Consequential Conditionals: Invited and Suppressed Inferences From Valued Outcomes.

Consequential conditionals are defined as "if P then Q" statements, where P is an action, and Q a predicted outcome of this action, which is either desirable or undesirable to the agent. Experiment 1 shows that desirable (viz. undesirable) outcomes invite an inference to the truth (viz. falsity) of their antecedent. Experiment 2 shows that the more extreme the outcome is, the stronger the invited inference is. Experiment 3 shows that modus ponens from premises "If A then C, A" can be suppressed with the introduction of a consequential conditional, "If C then Q," where Q is an undesirable outcome. Experiment 4 shows that the more undesirable Q is, the larger the suppression is. The authors discuss how these results can enrich current approaches of conditional inference on the basis of mental models, complementary necessary conditions, and conditional probabilities. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The development of reasoning with causal conditionals.

A total of 512 children in Grades 1 through 6 received a conditional inference task using causal conditionals (If cause P, then effect Q) and a generation of alternatives task. The inference task used premises for which there were few or many possible alternative causes. Results show a steady age-related increase in uncertainty responses to the two uncertain logical forms, affirmation of consequent (AC) and denial of antecedent (DA), and an increase in production of disabling conditions for modus ponens. More uncertainty responses were produced to AC and DA with premises with many possible alternatives. Individual differences in inference production were related to numbers of alternatives produced in the generation task. Results support the idea that both developmental and individual differences in reasoning can be at least partially explained by differential access to knowledge stored in long-term memory. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Conditional reasoning with inducements and advice

In an earlier study of conditional reasoning, Newstead et al. [Newstead, S.E., Ellis, C.E., Evans, J.St.B.T., Dennis, I., (1997). Conditional reasoning with realistic material. Thinking and Reasoning 3, 49-96] found that people drew more inferences from conditionals framed as inducements (threats and promises) than from conditionals phrased as advice (tips and warnings). The present study was designed to test the hypothesis that this difference arose from the fact that the speaker of an inducement is normally seen to have control over the consequent event whereas the giver of advice does not. In the experiment reported here, inducement and advice conditionals were constructed in brief contexts such that in either case the speaker could be seen to have high or low control. Participants drew many more conditional inferences of all kinds for high control than for low control conditionals in either context. A second finding of interest was that participants drew many more forward (antecedent to consequent) inferences than backward inferences with these kinds of realistic conditionals.     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities.

[Correction Notice: An erratum for this article was reported in Vol 29(6) of Journal of Experimental Psychology: Learning, Memory, and Cognition (see record 2007-16865-001). On page 684, Table 4, all correlations should have been identified as having a pp then q") as indicating a high conditional probability P(q|p). Participants estimated the probability that a given conditional is true (Experiments 1A, 1B, and 3) or judged whether a conditional was true or false (Experiments 2 and 4) given information about the frequencies of the relevant truth table cases. Judgments were strongly influenced by the ratio of pq to p?q cases, supporting the conditional probability account. In Experiments 1A, 1B, and 3, judgments were also affected by the frequency of pq cases, consistent with a version of mental model theory. Experiments 3 and 4 extended the results to thematic conditionals and showed that the pragmatic utility associated with believing a statement also affected the degree of belief in conditionals but not in logically equivalent quantified statements. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities": Correction to Oberauer and Wilhelm (2003).

Reports an error in "The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities" by Klaus Oberauer and Oliver Wilhelm (Journal of Experimental Psychology: Learning, Memory, and Cognition, 2003[Jul], Vol 29[4], 680-693). On page 684, Table 4, all correlations should have been identified as having a p2003-06626-018.) Five experiments were conducted to test the hypothesis that people understand conditional statements ("if p then q") as indicating a high conditional probability P(q|p). Participants estimated the probability that a given conditional is true (Experiments 1A, 1B, and 3) or judged whether a conditional was true or false (Experiments 2 and 4) given information about the frequencies of the relevant truth table cases. Judgments were strongly influenced by the ratio of pq to p?q cases, supporting the conditional probability account. In Experiments 1A, 1B, and 3, judgments were also affected by the frequency of pq cases, consistent with a version of mental model theory. Experiments 3 and 4 extended the results to thematic conditionals and showed that the pragmatic utility associated with believing a statement also affected the degree of belief in conditionals but not in logically equivalent quantified statements. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How people interpret conditionals: Shifts toward the conditional event.

We investigated how people interpret conditionals and how stable their interpretation is over a long series of trials. Participants were shown the colored patterns on each side of a 6-sided die and were asked how sure they were that a conditional holds of the side landing upward when the die is randomly thrown. Participants were presented with 71 trials consisting of all combinations of binary dimensions of shape (e.g., circles and squares) and color (e.g., blue and red) painted onto the sides of each die. In 2 experiments (N? = 66, N? = 65), the conditional event was the dominant interpretation, followed by conjunction, and material conditional responses were negligible. In both experiments, the percentage of participants giving a conditional event response increased from around 40% at the beginning of the task to nearly 80% at the end, with most participants shifting from a conjunction interpretation. The shift was moderated by the order of shape and color in each conditional's antecedent and consequent: Participants were more likely to shift if the antecedent referred to a color. In Experiment 2 we collected response times: Conditional event interpretations took longer to process than conjunction interpretations (mean difference = 500 ms). We discuss implications of our results for mental models theory and probabilistic theories of reasoning. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Counterfactual potency.

Counterfactual thoughts typically take the form of implied or explicit if–then statements. We propose that the multiplicative combination of “if likelihood” (the degree to which the antecedent condition of the counterfactual is perceived to be likely) and “then likelihood” (the perceived conditional likelihood of the outcome of the counterfactual, given the antecedent condition) determine the strength and impact of counterfactuals. This construct, termed counterfactual potency, is a reliable predictor of the degree of influence of counterfactual thinking upon judgments of regret, causation, and responsibility. Through 4 studies, we demonstrate the predictive power of this construct in a variety of contexts and show that it plays a causal role in determining the strength of the effects of counterfactual thought. Implications of counterfactual potency as a central factor of counterfactual influence are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Empirical evidence of Aristotle’s concepts of predication and opposition.

In the past four or five years I have been especially dependent on Aristotle's writings as I have initiated a series of experiments that can legitimately be called empirical efforts to prove Aristotelian conceptions to be true. In actuality, of course, I am trying to prove my own theory to be true—that is, worthy of consideration because it is consistent with observed human actions. However, by extension, I am surely seeking evidence for Aristotle's image of human cognition. There are two Aristotlelian conceptions that underwrite my theoretical and empirical efforts: predication and opposition. When we speak of a "predication" in cognition we refer to a process that is fundamentally creative. Predications deal in meanings; and the way in which we align meanings, lending the meaning of one concept to another is what predication is all about. Predication is the act of affirming, denying, or qualifying certain patterns of meaning in relation to other patterns of meaning. The second Aristotelian conception that I have been employing theoretically and investigating empirically is "opposition." Although association through frequent contact was recognized by Aristotle (1952b), he also appreciated that there is often an intrinsic tie of opposite meanings to be seen in human reason. In my own interpretation of Aristotle, I believe that we can see the ultimate necessity of predication stemming from the opositional ties of meanings like this. If I am cognizing within a congerie of interlacing meanings which relate to and, indeed, delimit the definitions of their opposite meanings, then it is up to me as a cognizer to continually "take a position" on just what I am going to affirm—or not! (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How to be sarcastic: The echoic reminder theory of verbal irony.

Positive statements, such as "A fine friend you are," can readily be used sarcastically. Negative statements, such as "You're a terrible friend," can be used sarcastically only under special circumstances. We account for this asymmetry in terms of echoic reminder theory, which asserts that listeners recognize sarcasm when they perceive that a speaker is alluding to some antecedent state of affairs. Positive statements do not require explicit antecedents because such statements may implicitly allude to societal norms and expectations, and these norms are almost invariably positive. Negative statements, however, cannot implicitly allude to such positive norms, and so they should require explicit antecedents if they are to be understood. An explicit victim of a sarcastically intended remark can provide such an antecedent and so should enable negative statements to be used sarcastically. Three experiments, involving scenarios with and without victims, provide support for this theory of sarcastic irony. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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., – q therefore – p ). These findings occurred with familiar and unfamiliar content, affirmative and negative conditionals, and conditional and biconditional relations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Biomechanical analysis of masticatory system configuration in Neandertals and Inuits

Johnson-Laird and Byrne (1991) present a theory of conditional inference based upon the manipulation of mental models. In the present paper, the theory is critically examined with regard to its ability to account for psychological data, principally with respect to the rate at which people draw the four basic inferences of modus ponens (MP), denial of the antecedent (DA), affirmation of the consequent (AC) and modus tollens (MT). It is argued first that the theory is unclear in its definition and in particular with regard to predictions of problem difficulty. Clarification and specification of principles are consequently provided here. Next, it is argued that there are a number of phenomena in the conditional reasoning literature for which the theory cannot account in its present form. Specifically, (a) the relatively frequency of DA and AC inferences on affirmative conditional is not as predicted by the theory, (b) differences occur between inferences on if then and only if rules beyond the capacity of the theory to explain and (c) there is no account of the "negative conclusion bias" observed when negated components are introduced into the rules. A number of revisions to the mental model theory of conditional reasoning are proposed in order to account for these findings.     

The primacy of thinking about possibilities in the development of reasoning.

One of the main tenets of the mental model theory is that when individuals reason, they think about possibilities. According to this theory, reasoning on what is possible from the truth of a sentence would be psychologically basic, whereas reasoning the other way round, on the truth or falsity of a sentence from a given state of affairs, would require some meta-ability. The present study tested the developmental corollary of this theory, which is that reasoning about possibilities should develop first, whereas the development of reasoning about truth-value should be delayed. For this purpose, 3rd, 6th, and 9th graders as well as adults were presented with tasks requiring them to evaluate either the possibilities compatible with conditional sentences or the truth-value of these sentences from these same possibilities. The results revealed 2 phenomena. First, the same developmental trend was observed in both tasks with 3 successive interpretational levels: conjunctive, biconditional, and then conditional. Second, there was a developmental lag between the 2 forms of reasoning—with developmental transitions from one level to the next occurring about 3 years later when reasoning about truth-value. The implications of these results for theories of cognitive development and of reasoning are discussed. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Putting Ifs to Work: Goal-Based Relevance in Conditional Directives.

Conditional directives are used by speakers to instruct hearers which actions are to be taken should certain events occur. The authors demonstrate that conditional directives are distinct from indicative conditionals in which speakers predict what is likely to be observed should certain events occur. The 1st set of experiments shows that goal structure determines what information speakers will select to test whether conditional directives have been followed but that these selections do not reflect their interpretations of the deontic necessity and sufficiency of the conditional relation. The 2nd set of experiments shows that formulations of conditional directives differ in how clearly speakers consider them to express their situation-specific intentions and that hearers accurately perceive what speakers intend them to do as a result of these formulations. The authors' findings illustrate a form of social rationality common in everyday interaction, which broadens normative conceptions of conditionals. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Representations as mediators of adolescent deductive reasoning

In Experiment 1, preadolescents, middle adolescents, and late adolescents were presented 3 deductive reasoning tasks. With some important exceptions, conditional reasoning improved with age on problems containing permission conditional relations, and reasoning fallacies increased with age on problems containing causal conditional relations. The results of Experiments 2a and 2b indicated that problem type (i.e., permission or causal) does not mediate the activation of conditional reasoning skills. Rather, valid conditional inferences are more common on problems for which plausible alternative antecedents can be generated than on problems for which alternative antecedent generation is difficult. Conditional rules for which alternative antecedent generation is difficult may be misrepresented as biconditionals, resulting in biconditional rather than conditional reasoning.     

Computational levels and conditional inference: Reply to Schroyens and Schaeken (2003).

This article is a reply to W. Schroyens and W. Schaeken's (2003; see record 2002-08431-014) critique of M. Oaksford, N. Chater, and J. Larkin's (2000; see record 2000-08540-005) conditional probability model (CP) of conditional inference. It is argued that their meta-analysis does not falsify CP because the evidence may bear on more than one computational level of explanation. Moreover, it is argued that CP provides a rational account of more of the data than W. Schroyens and W. Schaeken's mental models theory. Other points are also addressed. It is suggested that W. Schroyens and W. Schaeken's model and CP converge on the importance of probabilistic prior knowledge in conditional inference. This is consistent with the normative literature, which (like CP) treats conditionals in terms of subjective conditional probabilities. (PsycINFO Database Record (c) 2010 APA, all rights reserved)