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

Abstract

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Data Availability

The complete materials, collected data, and analysis code, are available at the following address https://osf.io/tuc8s/.

Notes

  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.

References

  1. Adams, E.W. 1996. A Primer of probability logic. Center for the study of language and information.

  2. Alonso-Ovalle, L. 2006. Disjunction in alternative semantics. Phd diss., UMass Amherst.

  3. Chierchia, G., D. Fox, and B. Spector. 2012. The grammatical view of scalar implicatures and the relationship between semantics and pragmatics. Semantics: an international handbook of natural language meaning, eds. Portner P., Maienborn C., and von Heusinger K. Berlin, Mouton de Gruyter.

  4. Ciardelli, I., J. Groenendijk, and F. Roelofsen. 2009. Attention! Might in inquisitive semantics. Proceedings of the 19th Conference on Semantics and Linguistic Theory (SALT), 91–108.

  5. Crupi, V., and A. Iacona. 2020. The evidential conditional. Erkenntnis :1–25.

  6. Crupi, V., B. Fitelson, and K. Tentori. 2008. Probability, confirmation, and the conjunction fallacy. Thinking & Reasoning 14(2): 182–199.

    Article  Google Scholar 

  7. Cummins, D.D. 1995. Naive theories and causal deduction. Memory and Cognition 23(5): 646–658.

    Article  Google Scholar 

  8. De Leeuw, J.R. 2015. jspsych: A javascript library for creating behavioral experiments in a web browser. Behavior Research Methods 47(1): 1–12.

    Article  Google Scholar 

  9. Evans, J.S.B.T. 1999. The influence of linguistic form on reasoning: the case of matching bias. The Quarterly Journal of Experimental Psychology 52 (1): 185–216.

    Article  Google Scholar 

  10. Grice, P. 1975. Logic and conversation. Syntax and semantics: Speech acts, eds. Cole P. and Morgan J. New York, Academic Press.

  11. Groenendijk, J. 2008. Inquisitive Semantics: Two possibilities for disjunction. Proceedings of the seventh international Tbilisi symposium on language, logic and computation.

  12. Johnson-Laird, P.N. 1983. Mental models: towards a cognitive science of language, inference and consciousness. Cambridge: Cambridge University Press.

    Google Scholar 

  13. Johnson-Laird, P.N., and M. Ragni. 2019. Possibilities as the foundation of reasoning. Cognition 193.

  14. Johnson-Laird, P.N., and F. Savary. 1999. Illusory inferences: a novel class of erroneous deductions. Cognition 71(3): 191–229.

    Article  Google Scholar 

  15. Johnson-Laird, P.N., S. Khemlani, and G.P. Goodwin. 2015. Logic, probability, and human reasoning. Trends in Cognitive Sciences 19 (4): 201–214.

    Article  Google Scholar 

  16. Kahneman, D., and A. Tversky. 1973. On the psychology of prediction. Psychological Review 80(4): 237–251.

    Article  Google Scholar 

  17. Khemlani, S., R.M.J. Byrne, and P.N. Johnson-Laird. 2018. Facts and possibilities: a model-based theory of sentential reasoning. Cognitive Science 42(6): 1887–1924.

    Article  Google Scholar 

  18. Koralus, P., and S. Mascarenhas. 2013. The erotetic theory of reasoning: bridges between formal semantics and the psychology of deductive inference. Philosophical Perspectives 27: 312–365.

    Article  Google Scholar 

  19. Koralus, P., and S. Mascarenhas. 2018. Illusory inferences in a question-based theory of reasoning. Pragmatics, truth, and underspecification: Towards an atlas of meaning, current research in the semantics/pragmatics interface, eds. Turner K. and Horn L., 300–322. Leiden, Brill. chap 10.

  20. Kratzer, A., and J. Shimoyama. 2002. Indeterminate pronouns: the view from Japanese. Third Tokyo conference on psycholinguistics.

  21. Mascarenhas, S. 2009. Inquisitive semantics and logic. Master’s thesis, ILLC.

  22. Mascarenhas, S. 2014. Formal semantics and the psychology of reasoning: Building new bridges and investigating interactions. PhD thesis, New York University.

  23. Mascarenhas, S., and P. Koralus. 2017. Illusory inferences with quantifiers. Thinking and Reasoning 23(1): 33–48.

    Article  Google Scholar 

  24. Mascarenhas, S., and L. Picat. 2019. Might as a generator of alternatives: the view from reasoning. Proceedings of SALT 29, UCLA, 549–561. https://doi.org/10.3765/salt.v29i0.4635.

  25. Oaksford, M., and N. Chater. 2007. Bayesian rationality: The probabilistic approach to human reasoning. Oxford: Oxford University Press.

    Book  Google Scholar 

  26. Picat, L. 2019. Inferences with disjunction, interpretation or reasoning? MA thesis (CogMaster), Ecole Normale Supérieure.

  27. Skovgaard-Olsen, N., H. Singmann, and K.C. Klauer. 2016. The relevance effect and conditionals. Cognition 150: 26–36.

    Article  Google Scholar 

  28. Spector, B. 2007. Scalar implicatures: exhaustivity and Gricean reasoning. Questions in dynamic semantics, eds. Aloni M., Dekker P., and Butler A.. Elsevier.

  29. Tentori, K., V. Crupi, N. Bonini, and D. Osherson. 2007. Comparison of confirmation measures. Cognition 103: 107–119.

    Article  Google Scholar 

  30. Tversky, A., and D. Kahneman. 1983. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review 90: 293–315.

    Article  Google Scholar 

  31. Walsh, C., and P.N. Johnson-Laird. 2004. Co-reference and reasoning. Memory and Cognition 32: 96–106.

    Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Mathias Sablé-Meyer.

Additional information

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1007/s13164-021-00543-8.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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).

Supplementary Information

Below is the link to the electronic supplementary material.

(PDF 103 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sablé-Meyer, M., Mascarenhas, S. Indirect illusory inferences from disjunction: a new bridge between deductive inference and representativeness. Rev.Phil.Psych. (2021). https://doi.org/10.1007/s13164-021-00543-8

Download citation