A Priori General Revelation

We rely greatly on specific revelation to determine aspects of God's character, and rightfully so. Even so, it is interesting to explore what we can determine about His character through only general revelation. We usually assume that we can determine that He exists and is good, but further proofs are possible, and can establish the logical necessity of the Trinity and the Incarnation.

Trinity 1) One cannot create that which is not already inside them. - The creative act is fundamentally an act of self-expression on the external. In order for an artist to create, or even duplicate, they must synthesize data, make it a part of themselves before they can recreate it.

2) God created all things. - A Creator Deity is logically inescapable, whether by causality or by any other proof. Taking this as given, such a Being would be the ultimate cause of all things, and their essences originate with Him. (From where else would they come?)

3) Relationships exist. - Relationships exist, and there is no reason for them to have to. Biology, human society, math, all aspects of existence occur in relation. Humans could exist as a hive entity, a solitary entity, atomistic entities or not at all just as easily.

4a) Therefore, relationships exist as a self-expression of God.
4b) God, then, must exist in relationship. - Relationship must spring from the Creator, and must have its roots in Him. It must be a part of Him for Him to express it in His creation.

5) God existed before all things. - The first cause/unmoved mover is by definition first, before all other things if causality is temporal.

6) Therefore, God exists in relationship to Himself. - God's relational existence must first be introspective, for there is no one else initially to have a relationship with. The Trinitarian model is the only one in contemporary religion that accommodates this while still recognizing the differentiation of Creator and creation, and explains the creative act.

Corollary: Creation is the building of new relationships, or a desire to extend relationships. Only a relational God has a real impetus toward creation.

Incarnation
1a) A Transcendent, Creator Entity [God] is not logistically constrained. - If a Creator wants something, He will make reality to suit those wishes. If He is restrained by something other than sheer logical constraints, He would have made reality differently.
1b) God will then do whatever He wants to the highest degree logically possible. - A Creator will not run out of money, or time, or effort. If He wants to do something, He will do it completely. He is only bound by His own nature, and hence truth.

2) God has a desire to know and be known by humanity. - Whether through prophets or scriptures (not a priori), or through His act of creation, God has shown an interest in a relationship with humanity.

3a) The finite can only understand the infinite insofar as the infinite reveals itself to the finite. - The 'flatland' example of transcendence, we cannot grasp things beyond our plane of existence, because we have no basis/definition for relation. It has to 'come down' to us, because we can't 'come up' to it.
3b) The most complete understanding possible for the finite of the infinite is for the infinite to become finite yet still remain infinite. - If the infinite were to wrap itself in the finite, the finite would be able to grasp the infinite. At least to the extent necessary for relationship. There is no higher level of understanding necessary or possible for the finite.

4) Therefore, God will become man in order to be known by man. - It takes God to wrap himself in flesh for a mind of flesh to wrap itself around God. If God wants to know and be known by man, then He will at some point become man. Therefore, the incarnation off Christ is logically inescapable, even without sin.