Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-10-05T08:43:35.192Z Has data issue: false hasContentIssue false

Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning

Published online by Cambridge University Press:  12 February 2009

Mike Oaksford
Affiliation:
School of Psychology, Birkbeck College London, London, WC1E 7HX, United Kingdomm.oaksford@bbk.ac.ukwww.bbk.ac.uk/psyc/staff/academic/moaksford
Nick Chater
Affiliation:
Division of Psychology and Language Sciences, and ESRC Centre for Economic Learning and Social Evolution, University College London, London, WC1E 6BT, United Kingdomn.chater@ucl.ac.ukwww.psychol.ucl.ac.uk/people/profiles/chater_nick.htm

Abstract

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards.

Bayesian Rationality argues that rationality is defined instead by the ability to reason about uncertainty. Although people are typically poor at numerical reasoning about probability, human thought is sensitive to subtle patterns of qualitative Bayesian, probabilistic reasoning. In Chapters 1–4 of Bayesian Rationality (Oaksford & Chater 2007), the case is made that cognition in general, and human everyday reasoning in particular, is best viewed as solving probabilistic, rather than logical, inference problems. In Chapters 5–7 the psychology of “deductive” reasoning is tackled head-on: It is argued that purportedly “logical” reasoning problems, revealing apparently irrational behaviour, are better understood from a probabilistic point of view. Data from conditional reasoning, Wason's selection task, and syllogistic inference are captured by recasting these problems probabilistically. The probabilistic approach makes a variety of novel predictions which have been experimentally confirmed. The book considers the implications of this work, and the wider “probabilistic turn” in cognitive science and artificial intelligence, for understanding human rationality.

Type
Main Articles
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, E. W. (1975) The logic of conditionals: An application of probability to deductive logic. Reidel.CrossRefGoogle Scholar
Adams, E. W. (1998) A primer of probability logic. CLSI Publications.Google Scholar
Anderson, J. R. (1990) The adaptive character of thought. Erlbaum.Google Scholar
Anderson, J. R. (1991a) Is human cognition adaptive? Behavioral and Brain Sciences 14:471–84; discussion 485–517.CrossRefGoogle Scholar
Anderson, J. R. (1991b) The adaptive nature of human categorization. Psychological Review 98:409–29.CrossRefGoogle Scholar
Anderson, J. R. & Matessa, M. (1998) The rational analysis of categorization and the ACT-R architecture. In: Rational models of cognition, ed. Oaksford, M. & Chater, N., pp. 197217. Oxford University Press.Google Scholar
Anderson, J. R. & Milson, R. (1989) Human memory: An adaptive perspective. Psychological Review 96:703–19.CrossRefGoogle Scholar
Anderson, J. R. & Schooler, L. J. (1991) Reflections of the environment in memory. Psychological Science 2:396408.CrossRefGoogle Scholar
Aristotle, (1980) Nicomachean ethics, trans. Ross, W. D.. Clarendon Press.Google Scholar
Baron, J. (1981) An analysis of confirmation bias. Paper presented at the 22nd Annual Meeting of the Psychonomic Society. 6–8 November, 1981, Philadelphia, PA.Google Scholar
Baron, J. (1985) Rationality and intelligence. Cambridge University Press.CrossRefGoogle Scholar
Barwise, J. & Cooper, R. (1981) Generalized quantifiers and natural language. Linguistics and Philosophy 4:159219.CrossRefGoogle Scholar
Bennett, J. (2003) A philosophical guide to conditionals. Oxford University Press.CrossRefGoogle Scholar
Bernoulli, J. (1713/2005) Ars conjectandi The art of conjecture, trans. Sylla, E. D.. Johns Hopkins University Press.Google Scholar
Boole, G. (1854/1958) An investigation of the laws of thought. Macmillan/Dover. (Reprinted by Dover, 1958).Google Scholar
Bovens, L. & Hartmann, S. (2003) Bayesian epistemology. Clarendon Press.Google Scholar
Braine, M. D. S. (1978) On the relation between the natural logic of reasoning and standard logic. Psychological Review 85:121.CrossRefGoogle Scholar
Chater, N., Crocker, M. & Pickering, M. (1998) The rational analysis of inquiry: The case of parsing: In: Rational models of cognition, ed. Oaksford, M. & Chater, N., pp. 441–68. Oxford University Press.Google Scholar
Chater, N. & Manning, C. D. (2006) Probabilistic models of language processing and acquisition. Trends in Cognitive Sciences 10:335–44.CrossRefGoogle ScholarPubMed
Chater, N. & Oaksford, M. (1999b) The probability heuristics model of syllogistic reasoning. Cognitive Psychology 38:191258.CrossRefGoogle ScholarPubMed
Cheng, P. W. & Holyoak, K. J. (1985) Pragmatic reasoning schemas. Cognitive Psychology 17:391416.CrossRefGoogle ScholarPubMed
Chomsky, N. (1957) Syntactic structures. Mouton.CrossRefGoogle Scholar
Chomsky, N. (1965) Aspects of the theory of syntax. MIT Press.Google Scholar
Cohen, L. J. (1981) Can human irrationality be experimentally demonstrated? Behavioral and Brain Sciences 4:317–70.CrossRefGoogle Scholar
Copeland, D. E. & Radvansky, G. A. (2004) Working memory and syllogistic reasoning. Quarterly Journal of Experimental Psychology 57A:1437–57.CrossRefGoogle Scholar
Cosmides, L. (1989) The logic of social exchange: Has natural selection shaped how humans reason? Studies with the Wason selection task. Cognition 31:187276.CrossRefGoogle ScholarPubMed
Cosmides, L. & Tooby, J. (2000) Evolutionary psychology and the emotions. In: Handbook of emotions, 2nd edition, ed. Lewis, M. & Haviland-Jones, J. M., pp. 91115. Guilford.Google Scholar
Courville, A. C., Daw, N. D. & Touretzky, D. S. (2006) Bayesian theories of conditioning in a changing world. Trends in Cognitive Sciences 10:294300.CrossRefGoogle Scholar
Daston, L. (1988) Classical probability in the enlightenment. Princeton University Press.CrossRefGoogle Scholar
Davidson, D. (1984) Inquiries into truth and interpretation. Oxford University Press.Google Scholar
Earman, J. (1992) Bayes or bust? MIT Press.Google Scholar
Edgington, D. (1995) On conditionals. Mind 104:235329.CrossRefGoogle Scholar
Evans, J. St. B. T. (1972) Reasoning with negatives. British Journal of Psychology 63:213–19.CrossRefGoogle Scholar
Evans, J. St. B. T. & Handley, S. J. (1999) The role of negation in conditional inference. Quarterly Journal of Experimental Psychology 52A 739–69.CrossRefGoogle Scholar
Evans, J. St. B. T., Handley, S. J., Harper, C. N. J. & Johnson-Laird, P. N. (1999) Reasoning about necessity and possibility: A test of the mental model theory of deduction. Journal of Experimental Psychology: Learning, Memory, and Cognition 25:14951513.Google Scholar
Evans, J. St .B. T., Handley, S. J. & Over, D. E. (2003) Conditionals and conditional probability. Journal of Experimental Psychology: Learning, Memory and Cognition 29321–55.Google ScholarPubMed
Evans, J. St. B. T. & Lynch, J. S. (1973) Matching bias in the selection task. British Journal of Psychology 64:391–97.CrossRefGoogle Scholar
Evans, J. St. B. T., Newstead, S. E. & Byrne, R. J. (1993) Human reasoning. Erlbaum.Google Scholar
Evans, J. St. B. T. & Over, D. E. (1996a) Rationality and reasoning. Psychology Press.Google Scholar
Evans, J. St. B. T. & Over, D. E. (1996b) Rationality in the selection task: Epistemic utility versus uncertainty reduction. Psychological Review 103:356–63.CrossRefGoogle Scholar
Evans, J. St. B. T. & Over, D. E. (2004) If. Oxford University Press.CrossRefGoogle Scholar
Fodor, J. A. (1983) The modularity of mind. MIT Press.CrossRefGoogle Scholar
Geurts, B. (2003) Reasoning with quantifiers. Cognition 86:223–51.CrossRefGoogle ScholarPubMed
Gigerenzer, G. & Goldstein, D. (1996) Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review 103:650–69.CrossRefGoogle ScholarPubMed
Gigerenzer, G. & Hoffrage, U. (1995) How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review 102(4):684704.CrossRefGoogle Scholar
Gigerenzer, G., Swijinck, Z., Porter, T., Daston, L., Beatty, J. & Kruger, L. (1989) The empire of chance. Cambridge University Press.CrossRefGoogle Scholar
Gigerenzer, G., Todd, P. & the ABC Research Group. (1999) Simple heuristics that make us smart. Oxford University Press.Google Scholar
Green, D. W. & Over, D. E. (1997) Causal inference, contingency tables and the selection task. Current Psychology of Cognition 16:459–87.Google Scholar
Green, D. W. & Over, D. E. (2000) Decision theoretical effects in testing a causal conditional. Current Psychology of Cognition 19:5168.Google Scholar
Griffiths, T. L. & Tenenbaum, J. B. (2005) Structure and strength in causal induction. Cognitive Psychology 51:354–84.CrossRefGoogle ScholarPubMed
Hacking, I. (1975) The emergence of probability. Cambridge University Press.Google Scholar
Hacking, I. (1990) The taming of chance. Cambridge University Press.CrossRefGoogle Scholar
Hattori, M. (2002) A quantitative model of optimal data selection in Wason's selection task. Quarterly Journal of Experimental Psychology 55A:1241–72.CrossRefGoogle Scholar
Henle, M. (1978) Foreword. In: Human reasoning, ed. Revlin, R. & Mayer, R. E.. Winston.Google Scholar
Horwich, P. (1982) Probability and evidence. Cambridge University Press.Google Scholar
Howson, C. & Urbach, P. (1993) Scientific reasoning: The Bayesian approach, 2nd edition. Open Court.Google Scholar
Inhelder, B. & Piaget, J. (1955) De la logique de l'enfant à la logique de l'adolescent. Presses Universitaires de France. (English version: The growth of logical thinking from childhood to adolescence. Routledge, 1958).Google Scholar
Jeffrey, R. C. (1983) The logic of decision, 2nd edition. University of Chicago Press.Google Scholar
Johnson-Laird, P. N. (1983) Mental models. Cambridge University Press.Google Scholar
Johnson-Laird, P. N. & Byrne, R. M. J. (1991) Deduction. Erlbaum.Google Scholar
Johnson-Laird, P. N. & Byrne, R. M. J. (2002) Conditionals: A theory of meaning, pragmatics, and inference. Psychological Review 109:646–78.CrossRefGoogle ScholarPubMed
Kahneman, D., Slovic, P. & Tversky, A., eds. (1982) Judgment under uncertainty: Heuristics and biases. Cambridge University Press.CrossRefGoogle Scholar
Kakade, S. & Dayan, P. (2002) Acquisition and extinction in autoshaping. Psychological Review 109:533–44.CrossRefGoogle ScholarPubMed
Kant, E. (1787/1961) Critique of pure reason, First edition, second impression, trans. Smith, N. K.. Macmillan.Google Scholar
Kirby, K. N. (1994) Probabilities and utilities of fictional outcomes in Wason's four card selection task. Cognition 51:128.CrossRefGoogle ScholarPubMed
Klauer, K. C. (1999) On the normative justification for information gain in Wason's selection task. Psychological Review 106:215–22.CrossRefGoogle Scholar
Knill, D. & Richards, W., eds. (1996) Perception as Bayesian inference. Cambridge University Press.CrossRefGoogle Scholar
Kuhn, T. (1962) The structure of scientific revolutions. University of Chicago Press.Google Scholar
Lakatos, I. (1970) Falsification and the methodology of scientific research programmes. In: Criticism and the growth of knowledge, ed. Lakatos, I. & Musgrave, A., pp. 91196. Cambridge University Press.CrossRefGoogle Scholar
Lindley, D. V. (1956) On a measure of the information provided by an experiment. Annals of Mathematical Statistics 27:9861005.CrossRefGoogle Scholar
Manktelow, K. I. & Over, D. E. (1987) Reasoning and rationality. Mind and Language 2:199219.CrossRefGoogle Scholar
Manktelow, K. I. & Over, D. E. (1991) Social roles and utilities in reasoning with deontic conditionals. Cognition 39:85105.CrossRefGoogle ScholarPubMed
Manktelow, K. I., Sutherland, E. J. & Over, D. E. (1995) Probabilistic factors in deontic reasoning. Thinking and Reasoning 1:201–20.CrossRefGoogle Scholar
McCarthy, J. & Hayes, P. J. (1969) Some philosophical problems from the standpoint of artificial intelligence. In: Machine intelligence, vol. 4, ed. Meltzer, B. & Michie, D.. Edinburgh University Press.Google Scholar
McClelland, J. L. (1998) Connectionist models and Bayesian inference. In: Rational models of cognition, ed. Oaksford, M. & Chater, N., pp. 2153. Oxford University Press.Google Scholar
McKenzie, C. R. M., Ferreira, V. S., Mikkelsen, L. A., McDermott, K. J. & Skrable, R. P. (2001) Do conditional statements target rare events? Organizational Behavior and Human Decision Processes 85:291309.CrossRefGoogle Scholar
McKenzie, C. R. M. & Mikkelsen, L. A. (2000) The psychological side of Hempel's paradox of confirmation. Psychonomic Bulletin and Review 7:360–66.CrossRefGoogle ScholarPubMed
McKenzie, C. R. M. & Mikkelsen, L. A. (2007) A Bayesian view of covariation assessment. Cognitive Psychology 54:3361.CrossRefGoogle ScholarPubMed
Nelson, J. D. (2005) Finding useful questions: On Bayesian diagnosticity, probability, impact, and information gain. Psychological Review 112(4):979–99.CrossRefGoogle ScholarPubMed
Newell, A., Shaw, J. C. & Simon, H. A. (1958) Chess-playing programs and the problem of complexity. IBM Journal of Research and Development 2:320–25.CrossRefGoogle Scholar
Newell, A. & Simon, H. A. (1972) Human problem solving. Prentice-Hall.Google Scholar
Newstead, S. E., Handley, S. J. & Buck, E. (1999) Falsifying mental models: Testing the predictions of theories of syllogistic reasoning. Memory and Cognition 27:344–54.CrossRefGoogle ScholarPubMed
Nickerson, R. S. (1996) Hempel's paradox and Wason's selection task: Logical and psychological puzzles of confirmation. Thinking and Reasoning 2:132.CrossRefGoogle Scholar
Novick, L. R. & Cheng, P. W. (2004) Assessing interactive causal influence. Psychological Review 111:455–85.CrossRefGoogle ScholarPubMed
Oaksford, M. (2004a) Conditional inference and constraint satisfaction: Reconciling probabilistic and mental models approaches? Paper presented at the 5th International Conference on Thinking, July 22–24, 2004. University of Leuven, Leuven, Belgium.Google Scholar
Oaksford, M. (2004b) Reasoning. In: Cognitive psychology, ed. Braisby, N. & Gellatly, A., pp. 418–55. Oxford University Press.Google Scholar
Oaksford, M. & Chater, N. (1991) Against logicist cognitive science. Mind and Language 6:138.CrossRefGoogle Scholar
Oaksford, M. & Chater, N. (1994) A rational analysis of the selection task as optimal data selection. Psychological Review 101:608–31.CrossRefGoogle Scholar
Oaksford, M. & Chater, N. (1996) Rational explanation of the selection task. Psychological Review 103:381–91.CrossRefGoogle Scholar
Oaksford, M. & Chater, N. (1998a) Rationality in an uncertain world. Psychology Press.Google Scholar
Oaksford, M. & Chater, N. eds. (1998b) Rational models of cognition. Oxford University Press.Google Scholar
Oaksford, M. & Chater, N. (2003a) Conditional probability and the cognitive science of conditional reasoning. Mind and Language 18:359–79.CrossRefGoogle Scholar
Oaksford, M. & Chater, N. (2003b) Optimal data selection: Revision, review, and reevaluation. Psychonomic Bulletin and Review 10:289318.CrossRefGoogle ScholarPubMed
Oaksford, M. & Chater, N. (2007) Bayesian rationality: The probabilistic approach to human reasoning. Oxford University Press.CrossRefGoogle Scholar
Oaksford, M. & Chater, N. (2008) Probability logic and the Modus Ponens–Modus Tollens asymmetry in conditional inference. In: The probabilistic mind: Prospects for Bayesian cognitive science, ed. Chater, N. & Oaksford, M., pp. 97120. Oxford University Press.CrossRefGoogle Scholar
Oaksford, M., Chater, N. & Grainger, B. (1999) Probabilistic effects in data selection. Thinking and Reasoning 5:193244.CrossRefGoogle Scholar
Oaksford, M., Chater, N., Grainger, B. & Larkin, J. (1997) Optimal data selection in the reduced array selection task (RAST). Journal of Experimental Psychology: Learning, Memory and Cognition 23:441–58.Google Scholar
Oaksford, M., Chater, N. & Larkin, J. (2000) Probabilities and polarity biases in conditional inference. Journal of Experimental Psychology: Learning, Memory and Cognition 26:883–89.Google ScholarPubMed
Oaksford, M. & Moussakowski, M. (2004) Negations and natural sampling in data selection: Ecological vs. heuristic explanations of matching bias. Memory and Cognition 32:570–81.CrossRefGoogle Scholar
Oaksford, M., Roberts, L. & Chater, N. (2002) Relative informativeness of quantifiers used in syllogistic reasoning. Memory and Cognition 30:138–49.CrossRefGoogle ScholarPubMed
Oaksford, M. & Stenning, K. (1992) Reasoning with conditionals containing negated constituents. Journal of Experimental Psychology: Learning, Memory and Cognition 18:835–54.Google ScholarPubMed
Oaksford, M. & Wakefield, M. (2003) Data selection and natural sampling: Probabilities do matter. Memory and Cognition 31:143–54.CrossRefGoogle ScholarPubMed
Oberauer, K., Weidenfeld, A. & Hörnig, R. (2004) Logical reasoning and probabilities: A comprehensive test of Oaksford and Chater (2001) Psychonomic Bulletin and Review 11:521–27.CrossRefGoogle ScholarPubMed
Oberauer, K. & Wilhelm, O. (2003) The meaning(s) of conditionals: Conditional probabilities, mental models and personal utilities. Journal of Experimental Psychology: Learning, Memory, and Cognition 29:680–93.Google ScholarPubMed
Oberauer, K., Wilhelm, O. & Diaz, R. R. (1999) Bayesian rationality for the Wason selection task? A test of optimal data selection theory. Thinking and Reasoning 5:115–44.CrossRefGoogle Scholar
Over, D. E. & Evans, J. St. B. T (1994) Hits and misses: Kirby on the selection task. Cognition 52:235–43.CrossRefGoogle ScholarPubMed
Over, D. E. & Jessop, A. (1998) Rational analysis of causal conditionals and the selection task. In: Rational models of cognition, ed. Oaksford, M. & Chater, N., pp. 399414. Oxford University Press.Google Scholar
Pearl, J. (1988) Probabilistic reasoning in intelligent systems. Morgan Kaufmann.Google Scholar
Pearl, J. (2000) Causality: Models, reasoning and inference. Cambridge University Press.Google Scholar
Perham, N. & Oaksford, M. (2005) Deontic reasoning with emotional content: Evolutionary psychology or decision theory? Cognitive Science 29:681718.CrossRefGoogle ScholarPubMed
Politzer, G. & Braine, M. D. (1991) Responses to inconsistent premises cannot count as suppression of valid inferences. Cognition 38:103–08.CrossRefGoogle Scholar
Popper, K. R. (1935/1959) The logic of scientific discovery. Basic Books.Google Scholar
Putnam, H. (1974) The “corroboration” of theories. In: The philosophy of Karl Popper, vol. 2, ed. Schilpp, A.. Open Court.Google Scholar
Pylyshyn, Z., ed. (1987) The robot's dilemma: The frame problem in artificial intelligence. Ablex.Google Scholar
Quine, W. V. O. (1953) From a logical point of view. Harvard University Press.Google Scholar
Ramsey, F. P. (1931/1990b) The foundations of mathematics and other logical essays. Routledge and Kegan Paul.Google Scholar
Reiter, R. (1980) A logic for default reasoning, Artificial Intelligence 13:81132.CrossRefGoogle Scholar
Rips, L. J. (1983) Cognitive processes in propositional reasoning. Psychological Review 90:3871.CrossRefGoogle Scholar
Rips, L. J. (1994) The psychology of proof. MIT Press.CrossRefGoogle Scholar
Rosch, E. (1975) Cognitive representation of semantic categories. Journal of experimental psychology: General 104:192233.CrossRefGoogle Scholar
Schroyens, W. & Schaeken, W. (2003) A critique of Oaksford, Chater and Larkin's (2000) conditional probability model of conditional reasoning. Journal of Experimental Psychology: Learning, Memory and Cognition 29:140–49.Google Scholar
Sober, E. (2002) Intelligent design and probability reasoning. International Journal for Philosophy of Religion 52:6580.CrossRefGoogle Scholar
Stewart, N., Chater, N. & Brown, G. D. A. (2006) Decision by sampling. Cognitive Psychology 53:126.CrossRefGoogle ScholarPubMed
Wagner, C. G. (2004) Modus tollens probabilized. British Journal for Philosophy of Science 55:747–53.CrossRefGoogle Scholar
Yama, H. (2001) Matching versus optimal data selection in the Wason selection task. Thinking and Reasoning 7:295311.CrossRefGoogle Scholar
Yuille, A. L. & Kersten, D. (2006) Vision as Bayesian Inference: Analysis by Synthesis? Trends in Cognitive Sciences 10:301–08.CrossRefGoogle ScholarPubMed
Zeelenberg, M., Van Dijk, W. W., Manstead, A. S. R. & Van der Pligt, J. (2000) On bad decisions and disconfirmed expectancies: The psychology of regret and disappointment. Cognition and Emotion 14:521–41.CrossRefGoogle Scholar