Subjects logic

Modus Ponens

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Modus Ponens


1. **State the problem:** We are given an argument with premises and a conclusion: - Premise 1: If Socrates is human, then Socrates is mortal. - Premise 2: Socrates is human. - Conclusion: Socrates is mortal. We need to find the argument form and determine if the argument is valid, meaning if the conclusion must be true when the premises are true. 2. **Identify the argument form:** Let $p$ = "Socrates is human" and $q$ = "Socrates is mortal". The argument can be rewritten as: - Premise 1: $p \to q$ - Premise 2: $p$ - Conclusion: $q$ 3. **Explain the rule used:** This is a classic form called *Modus Ponens*. The rule states: If $p \to q$ is true and $p$ is true, then $q$ must be true. 4. **Validity:** Since the argument follows Modus Ponens, it is a valid argument form. This means if the premises are true, the conclusion must be true. 5. **Final conclusion:** Yes, we can conclude that Socrates is mortal if the premises are true. **Answer:** The argument form is Modus Ponens ($p \to q$, $p$, therefore $q$), and the argument is valid.