One of my favorite reasoning tools, and a method which leads to endless new and enlightening formulations of scriptural truth, is equational substitution; that is, identifying an equality, and then substituting one side of the equality for the other in a scriptural assertion.

As an example of what I mean by equational reasoning, take the classic syllogism:

Socrates is a man.

All men are mortal.

Therefore: Socrates is mortal.

Notice what we have done here; we have identified that Socrates “is” a man, and therefore wherever we make statements about “all men,” we can replace “all men” with Socrates, and the result is a logically valid statement (that is, if the original statement is true, the new one is true too).

Using the colors, we can see that the lines “is” and “are” tell us that where we see the color on the right, we can replace it with the color on the left. So we see “green thing is orange thing” which means that wherever we see orange thing, we can replace it with green thing and discover something true.

Scripture does not use the language of formal logic, but it is a coherent system of logical statements, and we can apply these principles just the same.

For God did not send His Son into the world to condemn the world, but that the world through Him might be saved.

John 3:17

Here we see our first equality, and I’m going to color parts of the equation so we can more easily see things that are identical: the things that Jesus says are in some sense equal¹ to “not condemning the world.” Next:

Now we know that whatever the [Mosaic] Law says, it says to those who are under the law, that every mouth may be stopped, and all the world may become guilty before God.

Romans 3:19

This verse gives us the second equality: the things that the Law says are equal to “making the world guilty,” or in other words, to “condemning the world.” This is the important step, because we can now replace anywhere we see “condemning the world” with “the things that the Law says.”

So let’s substitute the pink “condemning the world” with the purple “the things that the Law says” in our first equality “the things that Jesus says = not condemning the world” (note that we have to be careful to leave the orange not where it is):

The things that Jesus says are not the things that the Law says.

Or in other words, we have discovered a new way to say a certain truth, which is that “Jesus does not teach the Law.”

This kind of equational reasoning is powerful:

Therefore, there is now no condemnation for those who are in Christ Jesus. (Romans 8:1)

This equation sets us up.

Whatsoever things the (Mosaic) Law says, it says to condemn. (Romans 3:19)

All the (Mosaic) Law is condemnation. Now substitute pink with purple.

Therefore, there is now no (Mosaic) Law for those in Christ Jesus.

Beautiful. We should keep a collection of inferences like these.

1. (I’m slightly conflating the english words “is” and “are” with the mathematical term “equal to” in this article, because what I really mean is “is an element of” a given set. For true equality, you can replace any occurrence of either side with the other side; but with set membership, you have to be a little more careful. For example, you can’t say “My car is red; the apple is red; the apple is my car.” What you would mean to say is “My car is a member of the set of red things; the apple is a member of the set of red things.” This doesn’t permit replacement of “red” with “my car” or “the apple.” What it does allow you to do is take statements about all red things, and apply them to both the apple and my car.) ↩︎