Reasoning with conditionals: Does every counterexample count? It’s frequency that counts

Abstract

A series of experiments investigated what determines people’s degree of belief in conditionals and their readiness to draw inferences from them. Information on the frequency of exceptions to conditional rules was contrasted with information about the number of different disabling conditions causing these exceptions. Experiments 1 and 2, using conditionals with arbitrary contents, revealed a strong effect of frequency information and no effect of disabling information. Experiment 3 established that, in the absence of frequency information, the disabling condition information used in Experiments 1 and 2 affected belief in the conditionals and inference acceptance, as has been found in many previous studies (Byrne, 1989; DeNeys, Schaeken, & d’Ydewalle, 2003b). Experiment 4 extended the results of Experiments 1 and 2 to everyday conditionals. The results show that belief in a conditional, and the confidence in inferences subsequently drawn from it, both depend on the subjective conditional probability of the consequent given the antecedent. This probability is estimated from the relative frequency of exceptions regardless of what causes them.

References

  1. Anderson, J. R. (1995).Cognitive psychology and its implications. New York: Freeman.

    Google Scholar 

  2. Byrne, R. M. (1989). Suppressing valid inferences with conditionals.Cognition,31, 61–83.

    Article  PubMed  Google Scholar 

  3. Byrne, R. M., Espino, O., &Santamaria, C. (1999). Counterexamples and the suppression of interferences.Journal of Memory & Language,40, 347–373.

    Article  Google Scholar 

  4. Cummins, D. D. (1995). Naive theories and causal deduction.Memory & Cognition,23, 646–658.

    Article  Google Scholar 

  5. Cummins, D. D., Lubart, T., Alksnis, O., &Rist, R. (1991). Conditional reasoning and causation.Memory & Cognition,19, 274–282.

    Article  Google Scholar 

  6. De Neys, W., Schaeken, W., &D’Ydewalle, G. (2002). Causal conditional reasoning and semantic memory retrieval: A test of the semantic memory framework.Memory & Cognition,30, 908–920.

    Article  Google Scholar 

  7. De Neys, W., Schaeken, W., &D’Ydewalle, G. (2003a). Causal conditional reasoning and strength of association: The disabling condition case.European Journal of Cognitive Psychology,15, 162–167.

    Google Scholar 

  8. De Neys, W., Schaeken, W., &D’Ydewalle, G. (2003b). Inference 1513. suppression and semantic memory retrieval: Every counterexample counts.Memory & Cognition,31, 581–595.

    Article  Google Scholar 

  9. De Neys, W., Schaeken, W., &D’Ydewalle, G. (2005). Working memory and everyday conditional reasoning: Retrieval and inhibition of stored counterexamples.Thinking & Reasoning,11, 349–381.

    Article  Google Scholar 

  10. Dieussaert, K., Schaeken, W., &D’Ydewalle, G. (2002). The relative contribution of content and context factors on the interpretation of conditionals.Experimental Psychology,49, 181–195.

    PubMed  Google Scholar 

  11. Evans, J. St. B. T., Handley, S. J., &Over, D. E. (2003). Conditionals and conditional probability.Journal of Experimental Psychology: Learning, Memory, & Cognition,29, 321–335.

    Article  Google Scholar 

  12. Evans, J. St. B. T., &Over, D. E. (2004).If. Oxford: Oxford University Press.

    Google Scholar 

  13. Evans, J. St. B. T., Over, D. E., &Handley, S. J. (2005). Suppositionals, extensionality, and conditionals: A critique of the mental model theory of Johnson-Laird and Byrne (2002).Psychological Review,112, 1040–1052.

    Article  PubMed  Google Scholar 

  14. Geiger, S. M., & Oberauer, K. (2006).How necessary is sufficiency for reasoning? A test of two probabilistic theories. Manuscript submitted for publication.

  15. Johnson-Laird, P. N. (2001). Mental models and deduction.Trends in Cognitive Sciences,5, 434–442.

    Article  PubMed  Google Scholar 

  16. Johnson-Laird, P. N., Legrenzi, P., Girotto, V., Legrenzi, M. S., &Caverni, J.-P. (1999). Naive probability: A mental model theory of extensional reasoning. Psychological Review, 106, 62–88.

    Article  PubMed  Google Scholar 

  17. Klaczynski, P. A. (2001). Analytic and heuristic processing influences on adolescent reasoning and decision making.Child Development,72, 844–871.

    Article  PubMed  Google Scholar 

  18. Markovits, H., &Barrouillet, P. (2002). The development of conditional reasoning: A mental model account.Developmental Review,22, 5–36.

    Article  Google Scholar 

  19. Markovits, H., &Potvin, F. (2001). Suppression of valid inferences and knowledge structures: The curious effect of producing alternative antecedents on reasoning with causal conditionals.Memory & Cognition,29, 736–744.

    Article  Google Scholar 

  20. Markovits, H., &Quinn, S. (2002). Efficiency of retrieval correlates with “logical” reasoning from causal conditional premises.Memory & Cognition,30, 696–706.

    Article  Google Scholar 

  21. Oaksford, M., &Chater, N. (1994). A rational analysis of the selection task as optimal data selection.Psychological Review,101, 608–631.

    Article  Google Scholar 

  22. Oaksford, M., &Chater, N. (2001). The probabilistic approach to human reasoning.Trends in Cognitive Sciences,5, 349–357.

    Article  PubMed  Google Scholar 

  23. Oaksford, M., Chater, N., &Larkin, J. (2000). Probabilities and polarity biases in conditional inference.Journal of Experimented Psychology: Learning, Memory, & Cognition,2B, 883–899.

    Article  Google Scholar 

  24. Oberauer, K. (2006). Reasoning with conditionals: A test of formal models of four theories.Cognitive Psychology,53, 238–283.

    Article  PubMed  Google Scholar 

  25. Oberauer, K., Geiger, S. M., Fischer, K., &Weidenfeld, A. (2007). Two meanings of “if ”? Individual differences in the interpretation of conditionals.Quarterly Journal of Experimental Psychology,60, 790–819.

    Article  Google Scholar 

  26. Oberauer, K., &Wilhelm, O. (2003). The meaning(s) of conditionals: Conditional probabilities, mental models, and personal utilities.Journal of Experimental Psychology: Learning, Memory, & Cognition,29, 680–693.

    Article  Google Scholar 

  27. Over, D. E., &Evans, J. St. B. T. (2003). The probability of conditionals: The psychological evidence.Mind & Language,18, 340–358.

    Article  Google Scholar 

  28. Quinn, S., &Markovits, H. (1998). Conditional reasoning, causality, and the structure of semantic memory: Strength of association as a predictive factor for content effects.Cognition,68, B93-B101.

    Article  PubMed  Google Scholar 

  29. Rottenstreich, Y., &Tversky, A. (1997). Unpacking, repacking, and anchoring: Advances in support theory.Psychological Review,104, 406–415.

    Article  PubMed  Google Scholar 

  30. Schroyens, W., Schaeken, W., &Handley, S. (2003). In search of counter-examples: Deductive rationality in human reasoning.Quarterly Journal of Experimental Psychology,56A, 1129–1145.

    Google Scholar 

  31. Thompson, V. (1995). Conditional reasoning: The necessary and sufficient conditions.Canadian Journal of Experimental Psychology,40, 1–60.

    Google Scholar 

  32. Thompson, V. (2000). Task specific nature of domain general reasoning.Cognition,76, 209–268.

    Article  PubMed  Google Scholar 

  33. Tversky, A., &Koehler, D. J. (1994). Support theory: A nonextensional representation of subjective probability.Psychological Review,101, 547–567.

    Article  Google Scholar 

  34. Verschueren, N., Schaeken, W., &D’Ydewalle, G. (2005). A dualprocess specification of causal conditional reasoning.Thinking & Reasoning,11, 239–278.

    Article  Google Scholar 

  35. Weidenfeld, A. (2004).Interpretation of and reasoning with conditionals: Probabilities, mental models, and causality. Unpublished doctoral dissertation, University of Potsdam.

  36. Weidenfeld, A., Oberauer, K., &Hörnig, R. (2005). Causal and noncausal conditionals: An integrated model of interpretation and reasoning.Quarterly Journal of Experimental Psychology,58A, 1479–1513.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sonja M. Geiger.

Additional information

This research was supported by Deutsche Forschungsgemeinschaft Grant FOR 375 1-1.

Electronic supplementary material

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Geiger, S.M., Oberauer, K. Reasoning with conditionals: Does every counterexample count? It’s frequency that counts. Mem Cogn 35, 2060–2074 (2007). https://doi.org/10.3758/BF03192938

Download citation

Keywords

  • Frequency Information
  • Conditional Statement
  • Cover Story
  • Modus Ponens
  • Probability Judgment