With the nine rules of inference and the ten rules of replacement taught in Lessons 13-17 of Intermediate Logic, we can construct a formal proof for any valid propositional argument. But for the benefit of the logic student, I introduce two additional rules in Lessons 18 and 19: the conditional proof, and the reductio ad absurdum. The conditional proof will often simplify a proof, especially one that has a conditional in the conclusion, making the proof shorter or easier to solve. The reductio ad absurdum method usually does not shorten a proof or make it that much easier to solve, but understanding the concept of reductio is beneficial for purposes outside of formal logic, such as understanding proofs in mathematics and apologetics.

Both conditional proof and reductio ad absurdum start with making assumptions. I want to clarify what happens with those assumptions. Continue reading Conditional Proof and Reductio ad Absurdum →