Inferences from the negation of counterfactual and semifactual conditionals

Our goal was to study how people understand the negation of counterfactuals (such as “Antonio denied/said that it is false that if Messi had played, then Barcelona would have won”) and semifactuals (such as “Antonio denied that even if Messi had played, Barcelona would have won”). Previous studies have shown that participants negated basic conditionals using small-scope interpretations by endorsing a new conditional with the negated consequent, but also by making large-scope interpretations, endorsing a conjunction with the negated consequent. Three experiments showed that when participants were asked whether the negation of a counterfactual (Experiments 1 and 2) or semifactual (Experiment 3) conditional was followed by a new conditional, they made a small-scope interpretation, endorsing the same conditional with the negated consequent (e.g., “if/even if Messi had played, Barcelona would not have won”). However, they also accepted the conditional with the negated antecedent for semifactuals (e.g., “even if Messi had not played, Barcelona would have won”). When participants were asked whether the negation of a counterfactual or semifactual conditional is followed by a conjunction, they endorsed the conjunction with both the negated antecedent and the consequent (e.g., “Messi did not play and Barcelona did not win”), but again they accepted the conjunction with the negated antecedent only for semifactuals (e.g., “Messi did not play and Barcelona did win”). These results have implications for the main theories of reasoning.

Similarities and differences in understanding negative and affirmative counterfactuals and causal assertions: Evidence from eye-tracking

Two eye-tracking experiments compared affirmative and negative counterfactuals, "if she had (not) arrived early, she would (not) have bought roses" and affirmative and negative causal assertions, "Because she arrived (did not arrive) early, she bought (did not buy) roses." When participants heard a counterfactual, they looked on screen at words corresponding to its conjecture ("roses"), and its presupposed facts ("no roses"), whereas for a causal assertion, they looked only at words corresponding to the facts. For counterfactuals, they looked at the conjecture first, and later the presupposed facts, and at the latter more than the former. The effect was more pronounced for negative counterfactuals than affirmative ones because the negative counterfactual's presupposed facts identify a specific item ("she bought roses"), whereas the affirmative counterfactual's presupposed facts do not ("she did not buy roses"). Hence, when participants were given a binary context, "she did not know whether to buy roses or carnations," they looked primarily at the presupposed facts for both sorts of counterfactuals. We discuss the implications for theories of negation, the dual meaning of counterfactuals, and their relation to causal assertions.

The relative difficulty of negations of conjunctions and disjunctions-a mental model perspective

A current issue in propositional reasoning is which of negated disjunctions and conjunctions are more difficult to understand. Using the possibility generation and evaluation tasks, we investigated how people make possibility inferences from negated compound assertions such as not (A and B) and not (A or B). We derive 4 different strategies of negation from the mental model theory (the enumerative negation, the eliminative negation, the element negation, and the clause negation) to predict the relative difficulty of possibility inference from not (A and B) and not (A or B). The results of three experiments convergently demonstrate that possibility inference from not (A or B) is harder than that from not (A and B). Moreover, an interpretation of negation as the complement of the set of possibilities allowed by a compound assertion is in line with the results of not (A and B) rather than not (A or B). The overall results favor the clause negation strategy over the other strategies.

Three Strategies for the Critical Use of Statistical Methods in Psychological Research

We present three strategies to replace the null hypothesis statistical significance testing approach in psychological research: (1) visual representation of cognitive processes and predictions, (2) visual representation of data distributions and choice of the appropriate distribution for analysis, and (3) model comparison. The three strategies have been proposed earlier, so we do not claim originality. Here we propose to combine the three strategies and use them not only as analytical and reporting tools but also to guide the design of research. The first strategy involves a visual representation of the cognitive processes involved in solving the task at hand in the form of a theory or model together with a representation of a pattern of predictions for each condition. The second approach is the GAMLSS approach, which consists of providing a visual representation of distributions to fit the data, and choosing the best distribution that fits the raw data for further analyses. The third strategy is the model comparison approach, which compares the model of the researcher with alternative models. We present a worked example in the field of reasoning, in which we follow the three strategies.

The negations of conjunctions, conditionals, and disjunctions

How do reasoners understand and formulate denials of compound assertions, such as conjunctions and disjunctions? A theory based on mental models postulates that individuals enumerate models of the various possibilities consistent with the assertions. It therefore predicts a novel interaction: in affirmations, conjunctions, A and B, which refer to one possibility, should be easier to understand than disjunctions, A or B, which refer to more than one possibility; in denials, conjunctions, not(A and B), which refer to more than one possibility, should be harder to understand than disjunctions, not(A or B), which do not. Conditionals are ambiguous and they should be of intermediate difficulty. Experiment 1 corroborated this trend with a task in which the participants selected which possibilities were consistent with assertions, such as: Bob denied that he wore a yellow shirt and he wore blue pants on Tuesday. Experiment 2 likewise showed that participants' own formulations of verbal denials yielded the same trend in which denials of conjunctions were harder than denials of conditionals, which in turn were harder than denials of disjunctions.