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The uncertain reasoner: Bayes, logic, and rationality

Published online by Cambridge University Press:  12 February 2009

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

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the “rational” explanation of cognition; and re-evaluate the empirical case for Bayesian rationality.

Type
Authors' Response
Information
Behavioral and Brain Sciences , Volume 32 , Issue 1 , February 2009 , pp. 105 - 120
Copyright
Copyright © Cambridge University Press 2009

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References

Adams, E. W. (1975) The logic of conditionals: An application of probability to deductive logic. Reidel.Google Scholar
Adams, E. W. (1998) A primer of probability logic. CLSI Publications.Google Scholar
Ali, N., Schlottmann, A., Shaw, A., Chater, N. & Oaksford, M. (in press) Causal discounting and conditional reasoning in children. In: Cognition and conditionals: Probability and logic in human thought, ed. Oaksford, M. & Chater, N.. Oxford University Press.Google Scholar
Anderson, A. & Belnap, N. D. (1975) Entailment: The logic of relevance and necessity, vol. 1. Princeton University Press.Google Scholar
Anderson, J. R. (1983) The architecture of cognition. Harvard University Press.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.Google Scholar
Ariely, D., Loewenstein, G. & Prelec, D. (2003) Coherent arbitrariness: Stable demand curves without stable preferences. Quarterly Journal of Economics 118:73–105.Google Scholar
Bennett, J. (2003) A philosophical guide to conditionals. Oxford University Press.Google Scholar
Blakemore, C., Adler, K. & Pointon, M. (1990) Vision: Coding and efficiency. Cambridge University Press.Google Scholar
Braine, M. D. S. & O'Brien, D. P. (1991) A theory of if: A lexical entry, reasoning program, and pragmatic principles. Psychological Review 98:182–203.Google Scholar
Carnap, R. (1950) The logical foundations of probability. University of Chicago Press.Google Scholar
Carroll, S. (2005) Endless forms most beautiful. W. W. Norton.Google Scholar
Chater, N. (1996) Reconciling simplicity and likelihood principles in perceptual organization. Psychological Review 103:566–81.Google Scholar
Chater, N. & Oaksford, M. (1999b) The probability heuristics model of syllogistic reasoning. Cognitive Psychology 38:191–258.CrossRefGoogle ScholarPubMed
Chater, N. & Oaksford, M. (2006) Mental mechanisms: Speculations on human causal learning and reasoning. In: Information sampling and adaptive cognition, ed. Fiedler, K. & Juslin, P., pp. 210–38. Cambridge University Press.Google Scholar
Chater, N. & Oaksford, M. eds. (2008a) The probabilistic mind: Prospects for Bayesian cognitive science. Oxford University Press.Google Scholar
Chater, N. & Oaksford, M. (2008b) The probabilistic mind: Where next? In: The probabilistic mind: Prospects for Bayesian cognitive science, ed. Chater, N. & Oaksford, M., pp. 501–14. Oxford University Press.Google Scholar
Chater, N., Oaksford, M., Heit, E. & Hahn, U. (in press) Inductive logic and empirical psychology. In: The handbook of philosophical logic, vol. 10, ed. Hartmann, S. & Woods, J.. Springer.Google Scholar
Chater, N., Oaksford, M., Nakisa, R. & Redington, M. (2003) Fast, frugal and rational: How rational norms explain behavior. Organizational Behavior and Human Decision Processes 90:63–86.Google Scholar
Chater, N., Tenenbaum, J. B. & Yuille, A. eds. (2006) Probabilistic models of cognition: Where next? Trends in Cognitive Sciences 10:335–44. [Special Issue.]Google Scholar
Chater, N. & Vitányi, P. (2002) Simplicity: A unifying principle in cognitive science? Trends in Cognitive Sciences 7:19–22.Google Scholar
Copeland, D. E. (2006) Theories of categorical reasoning and extended syllogisms. Thinking and Reasoning 12:379–412.Google Scholar
Copeland, D. E. & Radvansky, G. A. (2004) Working memory and syllogistic reasoning. Quarterly Journal of Experimental Psychology 57A:1437–57.Google Scholar
Cosmides, L. (1989) The logic of social exchange: Has natural selection shaped how humans reason? Studies with the Wason selection task. Cognition 31:187–276.Google Scholar
Dawes, R. M. (1979) The robust beauty of improper linear models in decision making. American Psychologist 34:571–82.Google Scholar
Dempster, A. P. (1968) A generalization of Bayesian inference. Journal of the Royal Statistical Society, Series B 30:205–47.Google Scholar
De Neys, W., Vartanian, O. & Goel, V. (2008) Smarter than we think: When our brains detect that we are biased. Psychological Science 19:483–89.Google Scholar
Domingos, P. & Pazzani, M. (1997) On the optimality of the simple Bayesian classifier under zero-one loss. Machine Learning 29:103–30.Google Scholar
Dowty, D. R., Wall, R. E. & Peters, S. (1981) Introduction to Montague semantics. Springer.Google Scholar
Doya, K., Ishii, S., Rao, R. P. N. & Pouget, A., eds. (2007) The Bayesian brain: Probabilistic approaches to neural coding. MIT Press.Google Scholar
Earman, J. (1992) Bayes or bust? MIT Press.Google Scholar
Edgington, D. (1995) On conditionals. Mind 104:235–329.Google Scholar
Evans, J. St. B. T. (1989) Bias in human reasoning: Causes and consequences. Erlbaum.Google Scholar
Evans, J. St. B. T. (2007) Hypothetical thinking: Dual processes in reasoning and judgement. Psychology Press.Google Scholar
Evans, J. St. B. T. & Frankish, K., eds. (in press) In two minds: Dual processes and beyond. Oxford University Press.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. (2004) If. Oxford University Press.Google Scholar
Field, H. (1978) A note on Jeffrey conditionalization. Philosophy of Science 45:361–67.Google Scholar
Fodor, J. A. (1968) Psychological explanation. Random House.Google Scholar
Friston, K. (2005) A theory of cortical responses. Philosophical Transactions of the Royal Society B 360:815–36.Google Scholar
Gärdenfors, P. (1986) Belief revisions and the Ramsey test for conditionals. Philosophical Review 95:81–93.Google Scholar
George, C. (1997) Reasoning from uncertain premises. Thinking and Reasoning 3:161–90.CrossRefGoogle Scholar
Gigerenzer, G. & Goldstein, D. (1996) Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review 103:650–69.Google Scholar
Gigerenzer, G., Todd, P. & the ABC Research Group. (1999) Simple heuristics that make us smart. Oxford University Press.Google Scholar
Glymour, C. (2001) The mind's arrow. MIT Press.CrossRefGoogle Scholar
Goel, V. (2007) The anatomy of deduction. Trends in Cognitive Science 11:435–41.Google Scholar
Gold, J. I. & Shadlen, M. N. (2000) Representation of a perceptual decision in developing oculomotor commands. Nature 404:390–94.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 19:51–68.Google Scholar
Gregory, R. L. (1970) The intelligent eye. Weidenfeld & Nicolson.Google Scholar
Grice, H. P. (1975) Logic and conversation. In: The logic of grammar, ed. Davidson, D. & Harman, G., pp. 64–75. Dickenson.Google Scholar
Griffiths, T. L., Steyvers, M. & Tenenbaum, J. B. (2007) Topics in semantic representation. Psychological Review 114:211–44.Google Scholar
Griffiths, T. L. & Tenenbaum, J. B. (2005) Structure and strength in causal induction. Cognitive Psychology 51:354–84.Google Scholar
Hahn, U. & Oaksford, M. (2007) The rationality of informal argumentation: A Bayesian approach to reasoning fallacies. Psychological Review 114:704–32.CrossRefGoogle ScholarPubMed
Harman, G. (1986) Change in view: Principles of reasoning. MIT Press.Google Scholar
Hawthorn, J. (2008) Inductive logic. In: Stanford Encyclopedia of Philosophy. Available at: http://plato.stanford.edu/entries/logic-inductive/.Google Scholar
Hilton, D. J., Kemmelmeier, M. & Bonnefon, J-F. (2005) Putting Ifs to work: Goal-based relevance in conditional directives. Journal of Experimental Psychology: General 134:388–405.Google Scholar
Hochberg, J. & McAlister, E. (1953) A quantitative approach to figure “goodness.” Journal of Experimental Psychology 46:361–64.Google Scholar
Houdé, O., Zago, L., Mellet, E., Moutier, S., Pineau, A., Mazoyer, B. & Tzourio-Mazoyer, N. (2000) Shifting from the perceptual brain to the logical brain: The neural impact of cognitive inhibition training. Journal of Cognitive Neuroscience 12:721–28.CrossRefGoogle Scholar
Hurley, S. & Nudds, M., eds. (2006) Rational animals? Oxford University Press.Google Scholar
Jacob, F. (1977) Evolution and tinkering. Science 196:1161–66.Google Scholar
Jacobs, R. A., Jordan, M. I., Nowlan, S. & Hinton, G. E. (1991) Adaptive mixtures of local experts. Neural Computation 3:1–12.Google Scholar
Jeffrey, R. C. (1967) Formal logic: Its scope and limits, 2nd edition.McGraw-Hill.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. (1992) Syllogs (computer program). Available at: http://webscript.princeton.edu/~mentmod/models.php.Google Scholar
Kemp, C. & Tenenbaum, J. B. (2008) The discovery of structural form. Proceedings of the National Academy of Sciences USA 105:10687–92.Google Scholar
Klauer, K. C. (1999) On the normative justification for information gain in Wason's selection task. Psychological Review 106:215–22.Google Scholar
Knill, D. & Richards, W., eds. (1996) Perception as Bayesian inference. Cambridge University Press.Google Scholar
Körding, K. P. & Wolpert, D. (2004) Bayesian integration in sensorimotor learning. Nature 427:244–47.Google Scholar
Kowalski, R. (1979) Algorithm = Logic + Control. Communications of the Association for Computing Machinery 22:424–36.Google Scholar
Krauth, J. (1982) Formulation and experimental verification of models in propositional reasoning. Quarterly Journal of Experimental Psychology 34:285–98.Google Scholar
Laplace, P. S. (1951) A philosophical essay on probabilities, trans. Truscott, F. W. & Emory, F. L.. Dover. (Original work published 1814).Google Scholar
Lauritzen, S. & Spiegelhalter, D. (1988) Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society B 50:157–224.Google Scholar
Leeuwenberg, E. & Boselie, F. (1988) Against the likelihood principle in visual form perception. Psychological Review 95:485–91.Google Scholar
Liu, I.-M. (2003) Conditional reasoning and conditionalization. Journal of Experimental Psychology: Learning, Memory, and Cognition 29:694–709.Google Scholar
Liu, I. M., Lo, K. C. & Wu, J. T. (1996) A probabilistic interpretation of “If-Then”. The Quarterly Journal of Experimental Psychology 49A:828–44.Google Scholar
Ma, W. J., Beck, J., Latham, P. & Pouget, A. (2006) Bayesian inference with probabilistic population codes. Nature Neuroscience 9:1432–38.Google Scholar
MacKay, D. J. C. (2003) Information theory, inference, and learning algorithms. Cambridge University Press.Google Scholar
Manning, C. & Schütze, H. (1999) Foundations of statistical natural language processing. MIT Press.Google Scholar
Marr, D. (1982) Vision: A computational investigation into the human representation and processing of visual information. Freeman.Google Scholar
Martignon, L. & Blackmond-Laskey, K. (1999) Bayesian benchmarks for fast and frugal heuristics. In: Simple heuristics that make us smart, ed. Gigerenzer, G., Todd, P. M. & the ABC Research Group, pp. 169–88. 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 85:291–309.Google 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.Google Scholar
McKenzie, C. R. M. & Mikkelsen, L. A. (2007) A Bayesian view of covariation assessment. Cognitive Psychology 54:33–61.Google Scholar
Milne, P. (1995) A Bayesian defence of Popperian science? Analysis 55:213–15.Google Scholar
Milne, P. (1996) log[P(h|eb)/P(h|b)] is the one true measure of confirmation. Philosophy of Science 63:21–26.Google Scholar
Moore, G. E. (1903) Principia ethica. Cambridge University Press.Google Scholar
Navarro, D. J., Griffiths, T. L., Steyvers, M. & Lee, M. D. (2006) Modeling individual differences using Dirichlet processes. Journal of Mathematical Psychology 50:101–22.Google Scholar
Nelson, J. D. (2005) Finding useful questions: On Bayesian diagnosticity, probability, impact, and information gain. Psychological Review 112(4):979–99.Google Scholar
Oaksford, M. & Chater, N. (1991) Against logicist cognitive science. Mind and Language 6:1–38.Google Scholar
Oaksford, M. & Chater, N. (1994) A rational analysis of the selection task as optimal data selection. Psychological Review 101:608–31.Google Scholar
Oaksford, M. & Chater, N. eds. (1998b) Rational models of cognition. Oxford University Press.Google Scholar
Oaksford, M. & Chater, N. (2002) Common sense reasoning, logic and human rationality. In: Common sense, reasoning and rationality, ed. Elio, R., pp. 174–214. Oxford University Press.Google Scholar
Oaksford, M. & Chater, N. (2007) Bayesian rationality: The probabilistic approach to human reasoning. Oxford University Press.Google 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. 97–120. Oxford University Press.Google Scholar
Oaksford, M. & Chater, N. (in press) Conditionals and constraint satisfaction: Reconciling mental models and probabilistic approaches? In: Cognition and conditionals: Probability and logic in human thought, ed. Oaksford, M. & Chater, N.. Oxford University Press.Google Scholar
Oaksford, M., Chater, N. & Grainger, B. (1999) Probabilistic effects in data selection. Thinking and Reasoning 5:193–244.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 Scholar
Oaksford, M. & Hahn, U. (2007) Induction, deduction and argument strength in human reasoning and argumentation. In: Inductive reasoning, ed. Feeney, A. & Heit, E.. pp. 269–301. Cambridge University Press.Google Scholar
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.Google Scholar
Oaksford, M. & Wakefield, M. (2003) Data selection and natural sampling: Probabilities do matter. Memory and Cognition 31:143–54.Google Scholar
Oberauer, K. (2006) Reasoning with conditionals: A test of formal models of four theories. Cognitive Psychology 53:238–83.Google Scholar
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.Google Scholar
Over, D. E., Hadjichristidis, C., Evans, J. St. B. T., Handley, S. J. & Sloman, S. A. (2007) The probability of causal conditionals. Cognitive Psychology 54:62–97.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
Rao, R. P. N., Olshausen, B. A. & Lewicki, M. S., eds. (2002) Probabilistic models of the brain: Perception and neural function. MIT Press.Google Scholar
Restall, G. (1996) Information flow and relevant logics. In: Logic, language and computation, ed. Seligman, J. & Westerståhl, D., pp. 463–78 CSLI Publications.Google Scholar
Rips, L. J. (1994) The psychology of proof. MIT Press.Google Scholar
Rissanen, J. J. (1989) Stochastic complexity and statistical inquiry. World Scientific.Google Scholar
Shafer, G. (1976) A mathematical theory of evidence. Princeton University Press.Google Scholar
Shannon, C. E. & Weaver, W. (1949) The mathematical theory of communication. University of Illinois Press.Google Scholar
Sher, S. & McKenzie, C. R. M. (2006) Information leakage from logically equivalent frames. Cognition 101:467–94.Google Scholar
Sloman, S. A. (1996) The empirical case for two systems of reasoning. Psychological Bulletin 119:3–22.Google Scholar
Sloman, S. A. (2005) Causal models. Oxford University Press.Google Scholar
Sobel, D. M., Tenenbaum, J. B. & Gopnik, A. (2004) Children's causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers. Cognitive Science 28:303–33.Google Scholar
Sobel, J. H. (2004) Probable modus ponens and modus tollens and updating on uncertain evidence. Unpublished manuscript, Department of Philosophy, University of Toronto, Scarborough. Available at: www.scar.toronto.ca/~sobel/Conf/Disconf.pdf.Google Scholar
Sober, E. (2002) Intelligent design and probability reasoning. International Journal for Philosophy of Religion 52:65–80.Google Scholar
Stanovich, K. E. (2008) Individual differences in reasoning and the algorithmic/intentional level distinction in cognitive science. In: Reasoning: Studies of human inference and its foundations, ed. Rips, L. & Adler, J., pp. 414–36. Cambridge University Press.Google Scholar
Stanovich, K. E. & West, R. F. (2000) Individual differences in reasoning: Implications for the rationality debate? Behavioral and Brain Sciences 23:645–65.Google Scholar
Stevenson, R. J. & Over, D. E. (1995) Deduction from uncertain premises. The Quarterly Journal of Experimental Psychology 48A:613–43.Google Scholar
Stewart, N., Chater, N. & Brown, G. D. A. (2006) Decision by sampling. Cognitive Psychology 53:1–26.Google Scholar
Tenenbaum, J. B. (1999) A Bayesian framework for concept learning. Doctoral dissertation, Brain and Cognitive Sciences Department, MIT.Google Scholar
Tenenbaum, J. B. & Griffths, T. L. (2001) Structure learning in human causal induction. In: Advances in neural information processing systems, vol. 13, ed. Keen, T. K., Dietterich, T. G. & Tresp, V., pp. 59–65. MIT Press.Google Scholar
Tenenbaum, J. B., Kemp, C. & Shafto, P. (2007) Theory based Bayesian models of inductive reasoning. In: Inducive reasoning, ed. Feeney, A. & Heit, E., pp. 167–204. Oxford University Press.Google Scholar
Thaler, R. H. (2005) Advances in behavioral finance, Vol. II. Princeton University Press.Google Scholar
Toussaint, M., Harmeling, S. & Storkey, A. (2006) Probabilistic inference for solving (PO)MDPs. Technical Report EDI-INF-RR-0934, University of Edinburgh.Google Scholar
Vitányi, P. M. B. & Li, M. (2000) Minimum description length induction, Bayesianism, and Kolmogorov complexity. IEEE Transactions on Information Theory IT-46446–64.Google Scholar
von Helmholtz, H. (1910/1925) Physiological optics. Volume III. The theory of the perception of vision. Dover. (Translated from 3rd German edition, 1910).Google Scholar
Walton, D. N. (1989) Informal logic. Cambridge University Press.Google Scholar
Williamson, J. & Gabbay, D., eds. (2003) Special issue on combining logic and probability. Journal of Applied Logic 1:135–308.Google Scholar
Zadeh, L. A. (1975) Fuzzy logic and approximate reasoning. Synthese 30:407–28.Google Scholar