
Contents
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Introduction Introduction
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Natural Language and Logic Natural Language and Logic
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Necessary Conditions and Sufficient Conditions with Binary Categories Necessary Conditions and Sufficient Conditions with Binary Categories
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Set Theory and Venn Diagrams Set Theory and Venn Diagrams
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Two-by-Two Tables Two-by-Two Tables
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Truth Tables Truth Tables
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Necessary Conditions and Sufficient Conditions with Fuzzy Sets Necessary Conditions and Sufficient Conditions with Fuzzy Sets
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Aggregation Aggregation
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Confronting Models with Data Confronting Models with Data
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Fit and Consistency Fit and Consistency
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Assessing Importance: Coverage and Trivialness Assessing Importance: Coverage and Trivialness
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Conclusion Conclusion
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References and Suggested Readings References and Suggested Readings
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2 Mathematical Prelude: A Selective Introduction to Logic and Set Theory for Social Scientists
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Published:September 2012
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Abstract
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.
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