Skip to main content

A Note on Why the Law of Transitivity is Important

by Hiram R. Diaz III

The Law of Transitivity and Scriptural Interpretation

In logic, if A is B and B is C, then A is C. This is called the law of transitivity. For A, B, and C we may substitute any logical subject. For example:

If Jesus (A) is Yahweh (B),
and Yahweh (B) is the One True God (C),
then Jesus (A) is the One True God (C).

We can apply this law when we read passages like Acts 5:1-4:

…a man named Ananias, with his wife Sapphira, sold a piece of property, and with his wife's knowledge he kept back for himself some of the proceeds and brought only a part of it and laid it at the apostles' feet. But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit and to keep back for yourself part of the proceeds of the land? While it remained unsold, did it not remain your own? And after it was sold, was it not at your disposal? Why is it that you have contrived this deed in your heart? You have not lied to man but to God.”

In contradiction to heretics who deny the personhood and deity of the Holy Spirit, Christians have always asserted this passage teaches the personhood and deity of the Holy Spirit. For when we substitute A, B, and C in the law of transitivity we get the following:

If the Holy Spirit (A) is the one to whom Ananias lied (B),
and the one to whom Ananias lied (B) is God (C),
then the Holy Spirit (A) is God (C).

We infer from the explicit statements of Scripture that the passage is implicitly telling us the Holy Spirit is God. The word implicitly simply means that there is no explicit statement of identity being made (e.g. “Ananias you have lied to the Holy Spirit, who is God.”).

Another example we may cite is found in Mark 1:1-3, which reads:

The beginning of the gospel of Jesus Christ, the Son of God.

As it is written in Isaiah the prophet,

“Behold, I send my messenger before your face,
who will prepare your way,
the voice of one crying in the wilderness:

‘Prepare the way of the Lord,
make his paths straight”

In contradiction to those who claim that the doctrine of the deity of Christ is false, we may use the law of transitivity, substituting for A, B, and C, and present the following argument:

If Jesus (A) is the one for whom John prepared the way (B),
and the one for whom John prepared the way (B) is Yahweh/the Lord (C),
then Jesus (A) is Yahweh/the Lord (C).

The law of transitivity demonstrates that Mark is implicitly identifying Jesus not as a mere man but as Yahweh in the flesh, the one for whom John prepared the way.

The examples above prove that the concluding propositions “The Holy Spirit is God” and “Jesus is Yahweh/the Lord” are logically necessitated by the explicit statements derived from the bible. If an enemy of the faith denies the proposition “The Holy Spirit is God,” then he implicitly denies the two Scriptural propositions derived from Acts 5:1-4. In other words, to deny that the Holy Spirit is God is to deny that the Scriptures are infallible. To deny that they are infallible, moreover, is to deny that they are the Word of God. Thus, if the Scriptures are the Word of God, then the Holy Spirit is God.

Testing Deviant Doctrinal Claims

The law of transitivity is also useful when we are evaluating the identity claims made by false teachers. For instance, the assertion “Jesus Christ is not God” may be restated as follows: “Jesus is only human.” From this we can substitute for A, B, and C, as follows:

If Jesus (A) is a mere human (B), 
and a mere human (B) is a sinner (C),
then Jesus (A) is a sinner (C).

Few if any heretical groups will espouse the conclusion that Jesus is a sinner, for they at least pay lip service to the teaching that Christ is the sinless sacrificial lamb of God. Nevetheless, their lip service is not enough to correct their error. Either Christ is not a sinner, and is therefore not a mere human; or Christ is a mere human and is, therefore, a sinner. The denier of Christ’s deity cannot have it both ways.