{"title":"An Update of Tarski: Two Usages of the Word “True”","authors":"Zhen Zhao","doi":"10.1007/s10849-022-09360-3","DOIUrl":null,"url":null,"abstract":"<p>This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, we do not need the hierarchy of languages. The truth predicate is mainly used for grammatical function. Tarski’s schema of the truth predicate is not necessary in this proposal. The schema of the word \"true\" is the schema of the truth operator. The liar paradox (and its cousins) can be solved in this way. In the appendix, I show a consistent model for both of the truth predicate and the truth operator.\n</p>","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"29 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic Language and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10849-022-09360-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, we do not need the hierarchy of languages. The truth predicate is mainly used for grammatical function. Tarski’s schema of the truth predicate is not necessary in this proposal. The schema of the word "true" is the schema of the truth operator. The liar paradox (and its cousins) can be solved in this way. In the appendix, I show a consistent model for both of the truth predicate and the truth operator.
期刊介绍：
The scope of the journal is the logical and computational foundations of natural, formal, and programming languages, as well as the different forms of human and mechanized inference. It covers the logical, linguistic, and information-theoretic parts of the cognitive sciences.
Examples of main subareas are Intentional Logics including Dynamic Logic; Nonmonotonic Logic and Belief Revision; Constructive Logics; Complexity Issues in Logic and Linguistics; Theoretical Problems of Logic Programming and Resolution; Categorial Grammar and Type Theory; Generalized Quantification; Information-Oriented Theories of Semantic Structure like Situation Semantics, Discourse Representation Theory, and Dynamic Semantics; Connectionist Models of Logical and Linguistic Structures. The emphasis is on the theoretical aspects of these areas.
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