Understanding Evidentness in Mathematics and Logic

Evidentness is a concept in the philosophy of mathematics and logic that refers to the idea that some mathematical truths are self-evident, meaning that their truth can be understood without needing to be proven.

For example, the statement "2 + 2 = 4" is considered to be self-evident, as it is a basic arithmetic fact that can be understood without needing to be proven. Similarly, the statement "all bachelors are unmarried" is also considered to be self-evident, as it follows logically from the definition of a bachelor.

The concept of evidentness is important in the philosophy of mathematics because it raises questions about the nature of mathematical truth and the role of proof in mathematics. Some philosophers argue that all mathematical truths can be derived from self-evident principles, while others argue that some mathematical truths cannot be proven and must be accepted as axiomatic.

In logic, the concept of evidentness is related to the idea of logical consequence, which refers to the relationship between a conclusion and its premises. A statement is considered to be logically consequential if it follows necessarily from its premises, meaning that it cannot be false if the premises are true. The concept of evidentness is important in logic because it helps to distinguish between statements that can be proven and those that cannot be proven.