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A Tale of Two CulturesQualitative and Quantitative Research in the Social Sciences$
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Gary Goertz and James Mahoney

Print publication date: 2012

Print ISBN-13: 9780691149707

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149707.001.0001

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Mathematical Prelude: A Selective Introduction to Logic and Set Theory for Social Scientists

Mathematical Prelude: A Selective Introduction to Logic and Set Theory for Social Scientists

Chapter:
(p.16) Chapter 2 Mathematical Prelude: A Selective Introduction to Logic and Set Theory for Social Scientists
Source:
A Tale of Two Cultures
Author(s):

Gary Goertz

James Mahoney

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691149707.003.0002

This chapter considers some key ideas from logic and set theory as they relate to qualitative research in the social sciences, including ideas concerning necessary and sufficient conditions. It also highlights a major contrast between qualitative and quantitative research: whereas quantitative research draws on mathematical tools associated with statistics and probability theory, qualitative research is often based on set theory and logic. The chapter first compares the natural language of logic in the qualitative culture with the language of probability and statistics in the quantitative culture. It then considers the necessary conditions and sufficient conditions as basis for qualitative methods, focusing on set theory and Venn diagrams, two-by-two tables, and truth tables. It also discusses the use of qualitative and quantitative aggregation techniques and concludes by explaining the criteria for assessing the “fit” of the model or the “importance” of a given causal factor.

Keywords:   logic, set theory, qualitative research, necessary condition, sufficient condition, quantitative research, statistics, probability theory, natural language, aggregation technique

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