Conditional Probability and the Cognitive Science of Conditional Reasoning

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context.

[1]  Nick Chater,et al.  Theories of reasoning and the computational explanation of everyday inference , 1995 .

[2]  Nick Chater,et al.  Rationality In An Uncertain World: Essays In The Cognitive Science Of Human Understanding , 1998 .

[3]  Nick Chater,et al.  Probabilities and Pragmatics in Conditional Inference: Suppression and Order Effects , 2003 .

[4]  N. Chater,et al.  RATIONAL EXPLANATION OF THE SELECTION TASK , 1996 .

[5]  In-mao Liu,et al.  A Probabilistic Interpretation of “If-Then” , 1996 .

[6]  Zenon W. Pylyshyn,et al.  Computation and Cognition: Toward a Foundation for Cognitive Science , 1984 .

[7]  Rosemary J. Stevenson,et al.  Deduction from Uncertain Premises , 1995 .

[8]  N. Chater,et al.  Against Logicist Cognitive Science , 1991 .

[9]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[10]  D. Lindley.  On a Measure of the Information Provided by an Experiment , 1956 .

[11]  N. Chater,et al.  Computational levels and conditional inference: Reply to Schroyens and Schaeken (2003) , 2003 .

[12]  F. Chua,et al.  Suppression of valid inferences: syntactic views, mental models, and relative salience , 1994, Cognition.

[13]  P. Johnson-Laird,et al.  Psychology of Reasoning: Structure and Content , 1972 .

[14]  L. Rips.  The Psychology of Proof , 1994 .

[15]  P. Horwich.  Probability and Evidence , 1972 .

[16]  M. Oaksford.  Thinking and the rational analysis of human reasoning , 1997 .

[17]  R. Nickerson.  Hempel's Paradox and Wason's Selection Task: Logical and Psychological Puzzles of Confirmation , 1996 .

[18]  G. d'Ydewalle,et al.  The processing of negations in conditional reasoning: A meta-analytic case study in mental model and/or mental logic theory , 2001 .

[19]  D. W. Green,et al.  Decision theoretic effects in testing a causal conditional , 2000 .

[20]  Keith Stenning,et al.  Reasoning theories and bounded rationality , 1993 .

[21]  N Chater,et al.  Probabilities and polarity biases in conditional inference. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[22]  John R. Anderson,et al.  The Adaptive Character of Thought , 1990 .

[23]  P. Cheng,et al.  Covariation in natural causal induction. , 1992, Psychological review.

[24]  Karl Christoph Klauer,et al.  On the Normative Justification for Information Gain in Wason's Selection Task. , 1999 .

[25]  David M. Riefer,et al.  Theoretical and empirical review of multinomial process tree modeling , 1999, Psychonomic bulletin & review.

[26]  W. Schroyens,et al.  A critique of Oaksford, Chater, and Larkin's (2000) conditional probability model of conditional reasoning. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[27]  Nick Chater,et al.  A rational analysis of the selection task as optimal data selection. , 1994 .

[28]  Masasi Hattori,et al.  A quantitative model of optimal data selection in Wason's selection task , 2002, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[29]  David E Over,et al.  Conditionals and conditional probability. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[30]  N. Chater,et al.  Probabilistic effects in data selection , 1999 .

[31]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[32]  Christian George,et al.  Reasoning From Uncertain Premises , 1997 .

[33]  L. Good,et al.  THE PARADOX OF CONFIRMATION* , 1960, The British Journal for the Philosophy of Science.

[34]  P. Cheng,et al.  Covariation in natural causal induction. , 1992 .

[35]  D. E. Over,et al.  Causal inference, contingency tables and the selection task , 1997 .

[36]  A meta-analytic review of conditional reasoning by model and/or rule: mental models theory revisited , 2001 .

[37]  N. Chater,et al.  Optimal data selection: Revision, review, and reevaluation , 2003, Psychonomic bulletin & review.

[38]  Jonathan Evans,et al.  Rationality in the selection task: Epistemic utility versus uncertainty reduction. , 1996 .

[39]  N. Chater,et al.  Optimal data selection in the reduced array selection task (RAST) , 1997 .

[40]  Philip N. Johnson-Laird,et al.  Quarterly Journal of Experimental Psychology Insight into a Logical Relation Insight into a Logical Relation , 2022 .

[41]  Jonathan Bennett.  Classifying Conditionals: The Traditional Way is Right , 1995 .

[42]  A. Tversky,et al.  Support theory: A nonextensional representation of subjective probability. , 1994 .

[43]  P C Wason,et al.  Reasoning about a Rule , 1968, The Quarterly journal of experimental psychology.

[44]  N. Chater,et al.  The probabilistic approach to human reasoning , 2001, Trends in Cognitive Sciences.

[45]  Ken Manktelow,et al.  Reasoning and Thinking , 1999 .

[46]  Walter Schaeken,et al.  Heuristic and analytic processes in propositional reasoning with negatives. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[47]  Nick Chater,et al.  Commonsense reasoning, logic, and human rationality , 2002 .