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.