The Logical Problem of the Trinity (LPT) by Jake Brancatella@The Muslim Metaphysician​

> P1 The Father is God
> P2 The Son is God
> P3 The Holy Spirit is God
> P4 The Father is not the Son
> P5 The Father is not the Holy Spirit
> P6 The Son is not the Holy Spirit
> P7 There is exactly one God

these 7 premises form an inconsistent set.
in other words, they cannot all be true.
However, Trinitarianism affirms all 7 premises.
what exactly is the problem? the basic problem is tritheism.

if Father, Son, and Holy Spirit are God, and not each other, it follows that there are 3 gods.

this then calls into question how the statements are to be analysed.
the key distinction is over the phrase "is God" in premises 1 to 3.

if "is God" is taken to be an "'is' of identity",
then by classical identity Father, Son, and Holy Spirit would be identical to each other, which would entail modalism.
modalism is a heresy. that's something Christians will want to avoid.

maybe it's an 'is' of relative identity?
this would mean that 2 things Father and Son could be identical to God and yet not identical to each other.
this violates classical identity and most people are reluctant to do so.

what about analysing "is God" in terms of predication?
well, if each person is ascribed the quality of divinity and they are not each other, then we are back to 3 gods.
no matter how similar they are in terms of their attributes, will, actions, etc.

there may be another option.

maybe each person "is God" in the sense that they are "parts" of God.
this is William Lane Craig's solution in an attempt to avoid tritheism.
however, this is clearly unorthodox as none of the persons is said to possess the divine nature.

what if all 7 premises are true and we accept that true contradictions exist?
this has recently been proposed by JC Beall, but involves denying the law of non-contradiction, which most people will be reluctant to do—most people will not be likely to reject the law of non-contradiction or the law of identity.

maybe the 7 premises are all true and they are only apparently contradictory, but not actually contradictory.
even if we cannot tell you how or why they aren't contradictory.
this is a form of mysterianism, which has been proposed by James Anderson.

this isn't technically a "solution" to the Logical Problem of the Trinity from the Classical paradigm.
rather, it is questioning whether or not a solution is required from an epistemological standpoint—"are mysteries acceptable in theology, and if so, when?"—How do we determine when something is actually contradictory vs. merely apparently?

questions to consider.

so, given the brief explanation of the Logical Problem of the Trinity and possible responses,
we are left with
1) modalism
2) denying classical identity with respect to this problem ('is' of identity option)
3) tritheism or partialism ('is' of predication option)
4) denying the Law of Non-Contradiction
5) affirming a form of mysterianism and arguing that the Logical Problem of the Trinity may be unsolvable, but Christians are still justified in affirming the doctrine of the Trinity.

admittedly, this is a brief sketch of the complexities of the problem and its various solutions proposed, but I hope you find this somewhat beneficial.

I, myself, am not satisfied with any of the above for reasons already stated.
this problem has been around since the 4th century when the doctrine was authoritatively established.

I don't think new solutions are coming.

May Allah guide us all.


addendum by mdthr:

Regarding the "Trinity",
either:
> **a)** we can know what the true belief is
> **b)** we can't know what the true belief is (it is rationally unknowable)

if **a**, either:
> **c)** we can know the true belief is not a contradiction
> **d)** we can know the true belief is a true contradiction (denying law of NC & law of identity)

if c, either:
> **e)** we know the belief is a statement of predication
> **f)** we know the belief is a statement of identity

if **e**, either:
> **e¹)** the belief is partialism (⅓+⅓+⅓=1)
> **e²)** the belief is social-trinitarianism (1+1+1=1)
> **e³)** the belief is tritheism (1+1+1=3)

if f, either:
> **f¹) **the belief is modalism (1|2|3=1)
> **f²)** the belief special-pleads/denies the law of identity (relative identity)

In light of the classical laws of logic, because of what the Trinity has historically claimed, leading to the Logical Problem of the Trinity,
we are left with the "options" of:
> **1)** left with heresies ***(e¹, e³, f¹),*** or
> **2)** what isn't a solution at all, nor acceptable to classical logic ***(e², f²)***
> **3)** or giving up and saying it's some type of mystery ***(b,d)***