Model-Based and Manipulative Abduction in Science

What I call theoretical abduction (sentential and model-based)certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanation occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. Many external things, usually inert from the epistemological point of view, can be transformed into what I callepistemic mediators, which are illustrated in the last part of the paper, together with an analysis of the related notions of ``perceptual and inceptual rehearsal' and of ``external representation'.     

Problems with Peirce's Concept of Abduction

Abductive reasoning takes place in forming``hypotheses' in order to explain ``facts.' Thus, theconcept of abduction promises an understanding ofcreativity in science and learning. It raises,however, also a lot of problems. Some of them will bediscussed in this paper. After analyzing thedifference between induction and abduction (1), Ishall discuss Peirce's claim that there is a ``logic'of abduction (2). The thesis is that this claim can beunderstood, if we make a clear distinction betweeninferential elements and perceptive elements ofabductive reasoning. For Peirce, the creative act offorming explanatory hypotheses and the emergence of``new ideas' belongs exclusively to the perceptive sideof abduction. Thus, it is necessary to study the roleof perception in abductive reasoning (3). A furtherproblem is the question whether there is arelationship between abduction and Peirce's concept of``theorematic reasoning' in mathematics (4). Both formsof reasoning could be connected, because both arebased on perception. The last problem concerns therole of instincts in explaining the success ofabductive reasoning in science, and the questionwhether the concept of instinct might be replaced bymethods of inquiry (5).     

Reasoning to Hypotheses: Where Do Questions Come?

Detectives and scientists are in the business of reasoning from observations to explanations. This they often do by raising cunning questionsduring their inquiries. But to substantiate this claim we need to know how questions arise and how they are nurtured into more specific hypotheses. I shall discuss what the problem is, and then introduce the so-called interrogative model of inquiry which makes use of an explicit logic of questions. On this view, a discovery processes can be represented as a model-based game in which an inquirer subjects a source of information to a series of strategically organized questions. Strategic principles and why-questions are especially important in heuristical reasoning. Why-questions have their own peculiar nature among questions. They indicate that the inquirer's expectations are somehow disappointed, and that is cognitively challenging. In a finished argument why-questions can be omitted, but in the search for more specific questions they are highly important. As a detetective example I shall analyze Sherlock Holmes reasoning in Silver Blace, the scientific one is A.R. Wallace's discovery of the principle of natural selection. In both of these examples the meaning of questions, especially of well-chosen why-questions, of strategic principles, and of highly structured background knowledge come to the fore. Good questions frequent those who have orderly expectations, based on experience and expertise (detectives!) or highly structured background theories (scientists!).     

Abductive Reasoning as a Way of Worldmaking

The author deals with the operational core oflogic, i.e. its diverse procedures ofinference, in order to show that logicallyfalse inferences may in fact be right because –in contrast to logical rationality – theyactually enlarge our knowledge of the world.This does not only mean that logically trueinferences say nothing about the world, butalso that all our inferences are inventedhypotheses the adequacy of which cannot beproved within logic but only pragmatically. Inconclusion the author demonstrates, through therelationship between rule-following andrationality, that it is most irrational to wantto exclude the irrational: it may, at times, bemost rational to think and infer irrationally.Focussing on the operational aspects of knowingas inferring does away with the hiatus betweenlogic and life, cognition and the world(reality) – or whatever other dualism one wantsto invoke –: knowing means inferring, inferringmeans rule-governed interpreting, interpretingis a constructive, synthetic act, and aconstruction that proves adequate (viable) inthe ``world of experience', in life, in thepraxis of living, is, to the constructivistmind, knowledge. It is the practice of livingwhich provides the orienting standards forconstructivist thinking and its judgments ofviability. The question of truth is replaced bythe question of viability, and viabilitydepends on the (right) kind of experiential fit.     

How to Get It. Diagrammatic Reasoning as a Tool of Knowledge Development and its Pragmatic Dimension

Discussions concerning belief revision, theorydevelopment, and ``creativity' in philosophy andAI, reveal a growing interest in Peirce'sconcept of abduction. Peirce introducedabduction in an attempt to providetheoretical dignity and clarification to thedifficult problem of knowledge generation. Hewrote that ``An Abduction is Originary inrespect to being the only kind of argumentwhich starts a new idea' (Peirce, CP 2.26).These discussions, however, led to considerabledebates about the precise way in which Peirce'sabduction can be used to explain knowledgegeneration (cf. Magnani, 1999; Hoffmann, 1999).The crucial question is that of understandinghow we can get the new elements capableof enlarging our theories. Under thesecircumstances, it might be helpful to step outof the entanglement and reconsider the basis ofthe problem that originally triggered Peirce'sinterest in abduction. This will lead us toanother Peircean concept, that of ``diagrammaticreasoning,' which I discuss here in the contextof his ``pragmatism.' In this way, I hope toreach a better understanding of thecontribution of ``abduction' to the knowledgegeneration process.     

科学发现的本质及其逻辑机制的再发现

不管对科学发现进行语义分析，还是对科学发现活动本身进行历史探究，我们都会发现，科学发现除了具有社会、历史和心理上的属性外，它在本质上乃是新假说的产生、选择、修正、接受和解释的逻辑过程，其逻辑机制正是皮尔士与汉森等所倡导的溯因推理。而且，现代认知科学的新成果促进了溯因推理形式的不断完善，人们意识到在新假说产生与选择中背景理论与背景知识的重要作用，创新了溯因推理的推理形式，令人满意地回答了溯因推理何以能够以及如何能够成为科学发现的逻辑的问题。     

Abduction as a Logic and Methodology of Discovery: the Importance of Strategies

There are various ``classical' argumentsagainst abduction as a logic of discovery,especially that (1) abduction is too weak amode of inference to be of any use, and (2) inbasic formulation of abduction the hypothesisis already presupposed to be known, so it isnot the way hypotheses are discovered in thefirst place. In this paper I argue, bybringing forth the idea of strategies,that these counter-arguments are weaker thanmay appear. The concept of strategiessuggests, inter alia, that many inferentialmoves are taken into account at the same time.This is especially important in abductivereasoning, which is basically a very weak modeof inference. The importance of strategicthinking can already be seen in Charles S.Peirce's early treatments of the topic, and N.R.Hanson's later writings on abductionalthough they did not use the concept of``strategies.' On the whole, I am arguing thatthe focus should be more on methodologicalprocesses, and not only on validityconsiderations, which have dominated thediscussion about abduction.     

Abduction aiming at empirical progress or eventruth approximationleading to a challenge for computational modelling

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and possibly new generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix'.     

略谈易卦与二进位制——兼与魏安明先生商榷

作者认为魏安明的论文《八卦作为一种无零二进制数符系统的解说》的卦序的二进制解说是一个自创的新解说,缺乏相应的原始文献支持。文章通过对易卦与二进制问题研究始末的介绍同,学术界已有共识;易卦系统本身是一种二进位制数表示方式,而古人是不经有自觉才是问题的关键,作者认为至迟雍易学中中国古人对此已经明确的自觉。     

Connecting Internal and External Representations: Spatial Transformations of Scientific Visualizations

Many scientific discoveries have depended on external diagrams or visualizations. Many scientists also report to use an internal mental representation or mental imagery to help them solve problems and reason. How do scientists connect these internal and external representations? We examined working scientists as they worked on external scientific visualizations. We coded the number and type of spatial transformations (mental operations that scientists used on internal or external representations or images) and found that there were a very large number of comparisons, either between different visualizations or between a visualization and the scientists’ internal mental representation. We found that when scientists compared visualization to visualization, the comparisons were based primarily on features. However, when scientists compared a visualization to their mental representation, they were attempting to align the two representations. We suggest that this alignment process is how scientists connect internal and external representations.     

The Emergence of Symbolic Algebra as a Shift in Predominant Models

Historians of science find it difficult to pinpoint to an exact period in which symbolic algebra came into existence. This can be explained partly because the historical process leading to this breakthrough in mathematics has been a complex and diffuse one. On the other hand, it might also be the case that in the early twentieth century, historians of mathematics over emphasized the achievements in algebraic procedures and underestimated the conceptual changes leading to symbolic algebra. This paper attempts to provide a more precise setting for the historical context in which this decisive step to symbolic reasoning took place. For that purpose we will consider algebraic problem solving as model-based reasoning and symbolic representation as a model. This allows us to characterize the emergence of symbolic algebra as a shift from a geometrical to a symbolic mode of representation. The use of the symbolic as a model will be situated in the context of mercantilism where merchant activity of exchange has led to reciprocal relations between money and wealth.

Remodeling the Past

In some of the papers in which she develops and defends the mental modelview of thought experiments in physics, Nersessian expresses the belief that her account has implications for thought experiments in other domains as well. In this paper, I argue, firstly, that counterfactual reasoning has a legitimate place in historical inquiry, and secondly, that the mental model view can account for such "alternative histories". I proceed as follows. Firstly, I review the main accounts of thought experiments in physics and point at some explanatory advantages of the mental model view. Subsequently, I argue that historians cannot dispense with counterfactual reasoning altogether and qualify a number of principled objections against the explicit use of alternative histories for theoretical purposes. Finally, I show that the mental model view can account for such thought experiments in history.     

论数学中的虚构主义

数学虚构主义是"数学实体不存在、数学中不存在真理、数学在世界的说明和科学事业中可有可无"的一种典型的当代数学反实在论的解释。通过对数学虚构主义的批判性分析,得出"数学虚构主义的反实在论规划整体上并不成功","数学在世界的说明和科学中是至关重要,而非可有可无"、"数学实体确实不存在"和"数学中存在真理,但其本质需进一步研究"的结论。     

数学视野中的中国古代历法--评曲安京著《中国历法与数学》

曲安京所著《中国历法与数学》一书，探讨中国古代历法中天文常数与算法的构造机理及其数学思想，对上元积年、渐近分数、内插法、历法中的公式化计算等历法中的重要数学问题进行了原创性的研究，提出了很有说服力的观点与论据。该书把数学史与天文史结合在一起的研究思路也是富有启发性的，是一部成果颇丰的交叉学科性学术著作。     

试论刘徽的数学思想方法

本文从三个方面论述了刘徽的数学思想方法:(1)刘徽的极限思想及其关于研究刘徽极限思想方法中的值得商榷的问题;(2)刘徽的数学方法——定义方法和证明方法及其特点和意义;(3)刘徽在数学研究中体现出来的科学精神。     

主体间的互动性与多主体认知推理模型的建构

认知往往是多个主体间相互作用的活动,建立多主体认知推理模型就必须考虑主体间互动问题.为此我们需要区分团体知识与公共知识,需要借助博弈论方法分析描述主体认知的动态性.这就使多主体认知推理模型的建立面临许多需要解决的技术问题.     

推理能力与逻辑规则--"沃森选择任务"论争的辨析

一直以来逻辑规则被认为是人们进行正确推理的依据.但是,1966年"沃森选择任务"(Wason selection task)实验的结果似乎表明人们的实际推理可能不遵守逻辑规则.这一问题已成为认知科学最重要的问题之一,逻辑学家和心理学家也一直争论到现在.本文通过分析各种理论对"沃森选择任务"的解释,表明人类的推理能力与逻辑规则并不冲突.