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"At least one" problem with "some" formal reasoning paradigms.

James R Schmidt1, A Thompson

  • 1Department of Psychology, University of Waterloo, Waterloo, Ontario, Canada. j4schmid@watarts.uwaterloo.ca

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Summary

Clarifying the logical meaning of "some" significantly reduced pragmatic interpretations and errors in reasoning tasks. This suggests using logically clarified quantifiers can improve logical reasoning and reduce common mistakes.

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Area of Science:

  • Cognitive Psychology
  • Formal Logic
  • Linguistics

Background:

  • The quantifier "some" in formal logic means "at least one, possibly all."
  • However, people often pragmatically interpret "some" as "some, but not all."
  • This pragmatic interpretation may contribute to errors in reasoning tasks.

Purpose of the Study:

  • To investigate if pragmatic interpretations of "some" explain errors in syllogistic reasoning.
  • To determine if using logically clarified quantifiers improves reasoning accuracy.

Main Methods:

  • Three experiments were conducted using immediate-inference and syllogistic reasoning tasks.
  • Participants were presented with either standard quantifiers or logically clarified quantifiers.
  • Performance was measured by the number of logical versus pragmatic responses.

Main Results:

  • Logically clarified quantifiers led to significantly more logical responses and fewer pragmatic responses on immediate-inference tasks.
  • This effect extended to a deductive task with false premises.
  • Clarified quantifiers reduced pragmatic and increased logical responses in syllogistic reasoning.

Conclusions:

  • Pragmatic interpretations of "some" contribute to errors in syllogistic reasoning.
  • Logically clarified quantifiers enhance logical reasoning accuracy.
  • Replacing standard quantifiers with clarified ones is recommended for education and research.