Second-order logic

Second-order logic expands on first-order logic by allowing not only statements about individual objects but also about sets or properties of those objects. While first-order logic can express relationships between specific entities (like “All humans are mortal”), second-order logic can quantify over properties (like “There exists a property that all humans share”). This added complexity enables richer and more expressive descriptions, facilitating discussions about concepts like mathematical structures or higher-level theories. However, it can also complicate formal proofs and interpretations, making second-order logic both powerful and challenging to work with in various fields, including mathematics and philosophy.