Reasoning with contrary-to-fact propositions

In the initial study, the ability of subjects at four age levels (10, 13, 15, 18 years) (1) to accept if-then premises as a basis for reasoning and (2) to reason correctly with if-then premises was examined. Half the subjects were assessed with four reasoning problems involving factually accurate premises. The other half received factually inaccurate premises which were derived from the preceding ones by altering a single term. Both tests included an abstract problem which preceded the concrete propositions. Results indicate that the 10 year olds, and to a lesser extent the 13 year olds, did have difficulty in accepting contrary-to-fact premises as a basis for reasoning. The 15 and 18 year olds did not, but did find reasoning correctly more difficult with contrary-to-fact premises. The second study examined the ability of 5 and 7 year olds to accept contrary-to-fact premises. Subjects were given factually false premises either alone or within a fantasy context. Results indicate that the fantasy context decreases the extent to which empirical knowledge interferes with accepting contrary-to-fact premises. This result supports the notion that a representational process may be involved in accepting contrary-to-fact premises.     

Getting the Most Out of Inconsistency

In this paper we look at two classic methods of deriving consequences from inconsistent premises: Rescher-Manor and Schotch-Jennings. The overall goal of the project is to confine the method of drawing consequences from inconsistent sets to those that do not require reference to any information outside of very general facts about the set of premises. Methods in belief revision often require imposing assumptions on premises, e.g., which are the important premises, how the premises relate in non-logical ways. Such assumptions enable one to select a reasonable collection of formulas from all the formulas of the language (the set of consequences of an inconsistent set). Basic versions of the classic methods only use logical relations between the premises. We compare and criticize each of the classic views with an eye to combining the views to get the most out of inconsistent premises. We do this in a way that will respect the theoretical grounding of each view while meeting our other restrictions.     

A curious belief-bias effect: reasoning with false premises and inhibition of real-life information

Many studies have shown that inferential behavior is strongly affected by access to real-life information about premises. However, it is also true that both children and adults can often make logically appropriate inferences that lead to empirically unbelievable conclusions. One way of reconciling these is to suppose that logical instructions allow inhibition of information about premises that would otherwise be retrieved during reasoning. On the basis of this idea, we hypothesized that it should be easier to endorse an empirically false conclusion on the basis of clearly false premises than on the basis of relatively believable premises. Two studies are presented that support this hypothesis.     

The Possibility of Inductive Moral Argumets

Abstract

Is it possible to have moral knowledge? ‘Moral justification skeptics’ hold it is not, because moral beliefs cannot have the sort of epistemic justification necessary for knowledge. This skeptical stance can be summed up in a single, eat argument, which includes the premise that ‘Inductive arguments from non-moral premises to moral conclusions are not possible.’ Other premises in the argument may rejected, but only at some cost. It would be noteworthy, therefore, if ‘inductive inferentialism’ about morals were show to be at least possible. Some philosophers may suppose that inductive moral argumets from non-moral premises cannot get off the ground, but I show that a perfectly legitimate inductive moral argument exists. This argument has on-moral premises and a moral conclusion, its premises are related to its conclusion in the right way, and it avoids some of the problems of other, better-know argumets from ‘Is’ to ‘Ought’.     

How falsity dispels fallacies

From certain sorts of premise, individuals reliably infer invalid conclusions. Two Experiments investigated a possible cause for these illusory inference: Reasoners fail to think about what is false. In Experiment 1, 24 undergraduates drew illusory and control inferences from premises based on exclusive disjunctions (“or else”). In one block, participants were instructed to falsify the premises of each illusory and control inference before making the inference. In the other block, participants did not receive these instructions. There were more correct answers for illusory disjunctions whose premises had been falsified than there were for illusory disjunctions that had not been falsified. A second Experiment introduced illusory inferences in a real world context that accentuated falsification of premises. Accuracy also improved. Knowledge of how to falsify premises and to consider their implications for true premises transferred to a new problem introduced at the end of the Experiment without the falsification instruction. The participants' ratings of the difficulty of the inferences showed that they did not err simply because illusory inferences are perceived to be more difficult than control problems. The model theory predicts these results because it postulates that the limitations of working memory preclude the representation of false information.     

The effects of belief on the spontaneous production of syllogistic conclusions

Two experiments examined the effects of subjects' beliefs on syllogistic inference. The first experiment showed that beliefs biased the spontaneous conclusions that subjects drew for themselves. These effects were more marked for indeterminate premises (which yield no non-trivial valid conclusions) than for determinate premises (which yield valid conclusions). There was also an effect of the nature of the beliefs: conclusions that were false by definition had a bigger effect on deductions than those that were false as a matter of fact. The second experiment replicated the finding for determinate syllogisms, using problems in moods in which the status of the valid conclusion could not be altered by conversion of the premises. Beliefs accordingly appear to affect the process of reasoning rather than the interpretation of premises.     

Effective elaboration and inferential reasoning

The present study investigated the effects of several variables on subjects’ abilities to draw inferences from two related premises. Contiguous presentation of the related sentences led to significantly higher inference scores than did noncontiguous presentation. The nature of the initial premise was also manipulated. For some subjects, the initial premise was relatively consistent with subjects’ semantic knowledge, whereas other subjects received initial premises that were somewhat arbitrary with respect to semantic knowledge. Inference scores were significantly higher for subjects who received the more consistent initial premises. This effect persists even when differential memory for the initial premises has been accounted for. The results suggest certain constraints on the nature of the knowledge one must possess in order to make appropriate inferences from material.     

小学儿童一维空间方位传递性推理能力的发展

研究了小学儿童一维空间方位传递性推理能力的发展水平及认知策略 ,同时 ,对心理模型理论进行了检验。被试为城市中等小学 7岁、9岁、11岁儿童各 2 4名 ,男女各半。 4种实验任务分别为三前提单模型、三前提双模型、四前提单模型和四前提双模型。采用个别实验 ,儿童在前提呈现的情况下进行推理。主要研究结果 :(1)从小学 7岁到 11岁 ,儿童的一维空间方位传递性推理能力明显提高 ,7岁儿童初步形成了一维空间方位推理能力 ,9岁和 11岁基本具有了这种能力 ;(2 )随着年龄增长 ,使用模型建构策略解决问题的儿童人次越来越多 ,绝大部分 11岁儿童都能使用这一策略进行推理。但即使儿童使用了模型建构策略 ,他们的推理成绩也没有反映出模型数量所造成的任务难度差异 ,即不符合心理模型理论关于模型数量的主要预期。     

Illusions in modal reasoning

According to the mental model theory, models represent what is true, but not what is false. One unexpected consequence is that certain inferences should have compelling, but invalid, conclusions. Three experiments corroborated the occurrence of such illusions in reasoning about possibilities. When problems had the heading "Only one of the premises is true," the participants considered the truth of each premise in turn, but neglected the fact that when one premise is true, the others are false. When two-premise problems had the heading "One of the premises is true and one is false," the participants still neglected the falsity of one of the premises. As predicted, however, the illusions were reduced when reasoners were told to check their conclusions against the constraint that only one of the premises was true. We discuss alternative explanations for illusory inferences and their implications for current theories of reasoning.     

小学儿童对日常生活事件时间关系推理能力的初探

探查小学儿童对含有“在什么之前”“同时”日常生活事件时间关系的推理发展过程及其影响因素。被试为7岁、9岁、11岁3个年龄组共54名小学儿童,每个年龄组18人。4种问题模式分别为带有传递关系的单模型问题、带有无关前提的单模型问题、含两个前提的单模型问题、有肯定答案的多模型问题。每种问题模式含3种具体探察任务。主要研究结果表明：在本实验条件下,（1）儿童对事件时间顺序关系的推理从7岁到9岁有快速发展的趋势;（2）单模型和多模型任务无显著差异,模型数量似乎不是影响儿童推理成绩的关键因素;（3）儿童能够主动采用5种策略解决问题。逆向关系传递策略是问题解决的有效策略。     

Affirming the consequent

The thesis of this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its premises at all favorably relevant to its conclusion. In support of this thesis I assume two premises and argue for a third. My two assumptions are these: (1) that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion certain relative to its premises (this is widely, if not universally, acknowledged by writers on logic), and (2) premises are favorably relevant to a conclusion only if it is certain or probable relative to them (I argued for this in an earlier paper). The premise I argue for in this paper is that an argument's possessing the form of affirming the consequent does not suffice to make its conclusion probable relative to its premises. To establish this third premise, I first refute a defense of the contrary position (namely, that an argument's possessing the form of affirming the consequent suffices to make its conclusion probable relative to its premises), then offer counterexamples to that position, and finally demonstrate the failure of several attempts to save it.An earlier draft of this paper was read at the meeting of the Association for Informal Logic and Critical Thinking at the meeting of the American Philosophical Association in Portland on March 27, 1992. I am indebted to Terry Parsons, John Woods, and this journal's anonymous referees for their comments.     

工作记忆、表达方式和同质性对线性三段论推理影响的眼动研究

采用眼动记录法,探讨了工作记忆、两个前提间的关系以及表达方式对线性三段论推理的影响。本实验采用2（表达方式：肯定、否定）×2（前提间的关系：同质、不同质）×2（工作记忆容量：高、低）的混合设计。通过分析总注视时间、第一次注视时间、第二次注视时间和回视,发现线性三段论推理过程既有语言加工的参与又有表象加工的参与。推理过程中的语言表征过程和空间关系的建立都受到工作记忆容量的影响,被试的工作记忆容量越高,就越容易建立语言表征和空间的关系。     

Deductive schemas with uncertain premises using qualitative probability expressions

The new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that contained non-numerical expressions (e.g., “the chances are high”) and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, even with sure premises), and (3) participants' interpretation of the conditional agreed with de Finetti's “conditional event” but not with the material conditional.     

Syllogistic inference

This paper reviews current psychological theories of syllogistic inference and establishes that despite their various merits they all contain deficiencies as theories of performance. It presents the results of two experiments, one using syllogisms and the other using three-term series problems, designed to elucidate how the arrangement of terms within the premises (the ‘figure’ of the premises) affects performance. These data are used in the construction of a theory based on the hypothesis that reasoners construct mental models of the premises, formulate informative conclusions about the relations in the model, and search for alternative models that are counterexamples to these conclusions. This theory, which has been implemented in several computer programs, predicts that two principal factors should affect performance: the figure of the premises, and the number of models that they call for. These predictions were confirmed by a third experiment.     

Reasoning from unfamiliar premises: a study with unschooled adults

A long tradition of research initiated by Luria in the 1930s has established that unschooled adults perform poorly on reasoning tasks. Particularly when the premises are unfamiliar, they adopt an inappropriate empirical bias. However, recent findings show that young children with little or no schooling reason competently if prompted to think of the unfamiliar premises as pertaining to a distant planet. We tested two groups of adults: illiterate, unschooled adults and adults with limited schooling. Both groups received problems that included either a premise with unknown content or a premise contradicting their everyday experience. When given a minimal prompt, both groups manifested the customary empirical bias. By contrast, when explicitly prompted to think of the unfamiliar premises as pertaining to a distant planet, they reasoned accurately and appropriately justified their conclusions in terms of the supplied premises.     

Children's memory for the premises in a transitive measurement task assessed by elicited and spontaneous justifications

Two experiments were conducted to test the hypothesis that children who fail to make the transitive inference do so because they do not recall the premises. In the first, 32% of the children who made an incorrect inference in a transitive measurement task justified their inference by the correct premises. In the second, where spontaneous justification was encouraged by testing dyads on the same task, the percentage was 15%. In neither experiment were there children who justified an incorrect inference by incorrect premises or a solo premise. The results are interpreted as showing that not only can incorrect inferers store the correct premises, but that they can also retrieve them adequately. The pattern and outcome of interactions between nontransitive and transitive inferers in the dyad sessions parallelled similar studies with conserver-nonconserver dyads. Both sets of data were taken as reinforcing the commonality between transitivity and the other concrete operations.     

Strategies in sentential reasoning

Four experiments examined the strategies that individuals develop in sentential reasoning. They led to the discovery of five different strategies. According to the theory proposed in the paper, each of the strategies depends on component tactics, which all normal adults possess, and which are based on mental models. Reasoners vary their use of tactics in ways that have no deterministic account. This variation leads different individuals to assemble different strategies, which include the construction of incremental diagrams corresponding to mental models, and the pursuit of the consequences of a single model step by step. Moreover, the difficulty of a problem (i.e., the number of mental models required by the premises) predisposes reasoners towards certain strategies. Likewise, the sentential connectives in the premises also bias reasoners towards certain strategies, e.g., conditional premises tend to elicit reasoning step by step whereas disjunctive premises tend to elicit incremental diagrams.     

Conditional reasoning with causal premises: Evidence for a retrieval model

This study examined the hypothesis that a key process in conditional reasoning with concrete premises involves on-line retrieval of information about potential alternate antecedents. Participants were asked to solve reasoning problems with causal conditional premises (If cause P then effect Q). These premises were inserted into short contexts. The availability of potential alternatives was varied from one context to another by adding statements that explicitly invalidated one or more of these alternatives (i.e., other causes that lead to the effect (Q). The invalidated alternatives differed in the degree of their semantic association to the consequent term (Q). The results show that the effect of invalidating one or more potential alternatives on the two uncertain logical forms, AC and DA, was largely determined by their relative associative strength. These results strongly support a model for conditional reasoning with causal premises that supposes that a key element in responding to the uncertain logical forms is on-line retrieval of at least one potential alternative antecedent.     

Intertemporal Disagreement and Empirical Slippery Slope Arguments

One prevalent type of slippery slope argument has the following form: (1) by doing some initial act now, we will bring it about that we subsequently do some more extreme version of this act, and (2) we should not bring it about that we do this further act, therefore (3) we should not do the initial act. Such arguments are frequently regarded as mistaken, often on the grounds that they rely on speculative or insufficiently strong empirical premises. In this article I point out another location at which these arguments may go wrong: I argue that, in their standard form, the truth of their empirical premises constitutes evidence for the falsity of their normative premises. If we will, as predicted, do the further act in the future, this gives us at least a prima facie reason to believe that the performance of this further act would be good, and thus something we should try to bring about. I end by briefly assessing the dialectic implications of my argument. I delineate a subset of slippery slope arguments against which my objection may be decisive, consider how the proponents of such arguments may evade my objection by adding further premises, and examine the likely plausibility of these additional premises.     

Children's syllogistic reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.