u/abenhaashim

Right. Before we get into this, we have to outline the seven basic propositions that the Trinity makes. Assume the following set S with propositions in natural language sentences:
(S1) The Father is God
(S2) The Son is God
(S3) The Holy Spirit is God
(S4) The Father is not the Son
(S5) The Father is not the Holy Spirit
(S6) The Son is not the Holy Spirit
(S7) There is exactly one God
We all know the whole shabang. Always repeated. Three co-eternal, co-equal divine persons that are not separate but distinct from each other and are one God, so three persons, one god. Does this claim actually hold up in classical logic? Firstly, let me make it absolutely clear that within this set itself, most people will say that there is not an explicit inconsistency, but rather a formal inconsistency. Basically, an explicit inconsistency is where within a set of propositions, there is explicitly a negation of another. For example:
(S1) Tom is a cat.
(S2) Tom is not a cat.
This would be an explicit inconsistency. However, a formal inconsistency is one where we point out the inconsistency from the members of the set using the rules of ordinary/classical logic. The three main laws of logic are the law of identity (A=A), the law of non-contradiction (P and not P), and the law of excluded middle (there is only two options and no 'sort of', e.g. the light is either on or off, not a middle option). However, what we'll be utilising here is Leibniz's law of identity. It is of two parts:

1. The Indiscernibility of Identicals: If x = y (x is identical to y), then x and y must share every property.
2. The Identity of Indiscernibles: If x and y share every property, then x = y (x is identical to y)
   This is what we call absolute identity and although this looks completely irrelevant to the trinity, you'll see why it is in a bit.
   Now we are concerned with the method of counting we use (yes, when it comes to Christians, you have to formalise your method of counting, duh 🙄). Our standard method of counting is called the CCM, or the classical counting method. Here's the formalisation by Beau Branson but I'll explain it less wordily right now:
   "Today we count F's by (1) logical subjects that are (2) discernible from (or at least, not identical to) one another, and are 'F'. That is, if x and y differ in any way, and are both F-ish, we count them as "two F's"
   In other words, assume we have x and y. If x and y are both apples, and they have any differing properties, then we count two apples. This is already given as how a three-year-old counts the number of wheels on his toy car.
   This is essential to our argument, which is the LPT (the Logical Problem of the Trinity). Below, I'll give the argument in logical symbols, so it may look like hieroglyphics but I'll translate it into natural language:
   (1) ∀x,y(Gx ∧ Gy ⇒ (x = y)) Formal regimentation of monotheism under the classical counting method/absolute identity
   (2) Gj ∧ Gf ⇒ (j = f) Universal instantiation from 1
   (3) j ≠ f Trinitarian claim
   (4) Gj ∧ Gf Trinitarian claim
   (5) j = f Modus ponens from (2) and (4)
   (6) ∴ j = f ∧ j ≠ f Contradiction — Conjunction of (3) and(5)
   Here's that represented in natural language:
   P1: For all x, y, if x is God and y is God, then x just is y. (Formal regimentation of monotheism under the classical counting method).
   P2: If Jesus is God and the Father is God, then Jesus just is the Father. (Universal Instantiation of P1)
   P3: Jesus is not identical to the Father. (Trinitarian claim)
   P4: Jesus is God and the Father is God. (Trinitarian claim)
   P5: Therefore, Jesus is identical to the Father. (Modus Ponens, P2 and P4)
   P6: Therefore, Jesus is identical to the Father and Jesus is not identical to the Father. (Conjunction, P3 and P5 - Contradiction)
   P7: Therefore, it is not the case that both ‘Jesus is God’ and ‘the Father is God’ can be true under the classical counting method. (From P6, by Reductio ad absurdum)
   P8: Therefore, to reject premise 1 is to deny either monotheism or the classical counting method itself. (Meta-logically unacceptable)
   Let's go through each premise one by one so we can understand what we're actually arguing.
   P1: For all x, y, if x is God and y is God, then x just is y. (Formal regimentation of monotheism under the classical counting method).
   This is really self-explanatory. If we were to regiment this with 'Apple', this obviously wouldn't make sense because we would count two apples and not say both apples are the same because they have differing properties. However, because we're denoting monotheism, then there needs to be exactly one God, and not two (polytheism is incoherent). Therefore, under Leibniz's law, if x and y are identical to God (bear every property of divinity), then x is identical to y.
   P2: If Jesus is God and the Father is God, then Jesus just is the Father. (Universal Instantiation of P1)
   This is just replacing x from premise 1 with Jesus and y from premise 1 with the Father, so we're applying the universal rule from P1 to two logical subjects, i.e. Jesus and the Father.
   P3: Jesus is not identical to the Father. (Trinitarian claim)
   This is what the trinitarian famously claims. For proof of this, we refer back to proposition four of set S: (S4) The Father is not the Son
   P4: Jesus is God and the Father is God. (Trinitarian claim)
   Again, this is what the trinitarian famously claims. For proof of this, we refer back to propositions one and two of set S:
   (S1) The Father is God
   (S2) The Son is God
   P5: Therefore, Jesus is identical to the Father. (Modus Ponens, P2 and P4)
   Modus ponens just denotes: if P, then Q. P, so Q. (For example: If the ground is wet, then it has rained. The ground is wet, so it has rained)
   From premise 2, which is a UI of premise 1, we said that if Jesus is God and the Father is God, then Jesus is identical to the Father. Premise 4 says that Jesus is God and the Father is God, so Jesus is identical to the Father.
   P6: Therefore, Jesus is identical to the Father and Jesus is not identical to the Father. (Conjunction, P3 and P5 - Contradiction)
   Here, we are combining two of our premises: P3 which says Jesus is not identical to the Father, which is the trinitarian claim, and P5 which says that it follows from P2 and P4 that Jesus is identical to the Father. Therefore, we have a logical contradiction.
   P7: Therefore, it is not the case that both ‘Jesus is God’ and ‘the Father is God’ can be true under the classical counting method. (From P6, by Reductio ad absurdum)
   We were applying our regimentation of the CCM (the standard way we count) all the way to P5, so if P5 contradicts the trinitarian claim in P3, then the propositions "Jesus is God" and "the Father is God" part of set S, cannot be true under the CCM, or basically, how we count. This means rejecting premise 1.
   P8: Therefore, to reject premise 1 is to deny either monotheism or the classical counting method itself. (Meta-logically unacceptable)
   Self-explanatory.
   Therefore, we find a formal inconsistency within set S. Either option is fatal to the trinity. If Jesus is identical to the Father, we call that the heresy of modalism and it does not conform with set S. If Jesus is not identical to the Father and are different in at least one way, and both of them are god or G-ish, then we count two god or two G-s, under the CCM which we showed earlier.
   (I have explained most of the simple stuff because people may not be familiar)

At the Council of Jerusalem, the apostles discuss the issue of circumcision for the gentiles. We see that at the end, they come to the conclusion that gentiles do not have to be circumcised. However, there is something peculiar that caught my eye. In Acts 15, James says:

*** “It is my judgment, therefore, that we should not make it difficult for the Gentiles who are turning to God. Instead we should write to them, telling them to abstain from food polluted by idols, from sexual immorality, from the meat of strangled animals and from blood. ***For the law of Moses has been preached in every city from the earliest times and is read in the synagogues on every Sabbath.” (Acts 15:19-21)

Here we see that James says gentiles must not eat food polluted by idols (widely interpreted to be food sacrificed to idols). We see in 1 Corinthians 8:

So then, about eating food sacrificed to idols: We know that “An idol is nothing at all in the world” and that “There is no God but one.”*** For even if there are so-called gods, whether in heaven or on earth (as indeed there are many “gods” and many “lords”), ***yet for us there is but one God, the Father, from whom all things came and for whom we live; and there is but one Lord, Jesus Christ, through whom all things came and through whom we live. (1 Corinthians 8: 4-6)

Paul is said to be permitting food sacrificed to idols here.

This creates a dichotomy because this issue really boils down to whether or not we must upkeep the laws of the old covenant.
Option 1: Paul is wrong, the apostles are right, and Christianity is false.
Option 2: Paul is right, the apostles are wrong, and Christianity is false.

Any contenders?