{"title":"Is English consequence compact?","authors":"A. Paseau, O. Griffiths","doi":"10.1002/THT3.492","DOIUrl":null,"url":null,"abstract":"By mimicking the standard definition for a formal language, we define what it is for a natural language to be compact. We set out a valid English argument none of whose finite subarguments is valid. We consider one by one objections to the argument's logical validity and then dismiss them. The conclusion is that English — and any other language with the capacity to express the argument — is not compact. This rules out a large class of logics as the correct foundational one, for example any sound and complete logic, and in particular first-order logic. The correct foundational logic is not compact.","PeriodicalId":44963,"journal":{"name":"Thought-A Journal of Philosophy","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/THT3.492","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Thought-A Journal of Philosophy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/THT3.492","RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 2
Abstract
By mimicking the standard definition for a formal language, we define what it is for a natural language to be compact. We set out a valid English argument none of whose finite subarguments is valid. We consider one by one objections to the argument's logical validity and then dismiss them. The conclusion is that English — and any other language with the capacity to express the argument — is not compact. This rules out a large class of logics as the correct foundational one, for example any sound and complete logic, and in particular first-order logic. The correct foundational logic is not compact.
期刊介绍：
Thought: A Journal of Philosophy is dedicated to the publication of short (of less than 4500 words), original, philosophical papers in the following areas: Logic, Philosophy of Maths, Philosophy of Mind, Epistemology, Philosophy of Language, Metaphysics, and Value Theory. All published papers will be analytic in style. We intend that readers of Thought will be exposed to the most central and significant issues and positions in contemporary philosophy that fall under its remit. We will publish only papers that exemplify the highest standard of clarity. Thought aims to give a response to all authors within eight weeks of submission. Thought employs a triple-blind review system: the author''s identity is not revealed to the editors and referees, and the referee''s identity is not revealed to the author. Every submitted paper is appraised by the Subject Editor of the relevant subject area. Papers that pass to the editors are read by at least two experts in the relevant subject area.
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