In this study on deduction, the authors argue that people reason by imagining the relevant state of affairs, ie building an internal model of it, formulating a tentative conclusion based on this model and then searching for alternative models.
The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)
Three experiments are reported which show that in certain contexts subjects reject instances of the valid modus ponens and modus tollens inference form in conditional arguments. For example, when a conditional premise, such as: If she meets her friend then she will go to a play, is accompanied by a conditional containing an additional requirement: If she has enough money then she will go to a play, subjects reject the inference from the categorical premise: She meets her friend, to the (...) conclusion: She will go to a play. Other contexts suppress the conditional fallacies. The first experiment demonstrates the effects of context on conditional reasoning. The second experiment shows that the inference suppression disappears when the categorical premise refers to both of the antecedents, such as: She meets her friend and she has enough money. In this case, subjects make both the valid inferences and the fallacies, regardless of the contextual information. The third experiment establishes that when subjects are given general information about the duration of a situation in which a conditional inducement was uttered, such as: If you shout then I will shoot you, they reject both the valid inferences and the fallacies. The results suggest that the interpretation of premises plays an even more central role in reasoning than has previously been admitted. Trois expériences montrent que dans certains contextes les sujets rejettent des instances valides de modus ponens et de modus tollens dans des énoncés conditionnels. Par exemple, quand une prémisse conditionnelle comme: Si elle rencontre son ami, alors elle ira jouer, est accompagnée par une phrase contenant une condition supplémentaire: Si elle a assez d'argent, alors elle ira jouer, les sujets rejettent l'inférence liant la prémisse catégorielle: Elle rencontre son ami, à la conclusion: Elle ira jouer. D'autres contextes éliminent également les inférences conditionnelles fallacieuses. La premiére expérience démontre l'effet du contexte sur la raisonnement conditionnel. La deuxiéme expérience montre que la suppression de l'inférence disparait quand la prémisse catégorielle fait référence aux deux antécédants, comme: Elle rencontre son ami et elle a assez d'argent. Dans ce cas, les sujets font aussi bien les inférences valides et fallacieuses, quelle que soit l'information contextuelle. La troisiéme expérience établit que quand l'on donne aux sujets des informations générales à propos de la durée d'une situation dans laquelle une conditionnelle a été prononcée, comme Si tu cries, alors je te tire dessus, ils rejettent autant les inférences valides que les inférences fallacieuses. Ces résultats suggèrent que l'interprétation des prémisses joue un rŏle encore plus central dans le raisonnement que l'on admettait auparavant. (shrink)
This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (...) (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities. (shrink)
When people understand a counterfactual such as “if the flowers had been roses, the trees would have been orange trees,” they think about the conjecture, “there were roses and orange trees,” and they also think about its opposite, the presupposed facts. We test whether people think about the opposite by representing alternates, for example, “poppies and apple trees,” or whether models can contain symbols, for example, “no roses and no orange trees.” We report the discovery of an inference‐to‐alternates effect—a tendency (...) to make an affirmative inference that refers to an alternate even from a negative minor premise, for example, “there were no orange trees, therefore there were poppies.” Nine experiments show the inference‐to‐alternates effect occurs in a binary context, but not a multiple context, and for direct and indirect reference; it can be induced and reduced by prior experience with similar inferences, and it also occurs for indicative conditionals. The results have implications for theories of counterfactual conditionals, and of negation. (shrink)
This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.
Four studies show that observers and readers imagine different alternatives to reality. When participants read a story about a protagonist who chose the more difficult of two tasks and failed, their counterfactual thoughts focused on the easier, unchosen task. But when they observed the performance of an individual who chose and failed the more difficult task, participants' counterfactual thoughts focused on alternative ways to solve the chosen task, as did the thoughts of individuals who acted out the event. We conclude (...) that these role effects may occur because participants' attention is engaged when they experience or observe an event more than when they read about it. (shrink)
We report two Experiments to compare counterfactual thoughts about how an outcome could have been different and causal explanations about why the outcome occurred. Experiment 1 showed that people generate counterfactual thoughts more often about controllable than uncontrollable events, whereas they generate causal explanations more often about unexpected than expected events. Counterfactual thoughts focus on specific factors, whereas causal explanations focus on both general and specific factors. Experiment 2 showed that in their spontaneous counterfactual thoughts, people focus on normal events (...) just as often as exceptional events, unlike in directed counterfactual thoughts. The findings are consistent with the suggestion that counterfactual thoughts tend to focus on how a specific unwanted outcome could have been prevented, whereas causal explanations tend to provide more general causal information that enables future understanding, prediction, and intervention in a wide range of situations. (shrink)
We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, “if she watered the plants they bloomed,” when beliefs about additional background conditions, for example, “if the sun shone they bloomed” decrease the frequency of inferences such as modus tollens (from “the plants did not bloom” to “therefore she did not water them”). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, “if she had watered the plants they would (...) have bloomed,” when beliefs about the known or presupposed facts, “she did not water the plants and they did not bloom” increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from “she did not water the plants” to “therefore they did not bloom”) is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new “switched‐suppression” effect for conditionals with negated components, for example, “if she had not watered the plants they would not have bloomed”: modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning. (shrink)
Semifactual thinking about what might have been the same, e.g., ''even if Philip had not chosen the chocolate ice-cream sundae, he would have developed an allergic reaction'' has been neglected compared to counterfactual thinking about what might have been different, e.g., ''if only Philip had not chosen the chocolate ice-cream sundae, he would not have developed an allergic reaction''. We report the first systematic comparison of the two sorts of thinking in two experiments. The first experiment showed that counterfactual ''if (...) only'' thoughts about an antecedent event lead people to judge the event to be more causally related to the outcome, whereas semifactual ''even if'' thoughts lead people to judge the antecedent event to be less causally related to the outcome. In addition, the experiment showed that generating counterfactual ''if only'' thoughts increases emotional reactions such as regret, whereas generating semifactual ''even if'' thoughts decreases such reactions. The second experiment, along with a replication experiment, showed that when people complete ''if only'' and ''even if'' sentence stems, they focus on different alternative antecedents to the outcome: ''if only'' thoughts focus on alternatives that would undo the outcome whereas ''even if'' thoughts focus on alternatives that would not undo it, from among a set of available alternative antecedents in which either all, some, or none would undo the outcome. The implications of the results for theories of thinking about what might have been are discussed. (shrink)
Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live (...) in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules. (shrink)
We report the results of two experiments that show that participants rely on both emotion and reason in moral judgments. Experiment 1 showed that when participants were primed to communicate feelings, they provided emotive justifications not only for personal dilemmas, e.g., pushing a man from a bridge that will result in his death but save the lives of five others, but also for impersonal dilemmas, e.g., hitting a switch on a runaway train that will result in the death of one (...) man but save the lives of five others; when they were primed to communicate thoughts, they provided non-emotive justifications for both personal and impersonal dilemmas. Experiment 2 showed that participants read about a protagonist's emotions more quickly when the protagonist was faced with a personal dilemma than an impersonal one, but they read about the protagonist's decision to act or not act equally quickly for personal and impersonal dilemmas. (shrink)
We examined how people think about how things could have turned out differently after they made a decision to cooperate or not in three social interactions: the Prisoner’s dilemma (Experiment 1), the Stag Hunt dilemma (Experiment 2), and the Chicken game (Experiment 3). We found that participants who took part in the game imagined the outcome would have been different if a different decision had been made by the other player, not themselves; they did so whether the outcome was good (...) or bad for them, their own choice had been to cooperate or not, and the other player’s choice had been to cooperate or not. Participants who only read about a fictional protagonist’s game imagined changes outside the protagonist’s control (such as the other player’s decision) after a good outcome but within the protagonist’s control (such as the protagonist’s decision) after a bad outcome. The implications for theories of counterfactual thinking and moral decision-making are discussed. (shrink)
People judge that an individual who attempts to harm someone but fails should be blamed and punished more when they imagine how things could have turned out worse, compared to when they imagine how things could have turned out the same, or when they think only about what happened. This moral counterfactual amplification effect occurs when people believe the protagonist had no reason for the attempt to harm, and not when the protagonist had a reason, as Experiment 1 shows. It (...) occurs for intentional failed attempts to harm and also for accidental near-misses, as Experiment 2 shows, but not for failed attempts in which the harm occurs anyway by another cause, for both general judgments about the event and specific judgments about the individual's actions, as Experiments 3 and 4 show. The implications for understanding the role of counterfactual thoughts in moral judgement are discussed. (shrink)
When people think about how a situation might have turned out differently, they tend to imagine counterfactual alternatives to their actions. We report the results of three experiments which show that people imagine alternatives to actions differently when they know about a reason for the action. The first experiment ( n = 36) compared reason - action sequences to cause - effect sequences. It showed that people do not imagine alternatives to reasons in the way they imagine alternatives to causes: (...) they imagine an alternative to an action more than an effect, and to a cause more than a reason. The second experiment ( n = 214) and the third experiment ( n = 190) both show that different sorts of reasons have different sorts of effects on how people imagine alternatives to actions. People imagine an alternative to an action (the protagonist went to a ball) less often when they know the reason for the action was an obligation (he had to participate in fundraising) compared to when they know about a weaker reason (he wanted to meet a famous violinist) or no reason. The second experiment shows the effect for a social obligation and the third experiment replicates and extends it to a health obligation. We interpret the results in terms of the possibilities that people keep in mind about actions and their reasons. (shrink)
How do people make deductions? The orthodox view in psychology is that they use formal rules of inference like those of a “natural deduction” system.Deductionargues that their logical competence depends, not on formal rules, but on mental models. They construct models of the situation described by the premises, using their linguistic knowledge and their general knowledge. They try to formulate a conclusion based on these models that maintains semantic information, that expresses it parsimoniously, and that makes explicit something not directly (...) stated by any premise. They then test the validity of the conclusion by searching for alternative models that might refute the conclusion. The theory also resolves long-standing puzzles about reasoning, including how nonmonotonic reasoning occurs in daily life. The book reports experiments on all the main domains of deduction, including inferences based on prepositional connectives such as “if” and “or,” inferences based on relations such as “in the same place as,” inferences based on quantifiers such as “none,” “any,” and “only,” and metalogical inferences based on assertions about the true and the false. Where the two theories make opposite predictions, the results confirm the model theory and run counter to the formal rule theories. Without exception, all of the experiments corroborate the two main predictions of the model theory: inferences requiring only one model are easier than those requiring multiple models, and erroneous conclusions are usually the result of constructing only one of the possible models of the premises. (shrink)
Participants acting as mock jurors made inferences about whether a person was a suspect in a murder based on an expert's testimony about the presence of objects at the crime scene and the disclosure that the testimony was true or false. Experiment 1 showed that participants made more correct inferences, and made inferences more quickly, when the truth or falsity of the expert's testimony was disclosed immediately after the testimony rather than when the disclosure was delayed. Experiment 2 showed no (...) advantage for prior disclosure over immediate disclosure. Experiment 3 showed that the pattern of inferences when there was no disclosure mirrored the pattern when it was disclosed that the expert's testimony was true rather than false. Participants made more correct inferences from true conjunctions than disjunctions, and from false disjunctions than conjunctions. We discuss the implications for theories of the mental representations and cognitive processes that underlie human reasoning. (shrink)
We resolve the two problems that Hardman raises. The first problem arises from a misunderstanding: the crucial distinction is between one-model and multiple-model problems. The second problem illuminates a deeper principle: conclusions depend on the procedures for interpreting models. We describe an algorithm that obviates the problem and empirical work that reveals a new view of syllogistic reasoning.
Van der Henst argues that the theory of mental models lacks a pragmatic component. He fills the gap with the notion that reasoners draw the most relevant conclusions. We agree, but argue that theories need an element of “nondeterminism.” It is often impossible to predict either what will be most relevant or which particular conclusion an individual will draw.