Law of detachment

Definition

The law of detachment is a logical rule that states if a conditional statement ("if p, then q") is true and the antecedent (p) is true, then the consequent (q) must also be true. It is a fundamental principle in deductive reasoning.

5 Must Know Facts For Your Next Test

1. 1. The law of detachment applies to statements in the form "if p, then q" where both parts are declarative sentences.
2. 2. It requires both the truth of "if p, then q" and the truth of p to conclude that q is true.
3. 3. This law is also known as modus ponens in formal logic.
4. 4. The antecedent (p) must be explicitly stated as true for the law of detachment to apply.
5. 5. It is used to derive specific conclusions from general premises in logical arguments.

Review Questions

• 1. What must be true for the law of detachment to be applied?
• 2. How does the law of detachment relate to conditional statements?
• 3. What alternative name is given to the law of detachment in formal logic?

Related terms

Modus Ponens: Another term for the law of detachment, stating that if "if p, then q" and "p" are both true, then "q" must be true

Conditional Statement: A statement composed of two parts, an antecedent and a consequent, usually formulated as "if p, then q"

Antecedent: The first part (p) of a conditional statement which precedes the consequence