I fell in love with formal logic in college. It felt like the proofs we did during geometry my freshman year of high school that the entire class hated but I loved. I loved it so much I did an independent study in advanced formal logic. I couldn’t get enough.
It was no surprise that when I got to teach philosophy at the local community college when we moved to Whidbey Island, WA, in 2000, my favorite class to teach was Logic. I wanted my students to love it like I did. Most didn’t, but some did.
One of the first rules you learn in logic (other than statements can’t be true and false at the same time in the same way, that A=A, and the importance of a distributed middle) is called modus ponens. (That’s Latin for “the mode of affirming.”). It goes like this:
P1) If A, then B
P2) A
C) B
In other words. If the conditional “if A, then B” is true, and A is true, then B has to be true. Doesn’t matter what A and B are. Plug any truth claim in for A and B, and it works. Example:
P1) If William Blake wrote “The Tyger,” then William Blake had red hair.
P2) If William Blake wrote “The Tyger.”
C) Therefore, William Blake had red hair.
I don’t know what color William Blake’s hair was in fact. But if P1 and P2 are true, he must have had red hair. If the archives say he had green hair (work with me here), we would know that either P1 or P2 must be false (probably P1).
There is a companion rule to modus ponens, called modus tollens (“the mode of removing”). It goes like this:
P1) If A, then B
P2) Not B.
C) Not A.
Modus tollens can be used to great effect to counter arguments that use modens ponens. For example, take this argument, proposed by the philosopher Gottfried Leibniz:
P1) If God exists, then this must be the best of all possible worlds.
P2) God exists.
C) This is the best of all possible worlds.
The famous philosophe (and athiest) was having none of it, of course. (He wrote the novel Candide to mock this idea.) Voltaire proposed this modification to Leibniz’s argument, using modus tollens:
P1) If God exists, then this must be the best of all possible worlds.
P2) This is not the best of all possible worlds.
C) Therefore, God does not exist.
There is a saying among logicians that “one man’s modus ponens is another man’s modus tollens.” And you can see why.
At first glance, it looks like Voltaire wins the round. Clearly, this is not the best of all possible worlds, right? Imagine this world, but without mosquitoes. Or earthquakes. Or the Kardashians. Clearly better, right?
It becomes obvious that “best of all possible worlds” is fuzzily defined. Best according to whom? What’s the metric being used to determine maximal goodness here?
What if the “best of all possible worlds” is decided by God and not us? If God is sovereign and omnipotent, then surely he is best able to judge what is best? If Psalm 115:3 is right, and “Our God is in the heavens; he does all that he pleases,” then isn’t that saying that this world is exactly what God has decreed it to be? Could it be that Leibniz was right?