无差别原则与贝叶斯疑难

无差别原则(the Principle of Indifference)作为确定基本概率的原则之一,在概率论、统计学和现代归纳逻辑中占居重要的地位。不过,有趣的是,人们对于无差别原则的质疑正如对它的使用一样一直没有间断。无差别原则的致命缺陷在于它会导致逻辑悖论,即无差别悖论。无差别原则的这种矛盾品格使18世纪的数学家、贝叶斯方法的创始人贝叶斯(T.Bayes)处于一种尴尬的境地。一、无差别原则“无差别原则”这个名称得自于现代归纳逻辑的创始人之一凯恩斯(John M.Keynes),但是事实上这个原则几乎是伴随概率概念一道出现的。早在18世纪初概率论处于草…     

弗雷格定理:一个导言

戈特洛布·弗雷格是现代数理逻辑的奠基人,也是分析哲学的创始人之一。他的大部分工作都致力于建立一种数学哲学———逻辑主义:算术真理都是逻辑真理。长久以来,哲学家一直认为,罗素悖论彻底瓦解了弗雷格的工作。然而实际的情况是,在弗雷格那里隐藏着另一个证明:算术公理可以纯粹逻辑地从休谟原则推出。休谟原则是说,概念F的数和概念G的数相同当且仅当存在F和G之间的一一对应关系。这一结果被称为弗雷格定理,它引发了一种新的逻辑主义的兴起。     

当代中国大众文化的逻辑悖论与价值引领

当代中国大众文化商品化、世俗化、生活化和符号化的表象之下,蕴涵着资本逻辑悖论、物化逻辑悖论、快感逻辑悖论和消费逻辑悖论的深层本质。面对我国大众文化的种种逻辑悖论和价值失范,必须加强对大众文化的政治价值、科学价值、道德价值、审美价值、生态价值的全方位引领。其引领的具体路径:一是高位吸引,提升文化品位;二是底线阻击,阻塞下滑通道;三是化人诉求,彰显教化功能;四是"情感"疏导,开辟认同新径;五是"立体"渗透,确保落地生根。     

略论市场逻辑及其伦理基础

市场逻辑是在特定制度约束条件下的个人权利的自由交易.作为现实的人的经济活动场所,市场充分体现了现实的人自由交换的需要,体现了人们对自身价值和创造力的肯定.自市场经济体制产生以来,各种伦理学说所关注的一个共同课题就是如何从伦理上为各自所设计的市场经济制度作辩护.基于市场逻辑的伦理原则为自由原则、平等原则、效率原则和秩序原则.     

《墨经》消解的五个悖论的起源及性质考论

中国古代典籍中究竟有没有出现过严格意义上的悖论，这是中国逻辑史和悖论研究领域中，学者们一直热衷讨论的重要问题。作为中国古代逻辑思想最为重要的代表性典籍，《墨经》讨论了言尽誖、非诽、学无益、知知之否之足用、仁义之为内外等悖论。本文通过准确考察这五个悖论的含义和基本来源，初步认定它们多来自儒家或道家的主张。墨家对这五个悖论形成了或语义或语用角度的理解，并运用逻辑分析的方法对其作了消解。通过分析悖论这一概念的含义和基本特征，可以看出，墨家所提炼和消解的这些悖论在本质上是逻辑矛盾，而儒家或道家所主张的论题则属于辩证矛盾，属于某种严格意义上的非逻辑悖论，即渗透了独特思想文化内涵的哲学悖论或科学文化悖论。区分两种不同悖论，或许更有助于把握墨家和先秦儒家、道家各自思想的特质。     

试论"真矛盾"及次协调逻辑的哲学价值

二十世纪后期以来,再也没有哪一种逻辑像次协调逻辑那样,在取得丰富研究成果的同时,也领略到了极为尖锐的批判,仿佛其本身就是一种意味深长的“矛盾”。依照次协调逻辑“真矛盾”的观点所构建的次协调逻辑系统,夷非所思地试图要容纳我们所认知的悖论、辩证矛盾、甚至逻辑矛盾。次协调逻辑试图要和悖论永久共存,但我们可以为了暂时的搁置这种矛盾,发展某理论的其他方面而接受这种逻辑技术。次协调逻辑在反映人脑的容错机制上具有重要的描述功能,这对提高计算机的智能化具有十分重要的实践意义。     

推类等于类比推理吗？

近10年来,中国古代的推类理论被普遍认为有助于说明中国古代逻辑与西方（亚里士多德）逻辑的不同。关于推类的逻辑本质——推类的前提与结论之间究竟是何种推理关系,一种流行的观点是将推类与类比推理等而视之。不过,伍非百、汪奠基、沈有鼎、刘培育、孙中原等对类同原则的适用范围与推类的逻辑本质做了更为全面与准确的诠释。通过分析中国古代的推类实践,可以从中揭示出类同原则的工作机制,从而在经验层面上进一步确认类同原则对于演绎、归纳和类比推理的普遍意义,最终证成推类与类比推理并不等同。     

费奇悖论的混合时态认知逻辑分析CSSCI

费奇悖论的形成原因是没有将证实原则和摩尔句子进行准确刻画。证实原则“真命题都是可知的”并不是指每个真命题都在当下可能被知道,而应该是指对每个真命题来说都存在一个时间点使得在这个时间点上此命题被知道。摩尔句子“p并且主体不知道p”应该是指“p并且在t时主体不知道p”。利用混合逻辑的技术可以对认知算子进行时间标记,进而可以形式化出证实原则和摩尔句子的准确思想,最终可以消解费奇悖论。     

形式化量子力学不必使用量子逻辑

一般认为,标准量子力学需要使用一套它自己的逻辑系统,即量子逻辑。量子逻辑采用与一般逻辑系统不同的语义规则,因此和古典逻辑无法兼容。此篇文章将呈现一套量子力学的严格形式基础,它是对古典二值逻辑之保守扩充;保守扩充意指比原先之逻辑系统强,但较强的原因为它有较多之词汇。此套逻辑为三值逻辑。古典逻辑中为真的句子仍然为真。古典逻辑中为假的句子将被区分为强性假与中性。第三个真值一中性一考虑了非本征态情况中之观察句。本文详列了物理的公理并显示它们具有一个模型。此提案的可行性说明了量子逻辑是不必要的,并且存在一个共同的逻辑架构可提供给数学、非量子物理及量子力学使用。     

中国近三十年逻辑悖论研究的主要特点与趋势

当代逻辑悖论研究有三个不同层面:一是特定领域某个或某组悖论的建构及其具体解悖方案研究;二是各种悖论及解悖方案的哲学研究;三是关于悖论的发现、解决及其功能的一般方法论研究。文革前,中国学界的逻辑悖论研究主要体现在莫绍揆、沈有鼎等学者在第一层面的研究上。中国学界关于逻     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.     

Severe Withdrawal (and Recovery)

The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals.     

A non-linear utility theory with multiple objectives

The aim of this paper is to make optimum several objectives at the same time which would enable a measurement of utility for several possible alternatives. The problem is solved if a strong or weak dominance exists between the alternatives, otherwise a set of incomparable alternatives would be present. Therefore, indifference curve analysis offers the outcome but as these indifference loci are difficult to determine only the characteristics of this analysis are maintained viz. decreasing marginal utility, non-linearity and even non-convexity. Indifference and reference point theory with the Minkowski min–max-metric only respond to these characteristics. Also the problem of generating alternatives during the process is taken into consideration. © 1998 John Wiley & Sons, Ltd.     

The Nature and Ethics of Indifference

Indifference is sometimes said to be a virtue. Perhaps more frequently it is said to be a vice. Yet who is indifferent; to what; and in what way is poorly understood, and frequently subject to controversy and confusion. This paper presents a framework for the interpretation and analysis of ethically significant forms of indifference in terms of how subjects of indifference are variously related to their objects in different circumstances; and how an indifferent orientation can be either more or less dynamic, or more or less sensitive to the nature and state of its object. The resulting analysis is located in a wider context of moral psychology and ethical theory; in particular with respect to work on the virtues of care, empathy and other forms of affective engagement. During the course of this discussion, a number of recent claims associated with the ethics of care and empathy are shown to be either misleading or implausible.     

DELAY‐AMOUNT TRADEOFFS IN CHOICES BY PIGEONS AND RATS: HYPERBOLIC VERSUS EXPONENTIAL DISCOUNTING

An adjusting‐delay procedure was used to study the choices of pigeons and rats when both delay and amount of reinforcement were varied. In different conditions, the choice alternatives included one versus two reinforcers, one versus three reinforcers, and three versus two reinforcers. The delay to one alternative (the standard alternative) was kept constant in a condition, and the delay to the other (the adjusting alternative) was increased or decreased many times a session so as to estimate an indifference point—a delay at which the two alternatives were chosen about equally often. Indifference functions were constructed by plotting the adjusting delay as a function of the standard delay for each pair of reinforcer amounts. The experiments were designed to test the prediction of a hyperbolic decay equation that the slopes of the indifference functions should increase as the ratio of the two reinforcer amounts increased. Consistent with the hyperbolic equation, the slopes of the indifference functions depended on the ratios of the two reinforcer amounts for both pigeons and rats. These results were not compatible with an exponential decay equation, which predicts slopes of 1 regardless of the reinforcer amounts. Combined with other data, these findings provide further evidence that delay discounting is well described by a hyperbolic equation for both species, but not by an exponential equation. Quantitative differences in the y‐intercepts of the indifference functions from the two species suggested that the rate at which reinforcer strength decreases with increasing delay may be four or five times slower for rats than for pigeons.     

Business is not just war. Transferring the principle of double effect from war to business

Abstract

In this article the validity of transferring the Principle of Double Effect from the just war tradition to the domain of business is critically reviewed. If a case can be build for sufficient analogies between war and business, the principle of double effect can legitimately be transferred from war to business. If, on the other hand it can be shown that there are aspects in which business differ substantially from just war, then the transfer to business of a principle developed within the context of war becomes more problematic. After exploring the nature of arguments of analogy and fallacious arguments of weak analogy some important disanalogies between war and business are highlighted. Given these disanalogies it is then contended that the just war background of the Principle of Double Effect had some bearing on both the content and manner of application of the Principle of Double Effect. Finally it is argued that these disanalogies require some revisions to the Principle of Double Effect with regard to both its content and its manner of application before it can be applied meaningfully to foreseeable negative side-effects of business.     

The Principle of Semantic Compositionality

The Principle of Semantic Compositionality (sometimes called Frege's Principle) is the principle that the meaning of a (syntactically complex) whole is a function only of the meanings of its (syntactic) parts together with the manner in which these parts were combined. This principle has been extremely influential throughout the history of formal semantics; it has had a tremendous impact upon modern linguistics ever since Montague Grammars became known; and it has more recently shown up as a guiding principle for a certain direction in cognitive science.Despite the fact that The Principle is vague or underspecified at a number of points — such as what meaning is, what counts as a part, what counts as a syntactic complex, what counts as combination — this has not stopped some people from viewing The Principle as obviously true, true almost by definition. And it has not stopped other people from viewing The Principle as false, almost pernicious in its effect. And some of these latter theorists think that it is an empirically false principle while others think of it as a methodologically wrong-headed way to proceed.In fact, there are approximately 318 arguments against The Principle which can be found in the literature, whereas there are only three (or maybe four) arguments proposed in favor of The Principle. This paper will adjudicate among these arguments. And at the end it will suggest some other way to look at what proponents of compositionality really want.     

The problem of invoking infinite polytheisms: a response to Raphael Lataster and Herman Philipse

Raphael Lataster and Herman Philipse present an argument which they think decisively demonstrates polytheism over monotheism, if theism is assumed. Far from being decisive, the argument depends on very controversial and likely false assumptions about how to treat infinities in probability. Moreover, these problems are well known. Here, we focus on three objections. First, the authors rely on both countable additivity and the Principle of Indifference, which contradict each other. Second, the authors rely on a particular way of dividing up the possibility space, when there are equally as reasonable alternative divisions which give different answers to the one the authors arrived at. Third, the authors’ argument proves too much, giving us an argument against many positions we should not be able to argue against so easily.     

RISKY CHOICE IN PIGEONS AND HUMANS: A CROSS‐SPECIES COMPARISON

Pigeon and human subjects were given repeated choices between variable and adjusting delays to token reinforcement that titrated in relation to a subject's recent choice patterns. Indifference curves were generated under two different procedures: immediate exchange, in which a token earned during each trial was exchanged immediately for access to the terminal reinforcer (food for pigeons, video clips for humans), and delayed exchange, in which tokens accumulated and were exchanged after 11 trials. The former was designed as an analogue of procedures typically used with nonhuman subjects, the latter as an analogue to procedures typically used with human participants. Under both procedure types, different variable‐delay schedules were manipulated systematically across conditions in ways that altered the reinforcer immediacy of the risky option. Under immediate‐exchange conditions, both humans and pigeons consistently preferred the variable delay, and indifference points were generally ordered in relation to relative reinforcer immediacies. Such risk sensitivity was greatly reduced under delayed‐exchange conditions. Choice and trial‐initiation response latencies varied directly with indifference points, suggesting that local analyses may provide useful ancillary measures of reinforcer value. On the whole, the results indicate that modifying procedural features brings choices of pigeons and humans into better accord, and that human—nonhuman differences on risky choice procedures reported in the literature may be at least partly a product of procedural differences.