What is the law of detachment?

The law of detachment, also known as the modus ponens, is a logical rule that is used to deduce a conclusion from a conditional statement. It states that if a conditional statement is true, then the consequent of the conditional statement can be inferred to be true if the antecedent is true.

For example, if the conditional statement "If it is raining, then the ground is wet" is true and it is indeed raining, then we can logically deduce that the ground is wet without any doubt. This is because the law of detachment allows us to reason that if the antecedent (it is raining) of the conditional statement is true, then the consequent (the ground is wet) must also be true.

The law of detachment is a foundational principle of logical reasoning and plays an important role in fields such as mathematics, science, and philosophy. It is also used in everyday situations when making decisions based on conditional statements or if-then statements.