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Refutation of Christian Theology (Trinity)

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The Christian doctrine of the Trinity faces well-known problems. On the one hand, the doctrine involves a commitment to monotheism, while on the other, it involves the claim that there are three distinct divine persons.
Among many of the arguments given for the trinity, the most vast and logically sustained is that of Mereology. Chistian theologians, for centuries, have been using this framework to philosophically substantiate their claims.
At its base, Mereology is a mathematical concept used to express the singularity-while at the same time its multiplicity- of numbers and objects. In this sense, it looks at the relationship of parts and wholes and the distinctions within them.
An example of this would be any abstract number, such a 1. Chrsitans would assert that this number is distinct from the number 13, but at the same time, shares the same essence. In this sense, each number is singular yet infinite at the same time.
Hence, christians would assert that the Godhead too is singular, yet there is an aspect of multiplicity within it.
The problem with this, however, is that Mereology looks at the parts and then forms the wholes. Therefore, the parts must always exist prior to the wholes...
..the whole is dependent on the parts

Taking the number 14 as an example, it composites an infinite amount of numbers to exist (1+13, 2+12, 0.0001+13.9999). Hence, 14 by its very nature is dependent on a sequence proceeding it to exist.
Furthermore, the Christians assert that each member in the Godhead is fully God, but not that there are three Gods, rather only one. This would entail that the totality of parts can conceivably be as large as each individual part of the whole. This, however, is pure nonsensical.
Moreover, Christans would assert that because this singular-multiplicity aspect exists within this physical word, it logically follows that the metaphysical too possess these qualities.
Hence, they would say, as @Jay_D007 said in a debate with Shabir ally, that “the only way we could make sense of this world is if God was triune”

Firstly, just because the physical world possesses characteristic x, does not necessitate that the metaphysical must also possess x:
P1: Whatever exists within the physical must exist within the metaphysical
P2: Death and mortality exists within the physical
C: Therefore Death and mortality must exist within the metaphysical

Even if we were to grant the premises, there exists a deeper problem...
Abstract objects, such as numbers, are represented as singular and infinite(∞), not singular and dual (2), or singular and plural (3).

Hence, If one were to rely on mereology to establish the trinity, they would in turn be destroying it, since the trinity is 3 distinct natures
Hence Jay’s statement about the trinity not only falls short, but is self contradictory.

Even if we were to accept philosophical bootstrapping, God would need to be infinitely district. In other words, there must be infinite distinctions within the Godhead, not just three
For this argument to work, one does not need to superimpose a trinity to make sense of this, rather all they need to prove is that there are real distinctions between the essences and energies of God. This solves nothing really as almost every religion believes these distinctions
To make this more clear note the words “only” and triune” in Jay’s statement. After what has already been established, both these terms are now laughable. Hence, relying on Mereology to prove a triune nature of God, while asserting that it is the “only” way, is foolish.
It would have been better to say: If we accept philosophical bootstrapping, the only way we could make sense of this world is if God had real distinctions. A necessary being with 3 distinct natures does level to a necessary being with an infinite distinct nature.
Given this, if one were to rely on mereological models to form an argument, they would have to prove the following put in axiomatic format:

1.1) There is only one divinity.
(1.2) On the model it must be false that ‘Father = Son’, ‘Son = Holy Spirit’ and ‘ Holy Spirit = Father’
(1.3) The word ‘. . . is wholly. . .’, it is true on the model that ‘the Father is wholly the Godhead’, ‘the Son is wholly the Godhead’, and ‘the Holy Spirit is wholly the Godhead’.

Hence, with these axoms, the following mereological models shall be analyzed
Model A: Social Trinitarianism

This model dictates that the Godhead is like a society or family with three members. This means that each member is a part of the whole (Godhead). For simplicity sake, “a part” in this context will be represented as “proper part”
‘G’= Godhead
‘F’=Father
‘H’ = Holy Spirit
‘S’ = Son
Circles = proper parts

Each of the members of the Trinity is (a proper part of) the Godhead and distinct from one another, thus, avoiding modalism.
A further look, however, shows that the mereological picture intended rules out any of the members being wholly the Godhead. Hence, for each of the members, there is some other non-identical entity which is not a part of it, but is a proper part of the Godhead.
On the Social Trinitarian mereology, then, the Godhead exists “over” each of the members. This model, therefore, fails axiom 1.3. This model also entails tritheism.
Model B:

Here, all the proper parts of the Godhead are connected and shared. If each of the members is composed of the same proper parts as each other, then they must be different guises for one and the same person. Without a doubt, this entails modalism, rejecting axiom 1.2
Model C:
Here,the only proper parts of the Godhead are the members themselves. This model fails axiom 1.3.If each of the divine members lack compositional level below that of the members then this is sufficient for it being false on the model that any of the persons is wholly 'G'
Model D:

Simply by flipping the model on its head, axiom 1.3 is now achieved. The problem, however, lies in that none of the persons are proper parts of the Godhead. Hence, as with Model B, this Model too incorporates modalism, and therefore axiom 1.2 is rejected.
Model Da:
As with Model D, this Model successfully achieves axiom 1.3. More than than, now that each person has proper parts, this Model avoids Modalism, and hence also achieves axom 1.2. However, this benefit comes at a cost.
Model Da involves proper parts which are not divine in the way the member itself is. More serious, however, is that the Godhead is a part of the members of the Trinity and not the other way around. This, then, entails panentheism within models D and Da into forms of panentheism
This is because the divinity of the members are formulated in their partial composition by a particular divine part. Furthermore, Models as such also entail tritheism and hence fails 1.1.
Problem #2: Christ has a body

A further problem here is that models A–Da depend on the members and the Godhead having all their proper parts in common and yet being non-identical. With the reincarnation, at least one proper part cannot be a proper part of the Godhead
Otherwise that would entail that the body of Christ is a proper part of each of the other members as well, and that is heretical (Patripassianism)

There has been a solution to rectify this problem
Here, the Christ’s body is given a proper part in relation to the Son, but not to any other member or Godhead. Since the arrows point downwards, the proper parts transfer up the line, but not down it. Hence, the Son is a proper part of the Godhead, but not the body of Christ.
This Model shares the same problems as Model D. Here, the Godhead has become a proper part of the members instead of the other way around. Furthermore, the Father has become a proper part of the Son.
To ensure that the body of Christ is a proper part of only the Son, the Son must not be a proper part of any of the other persons.
In conclusion, Mereological models fail at attempting to portray the trinity. If parts proceed the wholes, the wholes must be dependent on its parts. It in inconceivable that the individual of the parts equal to or exceed the totality of them (parts), hence the irrationality
does not level*
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