Probability and Instruction Effects in Syllogistic Conditional Reasoning
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.
[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.
[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.
@article{"International Journal of Business, Human and Social Sciences:60526", author = "Olimpia Matarazzo and Ivana Baldassarre", title = "Probability and Instruction Effects in Syllogistic Conditional Reasoning", 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.", volume = "2", number = "7", pages = "780-9", }
