James 2 and Its Connection to Mathematical Logic

I have heard many sermons on the issue of faith and good works as conveyed in the book of James. Each time I hear such a sermon I am led, as a mathematician, to connect the relevant Scripture and mathematical logic or, simply, logic. Making such a connection shows how science/mathematics provides compelling evidence for the accuracy of the Bible and the Christian worldview.

Some people consider mathematics to be the queen of the sciences. It is the language of the universe and it speaks with beauty and elegance. Mathematics functions amid the fundamentals of logic.

Logic and James 2: Faith without Good Works Is Dead

In the James 2:14–26 passage, the theme is stated in verse 17: “faith by itself, if it is not accompanied by action, is dead.” I gain insight into this passage by making a connection to logic. Consider the statements, P and Q. From these, others are obtained as follows:

A negation: not P.

A conditional: If P, then Q.

The contrapositive of the conditional: If not Q, then not P.

The converse of the conditional: If Q, then P.

Now, consider these statements derived from James 2:

P: I have faith in Christ.

Q: I do good works to serve God.

The logical statements would then have the following form:

A negation of P: I do not have faith in Christ (not P).

A negation of Q: I do not do good works to serve God (not Q).

A conditional: If I have faith, then I do good works (If P, then Q).

The contrapositive of the conditional: If I do not do good works, then I have no faith (If not Q, then not P).

The converse of the conditional: If I do good works, then I have faith (If Q, then P).

How are these three (conditional, contrapositive, converse) statements related? It is established in logic that a conditional and its contrapositive are equivalent, meaning that each time one is true, the other is true, as well. A conditional is not necessarily equivalent to its converse. Just because a conditional may be true, it does not follow that its converse is true, though it may be.

How does this logic lesson help lay people to resolve potential difficulties in the foregoing Bible passage? Pastors are usually focused on exegetical concerns, as they should be. Thus, I don’t fault them for virtually never presenting these logical statements together in sermons. However, some STEMM-oriented people may appreciate the connection.

Consider the statement: If you have faith, then you do good works (If P, then Q). To me, James is asserting this conditional in these passages. Now consider the contrapositive: If you do not do good works, then you do not have faith (If not P, then not Q). When I hear sermons on this issue, the pastor references the contrapositive, though not usually in words that are overt.

Now let’s look at the converse, which is not necessarily true: If you do good works, then you have faith (If Q, then P). In this statement we see one of the great controversies of religion—at least, it is one I struggled with in my life as a Protestant Christian. My upbringing compelled me to think that if I did good works I would then be a person of Christian faith. I felt like I could only earn favor from God by good works. After many years of Scripture reading and study, aided by my mathematical training, I finally came to peace from the idea stated profoundly in Ephesians 2:8–9, “For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God—not by works, so that no one can boast.” The following statements summarize my thinking about faith and works:

• I accept the Holy Bible as true.
• The Scripture in James 2:14–26 is true.
• The passage asserts, “If I have faith, then I do good works.”
• The statement, “If I do not do good works, then I have no faith,” is true because

it is the contrapositive of the statement in (3).

• The statement, “If I do good works, then I have faith,” is not necessarily true because it is the converse of (3). However, it will be true in the case of a Christian who has received faith as a gift from God.

As a mathematician, I find great meaning and peace in the logic of the James passage. The truth presented in the logic can stand alone without theological explanation. No exegetical sermon is necessary – although such a sermon provides elucidation to enhance our acceptance of this truth, especially for those without training in logic. I hope this brief explanation shows how the author in general revelation of mathematics and logic is the same God who is the author who gives us special revelation in the words of the Bible.

Resources

For more details on the logic, see the following works. They establish the equivalency of a conditional and its contrapositive by using truth tables.