论古典确定真理

Luca Castaldo, Carlo Nicolai
{"title":"论古典确定真理","authors":"Luca Castaldo, Carlo Nicolai","doi":"arxiv-2409.04316","DOIUrl":null,"url":null,"abstract":"{The paper studies classical, type-free theories of truth and\ndeterminateness. Recently, Volker Halbach and Kentaro Fujimoto proposed a novel\napproach to classical determinate truth, in which determinateness is\naxiomatized by a primitive predicate. In the paper we propose a different\nstrategy to develop theories of classical determinate truth in Halbach and\nFujimoto's sense featuring a \\emph{defined} determinateness predicate. This\nputs our theories of classical determinate truth in continuity with a standard\napproach to determinateness by authors such as Feferman and Reinhardt. The\ntheories entail all principles of Fujimoto and Halbach's theories, and are\nproof-theoretically equivalent to Halbach and Fujimoto's CD+. They will be\nshown to be logically equivalent to a class of natural theories of truth, the\n\\emph{classical closures of Kripke-Feferman truth}. The analysis of the\nproposed theories will also provide new insights on Fujimoto and Halbach's\ntheories: we show that the latter cannot prove most of the axioms of the\nclassical closures of Kripke-Feferman truth. This entails that, unlike what\nhappens in our theories of truth and determinateness, Fujimoto and Halbach's\n\\emph{inner theories} -- the sentences living under two layers of truth --\ncannot be closed under standard logical rules of inference.}","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Classical Determinate Truth\",\"authors\":\"Luca Castaldo, Carlo Nicolai\",\"doi\":\"arxiv-2409.04316\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"{The paper studies classical, type-free theories of truth and\\ndeterminateness. Recently, Volker Halbach and Kentaro Fujimoto proposed a novel\\napproach to classical determinate truth, in which determinateness is\\naxiomatized by a primitive predicate. In the paper we propose a different\\nstrategy to develop theories of classical determinate truth in Halbach and\\nFujimoto's sense featuring a \\\\emph{defined} determinateness predicate. This\\nputs our theories of classical determinate truth in continuity with a standard\\napproach to determinateness by authors such as Feferman and Reinhardt. The\\ntheories entail all principles of Fujimoto and Halbach's theories, and are\\nproof-theoretically equivalent to Halbach and Fujimoto's CD+. They will be\\nshown to be logically equivalent to a class of natural theories of truth, the\\n\\\\emph{classical closures of Kripke-Feferman truth}. The analysis of the\\nproposed theories will also provide new insights on Fujimoto and Halbach's\\ntheories: we show that the latter cannot prove most of the axioms of the\\nclassical closures of Kripke-Feferman truth. This entails that, unlike what\\nhappens in our theories of truth and determinateness, Fujimoto and Halbach's\\n\\\\emph{inner theories} -- the sentences living under two layers of truth --\\ncannot be closed under standard logical rules of inference.}\",\"PeriodicalId\":501306,\"journal\":{\"name\":\"arXiv - MATH - Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.04316\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.04316","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

{本文研究经典的无类型真理论和确定性理论。最近,沃尔克-哈尔巴赫(Volker Halbach)和藤本健太郎(Kentaro Fujimoto)提出了一种新颖的经典确定性真理方法,其中确定性被一个基元谓词消解了。在本文中,我们提出了一种不同的策略来发展哈尔巴赫和藤本意义上的经典确定性真理理论,其特点是一个(emph{defined}确定性谓词。这就使我们的经典确定性真理理论与费弗曼和莱因哈特等学者的确定性标准方法一脉相承。这些理论包含了藤本和哈尔巴赫理论的所有原则,并且在理论上等同于哈尔巴赫和藤本的 CD+。它们将被证明在逻辑上等同于一类自然的真理理论,即克里普克-费弗曼真理的经典闭包(the/emph{classical closures of Kripke-Feferman truth})。对所提理论的分析也将为藤本和哈尔巴赫的理论提供新的见解:我们证明后者无法证明克里普克-费弗曼真理的经典闭包的大部分公理。这就意味着,与我们的真理和确定性理论中的情况不同,藤本和哈尔巴赫的(emph{inner)理论--生活在两层真理之下的句子--无法在标准的逻辑推理规则下封闭。}
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Classical Determinate Truth
{The paper studies classical, type-free theories of truth and determinateness. Recently, Volker Halbach and Kentaro Fujimoto proposed a novel approach to classical determinate truth, in which determinateness is axiomatized by a primitive predicate. In the paper we propose a different strategy to develop theories of classical determinate truth in Halbach and Fujimoto's sense featuring a \emph{defined} determinateness predicate. This puts our theories of classical determinate truth in continuity with a standard approach to determinateness by authors such as Feferman and Reinhardt. The theories entail all principles of Fujimoto and Halbach's theories, and are proof-theoretically equivalent to Halbach and Fujimoto's CD+. They will be shown to be logically equivalent to a class of natural theories of truth, the \emph{classical closures of Kripke-Feferman truth}. The analysis of the proposed theories will also provide new insights on Fujimoto and Halbach's theories: we show that the latter cannot prove most of the axioms of the classical closures of Kripke-Feferman truth. This entails that, unlike what happens in our theories of truth and determinateness, Fujimoto and Halbach's \emph{inner theories} -- the sentences living under two layers of truth -- cannot be closed under standard logical rules of inference.}
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信