The Triune Knot:

Logical Structure of the Trinity in Western Christianity

by Gary Gillespie (as explained by Richard Purtill)
March 2025.

The trinitarian formula found in the Nicene Creed with the "filioque" clause ("and the Son") represents a logically coherent way to understand the persons of the Trinity as both equal and distinct.

The Nicene-Constantinopolitan Creed with Filioque

The Western version of the Nicene Creed includes the filioque clause, stating that the Holy Spirit "proceeds from the Father and the Son" (in Latin, "filioque" means "and the Son"). This was officially added to the Western creed in the 11th century, though it had been used in some regions earlier, and was one of the key theological issues leading to the Great Schism of 1054 between Eastern and Western Christianity.

The Logical Proof

The relational diagram demonstrates that three co-equal points can be differentiated solely by their relations to each other in the following arrangement:

1. The Father (top point) sends to both the Son and the Spirit
   (2 outputs, 0 inputs)
   
   
2. The Son (bottom right) receives from the Father and sends to the Spirit
   (1 input, 1 output)
   
   
3. The Holy Spirit (bottom left) receives from both the Father and the Son
   (0 outputs, 2 inputs)

This creates a logical system where:

• Each person has exactly 2 relations, maintaining their equality in nature
• Each person has a unique pattern of relations, ensuring their distinction
• The distinctions arise purely from their internal relations, not from any external reference
• Each person is uniquely identifiable by their relational position

This structure creates three logically distinct relational identities:

• The "originator" (Father - sends only)
• The "mediator" (Son - both receives and sends)
• The "receiver" (Spirit - receives only)

The key insight is that this appears to be the only way to create a system where three co-equal points can be differentiated purely by their relations while maintaining exactly two relations per point. Other arrangements either make the points indistinguishable (like a circle) or create inequality in the number of relations.

The Western Argument

The filioque formula isn't merely a historical addition but represents a logically necessary relationship if all three persons are to be both equal in essence and distinct in person. This logical consistency provides support for the Western understanding of the Trinity, suggesting it captures something fundamental about the necessary internal relations of the triune God.

The Eastern formula, where the Spirit proceeds from the Father alone (or from the Father through the Son), creates a different relationship structure that may not provide the same level of logical distinction between the three persons while maintaining their equality.

This logical argument doesn't resolve all theological considerations, but it presents a compelling case for the coherence of the Western trinitarian formula.