Find extra options or reason badly: An investigation of children's reasoning with incompatibility statements.

The false dilemma or dichotomy is a logical fallacy that occurs when interlocuters accept the premises in an incompatibility statement as being jointly exhaustive (i.e., leaving no third option), whereas that is in fact not the case. Brisson et al. [Memory & Cognition (2018), Vol. 46, pp. 657-670] investigated this fallacy in an adult sample and discovered a content effect that influenced participants' performance. The current study aimed to elaborate on these findings by establishing whether similar patterns could be observed with children. A number of age-appropriate incompatibility premises were constructed. For every item, four different inferential problems were presented (Affirm First, Affirm Second, Deny First, and Deny Second) with three potential answers to choose from (X, not X, or uncertainty regarding X). A sample of 192 volunteer children, with ages ranging from 8 to 13 years, was collected. Statistical analysis showed no significant effect for participants' age but did reveal main effects for premise validity and the amount of available "third options" (possibilities outside of the presented dichotomy). These results are a clear replication of the general effects on adults found by Brisson et al. Affirm inferences were also easy for children, Deny inferences were difficult (even more so than for adults), and content had a profound effect on participants' performance. Whenever more third options could be generated, children were less likely to fall into the false dilemma fallacy. Our findings thus further support the idea that reasoning with incompatibilities is influenced by the same semantic retrieval processes that have been previously related to human conditional reasoning.

Reasoning strategies predict use of very fast logical reasoning.

The dual strategy model proposes that people use one of two potential ways of processing information when making inferences. The statistical strategy generates a rapid probabilistic estimate based on associative access to a wide array of information, while the counterexample strategy uses a more focused representation, allowing for a search for potential counterexamples. In the following studies, we explore the hypothesis that individual differences in strategy use are related to the ability to make rapid intuitive logical judgments. In Study 1, we show that this is the case for rapid judgments requiring a distinction between simple logical form and for a novel form of judgment, the ability to identify inferences that are not linked to their premises (non sequiturs). In Study 2, we show that strategy use is related to the ability to make the kinds of rapid logical judgments previously examined over and above contributions of working memory capacity. Study 3 shows that strategy use explains individual variability in rapid logical responding with belief-biased inferences over and above the contribution of IQ. The results of Studies 2 and 3 indicate that under severe time constraint cognitive capacity is a very poor predictor of reasoning, while strategy use becomes a stronger predictor. These results extend the notion that people can make rapid intuitive "logical" judgments while highlighting the importance of strategy use as a key individual difference variable.

Reasoning strategies and semantic memory effects in deductive reasoning.

Growing evidence supports the dual-strategy model, which suggests that reasoners have access to both a statistical and a counterexample reasoning strategy. In this paper, we explore further the processes underlying strategy use. We report three studies, the aim of which was to clarify the relation between this model and two forms of everyday reasoning. One of the most robust effects found with conditional reasoning with meaningful premises is the effect of alternative antecedents on the endorsement of AC and DA inferences. In a first study, we presented participants with conditional reasoning problems having more or fewer accessible alternatives as well as our dual-strategy diagnostic questionnaire. As hypothesized, results showed that strategy use had an independent effect on the inferences made with the AC and DA forms, over and above the effect of the number of antecedents, but was not related to responding to the MP and the MT forms. In a second study, we found that this relation extended to reasoning from an incompatibility statement. Finally, a third study showed that this relationship did not hold with probabilistic rather than logical response instructions, suggesting that the way reasoners transform a probabilistic evaluation into a dichotomous judgment is a key determinant of strategy use.

The development of fast and slow inferential responding: Evidence for a parallel development of rule-based and belief-based intuitions.

Dual process theories postulate the existence of two levels of processing, Type 1, which uses belief-based cues to make very rapid inferences, and Type 2, which uses more conscious, working memory-based processes that are, in principle, capable of making rule-based judgments. There is a common assumption that Type 1 processes are more rapidly produced, while Type 2 processes take more time. Evidence for this assumption is mixed. Recently, Newman, Gibb, and Thompson (Journal of Experimental Psychology: Learning, Memory, and Cognition, 43(7): 1154, 2017) have provided clear evidence that very fast responses use a combination of both belief-based and rule-based cues. In these studies, we initially replicated this basic result with adults using a different methodology and extended them to examine in greater detail patterns of change with restricted time. The results also show the same combination of rule-based and belief-based cues in fast responses, and suggest that time constraints differentially affect each form of cue. We then examined the developmental pattern of both fast and slow responding. Children aged between 8 and 10 years of age were examined using the methodology of the initial study. Results show that both developmental patterns and the effect of reduced time on children produce parallel changes in both belief-based and rule-based responding. These results suggest the existence of two simultaneously developing processes, consistent with a dual-strategy model of reasoning.

Conflict Detection and Logical Complexity.

Empirical evidence for the capacity to detect conflict between biased reasoning and normative principles has led to the proposal that reasoners have an intuitive grasp of some basic logical principles. In two studies, we investigate the boundary conditions of these logical intuitions by manipulating the logical complexity of problems where logical validity and conclusion believability conflict or not. Results pointed to evidence for successful conflict detection on the basic Modus Ponens (MP) inference, but also showed evidence for such a phenomenon on the more complex Modus Tollens (MT) inference. This suggests that both the MP and the MT inferences are simple enough for reasoners to have an intuitive grasp of their logical structure. The boundaries of logical intuition might thus reside in problems of greater complexity than these inferences. We also observed that on the invalid Affirmation of the Consequent (AC) and Denial of the Antecedent (DA) inferences, participants showed higher accuracy on the inference that was expected to be more complex (DA), and no evidence for successful conflict detection was found on these forms. Implications for the logical intuition framework are discussed.

Reasoning from an incompatibility: False dilemma fallacies and content effects.

In the present studies, we investigated inferences from an incompatibility statement. Starting with two propositions that cannot be true at the same time, these inferences consist of deducing the falsity of one from the truth of the other or deducing the truth of one from the falsity of the other. Inferences of this latter form are relevant to human reasoning since they are the formal equivalent of a discourse manipulation called the false dilemma fallacy, often used in politics and advertising in order to force a choice between two selected options. Based on research on content-related variability in conditional reasoning, we predicted that content would have an impact on how reasoners treat incompatibility inferences. Like conditional inferences, they present two invalid forms for which the logical response is one of uncertainty. We predicted that participants would endorse a smaller proportion of the invalid incompatibility inferences when more counterexamples are available. In Study 1, we found the predicted pattern using causal premises translated into incompatibility statements with many and few counterexamples. In Study 2A, we replicated the content effects found in Study 1, but with premises for which the incompatibility statement is a non-causal relation between classes. These results suggest that the tendency to fall into the false dilemma fallacy is modulated by the background knowledge of the reasoner. They also provide additional evidence on the link between semantic information retrieval and deduction.

Interactions between inferential strategies and belief bias.

The dual strategy model of reasoning proposed by Verschueren, Schaeken, and d'Ydewalle (Thinking & Reasoning, 11(3), 239-278, 2005a; Memory & Cognition, 33(1), 107-119, 2005b) suggests that people can use either a statistical or a counterexample-based strategy to make deductive inferences. Subsequent studies have supported this distinction and investigated some properties of the two strategies. In the following, we examine the further hypothesis that reasoners using statistical strategies should be more vulnerable to the effects of conclusion belief. In each of three studies, participants were given abstract problems used to determine strategy use and three different forms of syllogism with believable and unbelievable conclusions. Responses, response times, and feeling of rightness (FOR) measures were taken. The results show that participants using a statistical strategy were more prone to the effects of conclusion belief across all three forms of reasoning. In addition, statistical reasoners took less time to make inferences than did counterexample reasoners. Patterns of variation in response times and FOR ratings between believable and unbelievable conclusions were very similar for both strategies, indicating that both statistical and counterexample reasoners were aware of conflict between conclusion belief and premise-based reasoning.

Logical reasoning versus information processing in the dual-strategy model of reasoning.

One of the major debates concerning the nature of inferential reasoning is between counterexample-based strategies such as mental model theory and statistical strategies underlying probabilistic models. The dual-strategy model, proposed by Verschueren, Schaeken, & d'Ydewalle (2005a, 2005b), which suggests that people might have access to both kinds of strategy has been supported by several recent studies. These have shown that statistical reasoners make inferences based on using information about premises in order to generate a likelihood estimate of conclusion probability. However, while results concerning counterexample reasoners are consistent with a counterexample detection model, these results could equally be interpreted as indicating a greater sensitivity to logical form. In order to distinguish these 2 interpretations, in Studies 1 and 2, we presented reasoners with Modus ponens (MP) inferences with statistical information about premise strength and in Studies 3 and 4, naturalistic MP inferences with premises having many disabling conditions. Statistical reasoners accepted the MP inference more often than counterexample reasoners in Studies 1 and 2, while the opposite pattern was observed in Studies 3 and 4. Results show that these strategies must be defined in terms of information processing, with no clear relations to "logical" reasoning. These results have additional implications for the underlying debate about the nature of human reasoning. (PsycINFO Database Record

How do pre-adolescent children interpret conditionals?

Studies examining children's basic understanding of conditionals have led to very different conclusions. On the one hand, conditional inference tasks suggest that young children are able to interpret familiar conditionals in a complex manner. In contrast, truth-table tasks suggest that before adolescence, children have limited (conjunctive) representations of conditionals. We hypothesized that the latter results are due to use of what are essentially arbitrary conditionals. To examine this, we gave a truth-table task using two kinds of conditional rules, Arbitrary and Imaginary categorical rules (If an animal is a bori, then it has red wings) to 9- and 12-year-olds. Results with the Arbitrary rules were consistent with those found in previous studies, with the most frequent interpretation being the Conjunctive one. However, among even the youngest children, the most frequent interpretation of the Imaginary categorical rules was the defective conditional, which is only found with much older adolescents with Arbitrary rules. These results suggest that working memory limitations are not an important developmental factor in how young children interpret conditional rules.

Additional evidence for a dual-strategy model of reasoning: Probabilistic reasoning is more invariant than reasoning about logical validity.

One of the major debates concerning the nature of inferential reasoning is between counterexample-based strategies such as mental model theory and the statistical strategies underlying probabilistic models. The dual-strategy model proposed by Verschueren, Schaeken, and d'Ydewalle (2005a, 2005b) suggests that people might have access to both kinds of strategies. One of the postulates of this approach is that statistical strategies correspond to low-cost, intuitive modes of evaluation, whereas counterexample strategies are higher-cost and more variable in use. We examined this hypothesis by using a deductive-updating paradigm. The results of Study 1 showed that individual differences in strategy use predict different levels of deductive updating on inferences about logical validity. Study 2 demonstrated no such variation when explicitly probabilistic inferences were examined. Study 3 showed that presenting updating problems with probabilistic inferences modified performance on subsequent problems using logical validity, whereas the opposite was not true. These results provide clear evidence that the processes used to make probabilistic inferences are less subject to variation than those used to make inferences of logical validity.

Deductive updating is not Bayesian.

One of the major debates concerning the nature of inferential reasoning is between counterexample-based theories such as mental model theory and probabilistic theories. This study looks at conclusion updating after the addition of statistical information to examine the hypothesis that deductive reasoning cannot be explained by probabilistic inferences. In Study 1, participants were given an initial "If P then Q rule" for a phenomenon on a recently discovered planet, told that "Q was true," and asked to make a judgment of either deductive validity or probabilistic likelihood of the putative conclusion that "P is true." They were then told the results of 1,000 observations. In the low-probability problem, 950 times P was false and Q was true, whereas 50 times P was true and Q was true. In the high-probability problem, these proportions were inverted. On the low-probability problem, probabilistic ratings and judgments of logical validity decreased. However, on the high-probability problem, probabilistic ratings remained high whereas judgments of logical validity significantly decreased. Confidence ratings were consistent with this different pattern for probabilistic and for deductive inferences. Study 2 replicated this result with another form of inference, "If P then Q. P is false." These results show that deductive updating is not explicable by Bayesian updating.

Metacognition and abstract reasoning.

The nature of people's meta-representations of deductive reasoning is critical to understanding how people control their own reasoning processes. We conducted two studies to examine whether people have a metacognitive representation of abstract validity and whether familiarity alone acts as a separate metacognitive cue. In Study 1, participants were asked to make a series of (1) abstract conditional inferences, (2) concrete conditional inferences with premises having many potential alternative antecedents and thus specifically conducive to the production of responses consistent with conditional logic, or (3) concrete problems with premises having relatively few potential alternative antecedents. Participants gave confidence ratings after each inference. Results show that confidence ratings were positively correlated with logical performance on abstract problems and concrete problems with many potential alternatives, but not with concrete problems with content less conducive to normative responses. Confidence ratings were higher with few alternatives than for abstract content. Study 2 used a generation of contrary-to-fact alternatives task to improve levels of abstract logical performance. The resulting increase in logical performance was mirrored by increases in mean confidence ratings. Results provide evidence for a metacognitive representation based on logical validity, and show that familiarity acts as a separate metacognitive cue.

Direct evidence for a dual process model of deductive inference.

In 2 experiments, we tested a strong version of a dual process theory of conditional inference (cf. Verschueren et al., 2005a, 2005b) that assumes that most reasoners have 2 strategies available, the choice of which is determined by situational variables, cognitive capacity, and metacognitive control. The statistical strategy evaluates inferences probabilistically, accepting those with high conditional probability. The counterexample strategy rejects inferences when a counterexample shows the inference to be invalid. To discriminate strategy use, we presented reasoners with conditional statements (if p, then q) and explicit statistical information about the relative frequency of the probability of p/q (50% vs. 90%). A statistical strategy would accept the more probable inferences more frequently, whereas the counterexample one would reject both. In Experiment 1, reasoners under time pressure used the statistical strategy more, but switched to the counterexample strategy when time constraints were removed; the former took less time than the latter. These data are consistent with the hypothesis that the statistical strategy is the default heuristic. Under a free-time condition, reasoners preferred the counterexample strategy and kept it when put under time pressure. Thus, it is not simply a lack of capacity that produces a statistical strategy; instead, it seems that time pressure disrupts the ability to make good metacognitive choices. In line with this conclusion, in a 2nd experiment, we measured reasoners' confidence in their performance; those under time pressure were less confident in the statistical than the counterexample strategy and more likely to switch strategies under free-time conditions.