Knowledge, proof and the Knower

Walter Dean, Hidenori Kurokawa
{"title":"Knowledge, proof and the Knower","authors":"Walter Dean, Hidenori Kurokawa","doi":"10.1145/1562814.1562828","DOIUrl":null,"url":null,"abstract":"The Knower Paradox demonstrates that any theory <i>T</i> which 1) extends Robinson arithmetic <i>Q</i>, 2) includes a predicate <i>K</i>(<i>x</i>) intended to formalize \"the formula with godel number <i>x</i> is known by agent <i>i</i>,\" and 3) contains certain elementary epistemic principles involving <i>K</i>(<i>x</i>) is inconsistent. The purpose of this paper is to show how this paradox may be redeveloped within a system of quantified explicit modal logic in the tradition of Artemov [4] and Fitting [10], [11] which we argue allows for a more faithful formulation of some of the epistemic principles on which it is based. Along the way, we isolate a principle -- the so-called Uniform Barcan Formula [UBF] -- which we show is required to derive an explicit counterpart of the axiom <b>U</b> (i.e. <i>K</i>(⌜<i>K</i>(⌝φ⌍) → φ⌍)) which was used in the original formulation of the Paradox. We argue that since there are independent epistemic reasons to be suspicious of UBF, the paradox may be resolved by abandoning this principle (and thereby <b>U</b> as well).","PeriodicalId":118894,"journal":{"name":"Theoretical Aspects of Rationality and Knowledge","volume":"16 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Aspects of Rationality and Knowledge","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1562814.1562828","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6

Abstract

The Knower Paradox demonstrates that any theory T which 1) extends Robinson arithmetic Q, 2) includes a predicate K(x) intended to formalize "the formula with godel number x is known by agent i," and 3) contains certain elementary epistemic principles involving K(x) is inconsistent. The purpose of this paper is to show how this paradox may be redeveloped within a system of quantified explicit modal logic in the tradition of Artemov [4] and Fitting [10], [11] which we argue allows for a more faithful formulation of some of the epistemic principles on which it is based. Along the way, we isolate a principle -- the so-called Uniform Barcan Formula [UBF] -- which we show is required to derive an explicit counterpart of the axiom U (i.e. K(⌜K(⌝φ⌍) → φ⌍)) which was used in the original formulation of the Paradox. We argue that since there are independent epistemic reasons to be suspicious of UBF, the paradox may be resolved by abandoning this principle (and thereby U as well).
知识,证据和知者
知者悖论证明,任何理论T, 1)扩展罗宾逊算术Q, 2)包含一个谓词K(x),旨在形式化“具有哥德尔数x的公式为智能体i所知”,3)包含涉及K(x)的某些基本认知原则是不一致的。本文的目的是展示如何在传统的Artemov[4]和Fitting[10]的量化显式模态逻辑系统中重新发展这一悖论,我们认为这允许对其所基于的一些认知原则进行更忠实的表述。在此过程中,我们分离出一个原理——所谓的统一巴尔肯公式[UBF]——我们证明需要它来推导出公理U的显式对应(即K(K(⌍)→φ⌍)),该公理在悖论的原始公式中使用。我们认为,由于存在独立的认知理由来怀疑UBF,因此可以通过放弃这一原则(因此也可以放弃U)来解决悖论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
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