Truth and Generalized Quantification*

Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All(?, ψ)—that is, All ?s are ψ—or Most(?, ψ). Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth predicate. In this paper I solve the problem by showing how Kleene's strong scheme, and Kripke's theory based on it, can in a natural way be extended to accommodate the full range of generalized quantifiers.     

Taking Degrees of Truth Seriously

This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the idea of truth degree and to some mathematical difficulties.     

A Contextual-Hierarchical Approach to Truth and the Liar Paradox

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad hoc nor unnatural.     

Jump Liars and Jourdain’s Card via the Relativized T-scheme

A relativized version of Tarski’s T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain’s card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in and only in those frames containing at least an n-jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain’s card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa. Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness. Presented by Heinrich Wansing     

Filtering Theories of Truth: Compositionality as a Criterion

The traditional way to filter out the implausible candidate solutions to the semantic paradoxes is to appeal to the so-called “cost/benefit analyses.” Yet it is often tedious and controversial to carry out such analyses in detail. Facing this, it would be helpful for us to rely upon some principles to filter out at least something, if not everything, from them. The proposal in this paper is thereby rather simple: We may use principles of compositionality as a “filter” for this purpose. The paper has four sections. In Section 2, the author uses the filter to examine Kripke’s fixed-point theory and to thereby show how it works. In Section 3, the author gives more examples from the classical theories of truth to demonstrate the power of the filter. In Section 4, the author addresses the skepticism concerning whether there is any consistent or non-trivial theory of truth that can survive this filtering procedure. A “nearly sufficient” condition for a theory of truth to survive this test is discussed in order to show that at least some consistent or non-trivial theories of truth do indeed survive the filtering procedure.     

Deflationary Truth and the Liar

Journal of Philosophical Logic -     

Modal Logic,Truth, and the Master Modality

In the paper (Braüner, 2001) we gave a minimal condition for the existence of a homophonic theory of truth for a modal or tense logic. In the present paper we generalise this result to arbitrary modal logics and we also show that a modal logic permits the existence of a homophonic theory of truth if and only if it permits the definition of a so-called master modality. Moreover, we explore a connection between the master modality and hybrid logic: We show that if attention is restricted to bidirectional frames, then the expressive power of the master modality is exactly what is needed to translate the bounded fragment of first-order logic into hybrid logic in a truth preserving way. We believe that this throws new light on Arthur Prior's fourth grade tense logic.     

Henkin Quantifiers and the Definability of Truth

Henkin quantifiers have been introduced in Henkin (1961). Walkoe (1970) studied basic model-theoretical properties of an extension L _* ¹(H) of ordinary first-order languages in which every sentence is a first-order sentence prefixed with a Henkin quantifier. In this paper we consider a generalization of Walkoe's languages: we close L _* ¹(H) with respect to Boolean operations, and obtain the language L ¹(H). At the next level, we consider an extension L _* ²(H) of L ¹(H) in which every sentence is an L ¹(H)-sentence prefixed with a Henkin quantifier. We repeat this construction to infinity. Using the (un)-definability of truth – in – N for these languages, we show that this hierarchy does not collapse. In addition, we compare some of the present results to the ones obtained by Kripke (1975), McGee (1991), and Hintikka (1996).     

The Logic of Pragmatic Truth

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed.     

语言标签和自我关联对新颖客体类别知觉的影响

类别知觉(Categorical perception)是人类最基本的认知活动之一, 探讨语言对类别知觉的影响是心理语言学领域的热门话题之一。在这个研究的3个实验中, 分别在高、低不同的语言标签表征强度下、高、低不同的客体自我关联程度下观察新颖客体类别知觉的过程。研究发现, 语言标签表征程度的增强可促进新颖客体类别知觉的右视野优势效应; 客体与自我关联程度的提高会促进左、右视野的类别知觉效应; 语言标签的表征程度和客体与自我关联程度同时增强时, 语言标签的作用依旧表现出来, 但与自我关联的影响产生权衡分配, 且其影响力并不足以产生右视野优势效应。     

The Need for Absolute Truth and Self-Rumination as Basic Suppressors in the Relationship Between Private Self-Consciousness and Mental Health

Self-reflection has not so far been shown to have any specific benefits for mental health except for self-knowledge. Recent research showed that the controversy concerning the relationship between self-reflection and mental health could completely be eliminated if self-rumination and the need for absolute truth, especially the need for absolute truth, were considered as suppressor variables. This research replicated these findings in a different sample and expanded these findings by showing that the same is true for private self-consciousness. The need for absolute truth as a new variable was shown to be highly important in understanding the effects of self-consciousness on mental health.     

Paradoxes and Failures of Cut

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning—one which takes meaning to be constituted by assertibility and deniability conditions—and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system—ST—that conservatively extends classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered and responded to.     

大学生偶发和外显编码中的自我参照效应

在自我参照范式中加入偶发编码加工方式,并采用R/K判断范式考察中国大学生在偶发编码和外显编码方式中的记忆成绩.结果发现:在R指标上,偶发编码方式和外显编码方式中均出现了自我参照效应和母亲参照效应;参照自我加工的记忆成绩显著高于参照母亲加工的记忆成绩;外显编码方式中的记忆成绩显著高于偶发编码方式的记忆成绩.结果提示,当需提高对信息的记忆成绩时,只要呈现自我线索就足够了,并不需要对其进行外显编码加工.     

On the Logical Positivists' Theory of Truth: The Fundamental Problem and a New Perspective

The present article purports to show that the protocol sentence debate, pursued by some leading members of the Vienna Circle in the mid-1930s, was essentially a controversy over the explanation and the real significance of the concept of truth. It is further shown that the fundamental issue underlying the discussions about the concept of truth was the relationship between form and content, as well as between logic/language and the world. R. Carnap was the philosopher who most explicitly and systematically attempted to come to grips with this problem. It is shown that the form-content distinction pervades the three most important phases of Carnap's philosophical development: the structuralist (in Der logische Aufbau der Welt), the syntactical and the semantical. His final semantical stance is essentially determined by the concept of linguistic frameworks. The article purports to demonstrate that this concept cannot be dispensed with in philosophy, but that Carnap failed to work out its ontological implications. Finally, the concept of an internal ontology is briefly delineated. This revised version was published online in August 2006 with corrections to the Cover Date.     

Truth Analysis of the Gettier Argument

Gettier (1963) presented the now famous Gettier problem as a challenge to epistemology. The methods Gettier used to construct his challenge, however, utilized certain principles of formal logic that are actually inappropriate for the natural language discourse of the Gettier cases. In that challenge to epistemology, Gettier also makes truth claims that would be considered controversial in analytic philosophy of language. The Gettier challenge has escaped scrutiny in these other relevant academic disciplines, however, because of its façade as an epistemological analysis. This article examines Gettier's methods with the analytical tools of logic and analytic philosophy of language.     

Courage in The Analects: A Genealogical Survey of the Confucian Virtue of Courage

The different meanings of “courage” in The Analects were expressed in Confucius’ remark on Zilu’s bravery. The typological analysis of courage in Mencius and Xunzi focused on the shaping of the personalities of brave persons. “Great courage” and “superior courage”, as the virtues of “great men” or “shi junzi 士君子 (intellectuals with noble characters)”, exhibit not only the uprightness of the “internal sagacity”, but also the rich implications of the “external kingship”. The prototype of these brave persons could be said to be between Zengzi’s courage and King Wen’s courage. The discussion entered a new stage of Neo-Confucianism in the Song and Ming dynasties, when admiration for “Yanzi’s great valor” became the key of various arguments. The order of “the three cardinal virtues” was also discussed because it concerned the relationship between “finished virtue” and “novice virtue”; hence, the virtue of courage became internalized as an essence of the internal virtuous life. At the turn of the 20th century, when China was trembling under the threat of foreign powers, intellectuals remodeled the tradition of courage by redefining “Confucius’ great valor”, as Liang Qichao did in representative fashion in his book Chinese Bushido. Hu Shi’s Lun Ru 论儒 (On Ru) was no more than a repetition of Liang’s opinion. In the theoretical structures of the modern Confucians, courage is hardly given a place. As one of the three cardinal virtues, bravery is but a concept. In a contemporary society where heroes and sages exist only in history books, do we need to talk about courage? How should it be discussed? These are questions which deserve our consideration.     

Reliability Beyond Theory and Into Practice

The critical reactions of Bentler (2009, doi:), Green and Yang (2009a, doi:; 2009b, doi:), and Revelle and Zinbarg (2009, doi:) to Sijtsma’s (2009, doi:) paper on Cronbach’s alpha are addressed. The dissemination of psychometric knowledge among substantive researchers is discussed.     

Expression,Truth, Predication,and Context: Two Perspectives

Abstract

This paper considers the challenge to understanding another that comes from the view that language is, in Cristina Lafont’s phrase, ‘world‐disclosing’. If different speakers understand and refer to the world from different holistically structured worldviews, it seems to follow that there can be no mutual understanding unless there is significant overlap between ‘worlds’. Gadamer’s hermeneutics, I claim, blocks this consequence while maintaining that language is indeed world‐disclosing. By holding that language is a medium in which the distinction between interpretation and object of interpretation is paradoxically both maintained and overcome, Gadamer shows us that the interpreter always thinks the object of interpretation as both transcending and immanent in her worldview. Mutual understanding becomes a matter of mutual recognition of such worldview‐(but not language‐) transcendent objects. Truth and meaning may on this view be characterized as ‘objective’, while retaining a significant element of relativity.