My Passion for Logic

I have a passion for seeing conditional statements (IF...THEN) applied properly.

Far too often, people mistakenly assume that the converse is logically equivalent to the original statement. For example, let's describe me as I walk from my car into my place of employment each morning:

"If it is raining, then I get wet."

This is a true statement, because I don't own an umbrella. You may be thinking, "Then go get an umbrella!" But logic is not about giving advice. It's about stating reality as it exists.

A common mistake is for people to think that the following statement, known as the "Converse," must also be true:

"If I am wet, then it is raining."

This is deceptively appealing. It feels right. But it's not logically equivalent. I could have become wet for a whole host of other reasons. Maybe I bought a coffee and spilled it on myself on the drive in. Or maybe it's done raining, but I fell in a puddle.

Another common error is illustrated in the following example. Let's assume the following statement is true:

"If it is sunny outside, then I am happy."

I live in one of the cloudiest cities in the U.S., so this time of year, just seeing the sun warms my heart!

However, the "Inverse" is not logically equivalent:

"If it is not sunny outside, then I am not happy."

Even if I don't see the sun, there are plenty of times during the long winter months that I'm happy anyway. Maybe one of my kids just gave me a big hug. Maybe I just finished reading a good book. It might be cloudy outside, but I'm still happy.

The key to evaluating logical statements is to use what's called the contrapositive. This combines the converse and inverse together.

Let's take a look at the first "IF...THEN" conditional statement in 1 John.

John writes, in 1:6, "If we say that we have fellowship with Him, and walk in darkness, we lie and do not practice the truth."

In conditional form, this may be written:

IF we say that we have fellowship with Jesus and walk in darkness, THEN we lie and do not practice the truth.

The contrapositive of this conditional statement is:

IF we are truthful, THEN we don't say we have fellowship with Jesus while we walk in darkness.

In my mind, the contrapositive feels a bit simpler, and it's logically equivalent to John's original statement.

If I am a truthful follower of Jesus, then I won't claim to be in fellowship with Jesus when I'm walking in darkness. This is a clear call to repentance. Get right with God, and then share your walk publicly.

This is not a perfectionistic command, but a firm reminder to get our private walk with Jesus right before proclaiming our faith to the masses. This is one reason Billy Graham has been such an effective evangelist. He has avoided the wrath of the public because he lived his life in such a way that he avoided scandal.

Do I have my private walk in order? I'd better before I proclaim my faith to others. Otherwise, my example may become a stumbling block on their pathway to faith.