Indirect illusory inferences from disjunction: a new bridge between deductive inference and representativeness


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.

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  1. 1.

    Formally, an exclusive disjunction in the first premise would amount to ((ab) ∧¬(cd)) ∨ ((cd) ∧¬(ab)), which does not validate the inference. The countermodel we present in the main text will do the job here too.

  2. 2.

    Our data do not answer the question to what extent non-matching causal connections can approach the acceptance rate found in matching cases. We thank the editor for pointing out this gap. We have shown that our model can successfully predict behavior observed in matching studies, with very high acceptance rates. We further conjecture that materials displaying higher degrees of connectedness than ours should approximate matching cases. The issue is not essential for the theoretical discussion to follow, so we leave it to further research.

  3. 3.

    There is an alternative view of these interpretive processes from linguistic semantics and pragmatics that considers them to be narrowly grammatical rather than the product of pragmatic reasoning (see for example Chierchia et al., 2012). Since mental model theory is squarely about reasoning, we take it that such a grammatical outlook on the extent to which the theory models these kinds of strengthened interpretations was not intended.

  4. 4.

    We are very grateful to an anonymous reviewer, whose detailed comments crucially shaped the discussion that follows.

  5. 5.

    Indeed, we find manifestations of this general confirmation mechanism in semantics as well. In particular, recent probabilistic approaches to conditionals propose semantics based entirely on confirmation-theoretic measures (e.g. Crupi and Iacona, 2020). Moreover, experimental work by Skovgaard-Olsen et al. (2016) shows the influence of confirmation-theoretic considerations on the interpretation of conditionals.


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The authors would like to thank Benjamin Spector, Ulrike Hahn, Vincenzo Crupi, Philippe Schlenker, Stanislas Dehaene, Christophe Pallier, Emmanuel Chemla, Lorenzo Ciccione, the LANG-REASON team at Ecole Normale Supérieure’s Department of Cognitive Studies, and two anonymous reviewers for helpful feedback.

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Correspondence to Mathias Sablé-Meyer.

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The research presented here was supported by Agence Nationale de la Recherche grants ANR-17-EURE-0017 (FrontCog, Department of Cognitive Studies, Ecole Normale Supérieure) and ANR-18-CE28-0008 (LANG-REASON; PI: Mascarenhas).

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Sablé-Meyer, M., Mascarenhas, S. Indirect illusory inferences from disjunction: a new bridge between deductive inference and representativeness. Rev.Phil.Psych. (2021).

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