Memory & Cognition

, Volume 35, Issue 8, pp 2060–2074 | Cite as

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

  • Sonja M. Geiger
  • Klaus Oberauer


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.


Frequency Information Conditional Statement Cover Story Modus Ponens Probability Judgment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material (10 kb)
Supplementary material, approximately 340 KB.


  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.CrossRefPubMedGoogle Scholar
  3. Byrne, R. M., Espino, O., &Santamaria, C. (1999). Counterexamples and the suppression of interferences.Journal of Memory & Language,40, 347–373.CrossRefGoogle Scholar
  4. Cummins, D. D. (1995). Naive theories and causal deduction.Memory & Cognition,23, 646–658.CrossRefGoogle Scholar
  5. Cummins, D. D., Lubart, T., Alksnis, O., &Rist, R. (1991). Conditional reasoning and causation.Memory & Cognition,19, 274–282.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.PubMedGoogle 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.CrossRefGoogle Scholar
  12. Evans, J. St. B. T., &Over, D. E. (2004).If. Oxford: Oxford University Press.CrossRefGoogle 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.CrossRefPubMedGoogle Scholar
  14. Geiger, S. M., & Oberauer, K. (2006).How necessary is sufficiency for reasoning? A test of two probabilistic theories. Manuscript submitted for publication.Google Scholar
  15. Johnson-Laird, P. N. (2001). Mental models and deduction.Trends in Cognitive Sciences,5, 434–442.CrossRefPubMedGoogle 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.CrossRefPubMedGoogle Scholar
  17. Klaczynski, P. A. (2001). Analytic and heuristic processing influences on adolescent reasoning and decision making.Child Development,72, 844–871.CrossRefPubMedGoogle Scholar
  18. Markovits, H., &Barrouillet, P. (2002). The development of conditional reasoning: A mental model account.Developmental Review,22, 5–36.CrossRefGoogle 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.CrossRefGoogle Scholar
  20. Markovits, H., &Quinn, S. (2002). Efficiency of retrieval correlates with “logical” reasoning from causal conditional premises.Memory & Cognition,30, 696–706.CrossRefGoogle Scholar
  21. Oaksford, M., &Chater, N. (1994). A rational analysis of the selection task as optimal data selection.Psychological Review,101, 608–631.CrossRefGoogle Scholar
  22. Oaksford, M., &Chater, N. (2001). The probabilistic approach to human reasoning.Trends in Cognitive Sciences,5, 349–357.CrossRefPubMedGoogle 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.CrossRefGoogle Scholar
  24. Oberauer, K. (2006). Reasoning with conditionals: A test of formal models of four theories.Cognitive Psychology,53, 238–283.CrossRefPubMedGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
  27. Over, D. E., &Evans, J. St. B. T. (2003). The probability of conditionals: The psychological evidence.Mind & Language,18, 340–358.CrossRefGoogle 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.CrossRefPubMedGoogle Scholar
  29. Rottenstreich, Y., &Tversky, A. (1997). Unpacking, repacking, and anchoring: Advances in support theory.Psychological Review,104, 406–415.CrossRefPubMedGoogle 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.CrossRefPubMedGoogle Scholar
  33. Tversky, A., &Koehler, D. J. (1994). Support theory: A nonextensional representation of subjective probability.Psychological Review,101, 547–567.CrossRefGoogle Scholar
  34. Verschueren, N., Schaeken, W., &D’Ydewalle, G. (2005). A dualprocess specification of causal conditional reasoning.Thinking & Reasoning,11, 239–278.CrossRefGoogle Scholar
  35. Weidenfeld, A. (2004).Interpretation of and reasoning with conditionals: Probabilities, mental models, and causality. Unpublished doctoral dissertation, University of Potsdam.Google Scholar
  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

Copyright information

© Psychonomic Society, Inc. 2007

Authors and Affiliations

  • Sonja M. Geiger
    • 1
  • Klaus Oberauer
    • 2
  1. 1.Department of PsychologyUniversity of PotsdamPotsdamGermany
  2. 2.University of BristolBristolEngland

Personalised recommendations