Transitivity Problem

The Trinity states that there are three divine persons (CCC ¶258):

• The Father \(F\)
• The Son \(S\)
• The Holy Spirit \(H\)

Let God be \(G\), we know of God the Father \(F\) and God the Son \(S\). Because God \(G\) and the Father \(F\) are in some sense "the same", we pick an equivalence relation to relate \(G\) to \(F\).

The naive choice, \(=\), is a good first start, so let us assert that:

\[G = F\] and \[G = S\]

By the transitivity of \(=\), we can conclude that \(F = S\), which is wrong. (Matt 11:27)

This is the transitivity problem of the Trinity.