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Why did logicians try to reduce the number of basic logical concepts through Ockham’s razor?

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logic: universal affirmative — Modern logic Representations of the universal affirmative, “All A's are B's” in modern logic.

In the context of modern logic, the effort to reduce basic logical concepts is driven by the pursuit of syntactic simplicity and theoretical elegance, often guided by the principle of Occam’s razor. This principle suggests that, all else being equal, a simpler theory—one relying on fewer assumptions or primitive concepts—is preferable to a more complex one.1

Logicians have sought to minimize the number of basic concepts to demonstrate that complex systems, such as mathematics, can be derived from a minimal set of logical foundations. For example, in propositional logic, while several logical connectives are commonly used, they are interdefinable. This allows for further reduction; the American logician Henry M. Sheffer demonstrated that all truth-functional connectives can be defined using only a single connective, the Sheffer stroke.234

By reducing the number of primitives, logicians aim to create more concise and rigorous systems. However, while this reduction is a valuable heuristic for developing elegant theories, it is not an absolute rule, and modern academics remain cautious about applying the criterion of simplicity too liberally to complex phenomena.1