Chapter

Counterexamples

Philip N. Johnson-Laird

in How We Reason

Published in print October 2008 | ISBN: 9780199551330
Published online March 2012 | e-ISBN: 9780191701580 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199551330.003.0016
Counterexamples

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This chapter describes the notion of counterexamples. Counterexamples are important for reasoning. A valid inference has a conclusion that must be true if its premises are true. A counterexample to a general proposition is one that states that the proposition is false. In particular, this chapter answers three questions: Do humans recognizes the force of counterexamples? In what circumstances, if any, do humans search for them? And does the model theory explain performance? The problems in the use of counterexamples are addressed. In addition, some studies of reasoning with propositional connectives that corroborate the use of counterexamples are described. The data reviewed can answer the three questions above. First, it can recognize the force of counterexamples because the principle can be grasped that a valid inference has no counterexamples. Second, the best recipe to elicit counterexamples appears to be to evaluate someone else's conclusion, to use simple premises that elicit multiple models of possibilities, and to ensure that the conclusion holds in at least one of these models. Finally, the model theory seems to explain the performance.

Keywords: counterexamples; reasoning; model theory; premise; proposition

Chapter.  6807 words.  Illustrated.

Subjects: Cognitive Psychology

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