An Oral Proof in a Geometry Class: How Linguistic Tools Can Help Map the Content of a Proof

Recommendations that teachers promote argument and discourse in their mathematics classrooms anticipate researchers' needs for methods for examining and analyzing such talk. One form of discourse is oral arguments, including proofs. We ask: How can we track the development of an oral argument by a teacher and her/his students? We illustrate a method that combines Systemic Functional Linguistics (SFL) and Toulmin's argumentation scheme to examine how speakers logically connect different parts of an argument. We suggest that conjunction analysis can aid a researcher to map the content of a proof that has been constructed in class discussion. Using data from a discussion of a geometry proof, we show that different types of conjunctions enabled the teacher and the students to connect various components of an argument and, also, different arguments. The article illustrates how conjunction analysis can support and deepen what Toulmin's scheme for arguments can reveal about oral discussions.     

Reflective Argumentation: A Cognitive Function of Arguing

Why do we formulate arguments? Usually, things such as persuading opponents, finding consensus, and justifying knowledge are listed as functions of arguments. But arguments can also be used to stimulate reflection on one’s own reasoning. Since this cognitive function of arguments should be important to improve the quality of people’s arguments and reasoning, for learning processes, for coping with “wicked problems,” and for the resolution of conflicts, it deserves to be studied in its own right. This contribution develops first steps towards a theory of reflective argumentation. It provides a definition of reflective argumentation, justifies its importance, delineates it from other cognitive functions of argumentation in a new classification of argument functions, and it discusses how reflection on one’s own reasoning can be stimulated by arguments.     

The Selective Laziness of Reasoning

Reasoning research suggests that people use more stringent criteria when they evaluate others' arguments than when they produce arguments themselves. To demonstrate this “selective laziness,” we used a choice blindness manipulation. In two experiments, participants had to produce a series of arguments in response to reasoning problems, and they were then asked to evaluate other people's arguments about the same problems. Unknown to the participants, in one of the trials, they were presented with their own argument as if it was someone else's. Among those participants who accepted the manipulation and thus thought they were evaluating someone else's argument, more than half (56% and 58%) rejected the arguments that were in fact their own. Moreover, participants were more likely to reject their own arguments for invalid than for valid answers. This demonstrates that people are more critical of other people's arguments than of their own, without being overly critical: They are better able to tell valid from invalid arguments when the arguments are someone else's rather than their own.     

Moral Reasoning and Rhetoric: The Acceptability of Arguments About AIDS-Related Dilemmas1

The disease AIDS has given rise to a host of social dilemmas. Here we explore the rhetoric that affects people's reasoning about actions taken in the face of such dilemmas. We presented a group of 514 undergraduates with vignettes depicting dilemmas having to do with the distribution of sexually explicit educational material to high school students and with the forced HIV blood testing of factory workers. Subjects rated the acceptability of arguments for and against courses of action taken by persons in the vignettes. The arguments embodied concerns typical of moral reasoning at each of Kohlberg's six stages. We found that the acceptability of stage-typical moral arguments about AIDS-related dilemmas depends on both the dilemma at hand and the course of action being argued for. We argue that knowledge of how people respond to different kinds of moral arguments concerning AIDS-related dilemmas is valuable for informing efforts to advocate humane and lifesaving policies to particular audiences.     

Properties of the diversity effect in category-based inductive reasoning

Four experiments investigated how people judge the plausibility of category-based arguments, focusing on the diversity effect, in which arguments with diverse premise categories are considered particularly strong. In Experiment 1 we show that priming people as to the nature of the blank property determines whether sensitivity to diversity is observed. In Experiment 2 we find that people's hypotheses about the nature of the blank property predict judgements of argument strength. In Experiment 3 we examine the effect of our priming methodology on people's tendency to bring knowledge about causality or similarity to bear when evaluating arguments, and in Experiment 4 we show that whether people's hypotheses about the nature of the blank property were causal predicted ratings of argument strength. Together these results suggest that diversity effects occur because diverse premises lead people to bring general features of the premise categories to mind. Although our findings are broadly consistent with Bayesian and Relevance-based approaches to category-based inductive reasoning, neither approach captures all of our findings.     

Why Doomsday Arguments are Better than Simulation Arguments

Inspired by anthropic reasoning behind Doomsday arguments, Nick Bostrom's Simulation Argument says: people who think advanced civilisations would run many fully‐conscious simulated minds should also think they're probably simulated minds themselves. However, Bostrom's conclusions can (and should) be resisted, especially by sympathisers with Doomsday or anthropic reasoning. This paper initially offers a posterior‐probabilistic ‘Doomsday lottery’ argument against Bostrom's conclusions. Suggestions are then offered for deriving anti‐simulation conclusions using weaker assumptions. Anti‐simulation arguments herein use more (epistemically and metaphysically) robust reference classes than Bostrom's argument, require no Principles of Indifference, abide better by the total evidence requirement, and yet use empirically plausible priors and likelihoods. However, while Doomsday arguments are probabilistically, epistemically and metaphysically stronger than the Simulation Argument, anthropic reasoning can (and should) refrain from embracing either.     

PALEY'S iPOD: THE COGNITIVE BASIS OF THE DESIGN ARGUMENT WITHIN NATURAL THEOLOGY

The argument from design stands as one of the most intuitively compelling arguments for the existence of a divine Creator. Yet, for many scientists and philosophers, Hume's critique and Darwin's theory of natural selection have definitely undermined the idea that we can draw any analogy from design in artifacts to design in nature. Here, we examine empirical studies from developmental and experimental psychology to investigate the cognitive basis of the design argument. From this it becomes clear that humans spontaneously discern purpose in nature. When constructed theologically and philosophically correctly, the design argument is not presented as conclusive evidence for God's existence but rather as an abductive, probabilistic argument. We examine the cognitive basis of probabilistic judgments in relationship to natural theology. Placing emphasis on how people assess improbable events, we clarify the intuitive appeal of Paley's watch analogy. We conclude that the reason why some scientists find the design argument compelling and others do not lies not in any intrinsic differences in assessing design in nature but rather in the prior probability they place on complexity being produced by chance events or by a Creator. This difference provides atheists and theists with a rational basis for disagreement.     

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.     

The everyday production of knowledge: individual differences in epistemological understanding and juror‐reasoning skill

This study investigated the untested assumption that people's everyday reasoning reflects different understandings of the nature of knowledge and knowing. The epistemological stances of 180 prospective jurors were assessed with an interview that probed the nature and source of the discrepant knowledge claims of two historical accounts. The researchers derived global epistemological levels from these interviews. The jurors also heard trials and offered justifications for their verdict choices. The researchers assessed these justifications for whether subjects could use various reasoning skills successfully. Epistemological level, but not educational level, age, or gender, predicted juror‐reasoning skills and degree of certainty about verdict choice. Epistemological level, mediated by the juror‐reasoning skills, was a better predictor of general argument skill than certainty about verdict choice and the amount of evidence used in arguing for a verdict. The results indicate that epistemological understandings underlie specific juror‐reasoning skills and overall argument ability. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

Inductive Reasoning in Alzheimer''s Disease

We evaluated knowledge of basic level and superordinate semantic relations and the role of cognitive resources during inductive reasoning in probable Alzheimer's disease (AD). Nineteen mildly demented AD patients and 17 healthy control subjects judged the truthfulness of arguments with a premise and a conclusion that contain familiar concepts coupled with "blank" predicates, such as "Spiders contain phosphatidylcholine; therefore all insects contain phosphatidylcholine." Like healthy control subjects, AD patients were relatively insensitive to the typicality of the premise category when judging the strength of arguments with a conclusion containing a basic-level concept, but were relatively sensitive to typicality during judgments of arguments containing a superordinate in the conclusion. Moreover, AD patients resembled control subjects in judging arguments with an immediate superordinate in the conclusion compared to arguments with a distant superordinate. AD patients differed from control subjects because they could not take advantage of two premises in an argument containing basic-level concepts. We conclude that semantic knowledge is sufficiently preserved in AD to support inductive reasoning, but that limited cognitive resources may interfere with AD patients' ability to consider the entire spectrum of information available during semantic challenges.     

A Bayesian approach to the argument from ignorance.

In this paper, we re-examine a classic informal reasoning fallacy, the so-called argumentam ad ignorantiam. We argue that the structure of some versions of this argument parallels examples of inductive reasoning that are widely viewed as unproblematic. Viewed probabilistically, these versions of the argument from ignorance constitute a legitimate form of reasoning; the textbook examples are inductive arguments that are not unsound but simply weak, due to the nature of the premises and conclusions involved. In an experiment, we demonstrated some of the variables affecting the strength of the argument, and conclude with some general considerations towards an empirical theory of argument strength.     

Expertise and error in diagnostic reasoning

An investigation is presented in which a computer simulation model (DIAGNOSER) is used to develop and test predictions for behavior of subjects in a task of medical diagnosis. The first experiment employed a process-tracing methodology in order to compare hypothesis generation and evaluation behavior of DIAGNOSER with individuals at different levels of expertise (students, trainees, experts). A second experiment performed with only DIAGNOSER identified conditions under which errors in reasoning in the first experiment could be related to interpretation of specific data items. Predictions derived from DIAGNOSER's performance were tested in a third experiment with a new sample of subjects. Data from the three experiments indicated that (1) form of diagnostic reasoning was similar for all subjects trained in medicine and for the simulation model, (2) substance of diagnostic reasoning employed by the simulation model was parable with that of the more expert subjects, and (3) errors in subjects' reasoning were attributable to deficiencies in disease knowledge and the interpretation of specific patient data cues predicted by the simulation model.     

条件推理:“演绎”与“概率”两种实验研究范式之比较

本研究通过推理心理学研究中的“演绎”和“概率”两种实验范式设计对同一个班级的大学生参与者(实验一中N=57,实验二中N=43)进行先后两次有关条件推理的实验研究后,得出如下主要结果:(1)推理者在对不同的“纯形式条件命题本身的认可度”以及对由它们各自建构的同类型推理题的推理结果之间的作答反应模式之间的差异都很小且具有较高的一致性;(2)对由不同的“含具体内容的假言命题”本身的认可度之间以及由它们建构的同类型条件推理题的推理结果之间具有较大的差异性;(3)推理者对“演绎”和“概率”两种不同实验范式分别建构的内容近似的推进题进行推理时具有大致相同的作答反应趋势。由此可以推论推理者在“概率推理实验范式”中的作答或推理结果可以被视为只是对“演绎推理实验范式”的相应推理题给出“概率解”的心理加工过程。     

Mathematical Reasoning: Adults' Ability to Make the Inductive-Deductive Distinction

In this study, I examined adults' ability to distinguish necessary deductive and indeterminate inductive forms of argument in mathematics. Only 30% of a sample of college students distinguished deductive and inductive forms of argument and experienced deductively derived conclusions as necessary and inductively derived conclusions as uncertain. Forty percent failed to distinguish deductive and inductive forms and experienced inductively derived and deductively derived conclusions as necessary. Thirty percent distinguished deductive and inductive arguments but experienced deductively derived and inductively derived conclusions as uncertain. As observed in other reasoning domains, the introduction of personal beliefs or knowledge about the argument content appeared to affect adult reasoners' application of knowledge about forms of argument and judgments of necessity. The results suggest the following conclusions. Adults' experience of the conclusions from mathematical inductive and deductive arguments as provisional conclusions or necessary conclusions depends on a complex coordination involving ability to attend to abstract premise-conclusion relations and beliefs about the nature of mathematical objects and regularities. Thus, two major achievements are involved, explaining the low numbers able to judge necessity in mathematics.     

Measurement and Computational Skepticism

Putnam and Searle famously argue against computational theories of mind on the skeptical ground that there is no fact of the matter as to what mathematical function a physical system is computing: both conclude (albeit for somewhat different reasons) that virtually any physical object computes every computable function, implements every program or automaton. There has been considerable discussion of Putnam's and Searle's arguments, though as yet there is little consensus as to what, if anything, is wrong with these arguments. In the present paper we show that an analogous line of reasoning can be raised against the numerical measurement (i.e., numerical representation) of physical magnitudes, and we argue that this result is a reductio ad absurdum of the challenge to computational skepticism. We then use this reductio to get clearer about both (i) what's wrong with Putnam's and Searle's arguments against computationalism, and (ii) what can be learned about both computational implementation and numerical measurement from the shortcomings of both sorts of skeptical argument.     

Do you see what I know? On reasons,perceptual evidence,and epistemic status

Our epistemology can shape the way we think about perception and experience. Speaking as an epistemologist, I should say that I don't necessarily think that this is a good thing. If we think that we need perceptual evidence to have perceptual knowledge or perceptual justification, we will naturally feel some pressure to think of experience as a source of reasons or evidence. In trying to explain how experience can provide us with evidence, we run the risk of either adopting a conception of evidence according to which our evidence isn't very much like the objects of our beliefs that figure in reasoning (e.g., by identifying our evidence with experiences or sensations) or the risk of accepting a picture of experience according to which our perceptions and perceptual experiences are quite similar to beliefs in terms of their objects and their representational powers. But I think we have good independent reasons to resist identifying our evidence with things that don't figure in our reasoning as premises and I think we have good independent reason to doubt that experience is sufficiently belief‐like to provide us with something premise‐like that can figure in reasoning. We should press pause. We shouldn't let questionable epistemological assumptions tell us how to do philosophy of mind. I don't think that we have good reason to think that we need the evidence of the senses to explain how perceptual justification or knowledge is possible. Part of my scepticism derives from the fact that I think we can have kinds of knowledge where the relevant knowledge is not evidentially grounded. Part of my scepticism derives from the fact that there don't seem to be many direct arguments for thinking that justification and knowledge always requires evidential support. In this paper, I shall consider the three arguments I've found for thinking that justification and knowledge do always require evidential support and explain why I don't find them convincing. I think that we can explain perceptual justification, rationality, and defeat without assuming that our experiences provide us with evidence. In the end, I think we can partially vindicate Davidson's (notorious) suggestion that our beliefs, not experiences, provide us with reasons for forming further beliefs. This idea turns out to be compatible with foundationalism once we understand that foundational status can come from something other than evidential support.     

Effects of Dyadic Interaction on Argumentive Reasoning

The object of this research was to provide an explicit test of the hypothesis that engagement in thinking about a topic enhances the quality of reasoning about that topic. Engagement took the form of a series of dyadic discussions of the topic of capital punishment. At both age levels examined--early adolescence and young adulthood-this dyadic interaction significantly enhanced quality of reasoning, relative to a more minimal, single-occasion dyadic engagement or a control condition limited to repeated elicitation of the participant's own opinions and arguments. The range of different arguments increased from pretest to posttest, suggesting a process of social transmission of new knowledge. In addition, however, 10 different types of qualitative improvement in the form of reasoning appeared in both age groups. Primary among them were a shift from 1 -sided to 2-sided arguments, arguments based within a framework of alternatives, and metacognitive awareness of coexistence of multiple views. Process analysis of the dialogues provided evidence of a variety of different forms of interaction contributing to change.     

The influence of power and reason on young Maya children's endorsement of testimony

Two important parenting strategies are to impose one's power and to use reasoning. The effect of these strategies on children's evaluation of testimony has received very little attention. Using the epistemic vigilance framework, we predict that when the reasoning cue is strong enough it should overcome the power cue. We test this prediction in a population for which anthropological data suggest that power is the prominent strategy while reasoning is rarely relied on in the interactions with children. In Experiment 1, 4‐ to 6‐year‐old children from a traditional Maya population are shown to endorse the testimony supported by a strong argument over that supported by a weak argument. In Experiment 2, the same participants are shown to follow the testimony of a dominant over that of a subordinate. The participants are then shown to endorse the testimony of a subordinate who provides a strong argument over that of a dominant who provides either a weak argument (Experiment 3) or no argument (Experiment 4). Thus, when the power and reasoning cues conflict, reasoning completely trumps power.