Catholics, and to my understanding other Trinitarian Christians, believe and teach what is borne by scripture [cf. Eph 4:4-5] i.e. there One God the Father, One God the Son, and one God the Holy Spirit.

The Father, being the Origin without origin is perhaps easier to grasp.

Why can't his Son have his own son and so on ad infinitum and therefore be a corresponding infinite number of spirits?

According to Catholic theology, why are there two and only two processions in the Godhead and therefore three and only three persons in one God?

  • I think your logic is backwards... there are three persons and therefore two processions.
    – curiousdannii
    Jan 29, 2015 at 0:18
  • @curiousdannii Agreed, especially in light of Peter Turner's answer. Jan 29, 2015 at 3:56
  • I recommend a review of this answer from Geremia: christianity.stackexchange.com/a/28414/10486 Jan 29, 2015 at 8:07
  • @curiousdannii My understanding, in a human way of thinking, is that it's the processions that give rise to the persons.
    – user13992
    Jan 29, 2015 at 20:25