One of the chief theological opponents of John Owen was Socinianism. Carl Trueman explains:
Socinianism takes it name from an uncle and a nephew, Laelius and Faustus Socinus, a couple of Italians, who in the 16th century decided to push the Reformation as they saw it to its logical conclusion. Remember what I said about the Reformers, they had a critical attitude towards the church’s tradition, but one that was appreciatative. The Socini would have none of that. The Socini were pretty much a “no creed but the Bible” sort of people.” As far as the Socinians were concerned, the church had gone wrong almost as soon as the canon was closed, and it went wrong because it allowed Greek philosophical language to intrude. The Socinians wanted to get rid of all philosophical language in Christian theology. They wanted to just go back to the bare texts of Scripture. The result was a theology that was (surprise, surprise) Unitarian. Guess what? If you get rid of all the Greek philosophical vocabulary in Christian theology, you cannot express God’s threeness-in-oneness in anything approximating a coherent way. You simply can’t do it. And historically it’s the case that whenever people have tried to purge Christianity of what we would call metaphysical language, philosophical language, it always ends up in Unitarianism.
Socinianism was not only Unitarian, but (obviously) denied the deity of Christ, the eternal damnation of the wicked, and the substitutionary atonement of Christ, among other things. And all this was done in an appeal to the “express words of Scripture.” Later Trueman summarizes part of Owen’s dilemma.
Socinianism . . . is particularly dangerous, of course, because it says it’s just following the sayings of Scripture. It’s a “Scripture alone” movement, which is principally what Owen wants to say he is.
Owen addressed this “scripture only” claim at the beginning of his Vindiciae Evangelicae:
MR BIDDLE having imposed upon himself the task of insinuating his abominations by applying the express words of Scripture in way of answer to his captious and sophistical queries, was much straitened in the very entrance, in that he could not find any text or tittle in them that is capable of being wrested to give the least color to those imperfections which the residue of men with whom he is, in the whole system of his doctrine, in compliance and communion, do charge them withal: as, that there are contradictions in them, though in things of less importance; that many things are or may be changed and altered in them; that some of the books of the Old Testament are lost; and that those that remain are not of any necessity to Christians, although they may be read with profit. Their subjecting them, also, and all their assertions, to the last judgment of reason, is of the same nature with the other. But it not being my purpose to pursue his opinions through all the secret windings and turnings of them, so [as] to drive them to their proper issue, but only to discover the sophistry and falseness of those insinuations which grossly and palpably overthrow the foundations of Christianity, I shall not force him to speak to any thing beyond what he hath expressly delivered himself unto.
In other words, Owen agrees that his theology does not go beyond what the Scripture says, and can show that Socinianism is not in accordance with the Scriptures, despite their so-called adherence to the “express words of Scripture.” In the end, such an appeal is really a means of denying the teachings of Scriptures. Trueman concludes,
I have a sneaking suspicion that a lot of contemporary Protestantism is functionally Socinian. Not only is it Unitarian, but also it pays no attention to what the Church has said over the centuries; it does not listen to it to see if there is any wisdom to be gleaned there from.
Immoderate 
I can see how a failure to “connect the dots” in Scripture would lead to Socinianism and Unitarianism, but I don’t quite “get” how that’s intrinsically coupled with church tradition and Greek philosophy and theological terms. The only thing I can figure out is that having a “cheat sheet,” more or less, of historical theological positions at least allows us to arrive at something correct more quickly.
Help?
Obviously the point is that John Owen’s exegesis depends on philosphy. Never mind that Socinianism and Unitarianism directly against the plain reading of Scripture and in fact depend on their own philosphy.
Well, Bert, it is too bad that we do not have Carl Trueman here to ask exactly what he meant. One thing should be made plain at the beginning, is that all theology is to some extent philosophical. My guess is that Trueman could have meant any number of things. First, I am not sure we can conceive of a Godhead with three Persons in one essence without the aid of the Greek philosophical categories given to us by the church of the past. I think we need the terms and categories ousia and hypostasis, in the sense that other ways of thinking about the Godhead will not work as nicely. We have no natural non-philosophical terms to communicate this mystery (water, the egg, etc–none of these cut it). Therefore we must have metaphysical terminology, and we should be very grateful that the Church worked this out for us. He mentions in the lectures the importance of a hermeneutic of trust for the traditional theology of the Church within the Reformed tradition, that trying to go without it is like reinventing the car. Trueman could also have in mind the fact that many who have problems with the philosophical aspects to the Church’s theology often, as Ryan said, have their own replacement theology, and all of this is in fact an attempt to conceal their own repudiation of the true theology those philosophical categories try to communicate. One theme you come across in many Reformation and post-Reformation theologians is that a distrust of the terminology we use for the Trinity is often veiling some incipient heretical view.
Unless Trueman himself stops by and clarifies this further, I think that one of these may be the idea he was after. Obviously the Greek philosophical we now use for the Trinity is not found in the Bible, so should we assume that they were Socinians/Unitarians? Obviously not. At the same time, I am not sure the authors of Scripture ever desired to or were even concerned to articulate the orthodox teaching in an explicit and coherent way. That did not serve the purpose of their writing and the things they were addressing.
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