, as is shown by providing a Henkin-style semantics for plural logic that does not resort to sets but takes a plural term to have plural reference. This semantics gives rise to a generalized notion of ontological commitment, which is used to develop some ideas of earlier critics of the alleged ontological innocence of plural logic.","PeriodicalId":232985,"journal":{"name":"The Many and the One","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129867548","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}
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