# Another way to appreciate CP

To every valid argument in propositional logic, there corresponds a conditional statement that is a tautology. For instance:

[(p > q) . ~q] > ~p is a conditional statement that spells out the premises of MT as an antecedent, and its conclusion as a consequent. If you do the truth table for this statement form (as opposed to doing it for the argument form (p > q) / ~q //~p), you will find a T under the second horseshoe all the way down.

Now, since it is a conditional statement and a tautology, we can establish its truth, as a logical truth, by the proof strategy CP. Begin as you always do, by assuming the antecedent. Work until you arrive at the consequent:

|1. (p > q) . ~ q                       ACP

|2. p > q                                    1 SM

|3. ~ q                                       1, CM, SM

|4. ~ p                                       2, 3 MT

5. [(p > q) . ~ q] > ~ p            CP 1-5

And here is another approach to appreciating how CP and IP work, written as a response paper in July 2014 by a student taking this course on-line.

Schaeffer – on CP and IP