The Stanford Encyclopaedia of Philosophy has two useful articles on the Trinity:
The latter has an interesting section on the various eisegesis-driven and illogical attempts to support, if not “prove,” Nicene/Chalcedonian “Orthodoxy” from the Old and New Testaments:
2. The Christian Bible
2.1 The Old Testament
No trinitarian doctrine is explicitly taught in the Old Testament. Sophisticated trinitarians grant this, holding that the doctrine was revealed by God only later, in New Testament times (c.50–c.100) and/or in the Patristic era (c. 100–800). They usually also add, though, that with hindsight, we can see that a number of texts either portray or forshadow the co-working of the Father, Son, and Holy Spirit.
For example, in Genesis 18, Yahweh appears to Abraham as three men, and the text has often been read as though the men spoke as one, with one voice. What is this, they urge, if not an appearance of, or even a triple temporary incarnation of the three persons within God's nature? (Other interpretations identify Yahweh with one of the men, the one who stays behind while the others travel to Sodom in Genesis 19.)
In numerous other passages, many Christian readers hold, the preincarnate Son of God is mentioned, or even appears in bodily form to do the bidding of his Father, and is (so they believe) sometimes called the “angel of the Lord”. Some have even identified the preincarnate Christ as Michael, protecting angel over Israel mentioned in the books of Daniel, Jude, and Revelation.
And in several passages, Yahweh refers to himself, or is referred to using plural terms. Non-trinitarians usually read this as a plural of majesty, a form of speech which occurs in many languages, or a conversation between God and angels, while trinitarians often read this as a conversation between the persons of the Trinity.
In sum, Christians read the Old Testament through the lens of the New. For example, the former speaks of God as working by his “word”, “wisdom”, or “spirit”. Some New Testament passages call Jesus Christ the word and wisdom of God, and in the Gospel of John, Jesus talks about the sending of another comforter or helper, the “Holy Spirit”. Thus, some Christians claim the door was open to positing two divine intelligent agents in addition to “the Father”, by, through, or in whom the Father acts, one of whom was incarnated in the man Jesus. In opposition, other Christian readers have taken these passages to involve anthropomorphization of divine attributes, urging that Greek speculations unfortunately encouraged the aforementioned hypostasizations.
2.2 The New Testament
The New Testament contains no explicit trinitarian doctrine. However, many Christian theologians, apologists, and philosophers hold that the doctrine can be inferred from what the New Testament does teach about God. But how may it be inferred? Is the inference deductive, or is it an inference to the best explanation? And is it based on what is implicitly taught there, or on what is merely assumed there? Many Christian theologians and apologists seem to hold it is a deductive inference.
In contrast, other Christians admit that their preferred doctrine of the Trinity not only (1) can't be inferred from the Bible alone, but also (2) that there's inadequate or no evidence for it there, and even (3) that what is taught in the Bible is incompatible with the doctrine. These Christians believe the doctrine solely on the authority of later doctrinal pronouncements of the True Christian Church (typically one of: the Catholic Church, the Eastern Orthodox tradition, or the mainstream of the Christian tradition, broadly understood). Some Catholic apologists have argued that this doctrine shows the necessity of the teaching authority of the Church, this doctrine being constitutive of Christianity but underivable from the Bible apart from the Church's guidance in interpreting it. This stance is not popular among Christians who are neither Catholic nor Eastern Orthodox. (2) would be the main sticking point, although some groups deny all three.
Many Christian apologists argue that the doctrine of the Trinity is “biblical” (i.e. either it is implicitly taught there, or it is the best explanation of what is taught there) using three sorts of arguments. They begin by claiming that the Father of Jesus Christ is the one true God taught in the Old Testament. They then argue that given what the Bible teaches about Christ and the Holy Spirit, they must be “fully divine” as well. Thus, we must, as it were, “move them within” the nature of the one God. Therefore, there are three fully divine persons “in God”. While this may be paradoxical, it is argued that this is what God has revealed to humankind through the Bible.
The types of arguments employed to show the “full divinity” of Christ and the Holy Spirit work as follows.
1. S did action A.
2. For any x, if x does action A, x is fully divine.
3. Therefore, S is fully divine.
E.g., A = non-culpably pronouncing the forgiveness of sins, non-culpably receiving worship, raising the dead, truly saying “Before Abraham was, I am”, creating the cosmos.
1. The Bible applies title or description “F” to S.
2. For any x, if the Bible applies title “F” to x, then x is fully divine.
3. Therefore, S is fully divine.
E.g., F = the first and the last, a god, the God, our savior
1. S has quality Q.
2. For any x, if x has quality Q, then x is fully divine.
3. S is fully divine.
E.g., Q = sinlessness, omniscience, the power to perform miracles, something Christians should be baptized in the name of
While such arguments are deductively valid, they suffer from a crucial ambiguity: What is meant by “fully divine”? Until this is made clear, it isn't clear which of the trinitarian theories is being argued for. A person being “fully divine” might, according to various theorists, amount to being constituted by the matter-like divine nature, being identical to God, being a mind of God, being a way God relates to himself or the world, and so on. Further, the epistemic status of each argument's second premise may depend on what “divine” means.
Opponents of these sorts of argument typically give biblical counterexamples to the second premise (e.g., humans who are called “gods” but aren't divine in the relevant sense, humans who are authorized by God to forgive sins but aren't divine in the relevant sense). In other cases, they also challenge the first premise (e.g., Jesus denied being omniscient, there are inadequate grounds to say that the Son of God created the cosmos).
Another form of argument runs as follows.
1. Passage E is a true prophecy predicting that the God of Israel, Yahweh, will do action A.
2. Passage F truly asserts that the prophecy in E was fulfilled in the life of Jesus Christ.
3. Therefore, Jesus Christ just is the God of Israel, Yahweh.
Opponents reply that this argument is invalid; it is possible for the premises to be true even though the conclusion is false. Even though the prediction “George W. Bush will conquer Iraq” may be said to be fulfilled by the actions of General Smith, it doesn't follow that Smith and Bush are one and the same. Rather, Smith acted as the agent of Bush. Similarly, Yahweh acts through his servant Jesus. Another disadvantage of this argument is that even if it is sound, the conclusion is undesirable. If Jesus and God are held to be (numerically) identical, and one adds that the Father is “fully divine” in this same sense, i.e. the Father is numerically identical to God, then it logically follows that Jesus just is (is numerically identical to) the Father. And yet, according to any trinitarian, some things are true of one that are not true of the other. This is why nearly all trinitarian theories decline to identify more than one of the three persons with God. On the other hand, some embrace this as a mystery —something which appears contradictory but is in fact true. (See main entry section 4.2.)
This traditional case for the divinity of Jesus and the Holy Spirit may be best construed not as a collection of deductive arguments, but rather as an inference to the best explanation, an attempt to infer what best explains all the biblical texts considered together. In this genre, however, alternate explanations are rarely explored in any detail, much less shown to be inferior.
Many arguments of the above types date back to ancient times, and have been repeated in similar forms whenever mainstream trinitarianism has been attacked (Beckwith 2007; Bowman 2007; Bowman and Komoszewski 2007; George 2006; Stuart 1834; Waterland 1856a-e). A number of well developed refutations of these arguments dating from the 17th to 19th centuries have been largely forgotten by present-day theologians, philosophers, and apologists (Burnap 1845; Clarke 1978; Crellius Racovian; Crellius 1691; Emlyn 1746; Haynes 1797; Lardner 1793; Lindsey 1776, 1818; Norton 1859; Nye 1691b; Priestley 1791a-c; Wilson 1846).