Reasoning with quantifiers

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity properties of quantified statements--properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning.     

归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

The macrostructure of informal arguments: A proposed model and analysis

Theories of informal reasoning and critical thinking often maintain that everyday, informal arguments can be classified into types based on the specific organization that the premises or reasons enter into in their support for the conclusion (Snoeck Henkemans, 2000; Vorobej, 1995b). Three general types are identified: convergent, coordinately linked, and subordinately linked arguments. There has been no empirical research, however, to determine whether these structural distinctions have any psychological reality. In the first two of four experiments, college students were presented with premise pairs from larger, informal arguments and were asked to judge the nature of the relationship between the premises in a pair. The judgments involved applying “tests” of linkage, subordination, and so on, that have been proposed in the theoretical literature on argument analysis (e.g., Walton, 1996a; Yanal, 1991). Results suggest that adults can effectively distinguish between linked (interdependent) and convergent relationships and can further distinguish between interdependencies that are full and those that are merely partial. Adults also distinguished between subordinate and nonsubordinate relations. Experiments 3 and 4 provide evidence that adults make use of information about argument structure in evaluating argument strength and in categorizing arguments. Experiment 4 further suggests that facility with macrostructure is only modestly related to deductive reasoning competence. Findings are framed in terms of a speculative account of how argument structure is identified and mentally represented.     

The Moral Dilemmas Debate, Deontic Logic, and the Impotence of Argument

In this paper I argue for modesty concerning what theoretical reason can accomplish in the moral dilemmas debate. Specifically, I contend that philosophers' conclusions for or against moral dilemmas are driven less by rational argument and more by how the moral world intuitively appears to them.I support this thesis by first considering an argument against moral dilemmas, the argument from deontic logic, and showing that its persuasive force depends on one's having already accepted its conclusion. I then make a different, and general, case that any argument in the moral dilemmas debate concerning the defeasibility of conflicting obligations can be marginalized by making not-unreasonable adjustments in the conditions for wrongdoing.These two strands of argument are related by the notion of inescapable wrongdoing. It is our standing intuitions about inescapable wrongdoing which make the relevant deontic logical principles plausible or implausible to us. And whether wrongdoing can be inescapable is central to deciding what the conditions for wrongdoing are. My conclusion is that the arguments in the moral dilemmas debate merely implement whatever standing intuition we have concerning inescapable wrongdoing, and that apart from any such intuition the arguments are unpersuasive.     

Two kinds of reasoning

According to one view of reasoning, people can evaluate arguments in at least two qualitatively different ways: in terms of their deductive correctness and in terms of their inductive strength. According to a second view, assessments of both correctness and strength are a function of an argument's position on a single psychological continuum (e.g., subjective conditional probability). A deductively correct argument is one with the maximum value on this continuum; a strong argument is one with a high value. The present experiment tested these theories by asking participants to evaluate the same set of arguments for correctness and strength. The results produced an interaction between type of argument and instructions: In some conditions, participants judged one argument deductively correct more often than a second, but judged the second argument inductively strong more often than the first. This finding supports the view that people have distinct ways to evaluate arguments.     

Defeasibility,Law, and Argumentation: A Critical View from an Interpretative Standpoint

The phenomenon of defeasibility has long been a central theme in legal literature. This essay aims to shed new light on that phenomenon by clarifying some fundamental conceptual issues. First, the most widespread definition of legal defeasibility is examined and criticized. The essay shows that such a definition is poorly constructed, inaccurate and generates many problems. Indeed, the definition hides the close relationship between legal defeasibility and legal interpretation. Second, this essay argues that no new definition is needed. I will show that from an interpretative standpoint, there is nothing special about legal defeasibility. Contrary to what some authors maintain, no unique or privileged source of legal defeasibility exists, nor are there privileged arguments to justify it. Specifically, legal defeasibility refers to interpretative outcomes deriving from interpretative arguments that, on the one hand, are very different from one another, and, on the other, are often employed to justify different interpretative outcomes. In the legal field, the problems related to defeasibility have little in common with the problems that this label covers in other areas—such as logic or epistemology—and they are nothing but the well-known problems related to legal interpretation. In conclusion, this paper argues that as far as legal argumentation is concerned, the notion of legal defeasibility lacks explanatory power, and it should be abandoned.

     

Algebraic Semantics for Deductive Systems

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics.     

Framing human inference by coherence based probability logic

We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.     

A formal account of Socratic-style argumentation

In traditional mathematical models of argumentation an argument often consists of a chain of rules or reasons, beginning with premisses and leading to a conclusion that is endorsed by the party that put forward the argument. In informal reasoning, however, one often encounters a specific class of counterarguments that until now has received little attention in argumentation formalisms. The idea is that instead of starting with the premisses, the argument starts with the propositions put forward by the counterparty, of which the absurdity is illustrated by showing their (defeasible) consequences. This way of argumentation (which we call S-arguments) is very akin to Socratic dialogues and critical interviews; it also has applications in modern philosophy. In this paper, various examples of S-arguments are provided, as well as a treatment of the problems that occur when trying to formalize them in existing formalisms. We also provide general guidelines that can serve as a basis for implementing S-arguments into various existing formalisms. In particular, we show how S-arguments can be implemented in Pollock's formalism, how they fit into Dung's abstract argumentation approach and how they are related to the issue of self-defeating arguments.     

Syllogistic reasoning and belief-bias inhibition in school children: evidence from a negative priming paradigm

Research on deductive reasoning in adolescents and adults has shown that errors in deductive logic are not necessarily due to a lack of logical ability but can stem from an executive failure to inhibit biases. Few studies have examined this dissociation in children. Here, we used a negative priming paradigm with 64 children (8-10 years old) to test the role of cognitive inhibition in syllogisms with belief-bias effects. On trials where negative priming was predicted, results were as follows: For the first syllogism (A), the strategy 'unbelievable-equals-invalid' had to be inhibited. The logic of the syllogism led to affirming a conclusion inconsistent with one's knowledge of the world, such as 'All elephants are light.' For the second syllogism (B), one's real-world knowledge and the syllogism's logic were congruent but the latter required affirming exactly what had been inhibited for A (i.e. that elephants are heavy). A negative priming effect on the A-B sequence was reflected in a significant drop in reasoning performance on B. This supports the idea that during cognitive development, inhibitory control is required for success on syllogisms where beliefs and logic interfere.     

非形式逻辑与演绎主义

非形式逻辑出现于上个世纪70年代,它首先是一种寻求更好的大学逻辑教学方式的努力。进而,非形式逻辑学者们逐渐开始触及和探讨越来越多的理论议题,即发展不依赖于形式逻辑的关于论证以及好论证的理解方式。在1998年世界哲学大会上,布莱尔和我阐释了非形式逻辑为哲学所带来的理论后果,其中一点我们称之为“演绎主义的终结”。那时我们并未给出演绎主义的定义,而只是把它等同于麦金泰尔的那个精炼的说法：“任何推理,不是演绎的,就是有缺陷的。”但现在看来,我们在当时就作出“演绎主义的终结”这一论断,显然是有点为时过早了。因为演绎主义似乎至今都还很有生命力,甚至在那些倾向于非形式逻辑的学者那里它也能得到支持：恩尼斯长期以来都辩护演绎主义是一种论证重构策略,格罗尔克更是致力于辩护它是一种论证评价理论。在本文中我将论证,非形式逻辑最好被理解为一种不诉诸于演绎技巧和演绎规范的逻辑研究。当我们意识到演绎和演绎主义已经如何深深地扎根于我们的哲学发展史中,并且牢牢地控制了我们关于逻辑研究的理解,我们就能明白非形式逻辑这一理论努力是多么的困难和重要。我将首先澄清“演绎主义”的意思,然后再分别考察那些赞成和反对演绎主义的论证,最后,我将表明非形式逻辑是从演绎主义中挽救逻辑的理论尝试。     

Blind Reasoning

The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of 'blind but blameless' reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible.     

The Relevance of Logic to Reasoning and Beleif Revision: Harman on 'Change in View'

In Change of View: Principles of Reasoning , Gilbert Harman argues that (i) all genuine reasoning is a matter of belief revision, and that, since (ii) logic is not "specially relevant" to belief revision, (iii) logic is not specially relevant to reasoning, either. Thus, Harman suggests, what is needed is a "theory of reasoning"–which, incidentally, will be psychologistic, telling us both how we do and how we should reason. I argue that Harman fails to establish the need for such a theory, because (a) reasoning is not always a matter of belief revision, and (b) logic is, in fact, of the utmost relevance to both reasoning and belief revision.     

归纳推理中的属性中心性效应

通过三个实验研究了属性的中心性程度对归纳推理的影响,结果表明,在归纳推理中存在属性中心性效应,中心属性比其他属性（次中心属性、再次中心属性）更能影响归纳推理。但属性中心性效应的出现受到了前提对象和结论对象相似性程度的制约,当前提对象和结论对象的相似程度高时,中心属性比其他属性更能影响归纳推理;随着相似性水平的降低,中心属性的归纳推理力度越来越弱,而次中心属性、再次中心属性的归纳推理力度则会依次表现出越来越强的趋势,到最后当前提对象和结论对象的属性完全不相似时,最次中心属性的归纳推理力度达到最高水平,而中心属性的归纳推理力度则降低到最低水平。由于再次中心属性的归纳推理力度的最高水平没有显著高于随机水平,而中心属性的归纳推理力度的最低水平却显著低于随机水平,因此,研究者认为,在前提对象和结论对象完全不相似的情况下,被试将确信不能采用中心属性来进行归纳推理的力度判断,而采用猜测的方式选择了肯定可以排除的项目之外的其他项目,这体现了具有不确定的归纳推理活动的过程的典型特征     

论八卦是八个逻辑范式

基于太极代数,本文证明八卦是八个逻辑范式,八卦中包含四对矛盾关系,其中"六子"构成辩证逻辑组。八卦是生命生产和思想生产都必须共同遵循的变化法则。学界似有这样的倾向,以为《周易》中只有类推逻辑而没有演绎逻辑,本文证明这种观点是不能成立的。八卦本质上就是演绎逻辑的,卦象的本质是逻辑法则。因此,基于卦象的联想或推理不能脱离八卦的逻辑内涵;否则,想象的灵活性必将导致卦象上的混淆,甚至使八卦沦为象数游戏的工具。     

Be Nice! How Simple Imperatives Simplify Imperative Logic

In a series of articles, P. Vranas recently proposed a new imperative logic. The strong and weak inferences of this logic are motivated by an appeal to a strong and weak ‘support by reasons’ that transfers from the premisses of an argument to its conclusion. They also combine nonmonotonic and monotonic reasoning patterns. I show that for any moral agent, Vranas’s proposal can be simplified enormously.     

Why should we abandon the mental logic hypothesis?

Two hypotheses on deductive reasoning are under development: mental logic and mental models. It is often accepted that there are overwhelming arguments to reject the mental logic hypothesis. I revise these arguments and claim that they are either not conclusive, or point at problems which are troublesome for the mental model hypothesis as well.     

Deduction from if-then personality signatures

Personality signatures are sets of if-then rules describing how a given person would feel or act in a specific situation. These rules can be used as the major premise of a deductive argument, but they are mostly processed for social cognition purposes; and this common usage is likely to leak into the way they are processed in a deductive reasoning context. It is hypothesised that agreement with a Modus Ponens argument featuring a personality signature as its major premise is affected by the reasoner's own propensity to display this personality signature. To test this prediction, Modus Ponens arguments were constructed from conditionally phrased items extracted from available personality scales. This allowed recording of (a) agreement with the conclusion of these arguments, and (b) the reasoner's propensity to display the personality signature, using as a proxy this reasoner's score on the personality scale without the items used in the argument. Three experiments (N = 256, N = 318, N = 298) applied this procedure to Fairness, Responsive Joy, and Self-Control. These experiments yielded very comparable effects, establishing that a reasoner's propensity to display a given personality signature determines this reasoner's agreement with the conclusion of a Modus Ponens argument featuring the personality signature.     

Conspiracy Accounts as Intergroup Theories: Challenging Dominant Understandings of Social Power and Political Legitimacy

Conspiracy accounting is often regarded as an atypical, pathological form of political reasoning, and little research has considered how ordinary social actors may refer to political conspiracies in the course of argument. In this article, we consider the spontaneous use of conspiracy narratives by politically engaged Greek citizens in interview discussions of the Macedonian crisis. Analysis revealed that conspiracy narratives were typically used to challenge dominant representations that attributed the Macedonian crisis to Greek xenophobic nationalism. Specifically, conspiracy accounts were used to dispute assumptions concerning Greece's majority status by representing the political opposition as a consortium rather than a single out‐group, by recasting the threat posed to Greece as a matter of realistic rather than symbolic competition, and by extending the historical frame of reference to encompass past and prospective future threats to the Greek people and the Greek state. In conclusion, we note how the use of conspiratorial reasoning may be used to construct complex causal arguments concerning intergroup relations and to challenge dominant ideological assumptions about social hierarchy and political legitimacy. In this respect, conspiratorial reasoning might be regarded as a prototypical form of intergroup representation.