As an example in Lewis's "Mere Christianity," he argues for objective morality with:
- Major: If you can judge one moral code (M1) to be better than another (M2) then objective morality exists.
- Minor: M1 is better than M2.
- Conclusion: Objective morality exists.
He then takes the conclusion of objective morality existing in this syllogism to prove God is real.
- Major: If objective morality exists, then God is real.
- Minor: Objective morality exists.
- Conclusion: God is real.
These are also both modus ponens. Are there different names for it if you are inserting arguments from different structures?