Indicative and counterfactual ‘only if’ conditionals

We report three experiments to test the possibilities reasoners think about when they understand a conditional of the form ‘A only if B’ compared to ‘if A then B’. The experiments examine conditionals in the indicative mood (e.g., A occurred only if B occurred) and counterfactuals in the subjunctive mood (A would have occurred only if B had occurred). The first experiment examines the conjunctions of events that reasoners judge to be consistent with conditionals, e.g., A and B, not-A and not-B. It shows that people think about one possibility to understand ‘if’ and two possibilities to understand ‘only if’; they think about two possibilities to understand counterfactual ‘if’ and ‘only if’. The second experiment shows that the possibilities people think about when they understand ‘only if’ are in a different temporal order (e.g., B and A) to the possibilities they think about for ‘if’ (A and B). The third experiment shows that people make different inferences from ‘only if’ and ‘if’ conditionals and counterfactuals. The implications of the results for theories of counterfactual conditionals are considered.     

Upward and Downward Counterfactual Thought After Loss: A Multiwave Controlled Longitudinal Study

Counterfactual thoughts, mental simulations about how a situation may have turned out differently (i.e., “if only …, then …”), can reduce mental health after stressful life-events. However, how specific counterfactual thought types relate to post-loss mental health problems is unclear. We hypothesized that self-referenced upward counterfactuals (i.e., “If only I had done …, then the current situation would be better”) may serve as cognitive avoidance, thereby perpetuating loss-related distress. Conversely, downward counterfactuals (i.e., “If … had happened, then the current situation could have been [even] worse”) may facilitate benefit finding, thereby reducing distress. In a longitudinal survey, self-referent, other-referent, and nonreferent upward counterfactuals, and nonreferent downward counterfactuals were assessed at baseline. Prolonged grief and depression symptoms were assessed at baseline, and 6- and 12-month follow-ups. Multiple regression analyses assessed associations between counterfactual thoughts and symptom levels in 65 recently bereaved people who generated counterfactual thoughts about the loss-event. Moderator analyses assessed the unicity of significant effects in the previous step, by comparing these effects in 59 people generating loss-related counterfactuals with those in 59 propensity-score matched participants generating counterfactuals about other negative life-events. Multivariate analyses showed that nonreferent upward counterfactuals were uniquely strongly positively associated with prolonged grief and depression symptoms concurrently. Self-referent upward counterfactuals were uniquely positively associated with prolonged grief and depression symptoms longitudinally. Moderator analyses confirmed that thinking about how one’s (in)actions could prevent a death uniquely exacerbated prolonged grief and depression severity. Prolonged grief treatment may be improved by targeting self-blame and guilt.     

Counterfactual and semifactual conditionals prime alternative possibilities

The authors examined in 3 experiments the comprehension of counterfactuals, such as "If it had rained, the plants would have bloomed," and semifactuals, such as "Even if it had rained, the plants would have bloomed," compared with indicative conditionals, "If it rained, the plants bloomed." The first experiment showed that people read the negative conjunction, "not p and not q" faster when it was primed by a counterfactual than when it was primed by an indicative conditional. They read the affirmative conjunction, "p and q" equally quickly when it was primed by either conditional. The 2nd experiment showed that people read the negated-antecedent conjunction, "not p and q" faster when it was primed by a semifactual conditional. The 3rd experiment corroborated these results in a direct comparison of counterfactuals and semifactuals. The authors discuss the implications of the results for the mental representations of different conditionals.     

Two causal theories of counterfactual conditionals

Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayes net theories as models of people's understanding of counterfactuals. Experiments 1-3 show that neither theory makes correct predictions about backtracking counterfactuals (in which the event of the if-clause occurs after the event of the then-clause), and Experiment 4 shows the same is true of forward counterfactuals. An amended version of one of the approaches, however, can provide a more accurate account of these data.     

Deductive reasoning with factual, possible, and counterfactual conditionals

We compared reasoners' inferences from conditionals based on possibilities in the present or the past (e.g., "If Linda had been in Dublin then Cathy would have been in Galway") with their inferences based on facts in the present or the past (e.g., "If Linda was in Dublin then Cathy was in Galway"). We propose that people construct a richer representation of conditionals that deal with possibilities rather than facts: Their models make explicit not only the suppositional case, in which Linda is in Dublin and Cathy is in Galway, but also the presupposed case, in which Linda is not in Dublin and Cathy is not in Galway. We report the results of four experiments that corroborate this model theory. The experiments show that reasoners make more inferences from conditionals based on possibilities rather than on facts when the inferences depend on the presupposed case. The results also show that reasoners generate different situations to verify and falsify conditionals based on possibilities and facts.     

The Suppression of Inferences From Counterfactual Conditionals

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.     

The probability of causal conditionals

Conditionals in natural language are central to reasoning and decision making. A theoretical proposal called the Ramsey test implies the conditional probability hypothesis: that the subjective probability of a natural language conditional, P(if p then q), is the conditional subjective probability, P(q/p). We report three experiments on causal indicative conditionals and related counterfactuals that support this hypothesis. We measured the probabilities people assigned to truth table cases, P(pq), P(p notq), P( notpq) and P( notp notq). From these ratings, we computed three independent predictors, P(p), P(q/p) and P(q/ notp), that we then entered into a regression equation with judged P(if p then q) as the dependent variable. In line with the conditional probability hypothesis, P(q/p) was by far the strongest predictor in our experiments. This result is inconsistent with the claim that causal conditionals are the material conditionals of elementary logic. Instead, it supports the Ramsey test hypothesis, implying that common processes underlie the use of conditionals in reasoning and judgments of conditional probability in decision making.     

The compatibility heuristic in non-categorical hypothetical reasoning: Inferences between conditionals and disjunctions

A new theory explains how people make hypothetical inferences from a premise consistent with several alternatives to a conclusion consistent with several alternatives. The key proposal is that people rely on a heuristic that identifies compatible possibilities. It is tested in 7 experiments that examine inferences between conditionals and disjunctions. Participants accepted inferences between conditionals and inclusive disjunctions when a compatible possibility was immediately available, in their binary judgments that a conclusion followed or not (Experiment 1a) and ternary judgments that included it was not possible to know (Experiment 1b). The compatibility effect was amplified when compatible possibilities were more readily available, e.g., for ‘A only if B’ conditionals (Experiment 2). It was eliminated when compatible possibilities were not available, e.g., for ‘if and only if A B’ bi-conditionals and exclusive disjunctions (Experiment 3). The compatibility heuristic occurs even for inferences based on implicit negation e.g., ‘A or B, therefore if C D’ (Experiment 4), and between universals ‘All A’s are B’s’ and disjunctions (Experiment 5a) and universals and conditionals (Experiment 5b). The implications of the results for alternative theories of the cognitive processes underlying hypothetical deductions are discussed.     

Questioning the preparatory function of counterfactual thinking

Why do individuals mentally modify reality (e.g., “If it hadn’t rained, we would have won the game”)? According to the dominant view, counterfactuals primarily serve to prepare future performance. In fact, individuals who have just failed a task tend to modify the uncontrollable features of their attempt (e.g., “If the rules of the game were different, I would have won it”), generating counterfactuals that are unlikely to play any preparatory role. By contrast, they generate prefactuals that focus on the controllable features of their ensuing behavior (e.g., “If I concentrate more, I will win the next game”). Here, we test whether this tendency is robust and general. Studies 1a and 1b replicate this tendency and show that it occurs regardless of whether individuals think about their failures or their successes. Study 2 shows that individuals generate relatively few controllable counterfactuals, unless explicitly prompted to do so. These results raise some questions regarding the generality of the dominant view according to which counterfactuals mainly serve a preparatory function.     

Reasoning counterfactually: making inferences about things that didn't happen

The authors investigated the relationship between reasoners' understanding of subjunctive conditionals (e.g., if p had happened, then q would have happened) and the inferences they were prepared to endorse. Reasoners who made a counterfactual interpretation of subjunctive statements (i.e., they judged the statement to imply that p and q did not happen) endorsed different inferences than those who did not. Those who made a counterfactual interpretation were more likely to (a) judge the situation in which p and q occurred to be inconsistent with the conditional statement and (b) make negative inferences such as modus tollens (i.e., approximately q therefore approximately p). These findings occurred with familiar and unfamiliar content, affirmative and negative conditionals, and conditional and biconditional relations.     

Some age norms for the “woodworth-wells's substitution test”

If we seek to analyse causation in terms of counterfactual conditionals then we must assume that there is a class of counterfactuals whose members (i) are all and only those we need to support our judgements of causation, (ii) have truth-conditions specifiable without any irreducible appeal to causation. I argue that (i) and (ii) are unlikely to be met by any counterfactual analysis of causation. I demonstrate this by isolating a class of counterfactuals called non-projective counterfactuals, or NP-counterfactuals, and indicate how counterfactual analyses of causation must appeal to them to account for the correct causal judgements we make. I show that the truth-conditions of NP-counterfactuals are specifiable only by irreducible appeal to causation. A dilemma then holds: if counterfactual analyses of causation eschew appeal to NP-counterfactuals they are empirically inadequate, but if they appeal to NP-counterfactuals they are circular and thus conceptually inadequate.     

On the Mental Representation of Conditional Sentences

Four experiments are reported which attempt to externalize subjects' mental representation of conditional sentences, using novel research methods. In Experiment 1, subjects were shown arrays of coloured shapes and asked to rate the degree to which they appeared to be true of conditional statements such as 'If the figure is green then it is a triangle'. The arrays contained different distributions of the four logically possible cases in which the antecedent or consequent is true or false: TT, TF, FT, and FF. For example, a blue triangle would be FT for the conditional quoted above. In Experiments 2 to 4, subjects were able to construct their own arrays to make conditionals either true or false with any distribution of the four cases they wished to choose. The presence and absence of negative components was varied, as was the form of the conditional, being either 'if then' as above or 'only if': 'The figure is green only if it is a triangle'. The first finding was that subjects represent conditionals in fuzzy way: conditionals that include some counter-example TF cases (Experiment 1) may be rated as true, and such cases are often included when subjects construct an array to make the rule true (Experiments 2 to 4). Other findings included a strong tendency to include psychologically irrelevant FT and FF cases in constructed arrays, presumably to show that conditional statements only apply some of the time. A tendency to construct cases in line with the 'matching bias' reported on analogous tasks in the literature was found, but only in Experiment 4, where the number of symbols available to construct each case was controlled. The findings are discussed in relation to the major contemporary theories of conditional reasoning based upon inference rules and mental models, neither of which can account for all the results.     

The differential effect of realistic and unrealistic counterfactual thinking on regret

Research has established that realistic counterfactual thinking can determine the intensity and the content of people's affective reactions to decision outcomes and events. Not much is known, however, about the affective consequences of counterfactual thinking that is unrealistic (i.e., that does not correspond to the main causes of a negative outcome). In three experiments, we investigate the influence of realistic and unrealistic counterfactuals on experienced regret after negative outcomes. In Experiment 1, we found that participants who thought unrealistically about a poor outcome reported less regret than those who thought realistically about it. In Experiments 2a and 2b, we replicated this finding and we showed that the decrease in regret was associated with a shift in the causal attributions of the poor outcome. Participants who thought unrealistically attributed it more to external circumstances and less to their own behaviours than those who thought realistically about it. We discuss the implications of these findings for the role of counterfactuals as self-serving biases and the functionality of regret as a counterfactual emotion.     

When can we say 'if'?

In this study, we focus on the conditions which permit people to assert a conditional statement of the form 'if p then q' with conversational relevance. In a broadly decision-theoretic approach, also drawing on hypothetical thinking theory [Evans, J. St. B. T. (2007). Hypothetical thinking: Dual processes in reasoning and judgement. Hove, UK: Psychology Press.], we predicted that conditional tips and promises would appear more useful and persuasive and be more likely to encourage an action p when (a) the conditional link from p to q was stronger, (b) the cost of the action p was lower and (c) the benefit of the consequence q was higher. Similarly, we predicted that conditional warnings and threats would be seen as more useful and persuasive and more likely to discourage an action p when (a) the conditional link from p to q was stronger, (b) the benefit of the action p was lower and (c) the cost of the consequence q was higher. All predictions were strongly confirmed, suggesting that such conditionals may best be asserted when they are of high relevance to the goals of the listener.     

When will is not the same as should: The role of modals in reasoning with legal conditionals

Naïve reasoners reject logically valid conclusions from conditional rules if they can think of exceptions in which the antecedent is true, but the consequent is not. However, when reasoning with legal conditionals (e.g., “If a person kills another human, then this person should be punished for manslaughter”) people hardly consider exceptions but evaluate conclusions depending on their own sense of justice. We show that participants’ reluctance to consider exceptions in legal reasoning depends on the modal auxiliary used. In two experiments we phrased legal conditionals either with the modal “should” (i.e., “ . . . then this person should be punished”), or with “will” (i.e., “ . . . then this person will be punished”) and presented them as modus ponens or modus tollens inferences. Participants had to decide whether the offender should or will be punished (modus ponens) or whether the offender indeed committed the offence (modus tollens). For modus ponens inferences phrased with “should” we replicate previous findings showing that participants select conclusions on the basis of their own sense of justice (Experiments 1 and 2). Yet, when the legal conditional is phrased with the modal “will” this effect is attenuated (Experiments 1 and 2), and exceptions are considered (Experiment 1). The modal auxiliary did not affect modus tollens inferences.     

Theories of conditional reasoning: a developmental examination of competing hypotheses

Children and adolescents were presented with problems that contained deontic (i.e., if action p is taken, then precondition q must be met) or causal (i.e., if event p occurs, then event q will transpire) conditionals and that varied in the ease with which alternative antecedents could be activated. Results showed that inferences were linked to the availability of alternative antecedents and the generation of "disabling" conditions (claims that the conditionals were false under specific circumstances). Age-related developments were found only on problems involving indeterminate inferences. Correlations among inferences differed for children and adolescents. The findings provide stronger support for domain-general theories than for domain-specific theories of reasoning and suggest, under some conditions, age-related changes in the roles of implicit and explicit processing.     

Putting words in perspective

In this article, we explore the nature of the conceptual knowledge retrieved when people use words to think about objects. If conceptual knowledge is used to simulate and guide action in the world, then how one can interact with an object should be reflected in the speed of retrieval and the content that is retrieved. This prediction was tested in three experiments in which a part verification procedure was used. Experiments 1 and 2 demonstrated that speed of part verification varied with the perspective imposed on the object by the language used to name the object (e.g., "You are driving a car" or "You are fueling a car"). In Experiment 3, parts were chosen so that actions directed toward them (on the real object) require movement upward (e.g., the roof of a car) or downward (e.g., the wheels of a car). Orthogonally, responding "yes" required an upward or a downward movement to a response button. Responding in a direction incompatible with the part's location (e.g., responding downward to verify that a car has a roof) was slow relative to responding in a direction compatible with the part's location. These results provide a strong link between concept knowledge and situated action.     

对相容和不相容析取关系下析取句与条件句之间推理的比较

研究析取句和条件句之间的推理能检验推理心理学中的主要理论解释。一个实验考察了析取句和条件句中两个基本成分之间的关系(相容析取与不相容析取)和推理方向(由析取句推条件句与由条件句推析取句)对析取句与其等值的条件句之间推理的影响。结果发现,推理方向的影响取决于条件句和析取句中基本成分间的关系,在不相容析取关系下的推理成绩好于在相容析取关系下的推理成绩。现有的推理理论不能解释被试的整体反应模式,作者提出的特殊知识启发式与一般的句法意义对比启发式的竞争能统一解释被试的主导反应模式。     

Indicatives,Subjunctives, and the Falsity of the Antecedent

It is widely held that there are important differences between indicative conditionals (e.g., “If the authors are linguists, they have written a linguistics paper”) and subjunctive conditionals (e.g., “If the authors had been linguists, they would have written a linguistics paper”). A central difference is that indicatives and subjunctives convey different stances toward the truth of their antecedents. Indicatives (often) convey neutrality: for example, about whether the authors in question are linguists. Subjunctives (often) convey the falsity of the antecedent: for example, that the authors in question are not linguists. This paper tests prominent accounts of how these different stances are conveyed: whether by presupposition or conversational implicature. Experiment 1 tests the presupposition account by investigating whether the stances project—remain constant—when embedded under operators like negations, possibility modals, and interrogatives, a key characteristic of presuppositions. Experiment 2 tests the conversational-implicature account by investigating whether the stances can be cancelled without producing a contradiction, a key characteristic of implicatures. The results provide evidence that both stances—neutrality about the antecedent in indicatives and the falsity of the antecedent in subjunctives—are conveyed by conversational implicatures.