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Explore the extension of proof-theoretic logical pluralism through an examination of harmony conditions and their role in determining admissible logics. Delve into Ferrari and Orlandelli's (2019) framework where harmonious logics must possess connectives that are unique and conservative, enabling a balanced pluralism with variance at both validity and connective meaning levels. Investigate how this system can be expanded to create a three-level logical pluralism by allowing multiple notions of uniqueness in harmony definitions or multiple concepts of harmony itself. Analyze how this extension generates pluralism at the levels of validity, connective meanings, and admissibility conditions while maintaining the core principles of balance and usefulness as fundamental constraints. Examine the theoretical implications of this expanded framework for understanding logical diversity and the criteria that govern which logical systems should be considered admissible within a pluralistic approach to logic.
