A Logical Analysis of the Doctrine of the Trinity

The doctrine of the Trinity has become one of the most central doctrines in Christian theology. However, it is also one of the doctrines that receives the most criticism. Some Christians seem to agree with these criticisms against the doctrine. The most common strain of nontrinitarian Christianity is Unitarianism, which teaches that God is one person. Here, I will give a logical analysis of the doctrine of the Trinity.


The Nicene Creed (also called the Nicene-Constantinopolitan Creed) defined the concept of the Trinity as it has most commonly been understood through Christian history. If you want to see a full copy of the Nicene Creed, see the version offered online by the Orthodox Church in America (OCA). In this creed, Jesus is described as being “of one essence with the Father.” The Holy Spirit is usually described in the same way by Trinitarian theologians. Also in the Nicene Creed, the generation of each member of the Trinity is mentioned: the Father unbegotten, the Son begotten, and the Holy Spirit proceeding. This difference of generation is the most widely accepted difference by Trinitarian scholars, at least as far as I have observed.


Although the idea that God is three in one is usually seen as a contradiction by critics insofar that 3 is not equal to 1 or in that 1 + 1 +1 is equal to 3, not 1, these are misunderstandings because Trinitarianism does not teach that God is three and one in the same sense. I have already mentioned that the Trinity can be described in terms of persons and of essence. In other words, the Trinity is said to be three in persons and one in essence. If the doctrine were to state that God is three in essence and one in essence, this would be an undeniable contradiction.

However, this does not immediately end the argument against the logical coherency of the doctrine of the Trinity. A common diagram used to describe the Trinity is this:

In this diagram, there lies a very fatal incoherency. Each member of the Trinity is identified as God. However, each member, or person, is also described as not each other. This goes against the Transitive Law: if a and b are both equal to c, then a and b must also be equal to each other. Replacing a and b with the Father and the Son and c with God, it becomes clear how this description of the Trinity is logically incoherent. Of course, we can expand this statement to include four terms so that: if a (the Father), b (the Son), and c (the Holy Spirit) are all equal to d (God), then they must all also be equal to each other.

If God (noun) is replaced with divine or fully divine (adjectives), there is still an issue, although it may not be as obvious. It is true that the above line of reasoning does not apply if God simply means divine. In other words, the Father, the Son, and the Holy Spirit could all be divine at the same time just as John, Jack, and Jill can all be described as human without their being a logical contradiction. However, John, Jack, and Jill can all also be described as humans; and each can be said to be a human. In other words, they are separate humans. Similarly, if the Father, the Son, and the Holy Spirit are all divine, it does not follow that they are all the same God; and if they are all said to be the same God, the logical incoherency presented in the above paragraph applies.

Of course, there are ways to get around this, but it is not proper to try to describe the Trinity in such a way that it is logically coherent for the sake of making it logically coherent. This is because even demonstrating that three can be one does not mean that God must necessarily be three in one. In other words, any description of the Trinity, for it to be meaningful, must be based off of a source, such as the Bible. Furthermore, any description must retain the individuality and personality of each of the three persons; otherwise, the description only makes God three in one in a way that fails to recognize that the three persons are actually persons.


With all of that said, there seems to be much difficulty in demonstrating the logical coherency of the doctrine of the Trinity. Despite this, it has become one of the core doctrines of the Christian faith. This is likely because the Trinity is considered by many Christian scholars to be essential to the theology of salvation and of the nature of God and to be one of the most unique doctrines of Christianity that sets it apart from other religions.

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