Formal proofs of validity are challenging. Unlike truth tables (longer and shorter), completing formal proofs is not merely a question of following all the steps correctly; they require some creativity. Consequently, students may have more difficulty solving them. But some students enjoy the challenge of figuring out how to prove the conclusion. It is very much like solving puzzles, and can be an enjoyable challenge. This is how the instructor should present them. I have found that many of my students over the years have risen to the challenge, done exceptionally well with formal proofs, and enjoyed them.

Formal proofs of validity give students practice thinking in a straight line. The process teaches them how to connect premises in a proper way in order to reach the desired conclusion. For example, consider this argument:

If we want to send a manned mission to Mars then it must be either funded by taxpayers or privately funded. We want to send a manned mission to Mars and other planets. It should not be funded by taxpayers. Therefore a Mars program must be privately funded.

How do I get to that conclusion? The argument can be symbolized as follows:

M ⊃ (T v P) M • O ~T ∴ P

This can be shown to be valid by truth table, but how to we prove the conclusion by connecting the premises? In the video below, I work through the proof, showing how to connect the premises using the rules of inference to reach the desired conclusion.

Trouble with video? YouTube version HERE.

Thank you, Mr. Nance for all of your posts on this blog! It has been a real help in our studies at home!