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Individuating Logics: A Category-Theoretic Approach
1University of Vienna.
Thought (Hoboken, N.J.)
|November 1, 2019
Summary
This paper argues against purely syntactic or semantic views of logical theories, proposing a combined approach. A novel category-theoretic method, institutions, unifies distinct logical systems for better understanding.
Area of Science:
- Philosophy of Logic
- Theoretical Computer Science
Background:
- A debate exists on whether logical theories should be understood syntactically or semantically.
- Previous work proposed purely semantic (Wigglesworth, 2017) or purely syntactic (Woods, 2018) approaches.
Purpose of the Study:
- To critique existing purely syntactic and semantic approaches to logical theories.
- To propose a novel, combined syntactic-semantic framework for understanding logical theories.
Main Methods:
- Analysis of the limitations of purely syntactic and purely semantic accounts.
- Development of a combined approach based on the category-theoretic notion of institutions.
Main Results:
- Purely syntactic and semantic approaches inadequately distinguish between distinct logical theories.
- A category-theoretic approach using institutions offers a more robust framework for logical theories.
Conclusions:
- A combined syntactic-semantic approach is necessary for a comprehensive understanding of logical theories.
- The concept of institutions provides a promising foundation for this integrated approach in logic.
Keywords:
anti‐exceptionalismcategorical equivalenceinstitutionsphilosophy of logictheoretical equivalenceMore Related Videos
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