Logical Approaches to Human Deductive Reasoning

doi:10.1017/CBO9780511814273.011

9 - Logical Approaches to Human Deductive Reasoning

Published online by Cambridge University Press: 05 June 2012

Lance J. Rips

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Jonathan E. Adler and

Lance J. Rips

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Lance J. Rips: Affiliation:
Northwestern University
Jonathan E. Adler: Affiliation:
Brooklyn College, City University of New York
Lance J. Rips: Affiliation:
Northwestern University, Illinois

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Summary

The idea that formal logic bears a close relationship to human reasoning is extremely controversial within cognitive science. For example, Wason and Johnson-Laird (1972: 245) concluded their influential study of reasoning by stating that “only gradually did we realize first that there was no existing formal calculus which correctly modeled our subjects' inferences, and second that no purely formal system would succeed.” This kind of opposition is based on evidence that subjects' judgments about an argument sometimes depart from the answer that the experimenter derived by translating the argument into some system of logic and assessing its correctness within that system. The strength of this evidence, however, clearly depends on the system the investigator uses. If the investigator's conception is too narrow, what is classified as nonlogical behavior may turn out logical after all. To evaluate the evidence, we need some clear idea of what logic has to offer.

Most cognitive theories that contain a logic-like component (e.g., Braine 1978; Johnson-Laird 1975; Osherson 1974, 1975, 1976; Rips 1983) are based on the notion of proof, particularly the “natural deduction” proofs originally devised by Gentzen (1935/1969) and Jaskowski (1934). The basic notion is familiar to anyone who has taken a high school mathematics course: If you want to know whether a particular argument is deductively correct, you can find out by taking its premises as given and then trying to derive its conclusion by applying a specified set of rules.

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Type: Chapter
Information: Reasoning
Studies of Human Inference and its Foundations
, pp. 187 - 205

DOI: https://doi.org/10.1017/CBO9780511814273.011 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2008

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References

Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: Harvard University Press.Google Scholar

Braine, M. D. S. (1978). On the relation between the natural logic of reasoning and standard logic. Psychological Review, 85, 1–21.Google Scholar

Braine, M. D. S., Reiser, B. J., Rumain, B. (1984). Some empirical justification for a theory of natural propositional reasoning. Psychology of Learning and Motivation, 18, 313–371. Orlando, FL: Academic Press.Google Scholar

Collins, A. M., and Loftus, E. F. (1975). A spreading activation theory of semantic precessing. Psychological Review, 13, 1–50.Google Scholar

Copi, I. M. (1954). Symbolic logic. New York: Macmillan.Google Scholar

Dowty, D. R. (1993). Categorial grammar, reasoning, and cognition. Paper presented at the 29th regional meeting of the Chicago Linguistics Society.Google Scholar

Fine, K. (1985a). Natural deduction and arbitrary objects. Journal of Philosophical Logic, 14, 57–107.CrossRef Google Scholar

Fine, K. (1985b). Reasoning with arbitrary objects. Oxford: Blackwells.Google Scholar

Gazdar, G. (1979). Pragmatics. New York: Academic Press.Google Scholar

Gentzen, G. (1969). Investigations into logical deduction. In Szabo, M. E. (ed.), The collected papers of Gerhard Gentzen. Amsterdam: North Holland. (Originally published 1935)Google Scholar

Gilhooly, K. J., Logie, R. H., Wetherick, N. E., and Wynn, V. (1993). Working memory and strategies in syllogistic reasoning task. Memory and Cognition, 21, 115–124.CrossRef Google Scholar

Grice, H. P. (1989). Studies in the way of words. Cambridge, MA: Harvard University Press.Google Scholar

Hitch, G. J., & Baddeley, A. D. (1976). Verbal reasoning and working memory. Quarterly Journal of Experimental Psychology, 28, 603–621.CrossRef Google Scholar

Jaskowski, S. (1934). On the rules of supposition in formal logic. Studia Logica, 1, 5–32.Google Scholar

Johnson-Laird, P. N. (1975). Models of deduction. In Falmagne, R. J. (ed.), Reasoning: Representation and process in children and adults. Hillsdale, NJ: Erlbaum.Google Scholar

Johnson-Laird, P. N. (1983). Mental models. Cambridge, MA: Harvard University Press.Google Scholar

Johnson-Laird, P. N., & Byrne, R. M. J. (1991). Deduction. Hillsdale, NJ: Erlbaum.Google Scholar

Johnson-Laird, P. N., Byrne, R. M. J., & Schaeken, W. (1992). Propositional reasoning by model. Psychological Review, 96, 658–673.Google Scholar

McCawley, J. D. (1981). Everything linguists have always wanted to know about logic but were ashamed to ask. Chicago: University of Chicago Press.Google Scholar

Newell, A., Shaw, J. C., & Simon, H. A. (1957). Empirical explorations with the Logic Theory Machine. In Proceedings of the Joint Computer Conference.Google Scholar

Osherson, D. N. (1974). Logical abilities in children, vol. 2. Hillsdale, NJ: Erlbaum.Google Scholar

Osherson, D. N. (1975). Logical abilities in children, vol. 3. Hillsdale, NJ: Erlbaum.Google Scholar

Osherson, D. N. (1976). Logical abilities in children, vol. 4. Hillsdale, NJ: Erlbaum.Google Scholar

Pelletier, F. J. (1977). Or. Theoretical linguistics, 4, 61–74.Google Scholar

Prawitz, D. (1965). Natural deduction: A proof-theoretical study. Stockholm: Almqvist and Wiksell.Google Scholar

Rips, L. J. (1983). Cognitive processes in propositional reasoning. Psychological Review, 90, 38–71.CrossRef Google Scholar

Rips, L. J. (1994). The psychology of proof: Deduction in human thinking. Cambridge, MA: MIT Press.Google Scholar

Rips, L. J. (1999). Human modes of quantificational reasoning. In Cooper, S. B. & Truss, J. K. (Eds.), Models and computability. Cambridge, England: Cambridge University Press.CrossRef Google Scholar

Rips, L. J. (2000). The cognitive nature of instantiation. Journal of Memory and Language, 43, 20–43.CrossRef Google Scholar

Rips, L. J., & Conrad, F. G. (1983). Individual differences in deduction. Cognition and Brain Theory, 6, 259–285.Google Scholar

Sperber, D., & Wilson, D. (1986). Relevance. Cambridge, MA: Harvard University Press.Google Scholar

Störring, G. (1908). Experimentelle Untersuchungen über einfache Schlussprozesse. Archiv für die Gesamte Psychologie, 11, 1–127.Google Scholar

Tarski, A. (1956). On the concept of truth in formalized languages. In Logic, semantics, metamathematics. Oxford: Oxford University Press. (Originally published 1936)Google Scholar

Thomason, R. H. (1970). Symbolic logic. New York: Macmillan.Google Scholar

Ungar, A. M. (1992). Normalization, cut-elimination, and the theory of proofs. Stanford, CA: CSLI.Google Scholar

Wason, P. C., & Johnson-Laird, P. N. (1972). The psychology of reasoning. Cambridge, MA: Harvard University Press.Google Scholar

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