We provide a new link between deductive and probabilistic reasoning fallacies. Illusory inferences from disjunction are a broad class of deductive fallacies traditionally explained by recourse to a matching procedure that looks for content overlap between premises. In two behavioral experiments, we show that this phenomenon is instead sensitive to real-world causal dependencies and not to exact content overlap. A group of participants rated the strength of the causal dependence between pairs of sentences. This measure is a near perfect predictor of fallacious reasoning by an independent group of participants in illusory inference tasks with the same materials. In light of these results, we argue that all extant accounts of these deductive fallacies require non-trivial adjustments. Crucially, these novel indirect illusory inferences from disjunction bear a structural similarity to seemingly unrelated probabilistic reasoning problems, in particular the conjunction fallacy from the heuristics and biases literature. This structural connection was entirely obscure in previous work on these deductive problems, due to the theoretical and empirical focus on content overlap. We argue that this structural parallelism provides arguments against the need for rich descriptions and individuating information in the conjunction fallacy, and we outline a unified theory of deductive illusory inferences from disjunction and the conjunction fallacy, in terms of Bayesian confirmation theory.
The conjunction fallacy is the well-documented empirical finding that subjects sometimes rate a conjunction A&B as more probable than one of its conjuncts, A. Most explanations appeal in some way to the fact that B has a high probability. But Tentori et al. (2013) have recently challenged such approaches, reporting experiments which find that (1) when B is confirmed by relevant evidence despite having low probability, the fallacy is common, and (2) when B has a high probability but has not been confirmed by relevant evidence, the fallacy is less common. They conclude that degree of confirmation, rather than probability, is the central determinant of the conjunction fallacy. In this paper, we address a confound in these experiments: Tentori et al. (2013) failed to control for the fact that their (1)-situations make B conversationally relevant, while their (2)-situations do not. Hence their results are consistent with the hypothesis that conversationally relevant high probability is an important driver of the conjunction fallacy. Inspired by recent theoretical work that appeals to conversational relevance to explain the conjunction fallacy, we report on two experiments that control for this issue by making B relevant without changing its degree of probability or confirmation. We find that doing so increases the rate of the fallacy in (2)-situations, and leads to comparable fallacy-rates as (1)-situations. This suggests that (non-probabilistic) conversational relevance indeed plays a role in the conjunction fallacy, and paves the way toward further work on the interplay between relevance and confirmation.
We show that probabilistic decision-making behavior characteristic of reasoning by representativeness or typicality arises in minimalistic settings lacking many of the features previously thought to be necessary conditions for the phenomenon. Specifically, we develop a version of a classical experiment by Kahneman and Tversky (1973) on base-rate neglect, where participants have full access to the probabilistic distribution, conveyed entirely visually and without reliance on familiar stereotypes, rich descriptions, or individuating information. We argue that the notion of evidential support as studied in (Bayesian) confirmation theory offers a good account of our experimental findings, as has been proposed for related data points from the representativeness literature. In a nutshell, when faced with competing alternatives to choose from, humans are sometimes less interested in picking the option with the highest probability of being true (posterior probability), and instead choose the option best supported by available evidence. We point out that this theoretical avenue is descriptively powerful, but has an as-yet unclear explanatory dimension. Building on approaches to reasoning from linguistic semantics, we propose that the chief trigger of confirmation-theoretic mechanisms in deliberate reasoning is a linguistically-motivated tendency to interpret certain experimental setups as intrinsically contrastive, in a way best cashed out by modern linguistic semantic theories of questions. These questions generate pragmatic pressures for interpreting surrounding information as having been meant to help answer the question, which will naturally give rise to confirmation-theoretic effects, very plausibly as a byproduct of iterated Bayesian update as proposed by modern Bayesian theories of relevance-based reasoning in pragmatics. Our experiment provides preliminary but tantalizing evidence in favor of this hypothesis, as participants displayed significantly more confirmation-theoretic behavior in a condition that highlighted the question-like, contrastive nature of the task.
We introduce purely visual paradigms that convey the logical structure of illusory inferences from disjunction: (a AND b) OR c, a |- b. Although the logical information was conveyed entirely via non-linguistic means, we found that the visual paradigms induce reasoning fallacies, though less attractive than their linguistic counterparts. The visual paradigms highlight the role of alternative-based reasoning, or question-answer dynamics, as they control for narrowly interpretive processes that confound the study of their linguistic counterparts. To our knowledge, this is the first work to develop visual paradigms that represent reasoning fallacies committed by adults and involve multiple logical operators non-trivially embedded. Previous studies focused on pre-verbal children or non-human animals, and for this reason limited the scope of research to visually representing logically simple, valid inferences.
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