Probability and Instruction Effects in Syllogistic Conditional Reasoning

Authors: Olimpia Matarazzo, Ivana Baldassarre

Abstract:

The main aim of this study was to examine whether people understand indicative conditionals on the basis of syntactic factors or on the basis of subjective conditional probability. The second aim was to investigate whether the conditional probability of q given p depends on the antecedent and consequent sizes or derives from inductive processes leading to establish a link of plausible cooccurrence between events semantically or experientially associated. These competing hypotheses have been tested through a 3 x 2 x 2 x 2 mixed design involving the manipulation of four variables: type of instructions (“Consider the following statement to be true", “Read the following statement" and condition with no conditional statement); antecedent size (high/low); consequent size (high/low); statement probability (high/low). The first variable was between-subjects, the others were within-subjects. The inferences investigated were Modus Ponens and Modus Tollens. Ninety undergraduates of the Second University of Naples, without any prior knowledge of logic or conditional reasoning, participated in this study. Results suggest that people understand conditionals in a syntactic way rather than in a probabilistic way, even though the perception of the conditional probability of q given p is at least partially involved in the conditionals- comprehension. They also showed that, in presence of a conditional syllogism, inferences are not affected by the antecedent or consequent sizes. From a theoretical point of view these findings suggest that it would be inappropriate to abandon the idea that conditionals are naturally understood in a syntactic way for the idea that they are understood in a probabilistic way.

Keywords: Conditionals, conditional probability, conditional syllogism, inferential task.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077379

References:

[1] D. Edgington, "On conditional," Mind, vol. 104, pp. 235-329, 1995.
[2] J. ST. B. T. Evans, D.E. Over, and S.J. Handley, "Supposition, extensionality and conditionals: A critique of the mental model theory of Johnson-Laird and Byrne (2002)," Psychological Review, vol. 112, no. 4, pp. 1042-1052, 2005.
[3] J. St. B. T. Evans, "Logic and Human Reasoning: An Assessment of the Deduction Paradigm," Psychological Bulletin, vol. 128, no. 6, pp. 978- 996, 2002.
[4] W. V. Quine, Methods of logic. New York: Holt, 1950.
[5] F. P. Ramsey, The foundations of mathematics and other logical essays. London: Routledge, 1931.
[6] R. Stalnaker, "A Theory of Conditionals," American Philosophical Quarterly Monograph Series, vol. 2, pp. 98-112, 1968.
[7] M. D. S. Braine and D. P. O-Brien, "A theory of if: A lexical entry, reasoning program, and pragmatic principles," Psychological Review, vol. 98, no. 2, pp. 182-203, 1991.
[8] L. Rips, The Psychology of Proof. Cambridge, MA: MIT Press, 1994.
[9] P. N. Johnson-Laird, Mental models. Toward s a cognitive science of language, inference and consciousness. Cambridge: Cambridge University Press, 1983.
[10] P. N. Johnson-Laird and R. M. J. Byrne, "Conditionals: A Theory of Meaning, Pragmatics, and Inference," Psychological Review, vol. 109, no. 4, pp. 646-678, 2002.
[11] P. Barrouillet and J.-F. Lecas, "How can mental models account for content effects in conditional reasoning? A developmental perspective," Cognition, vol. 67, no. 3, pp. 209-253, 1998.
[12] K. Dieussaert, W. Schaeken, and G. d-Ydewalle, "The Relative Contribution of Content and Context Factors on the Interpretation of Conditionals," Experimental Psychology, vol. 49, no.3, pp. 181-195, 2002.
[13] S. Quinn and H. Markovits, "Conditional reasoning with causal premises: evidence for a retrieval model," Thinking and reasoning, vol.. 8, no. 3, pp. 179-191, 2002.
[14] N. Verschueren, W. J. Schroyens, and W. Schaeken, Necessity and sufficiency in abstract conditional reasoning The European journal of cognitive psychology, vol. 18, no. 2, pp. 255-276, 2006.
[15] J. St. B. T. Evans, "Theories of Human Reasoning: The Fragmented State of the Art" Theory & Psychology, vol. 1, no.1, pp. 83-105, 1991.
[16] D.D. Cummins, "Naive theories and causal deduction," Memory & Cognition, vol. 23, no. 5, pp. 646-658, 1995.
[17] S.E. Newstead, C.M. Ellis, J. Evans, and I. Dennis, "Conditional Reasoning with Realistic Material," Thinking and Reasoning, vol. 3, no. 1, pp. 49-76, 1997.
[18] K. Oberauer, O. Wilhelm, "The meaning(s) of conditionals - conditional probabilities, mental models, and personal utilities," Journal of Experimental Psychology: Learning, Memory, and Cognition, vol. 29, no.4, pp. 680-639, 2003.
[19] K. Oberauer, S. M. Geiger, K. Fischer, and A. Weidenfeld, "Two meanings of "if"? Individual differences in the interpretation of conditionals," Quarterly journal of experimental psychology, vol.60, no. 6, pp. 790-819, 2007.
[20] N. Chater, J. B. Tenenbaum, A. Yuille, "Probabilistic models of cognition: Where next?," Trends in Cognitive Sciences, vol. 10, no. 7, pp. 335-344, 2006.
[21] J. St. B.T. Evans, S. J. Handley, and D. E. Over, "Conditionals and Conditional Probability," Journal of Experimental Psychology: Learning, Memory and Cognition, vol. 29, no. 2, pp. 321-335, 2003.
[22] I. M. Liu, "Conditional reasoning and conditionalization," Journal of Experimental Psychology: Learning, Memory and Cognition, vol. 29, no. 4, pp. 694-709, 2003.
[23] I. M. Liu, K.C. Lo, and J.T. Wu, "A probabilistic interpretation of "ifthen"," Quarterly Journal of Experimental Psychology A, vol. 49, no.3, pp. 828-844, 1996.
[24] M. Oaksford and N. Chater, "The Probabilistic Approach to Human Reasoning," Trends in Cognitive Sciences, vol. 5, no. 8, pp. 349-357, 2001.
[25] M. Oaksford and N. Chater, "Modelling probabilistic effects in conditional. inference: Validating search or conditional probability?," Psychologica, vol. 32, pp. 217-242, 2003.
[26] M. Oaksford and N. Chater, Bayesian Rationality. Oxford: Oxford University Press, 2006.
[27] M. Oaksford, N. Chater, and J. Larkin, "Probabilities and polarity biases in conditional inferences," Journal of Experimental Psychology: Learning, Memory and Cognition, vol. 29, no. 4, pp. 680-693, 2000.
[28] D. E. Over, J. St. B.T. Evans, "The Probability of Conditionals: The Psychological Evidence," Mind & Language, vol. 18, no. 4, pp. 340- 358, 2003.