悖论可同时兼含“两类矛盾”吗?——兼评黄展骥先生的悖论观

逻辑矛盾、辩证矛盾是两类根本不同的矛盾,这在学术界似乎已成定论。然而,悖论是什么?它内含什么矛盾?这些问题在悖论研究中迄今尚未取得共识。黄展骥先生在《悖论内含什么“矛盾”?》一文中对此做了评述,并提出了自己的观点。笔者认为,黄先生关于悖论可同时兼含“两类矛盾”的观点,是不能成立的。他在论述中出现的逻辑混乱,既与混淆悖论和其他两类矛盾有关,又与他没有分开悖论的矛盾归属和悖论的构成问题有关。下面,先指出黄先生论述中不应有的混乱及产生这一混乱的原因,然后论述悖论的矛盾归属和它的构成问题。 一、不应该出现的逻辑混乱。黄先生认为,“‘悖论’是极殊的逻辑矛盾(甲)而非辩证     

认证悖论和绿蓝悖论

“悖论”(Paradox)一词是有岐义的。在关于演绎逻辑的讨论中,悖论是指一种特殊的逻辑矛盾,即:从命题A可推出非A.从非A又可推出A。但在关于归纳逻辑的讨论中,悖论不仅包括一切逻辑矛盾,而且包括那些与人们的直觉或常识相违的推论亦即怪论。这种广义的悖论在归纳逻辑中是为数不少的,其中最基本的并且至今悬而未决的悖论包括认证悖论和绿蓝悖论。下面我们分别介绍这两个归纳悖论。一、认证悖论认证悖论(the Paradoxes of Confirmation)是由著名逻辑学家和科学哲学家亨佩尔(CarlG.Hem. Pel)于1937年首先提出,以后他又在“认证逻辑研究”(即[1],此文最早发表于1945年)和     

两类有代表性的悖论——悖论漫谈之二

悖论从形态上可分为两类,即逻辑悖论与语义悖论。罗素不赞成把悖论划分为两类,因为他认为所有悖论的产生都是同一种错误的结果,即都是由于违反“恶性循环原则”(一个“集合”自身必不是这个“集合”的元素)而造成的。他的观点不是没有道理的,从悖论的特征及其形成的深层原因看,确实这种划分并不重要。但是这种划分又是可能的;逻辑悖论导致了集合论的发展,而语义悖论则导致了语义学的发展。     

关于中国逻辑史是否应当是中国形式逻辑史的一场争论

在1980年的中国逻辑史第一次学术讨论会上,曾就中国逻辑史的对象和范围进行了讨论。当时大家除对辩证逻辑的性质持有不同意见外,一致承认中国古代有相当丰富的属于(传统)形式逻辑范围的思想和理论,中国逻辑史应当主要是中国形式逻辑思想发展史。因此,大家一致同意以形式逻辑为范围选编一部《中国逻辑史资料选》(五卷本),并在此基础上开始编写一部《中国逻辑史》(五卷本)。现在这两大部著作都早已完稿,著作已经出版,资料亦将出齐。这两年来,由于国外有关“非形式逻辑”、“内涵逻辑”、“语义学”新概念、新观点的进一步引入,一些同志在中国逻辑史的对象和范围问题上提出了不同的。等解和论点,从而引起了一场关于中国逻辑史是否应当是中国形式逻辑思想发展史的争论,理其中主要有三种不同的观点:(1)“非形式逻辑史”;(2)“语义学史”或“古汉语语义学史”     

中国古代典籍中有严格悖论吗?

讨论严格悖论之有无,首先需明确“严格悖论”的涵义。悖论在自然语言中是一个多义词,某些似是而非或似非而是的论点,与通常见解相对立的论证,思维中出现的各种疑难,乃至某些普通的自相矛盾的话语,都曾被人们称为“悖论”。严格意义上的悖论有二个特征:(1)语义特征:同一命题(在一定背景知识下)的真假互推,或者说真值相反的矛盾命题之     

国内悖论研究概述

悖论作为一种特殊的思维矛盾,几乎涉及抽象科学理论的每个领域。由于逻辑、数学、语言学和哲学,以及某些现代科学(如一般系统论、量子力学、相对论等)都是抽象程度较高的理论,它们在不同方面、不同层次、不同程度上均涉及对人类思维本性的研究,因而,在这些科学理论体系中就相继出现了悖论。然而,把悖论作为一个相对独立的范畴进行研究,一直是逻辑界和数学界争论不休的哲学问题。在国外,悖论研究已有八十多年的历史。值得介绍的理论有:罗素的“类型论”、塔尔斯基的“语言层次论”、哥德尔的“不完全性定理”、赫兹贝格的“朴素语义学”、雷歇尔和布兰登的“不协调逻辑”、普里斯特和罗特列的“超协调逻辑”,等等。在国內,近些年来有的同志已经开始对悖论进行思考和研究,现将有关理论问题概述如下。     

悖论内含什么“矛盾”?——“逻辑”、“辩证”还是“中介”矛盾

“悖论”是什么?它就是挑战(或违背)常识的“大”理。所谓“挑战”,就有“矛盾”存在。所谓“矛盾”,当然是指“逻辑矛盾”:某一属性既属于同时又不属于同一对象。 这个简朴的“悖论”定义,比日常理解(和普遍辞典)只多添一个“大”字。无论是我这个定义,还是历来的绝大多数的权威定义,都认定“矛盾”就是“逻辑矛盾”,所以不时都可以省略“逻辑”一词,只不过,大家都认为,悖论不是普通的矛盾,而是一种“特殊”的矛盾。我要补充的是,     

我国在校青少年逻辑推理能力发展的研究

思维的研究是一个十分重要的问题。尽管心理学家们早就“以为逻辑的法则就是思想的法则,思想的历程也象三段论法的历程那么明朗。”然而,长期来终因研究方法上的推论多于实验、瞑想代替观察、而使其在心理学的大殿中徘徊不前。直到本世纪的六十年代,日内瓦学派针对符茨堡学派“思维是逻辑的一面镜子”的论点,在其大量实验数据的基础上提出了“逻辑是思维的一面镜子”的观点以后,从逻辑思维的发展,进行青少年思维能力变化的研究,受到了人们普遍的关注和重视。     

说谎者悖论的恶性循环

一、引论承袭彭加勒的思想,罗素提出:“所有的悖论都源自于这样的事实,指称某个类的整体的表达式自身又表示这个类中某个元素。”(Russell,p.101)这便是被后人称为悖论根源于“循环”的思想。这一思想对悖论———尤其是语义悖论———后来的研究产生了重要影响:在诸多处理语义     

艾勒悖论(Allais Paradox)另释

艾勒悖论违背了期望效用(Expected Utility)理论的独立性(independence)原则,成为欲推翻期望效用理论的杠杆。“齐当别”抉择模型不将风险决策行为看成是追求某种“最大期望值”的抉择反应,而将其看成是“最好可能结果之间的取舍”或者“最坏可能结果之间的取舍”。此项研究设计了一“判断”技术,并用此对艾勒设计的选择问题加以检验。实验表明,判断结果所示的“齐当别”策略能满意地对艾勒选择题作出解释。     

Anti-realism and Epistemic Accessibility

I argue that Fitch’s ‘paradox of knowability’ presents no special problem for the epistemic anti-realist who believes that reality is epistemically accessible to us. For the claim which is the target of the argument (If p then it is possible to know p) is not a commitment of anti-realism. The epistemic anti-realist’s commitment is (or should be) to the recognizability of the states of affairs which render true propositions true, not to the knowability of the propositions themselves. A formal apparatus for discussing the recognizability of states of affairs is offered, and other prima facie similar approaches to the paradox argument are reviewed.     

The Logic of Group Decisions: Judgment Aggregation

Judgment aggregation studies how individual opinions on a given set of propositions can be aggregated to form a consistent group judgment on the same propositions. Despite the simplicity of the problem, seemingly natural aggregation procedures fail to return consistent collective outcomes, leading to what is now known as the doctrinal paradox. The first occurrences of the paradox were discovered in the legal realm. However, the interest of judgment aggregation is much broader and extends to political philosophy, epistemology, social choice theory, and computer science. The aim of this paper is to provide a concise survey of the discipline and to outline some of the most pressing questions and future lines of research.     

Making Sense of Truth-Makers

This essay argues that propositions are made true by facts. A proposition is the sense expressed by a statement (sentence token used to make a truth claim). Facts are positive or negative constitutive properties of the domain of discourse (usually the actual world). The presence of horses is a positive constitutive property of the world; the absence of unicorns is a negative one. This notion of constitutive properties accords well with the Hume-Kant claim that existence is not a property of any individual said to exist. While Frege held existence to be a property of concepts and Russell held it to be a property of propositional functions, our view sees existence as a property of a domain of discourse. To say that Native Dancer exists is simply to say that the world is characterized by the presence of Native Dancer; to say that Pegasus does not exist is to say the world is characterized by the absence of Pegasus. Such properties of presence and absence are facts. Facts make true propositions true; nothing makes false propositions false (they simply fail to be made true). Facts are not items in the world; they are (constitutive) properties of the world.     

Moore's Paradox and the Structure of Conscious Belief

Propositions such as are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore's paradox. Sydney Shoemaker has recently argued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker's own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account is the claim that conscious beliefs are always partly about themselves; it will be shown to follow from this that conscious beliefs in Moorean propositions are self-contradictory.     

A defense of middle knowledge

Conclusion Adams has not demonstrated that conditionals of freedom are necessarily false, just as I have not demonstrated that they are possibly true. According to Adams, we have good reason to think that they are not possibly true because we do not know what it is for them to be true. This is basically the claim that we cannot explain conditionals of freedom without reference to what would happen in certain situations. I argued that similar considerations apply to propositions about future free choices. We cannot explain propositions about future free choices without reference to what will happen. Neither conditionals of freedom nor propositions about future free choices are true in virtue of corresponding to actual states of affairs or any states of affairs that are necessitated by certain other states of affairs. In both instances we must appeal to states of affairs that are not determined to be actual by either the present states of affairs or the antecedent of the counterfactual. I do not consider this difficulty with propositions about future free choices to be a sufficient reason to reject the possibility of them being true. They are true because they correspond to what will happen. But then I also do not believe that Adams' reasons are sufficient to reject the possibility of true conditionals of freedom. They are true because they correspond with what would happen in certain counterfactual situations. Hence it is no more difficult to understand what it is for conditionals of freedom to be true than it is to understand what it is for propositions about future free choices to be true. I conclude that, contrary to Adams, it is possible for God to have middle knowledge.     

A Classical Prejudice?

In this paper, I reassess Floridi’s solution to the Bar-Hillel–Carnap paradox (the information yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions) and that, unless we accept the additional non-falsity thesis (information cannot be false), there is no reason to presuppose that there is no such thing like contradictory information.     

Deutscher's problem is not Popper's problem

The so-called knowability paradox results from Fitch's argument that if there are any unknown truths, then there are unknowable truths. This threatens recent versions of semantical antirealism, the central thesis of which is that truth is epistemic. When this is taken to mean that all truths are knowable, antirealism is thus committed to the conclusion that no truths are unknown. The correct antirealistic response to the paradox should be to deny that the fundamental thesis of the epistemic nature of truth entails the knowability of all truths. Correctly understood, the antirealistic conditions on a proposition's truth do not require that the proposition possess a verification-procedure which, when executed under the given conditions, issues in an agent's recognition of truth, but merely that there be a verification-procedure which, under these conditions, takes the value true. The knowability paradox and the related idealism problem (that antirealism seems, but is not, committed to the necessary existence of an epistemic agent) draw attention to the fact that certain propositions, those that are about verification-procedures themselves, may under certain conditions take the value true despite their unperformability under these circumstances. Thus these propositions' procedures can only be performed when the propositions are false, and they gain the appearance of antirealistic impossibility (e.g., that there is an unknown truth). This differs from the unperformability that antirealists object to, pertaining merely to matters of execution rather than to the logical structure of the procedures themselves. The force of antirealism's notion of epistemic truth is piecemeal, rather than consisting in a blanket characterization of truth as knowable.     

The Trouble with Tarski

As a result of thinking ( pace Tarski, wrongly) that it is propositions, not sentences, that are true or false, it has been supposed (also wrongly) that propositions such as that 'Snow is white' is true if and only if snow is white are necessarily true. But changing the rules for the use of the words in a sentence has no effect on the truth of the proposition, only on what proposition it formulates. Many similar statements, e.g., that 'plus' does not mean plus, are only pragmatically contradictory: if this were true, it would be impossible to say so in these words. One should distinguish between sentences that express necessary truths, and sentences that necessarily express truths. It follows that many well known accounts of necessity are wrong, that the truth of an analytic proposition does not follow from the definitions of the words in the sentence that expresses it, that it is not helpful to define meaning in terms of truth, that truth is not relative to language, and that conventionalism is false. This paper is a move in the direction of establishing the eternity of truth.     

Causal empiricism and mental events

Conclusion The present paradox illustrates a deep interconnection between two superficially unrelated metaphysical problems: the nature of mental events and the analysis of causation. I have not tried to resolve the paradox, but only to explain it and to describe the available tactics for resolving it. Although I have also mentioned some of the various considerations that might be advanced in the pursuit of these tactics, I do not claim to have canvassed all such considerations. Since the list of tactics itself is exhaustive, however, and since the four propositions of the paradox are jointly inconsistent, it follows that at least one of these tactics must be correct.     

Field's Paradox and Its Medieval Solution

Hartry Field's revised logic for the theory of truth in his new book, Saving Truth from Paradox, seeking to preserve Tarski's T-scheme, does not admit a full theory of negation. In response, Crispin Wright proposed that the negation of a proposition is the proposition saying that some proposition inconsistent with the first is true. For this to work, we have to show that this proposition is entailed by any proposition incompatible with the first, that is, that it is the weakest proposition incompatible with the proposition whose negation it should be. To show that his proposal gave a full intuitionist theory of negation, Wright appealed to two principles, about incompatibility and entailment, and using them Field formulated a paradox of validity (or more precisely, of inconsistency).

The medieval mathematician, theologian and logician, Thomas Bradwardine, writing in the fourteenth century, proposed a solution to the paradoxes of truth which does not require any revision of logic. The key principle behind Bradwardine's solution is a pluralist doctrine of meaning, or signification, that propositions can mean more than they explicitly say. In particular, he proposed that signification is closed under entailment. In light of this, Bradwardine revised the truth-rules, in particular, refining the T-scheme, so that a proposition is true only if everything that it signifies obtains. Thereby, he was able to show that any proposition which signifies that it itself is false, also signifies that it is true, and consequently is false and not true. I show that Bradwardine's solution is also able to deal with Field's paradox and others of a similar nature. Hence Field's logical revisions are unnecessary to save truth from paradox.