Could you give real-world examples of the arguments to prove in Intermediate Logic Lesson 18, number 7) U / ∴ W ⊃ W, and number 8) X / ∴ Y ⊃ X, showing how they would be used, or explain them a bit? Thank you.
Thanks for the great question! These two arguments are unusual, so I am not surprised that you are asking about them.
A real-world example for #7 might be Esther 4:16, “I will go to the king which is against the law; if I perish, then I perish!” This argument form basically shows that any proposition implies a tautology.
An example for #8 could be, “God created all things. So even if evolution can be used to explain some fossils, it’s still true that God created all things.” The form of this argument shows that if a proposition is given, any other proposition implies it.
To be honest, my purposes for including those two problems were: 1) to show how very strange the conditional proof is, and 2) to show how this method can be used to simplify otherwise difficult proofs.