Are there advantages of modern symbolic logic over classical logic (categorical syllogisms)?

Yes, there are several advantages of modern symbolic logic over classical logic (categorical syllogisms). Modern symbolic logic, also known as propositional logic or predicate logic, offers several features and advantages that make it more flexible and powerful compared to classical logic.

1. Expressive Power: Symbolic logic allows for the representation of more complex and nuanced arguments. It enables the expression of logical relationships that cannot be captured in categorical syllogisms. Symbolic logic can handle statements with multiple variables, quantifiers, and complex logical operators, allowing for a more precise and comprehensive analysis of arguments.

2. Formalized Syntax and Semantics: Symbolic logic has a well-defined syntax and semantics, which makes it easier to study and apply. The use of formal symbols and rules for constructing logical sentences provides a precise and consistent framework for reasoning. It allows for the analysis of arguments in a systematic and rigorous manner.

3. Boolean Algebra: Symbolic logic is closely related to Boolean algebra, which provides a mathematical foundation for analyzing logical relationships. Boolean algebra allows for the manipulation and simplification of logical expressions, enabling the identification of logical equivalences and contradictions. This algebraic aspect of symbolic logic facilitates the simplification and evaluation of complex arguments.

4. Automation and Computational Applications: Symbolic logic is particularly suitable for automation and computational applications. The formal structure and standardization of symbolic logic make it amenable to computer programming and automated reasoning. Symbolic logic forms the basis for automated theorem proving, logic programming, and artificial intelligence systems that can reason and make inferences automatically.

5. Consistency and Completeness: Symbolic logic has been extensively studied, leading to the development of various proof systems and theories. These developments have resulted in the establishment of consistency and completeness results, which prove that symbolic logic is both sound (only valid arguments can be proven) and complete (all valid arguments can be proven).

Overall, modern symbolic logic provides a more advanced and sophisticated framework for analyzing and understanding arguments. Its expressive power, formalized syntax and semantics, connection to Boolean algebra, automation capabilities, and consistency and completeness results make it advantageous over classical logic (categorical syllogisms).