克林强三值模式与修正过程

真之修正理论主要在经典二值模式下展开修正过程,但这种过程同时也兼容非经典赋值模式。本文在克林强三值这一典型的非经典赋值模式下规定修正过程,并利用这种过程对带真谓词的语句尤其是悖论语句进行了分析。由此给出了这些语句的一个更多样化的分类。这表明克林强三值赋值下的修正理论不但是一个包容性更强的修正理论,而且还为古普塔提出的真谓词的描述性问题提供了一个更全面的解决方案。     

公理化真与说谎者悖论

公理化真理论把真看作一个原始谓词,并用一组公理和规则给出真谓词的意义,真首先是语形概念。在公理化真理论的标准模型中,一个定理可解释为真。因此模型真和语形真在概念上需要作出区分。通过不同的技术手段大部分公理化真理论都能较好地处理悖论,但DT和KF系统同时证明"说谎者语句λ"与"λ不是真的",此时语形真和模型真产生了冲突。莫德林和费弗曼等国外学者从哲学解释或技术上对此进行的辩护都存在不足之处,本文通过从语义视角入手建立起一种真对应关系后指出,这一受到质疑的结论既不应归结为形式技术问题,不是一个意外的推论,也不必从其他哲学角度进行辩护,问题是由克里普克语义真理论自身在处理强化说谎者悖论时失效所导致的。KF系统两种真的冲突,反而以形式方法揭示了当内、外逻辑不一致时,真理论所具有的性质。     

以谓词表达模态

以谓词表达模态,在表达力上比算子具有更明显的优势,但蒙塔古悖论和语义的不完善曾使模态谓词遭遇技术困境。采用"模态"与"真"相结合的研究策略,不仅可以在语形上利用真谓词限制模态谓词的表达力实现模态谓词的相容性,亦能在语义上借助语义真理论定义模态谓词的可能世界语义学。因此,以谓词表达模态可以促进模态逻辑的研究,实现各种模态概念与真概念的结合,体现真概念在逻辑研究中的基础性地位。     

邻域语义与修正真理论

古普塔和赫兹伯格在1982年各自独立地提出了修正真理论,建立了可用于分析真与相关悖论的修正序列。修正真理论根据语句在所有修正序列中的表现,对语句进行分类。然而,修正真理论在某些语句的分类上不能令人满意,如修正真理论把柯瑞悖论的逆命题断定为绝对地真,这与直觉不一致。本文将从两种路径引入邻域语义研究修正真理论。路径一是在基模型上引入邻域基模型,建立邻域基模型修正序列。这类修正序列比经典修正序列更多,增加的修正序列可使包括柯瑞悖论的逆命题在内的一些语句的病态呈现出来。路径二是通过引入邻域语义模型,使得对任意不含模态词的公式φ,模态公式□φ在后继阶段的真值可以反映φ在上一阶段的真值,并且□φ在极限阶段的真值可以反映φ在至这个极限阶前是否稳定真。从而可以通过□φ的真值来限定Tφ的真值,使得满足相应限制的模型类表示了相应的修正序列。本文最后将对两个路径进行整合,构造出能表示邻域基模型修正序列的整体修正序列模型。     

说谎者悖论的一个新解决方案的纲要(英文)

首先,本文在第二节中提出了谎者悖论所包含的一些问题,比如加强的说谎者悖论,Curry悖论,Yablo悖论,偶然的说谎者悖论,以及塔尔斯基的真不可定义性定理。其次,在第三节简单介绍了塔尔斯基的分层理论,并且指出了他方案的一个最大不足之处就是把一个真谓词分成了很多个个真谓词,这和我们的直观很不符合。之后在第四节介绍了我的一个解悖方案,并讨论了它的一些性质,比如可靠性,完全性,以及我的方案和塔尔斯基方案的区别。第五节说明了第二节中提到的一些问题在我的这个方案下如何处理。     

悖论,类型论以及解救悖论的其它方法(续)

罗素的观点看来是主张,类型论提供了避免一切悖论的方法,此外类型论在本质上还是这种方法的理论基础。让我们依次来考虑这两点。晚近的作者在所谓“语义悖论”和集合论悖论之间作出了区分,而罗素没有这样做。埃匹曼尼德悖论被称为语义悖论,因为它在本质上涉及到真的概念(谎话是不真的);并且“真”被称作一种语义关系,因为它是     

当代形式真理论中不动点方法和修正方法的比较研究

当代形式真理论试图寻求恰当的模型来刻画真谓词,在克里普克之后,不动点方法及其修正方法是最主要的两种方法,这两种方式表面上大相径庭,应用时所获得的理论也大不一样。然而,通过对不动点方法、修正方法的比较和对比,本文试图说明这两种方法在最根本的特征上是一致的。这种一致性主要体现在两种方法都是通过叠置地构建模型序列刻画真谓词,这契合人们对真理的认识过程,是不动点方法和修正方法在过去四十年具有强大生命力的根本原因。     

说谎者悖论及其相关悖论的一种解决

依本文之见,说谎者悖论以及某些与之相关的悖论之被导出源于对某些不合理的前提的接受;而这些前提之被接受又源于对＂是真的＂与＂是假的＂这两个词的关键语义特性缺乏认识。本文为决定这些语义特性的基础提供了说明;这一基础包含两个论点,第一,每一语句均有其含义;第二,每一语句陈说的字面内容是一个命题态度的内容,因而具有某种一般形式。借助于这一基础,本文为这两个词构造了一个不同于传统意义上的塔尔斯基式真理理论的意义理论以说明这些特性,并借助于该理论论证说谎者悖论及其某些相关悖论的导出没有根据。     

面向认知冲突的弗协调置信逻辑

若限制一般意义的矛盾律,就会得到一种非亚氏(non-Aristotelian)逻辑,即弗协调(paraconsistent)逻辑。以弗协调逻辑系统C1为基础,对之进行语法和语义扩张,即可得到弗协调置信逻辑系统C1D。这种特殊的认知逻辑可以容忍认知冲突,若以之为基础逻辑,知识或信念的暂时不协调将不会导致逻辑上的无意义(不足道)。基于该系统的特异逻辑性质,相信一个陈述及其否定在逻辑上将变得并非不可能。该系统作为处理悖论的容悖路径,尽管在实质上没有排除掉悖论,但在那些认知悖论彻底解决之前,却可为理性认知提供一个可靠的逻辑基础。     

真与悖论的逻辑分析:从目的论解释到定量描述

根据克莱因观点,近代科学的兴起源于伽利略在研究目标上的一个新设定:对科学现象获得独立于目的论解释的定量描述。本文论证了同样精神的目标设定正发生在真理论领域。塔斯基、克里普克、弗里德曼和谢尔德的真理论以消除悖论为基本目的是典型的目的论解释性理论,而古普塔和赫兹伯格的真理论则通过悖论的周期性特征把定量分析引入到悖论的研究之中。而对悖论的矛盾性刻画把定量描述引向深入。本文呈现了现代真理论的这一变革进程,预示了真理论的发展方向。     

真值条件内容非实在论

错误论和非事实论是用语义方式表述的两种不同形态的非实在论,当中涉及"真"、"假"、"指称"、"真值条件"这样的语义概念。布高西昂认为,针对真值条件内容概念的错误论和非事实论是内在地不一致的,从而可以先验地予以拒绝。本文详细分析布高西昂的论证,揭示其论证的缺陷,以及分析布高西昂与其批评者达维特之间的争议,消除他们对用于表述非实在论的语义概念的误解,尝试为真值条件内容非实在论给出一致的表述。     

What Truth Depends on

What kinds of sentences with truth predicate may be inserted plausibly and consistently into the T-scheme? We state an answer in terms of dependence: those sentences which depend directly or indirectly on non-semantic states of affairs (only). In order to make this precise we introduce a theory of dependence according to which a sentence φ is said to depend on a set Φ of sentences iff the truth value of φ supervenes on the presence or absence of the sentences of Φ in/from the extension of the truth predicate. Both φ and the members of Φ are allowed to contain the truth predicate. On that basis we are able define notions such as ungroundedness or self-referentiality within a classical semantics, and we can show that there is an adequate definition of truth for the class of sentences which depend on non-semantic states of affairs.     

Gödelizing the Yablo Sequence

We investigate what happens when ‘truth’ is replaced with ‘provability’ in Yablo’s paradox. By diagonalization, appropriate sequences of sentences can be constructed. Such sequences contain no sentence decided by the background consistent and sufficiently strong arithmetical theory. If the provability predicate satisfies the derivability conditions, each such sentence is provably equivalent to the consistency statement and to the Gödel sentence. Thus each two such sentences are provably equivalent to each other. The same holds for the arithmetization of the existential Yablo paradox. We also look at a formulation which employs Rosser’s provability predicate.     

Accepting inconsistencies from the paradoxes

It has been proposed that the law of non-contradiction be revised to permit the simultaneous truth and falsity of the key sentences of the logical paradoxes, e.g., This sentence is false. In an attempt to show to what extent this bizarre suggestion of inconsistent models or truth-value gluts is a coherent suggestion it is proved that a first-order language for number theory can be semantically closed by having its own global truth predicate under some non-standard interpretation and thus that it actually can contain the Liar sentence. It is proved that in this interpretation the Liar sentence is both true and false, although not every sentence is.     

Fuzzy Logic and Arithmetical Hierarchy III

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satisfiable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated.     

Truth as Translation – Part B

This is the second part of a paper dealing with truth and translation. In Part A a revised version of Tarski's Convention T has been presented, which explicitly refers to a translation mapping from the object language to the metalanguage; the vague notion of a translation has been replaced by a precise definition. At the end of Part A it has been shown that interpreted languages exist, which allow for vicious self-reference but which nevertheless contain their own truth predicate – this is possible if truth is based on a nonstandard translation mapping. However, this result has only been proved for languages without quantifiers. In Part B we now extend the result to first-order languages, and we show that this can be done in three different ways. In each case, the addition of a truth predicate to an interpreted language with a high degree of expressiveness leads to changes in the ontology of the language.     

Probability for the Revision Theory of Truth

Journal of Philosophical Logic - We investigate how to assign probabilities to sentences that contain a type-free truth predicate. These probability values track how often a sentence is satisfied...     

Reasoning with Truth

The aim of the paper is to formulate rules of inference for the predicate 'is true' applied to sentences. A distinction is recognised between (ordinary) truth and definite truth and consequently between two notions of validity, depending on whether truth or definite truth is the property preserved in valid arguments. Appropriate sets of rules of inference governing the two predicates are devised. In each case the consequence relation is in harmony with the respective predicate. Particularly appealing is a set of ND rules for ordinary truth in which premises and assumptions play different roles, premises being taken to assert definite truth, assumptions to suppose truth. This set of rules can be said to capture everyday reasoning with truth. Also presented are formal characterisations, in the meta-language and in the object language, of paradoxical and 'truth teller'-like sentences.     

An Intensional Theory of Truth: An Informal Report

Saul Kripke’s theory of truth suffers from expressive limitations – in particular, there are no extensional operators within that framework that allow one to characterize those sentences that fail to receive a truth value within the framework. Especially worrisome is the fact that there is no operator that outputs true on exactly the paradoxical sentences. In this paper I extend Kripke’s approach via the addition of extensional operators, which allows us to characterize many (but not all) such sentences, including the paradoxical ones.     

Relative truth and the first person

In recent work on context-dependency, it has been argued that certain types of sentences give rise to a notion of relative truth. In particular, sentences containing predicates of personal taste and moral or aesthetic evaluation as well as epistemic modals are held to express a proposition (relative to a context of use) which is true or false not only relative to a world of evaluation, but other parameters as well, such as standards of taste or knowledge or an agent. I will argue that the sentences that apparently give rise to relative truth should be understood by relating them in a certain way to the first person. More precisely, such sentences express what I will call ‘first-person-based genericity’, a form of generalization that is based on an essential first-person application of the predicate. The account differs from standard relative truth account in crucial respects: it is not the truth of the proposition expressed that is relative to the first person; the proposition expressed by a sentence with a predicate of taste rather has absolute truth conditions. Instead it is the propositional content itself that requires a first-personal cognitive access whenever it is entertained. This account, I will argue, avoids a range of problems that standard relative truth theories of the sentences in question face and explains a number of further peculiarities that such sentences display.