Does the concept of the Triune God violate the Law of Identity and the Law of Non-Contradiction?

Why do you assume that theology and logic/critical thinking are mutually exclusive?   Since the Son of God is the logos (logic) of God ( John 1:1),  incompatibility with theology is impossible. 

Since much of theology is the study of gods, and all gods and doctrines are man-made,  its no surprise that there are contradictions along the way. Also, the majority of arguments for the existence of God are flawed,  and often commit logical fallacies.

Your argument is "non sequitor".   The assertion that "all gods and doctrines are man made" excludes the possible truth that there is a God that is not "man made".  Furthermore, it does not follow that "all gods and doctrines are man-made" simply because of the premise that "much of theology is the study of gods".  The God described in the Bible assumes existence without argument. 

[To R. K. Borill]

Indeed, a god may well exist, and this is the million dollar question, so to speak. However, there are arguments for the existence of a "creator" god, and also arguments for a SPECIFIC god, over all other gods. Since the man-made arguments for said god/gods often contradict one another, they cannot all be correct (although they could all be wrong).

Regardless of the actual existence of a god, ALL doctrines, without exception, are man-made.

When people claim that the Bible is the Word of God, the only known truth is that the Bible is the word of man, who CLAIMS it is the Word of God. It's important to make this distinction.

We can ignore (for the moment) the split in belief of those who believe that God is the Father and Jesus is the Son, and those who believe that Jesus IS God (albeit in a different format).

You cannot ignore this distinction if you want to properly analyze the Trinity. The Trinity states that all three persons are distinct, but share in the essence of God. 

When you say Jesus is God "in a different format" you imply that Jesus is God taking another form. This is not Trinitarianism, but another philosophy called modalism.

 Yes, true, although there are many people who belive in the Trinity, yet unknowingly subscribe to modalism.

They get confused, and offer this line :  " it is understood only by those who have the Holy Spirit." 🙂

[To Jim]

Yes, there are people who will say they are a Trinitarian although there are other schools of thought that describe them better. Its not uncommon for Trinitarians to not understand the Trinity, which goes to show how difficult the concept is to grasp!

I felt the distinction was appropriate to answer the question properly 

Well, they only need to ask one question.

Do Jesus, God & Holy Spirit each have a unique identity?

Multiple identities would need to be unique identities. A unique identity would require an independent will. Of course each independent will could align with the others, but because they are independent, they could differ. 

So we effectively have 3 gods. 

That is however how you chosen to conceive of them to begin with.  You have 3 gods because you have demanded this be so, otherwise they do not have in your view separate personalities.  By asserting that they have completely separate wills to count as a person, you set up a double-bind for everyone.

If two separate people agree on the same outcome, that does not mean that they actually do not have their separate wills but they could be said to be 'of one will'.  It is highly implied by the fact that the Devil bothered to tempt Jesus, that a split in the godhead would be theoretically possible but has in fact never actually happened.  It is up there with the god creates boulder too heavy for him to lift. 

The other key difference here is that must be remembered the three persons by virtue of their arriving separately at the same unified will are also sustained as parts of one person.  If you could convince one of the persons of the trinity to dissent against the other two, it would seem therefore that you could destroy God.  I guess that is the devil's idea of victory, to force dissension among the Trinity so their wills no longer perfectly align and God is thus destroyed. 

OK, you can build your own model here, just by answering a few Yes/No questions.

#1 Are the Father, the Son and the Holy Spirit individual beings/persons/entities, each with a unique identity? Yes, or No?

#2 Are the Father, the Son and the Holy Spirit each omnipotent, omniscient and eternal? Yes, or No?

#3 Do the Father, the Son and the Holy Spirit each have an independent will? Yes or No?

Let me know what you decide. Every question is fair, but important.

Yes, Inquisitor Jim. (:

1> Yes.

2> No, they only possess those characteristics in combination.  Apart from each-other they do not even exist.

3> Yes. 

1 is an interesting number I thought.  If you divide 1 into 3, what you get is 0.33333r, an infinite line of 3s, which amusingly means that when anyone says God is 1 (say Muslims), they are really also saying that God is 3, because that is how mathematics work.  Because 1 is actually 3 sets of infinite 3s (InfinityX3). 

It's like "God exists outside of time", yet God is supposed to have existed eternally, therefore God must be inside of time .... or

If God is a spirit (immaterial) , then God is composed of nothing ... and so on.

Just 2 out of the 9,437 reasons why God is impossible :)

[To Jim]

It's like "God exists outside of time", yet God is supposed to have existed eternally, therefore God must be inside of time.

Im surprised you still haven't found the flaw in your own reasoning. Hmmmmm is it possible that your understanding of outside space is not what thesists are talking about? Maybe that's why you avoided answering my last comment, because you know your argument relies on a definition of outside spacetime nobody is using except for you. 

The fallacies in your reasoning are so evident that I suspect you're not taking these discussions seriously. You've insisted on using a definition that was not intended (equivocation fallacy) in order to make the position easier to attack (definist fallacy), making the argument as a whole a strawman. 

You have yet to demonstrate that the definition of outside spacetime I and many others have offered is incoherent. I'll be waiting....

[To Jim]

It's like "God exists outside of time", yet God is supposed to have existed eternally, therefore God must be inside of time ....

Perhaps you can be clearer about how this shows that God’s existence is a matter of impossibility. Supposing that God has existed eternally and hence inside of time, it would be false that God exists outside of time. If one of the two views about God is true, the other is false. Where does the impossibility of God's existence figure into any of that?

What would be impossible is a position that says both that God is outside of time and that God is inside of time. But which theistic tradition maintains that position about God?

If God is a spirit (immaterial), then God is composed of nothing ... and so on.

Being immaterial is not sufficient for being composed of nothing. There are such things as metaphysical parts. For instance, metaphysical parts can be act and potency, essence and existence, and genus and species. There is nothing about composition per se that requires some or all of the parts involved to be parcels of matter.

The killer test is to ask if the 3 persons each have a unique identity, if so, they cannot be one God. They can each be God in a different format, in which case they all share a common identity.

Also, is each person omnipotent? If so, then that's 3 gods, not 1 God. 

Again, we have a problem. Two or more co-existing omnipotent entities is a logical contradiction,  as each would limit the other's power, thus making them NOT omnipotent.

[To Jim]

Most trinity believers that I have talk to believe they are 3 unique personality and 3 co-equal in everything. That is part of the problem with he Modern version of it. If you go back and read the writing of the father of the doctrine. What he taught is no where near what modern version teaches. He never taught they was co-equal and taught they was 3 that are one in purpose and not united in essence. Essentially 3 gods united in 1 purpose.

"Again, we have a problem. Two or more co-existing omnipotent entities is a logical contradiction,  as each would limit the other's power, thus making them NOT omnipotent."

I don't see how you figure this is problematic for Christianity. The Bible describes the will of Jesus and the holy Spirit as being the will of the fathers.

Both Jesus and the holy spirit are described as being "sent forth" or "proceeding from" the father. So there's no question as to which member of the Godhead is the prime being. The will of Jesus and the spirit is the will of the father. This also explains what is meant by one God in three persons. They are one God in that they have a single unified will.

I don't see how this violates any of the logical axioms you mentioned.

"I don't see how you figure this is problematic for Christianity."

It's not a problem for Christianity, but it you give precedence to logic, then two co-existing omnipotent beings IS a logical contradiction. If we have the strongest man in the world (A), there cannot be another man (B) who is the strongest man. In other words, B cannot be A, and A cannot be B. It's the same with any superlative.

If we now move to Christianity, the one important thing to remember is that God is anything you want it to be. So, it's nice to say that the 3 persons have a unified will, but if each of the 3 persons has an independent will, a free will, then theoretically the wills could oppose each other.

So, I said "God is anything you want it to be." Look at these 2 accounts from religious organisations :

Here's an example, from www.intouchuk.org/Read/th. . . :
  
#1 .."While there's only one God, the Godhead consists of three distinct persons—the Father, Son, and Holy Spirit. All are equally omniscient, OMNIPOTENT, omnipresent, eternal, and unchanging, but each one has unique functions."

Realising the error of the logical impossibility of 3 co-existing omnipotent beings, we then had this, from www.gotquestions.org/Trin. . . :

#2 .."There is subordination within the Trinity. Scripture shows that the Holy Spirit is subordinate to the Father and the Son, and the Son is subordinate to the Father."  

Obviously #1 and #2 are contradictory, so they cannot both be correct.

#1 is logically impossible, therefore untrue.

#2 is at least logically possible, so as a claim, it is fine. 

Of course this whole concept is untestable and unfalsifiable, but that's normal for any religious claim.

The reason it is not a contradiction is because each persons are all unified with a single will. So whatever Jesus does is done in accordance to the father.whatever the father does is in accordance with the son, and so it is with each member. , That means each member is equally omnipotent, and that would not be a logical contradiction in that