Initial models in conditionals: evidence from priming

We examined the comprehension of different types of conditionals. We measured the reading time of sentences primed by different types of conditionals (Experiments 1 and 2). We found that the participants read not-p and not-q faster when it was primed by the conditional form p if q and they were slower to read p and q when it was primed by the conditional form p only if q. This effect disappeared in the second experiment, where the order of the elements was reversed (q and p and not-q and not-p). These results suggest that the conditional form p if q elicits an initial representation "from p to q" with two possibilities, while the conditional form p only if q elicits a reverse representation with only one possibility. The third experiment showed that there were effects of the order only for the conditional if p then q, which confirms the reverse representation hypothesis. We discuss the implications of these results for different theories of conditional comprehension.     

People think about what is true for conditionals,not what is false: Only true possibilities prime the comprehension of “if”

We report the results of two priming experiments that examine the comprehension of conditionals—for example, “if there are apples then there are oranges”—and biconditionals—for example, “if and only if there are apples then there are oranges”. The first experiment showed that participants read a biconditional faster when it was primed by a true possibility, “there were apples and there were oranges” than when it was primed by a false possibility, “there were no apples and there were oranges”; a conditional was primed equally by both possibilities. The second experiment showed that participants read the negated-antecedent conjunction faster when it was primed by a conditional than when it was primed by a biconditional; the affirmative conjunction was primed equally by both connectives. The experiments show that (a) when people understand “if A then B”, they access the true possibilities, “A and B”, and “not-A and B”, and (b) when they understand “if and only if A then B” they access “A and B”, but they do not access “not-A and B”. We discuss their implications for current theories of reasoning.     

The negated conditional: a litmus test for the suppositional conditional?

Under the suppositional account of conditionals, when people think about a conditional assertion, "if p then q," they engage in a mental simulation in which they imagine p holds and evaluate the probability that q holds under this supposition. One implication of this account is that belief in a conditional equates to conditional probability [P(q/p)]. In this paper, the authors examine a further implication of this analysis with respect to the wide-scope negation of conditional assertions, "it is not the case that if p then q." Under the suppositional account, nothing categorically follows from the negation of a conditional, other than a second conditional, "if p then not-q." In contrast, according to the mental model theory, a negated conditional is consistent only with the determinate state of affairs, p and not-q. In 4 experiments, the authors compare the contrasting predictions that arise from each of these accounts. The findings are consistent with the suppositional theory but are incongruent with the mental model theory of conditionals.     

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.     

Priming effect on the exceptive conditional ‘except if’

Here we report the results of one priming experiment that examines the comprehension of exceptive conditionals—for example, ‘Mary will go out tonight except if she has an exam tomorrow’—and indicative conditionals—for example, ‘Mary will not go out tonight if she has an exam tomorrow’. The experiment showed that participants read the true possibility ‘Mary is not going out tonight and she has an exam tomorrow’ faster when it was primed by an exceptive conditional than when it was primed by an indicative; other possibilities (‘Mary is going out tonight and she does not have an exam tomorrow’, ‘Mary is going out tonight and she has an exam tomorrow’ and ‘Mary is not going out tonight and she does not have an exam tomorrow’) were primed equally by both connectives. The experiments showed that (1) when people understand ‘B except if A’, they access the true possibilities ‘not-A & B’ and ‘A & not-B’, and (2) when they understand ‘B, if not-A’ they access ‘not-A & B’, but they do not access ‘A & not-B’. We discuss the implications of this for current theories of reasoning.     

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.     

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.     

Causal conditionals and counterfactuals

Causal counterfactuals e.g., 'if the ignition key had been turned then the car would have started' and causal conditionals e.g., 'if the ignition key was turned then the car started' are understood by thinking about multiple possibilities of different sorts, as shown in six experiments using converging evidence from three different types of measures. Experiments 1a and 1b showed that conditionals that comprise enabling causes, e.g., 'if the ignition key was turned then the car started' primed people to read quickly conjunctions referring to the possibility of the enabler occurring without the outcome, e.g., 'the ignition key was turned and the car did not start'. Experiments 2a and 2b showed that people paraphrased causal conditionals by using causal or temporal connectives (because, when), whereas they paraphrased causal counterfactuals by using subjunctive constructions (had…would have). Experiments 3a and 3b showed that people made different inferences from counterfactuals presented with enabling conditions compared to none. The implications of the results for alternative theories of conditionals are discussed.     

条件推理的语义关系表达形式效应

作者用以大学生为被试的实验考察, 基本条件句语义关系表达形式(充分关系、必要关系和析取关系表达形式)和作为心理模型外显建构的可能性判断任务对条件推理的可能影响。实验结果发现, 条件推理的语义关系表达形式效应显著, 条件句语义关系表达形式对被试条件推理有显著的影响, 条件推理成绩随条件句语义关系表达的外显程度增加而增加; 被试在可能性判断任务中对条件句所含心理模型的外显建构并没有明显改善条件推理的成绩; 在有可能性判断任务条件下, 被试外显心理模型建构的成绩变化模式并不能一致地预测条件推理成绩的变化模式。这些结果说明, 人们的条件推理可能并不是完全基于心理模型建构, 而是还受对条件句前后件之间语义关系理解的影响; 条件句表达形式中语义关系的外显内隐模式影响对条件句语义关系的知觉理解难易, 从而影响相应条件推理的成绩。     

The influence of clause order,congruency, and probability on the processing of conditionals

Conditional information can be equally asserted in the forms if p, then q (e.g., “if I am ill, I will miss work tomorrow”) and q, if p (e.g., “I will miss work tomorrow, if I am ill”). While this type of clause order manipulation has previously been found to have no influence on the ultimate conclusions participants draw from conditional rules, we used self-paced reading to examine how it affects the real time incremental processing of everyday conditional statements. Experiment 1 revealed that clause order interacts with presuppositional congruency as readers hypothetically represent counterfactual statements. When if p, then q counterfactuals contained a presupposition that was incongruent with prior context, these statements took longer to read than when the presupposition was congruent, but for q, if p conditionals there was no such congruency effect. Experiment 2 revealed that reading times were influenced by the subjective probability of an indicative conditional regardless of clause order, with a penalty observed for low-probability statements relative to high-probability statements in both conditional clause orders. These data reveal a dissociation whereby clause order mediates the effect of suppositional congruency on reading times, but does not mediate the effect of subjective probability.     

Conditions for the acceptance of deontic conditionals.

Recent psychological research has investigated how people assess the probability of an indicative conditional. Most people give the conditional probability of q given p as the probability of if p then q. Asking about the probability of an indicative conditional, one is in effect asking about its acceptability. But on what basis are deontic conditionals judged to be acceptable or unacceptable? Using a decision theoretic analysis, we argue that a deontic conditional, of the form if p then must q or if p then may q, will be judged acceptable to the extent that the p & q possibility is preferred to the p & not-q possibility. Two experiments are reported in which this prediction was upheld. There was also evidence that the pragmatic suitability of permission rules is partly determined by evaluations of the not-p & q possibility. Implications of these results for theories of deontic reasoning are discussed.     

充分条件句语义关系知觉对条件推理的影响

作者通过实验考察了大学生被试对五种充分条件句语义关系知觉对其条件推理的影响。两个实验的结果表明,被试对条件句中前后件之间语义关系的知觉理解影响和调节其相应的条件推理的成绩。实验1新发现,被试对充分条件句后件对前件必要性的知觉理解存在难易差异,对许可句和定义句的后件必要性容易知觉,对偶然句、义务句和因果句的后件必要性难以知觉。实验2新发现,被试对充分条件句后件对前件必要性的知觉理解的难易差异导致被试在否定后件式推理成绩上的差异,对许可句和定义句的否定后件式推理成绩显著高于对偶然句、义务句和因果句的否定后件式推理成绩,对充分条件句否定后件式推理成绩随对后件必要性知觉增加而增加。     

The Probability of Iterated Conditionals

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the “imported,” noniterated form, If p and q, then r, using a probability evaluation task and a truth‐table task, and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the “new paradigm” that takes this conditional as a starting point.     

On the basis of belief in causal and diagnostic conditionals

According to the suppositional theory of conditionals, people assess their belief in a conditional statement of the form “if p then q” by conducting a mental simulation on the supposition of p in which they assess their degree of belief in q. This leads to them to the judge the probability of a conditional statement to be equal to the conditional probability, P(q|p). Evidence for this conditional probability hypothesis has been adduced in earlier studies for abstract, causal, and counterfactual conditionals. For the realistic conditionals, it is natural to assume that people perform such mental simulations by building causal mental models from prior causes to later effects. However, in the present study we show that the conditional probability hypothesis extends to diagnostic conditionals, which relate effects to causes. This new finding presents a major challenge for theoretical accounts of the mental processing of conditional statements.     

Priming effect in affirmative complex conditional connectives

We report the results of an experiment that examined the mental representations underlying the comprehension of complex conditional connectives (such as “A, on condition that B”) and the conditional if (such as “A, if B”). The mental representations during the comprehension stage were analysed using a “priming methodology”. The experiment showed that participants read the possibility “A and not-B” faster when it was primed by “A, if B” than when it was primed by “A, on condition that B”. The finding suggests that people understand the sentence “A, on condition that B” as biconditional; other possibilities (“A and B”, “not-A and B”, “not-A and not-B”) were primed equally by both connectives. We discuss the implications of this for current theories of reasoning.     

On the basis of belief in causal and diagnostic conditionals

According to the suppositional theory of conditionals, people assess their belief in a conditional statement of the form “if p then q” by conducting a mental simulation on the supposition of p in which they assess their degree of belief in q. This leads to them to the judge the probability of a conditional statement to be equal to the conditional probability, P(q|p). Evidence for this conditional probability hypothesis has been adduced in earlier studies for abstract, causal, and counterfactual conditionals. For the realistic conditionals, it is natural to assume that people perform such mental simulations by building causal mental models from prior causes to later effects. However, in the present study we show that the conditional probability hypothesis extends to diagnostic conditionals, which relate effects to causes. This new finding presents a major challenge for theoretical accounts of the mental processing of conditional statements.     

Suppositions, extensionality, and conditionals: a critique of the mental model theory of Johnson-Laird And Byrne (2002)

P. N. Johnson-Laird and R. M. J. Byrne proposed an influential theory of conditionals in which mental models represent logical possibilities and inferences are drawn from the extensions of possibilities that are used to represent conditionals. In this article, the authors argue that the extensional semantics underlying this theory is equivalent to that of the material, truth-functional conditional, at least for what they term "basic" conditionals, concerning arbitrary problem content. On the basis of both logical argument and psychological evidence, the authors propose that this approach is fundamentally mistaken and that conditionals must be viewed within a suppositional theory based on what philosophical logicians call the Ramsey test. The Johnson-Laird and Byrne theory is critically examined with respect to its account of basic conditionals, nonbasic conditionals, and counterfactuals.     

Probabilities of counterfactuals and counterfactual probabilities

Probabilities figure centrally in much of the literature on the semantics of conditionals. I find this surprising: it accords a special status to conditionals that other parts of language apparently do not share. I critically discuss two notable ‘probabilities first’ accounts of counterfactuals, due to Edgington and Leitgeb. According to Edgington, counterfactuals lack truth values but have probabilities. I argue that this combination gives rise to a number of problems. According to Leitgeb, counterfactuals have truth conditions-roughly, a counterfactual is true when the corresponding conditional chance is sufficiently high. I argue that problems arise from the disparity between truth and high chance, between approximate truth and high chance, and from counterfactuals for which the corresponding conditional chances are undefined. However, Edgington, Leitgeb and I can unite in opposition to Stalnaker and Lewis-style ‘similarity’ accounts of counterfactuals.     

Word for word: Multiple lexical access in speech production

We report an experiment in which we test the possible influence of the tense of the verb and explicit negatives with indicative conditionals. We tested the effects of systematically negating the constituents of four fundamental inferences based on conditionals in three different tenses (present tense, past tense, future tense): Modus Ponens (i.e., inferences of the form: if p then q; p; therefore q), Modus Tollens (if p then q; not-q; therefore not-p), Affirmation of the Consequent (if p then q; q; therefore p), and Denial of the Antecedent (if p then q; not-p; therefore not-q). The latter two inferences are invalid for true conditionals, but are valid for bi-conditionals (if, and only if, p then q). The participants drew their own conclusions from premises about letters and numbers on cards. We discuss the results in relation to an affirmation premise bias, a negative conclusion bias, and a double negation effect. We outline the importance of our findings for theories about conditional and counterfactual thinking.