The law of contraposition is that a conditional statement is equivalent to the contrapositive of that statement. Whoa! Those are a lot of big words. Let’s give you an example to help out with that.
Let’s say you accept the statement “If you are a boy, then you are made of snips and snails” as true. The law of contraposition states that you must also accept the statement “If you are not made of snips and snails, then you are not a boy” as true.
More formally, one says that if A implies B, then ‘not B’ implies ‘not A’. You can visualize this using the following diagram. If you are inside A, then you are definitely inside B. If you are outside B, then you are definitely in the shaded region representing ‘outside A’.
The transitive property of statements is known as syllogism in the logic world. If you have two or more implications that are true, you can come to conclusions using deductive reasoning. Let’s add to our example above to get an idea.
Now, let’s suppose that we accept the statement “If you are made of snips and snails, then you are absolutely disgusting” as true. Then, using deductive reasoning, we must also accept the statement “If you are a boy, then you are absolutely disgusting” as true.
Again, more formally, if you accept that A implies B and you accept that B implies C, then you must also accept that A implies C. This can be visualized by the graph below. If you are in A, then you are definitely in B. If you are in B then you are definitely in C. Thus, if you are in A, then you are definitely in C.
Now, let’s have some fun with a few of my favorite versus in the Bible and use the law of contraposition and some syllogism. First, let’s have a look at Luke 14:26. This is the spoken word of Jesus.
“If anyone comes to me and does not hate father and mother, wife and children, brothers and sisters–
yes, even their own life–such a person cannot be my disciple.”
I’m going to choose brother here to make things simple. From Luke 14:26 we get the statement “If you do not hate your brother, you cannot be a disciple of Jesus.” Using the law of contraposition, we find that “If you are a disciple of Jesus, then you hate your brother.” Hang on, the fun is just beginning.
To illustrate some syllogism, we’re going to now look at one of my other favorite verses in the New Testament: 1 John 3:15.
“Anyone who hates a brother or sister is a murderer, and you know that no murderer has eternal life residing in him.”
Now let’s get all of our statements in a row and use some syllogism.
- “If you are a disciple of Jesus, then you hate your brother.”
- “If you hate your brother, you are a muderer.”
- “If you are a murderer, you have no eternal life residing in you.
This deductive reasoning could get tough since we have to use one more level of syllogism than previously illustrated. Think of a larger set D that encompasses all of C. So, if A implies B, B implies C, and C implies D, then A implies D.
Aha! I think we have something here. Given the statements above, we have “If you are a disciple of Jesus, you have no eternal life residing in you.”
THE WORD OF GOD! Can I hear an “AMEN”? Maybe a “RAMEN”?
The fact that some of you want to immediately go to the Bible and try and put this into some sort of context so that you can refute this is ironic to me. I don’t even believe this statement, so you don’t have to convince me. In order to believe the statement at all, one would have to put some kind of weight to the Bible. Because one can take two verses from the Bible and come up with such a statement, I don’t place any weight in the Bible. I’m still trying to figure out why most of you do.