In your answer to the meaning of "orthodox" in the OPC's name (see Meaning of Orthodox), you rightly say that it (generally) means "correct doctrine". However, your etymology of the word is not quite correct. The Greek word "doxa" means "worship" as in "correct worship." Clearly there's a relation between the two (the "regulative principle" applies to doctrine as well as worship) but there's a difference also.
There are two questions involved here: First, does "Orthodox" mean (or primarily mean) "correct doctrine" or "correct worship"? Second, what does "Orthodox" mean in the name "Orthodox Presbyterian Church"? In response to the first question two points were made:
(1) All the standard dictionaries - including The New Oxford American Dictionary (2001) and the Random House Unabridged Dictionary (1999) - when tracing the etymology of "orthodox" (from "ortho" + "doxa") give the original meaning (and current meaning) as "correct doctrine" rather than as "correct worship." (2) Those who argue for "correct worship" as a possible meaning of "orthodox" (a) admit that "correct doctrine" is a correct meaning and (b) are almost always spokesman for the Eastern Orthodox Church, which has a tradition (for good or ill) of emphasizing worship over doctrine. (For further discussion of these points, see "Orthodox" Revisited - Part 1 and Part 2.)
That then leaves us with the important question that we will consider next: "What does 'Orthodox' mean in the name 'Orthodox Presbyterian Church'?" So far as the context of the late 1930's is concerned, I think most people would agree that the focus was not upon "correct worship" (in contrast to the "incorrect worship" of Liberal Protestantism), but upon "correct doctrine" (in contrast to the "incorrect doctrine" of Liberal Protestantism).
J. Gresham Machen's Christianity and Liberalism thus dealt not with "the regulative principle of worship" but with the radical doctrinal unbelief characteristic of Liberal Protestantism. This important book defining the crucial issues of the day was primarily concerned with "correct doctrine," not with "correct worship." (Machen was one of the founders of what a few years later became known as the Orthodox Presbyterian Church.)
I think you'll find the following assessment by two of Machen's contemporaries who were neither "orthodox" Christians nor Liberal Protestants to be of interest. The first of these is Walter Lippman, who in his book A Preface to Morals (1929) wrote at some length about the controversy and Machen's book:
Fundamentalism is ... avowedly a reaction within the Protestant communions against what the President of the World's Christian Fundamentalist Association rather accurately described as 'that weasel method of sucking the meaning out of words, and then presenting the empty shells in an attempt to palm them off as giving the Christian faith a new and another interpretation.'...
There is ... a reasoned case against the modernists... [T]his case has been stated in a little book called Christianity and Liberalism by a man who is both a scholar and a gentleman. The author is Professor J. Gresham Machen of the Princeton Theological Seminary. It is an admirable book. For its acumen, for its saliency, and for its wit, this cool and stringent defense of orthodox Protestantism is, I think, the best popular argument produced by either side in the current controversy. We shall do well to listen to Dr. Machen...
Dr. Machen insists, rightly I think, that the historic influence of Christianity on the mass of men has depended upon their belief that an historic drama was enacted in Palestine nineteen hundred years ago during the reign of the Emperor Tiberius. The veracity of that story was [is?] fundamental to the Christian Church... The fundamentalist goes to the very heart of the matter, therefore, when he insists that you have destroyed the popular foundations of religion if you make your gospel a symbolic record of experience, and reject it as an actual record of events.
The liberals have yet to answer Dr. Machen when he [argues that "the] Christian movement at its inception was not just a way of life in the modern sense, but a way of life founded upon a message. It was based, not upon mere feeling, not upon a mere program of work, but on an account of facts." It was based on the story of the birth, the life, the ministry, the death, and the resurrection of Jesus Christ. That story set forth the facts which certify the Christian experience.
Modernism, which in varying degree casts doubt upon the truth of that story, may therefore be defined as an attempt to preserve selected parts of the experience after the facts which inspired it have been rejected. The orthodox believer may be mistaken as to the facts in which he believes. But he is not mistaken in thinking that you cannot ... have a faith of which the only foundation is their need and desire to believe. The historic churches, without any important exceptions, I think, have founded faith on clear statements about matters of fact, historic events..."
--Walter Lippmann, A Preface to Morals (1929).
Similarly, the irreverent H.L. Mencken in his newspaper article "Dr. Fundamentalist" in 1937 had much praise for Machen:
The Rev. J. Gresham Machen, D.D. ... was actually a man of great learning, and, what is more, of sharp intelligence. What caused him to quit the Princeton Theological Seminary and found a seminary of his own was his complete inability, as a theologian, to square the disingenuous evasions of Modernism with the fundamentals of Christian doctrine. He saw clearly that the only effects that could follow diluting and polluting Christianity in the Modernist manner would be its complete abandonment and ruin. Either it was true or it was not true. If, as he believed, it was true, then there could be no compromise with persons who sought to whittle away its essential postulates, however respectable their motives.
Thus he fell out with the reformers who [were] trying... to convert the Presbyterian Church into a kind of literary and social club, devoted vaguely to good works. His one and only purpose was to hold [the Church] resolutely to what he conceived to be the true faith. When that enterprise met with opposition, he fought vigorously, and though he lost in the end and was forced out of Princeton it must be manifest that he marched off to Philadelphia with all the honors of war...
... I never had the honor of meeting him. Moreover, the doctrine that he preached seemed to me... to be excessively dubious... But Dr. Machen had the same clear right to believe in it that I have to disbelieve in it, and though I could not yield to his reasoning I could at least admire, and did greatly admire, his remarkable clarity and cogency as an apologist, allowing him his primary assumptions...
... [H]is opponents... essayed to overhaul the scriptural authority which lay at the bottom of the whole matter, retaining what coincided with their private notions and rejecting whatever upset them.
Upon this contumacy Dr. Machen fell with loud shouts of alarm. He denied absolutely that anyone had a right to revise and sophisticate Holy Writ. Either it was the Word of God or it was not the Word of God, and if it was, then it was equally authoritative in all its details, and had to be accepted or rejected as a whole. Anyone was free to reject it, but no one was free to mutilate it or to read things into it that were not there.
Thus the issue with the Modernists was clearly joined, and Dr. Machen argued them quite out of court, and sent them scurrying... His operations... at least disposed of those who proposed to read [Holy Writ] as they might read a newspaper, believing what they chose and rejecting what they chose...
It is my belief, as a friendly neutral in all such high and ghostly matters, that the body of doctrine known as Modernism is completely incompatible, not only with anything rationally describable as Christianity, but also with anything deserving to pass as religion in general. Religion, if it is to retain any genuine significance, can never be reduced to a series of sweet attitudes, possible to anyone not actually in jail for felony. It is, on the contrary, a corpus of powerful and profound convictions, many of them not open to logical analysis... It is potent in a man in proportion as he is willing to... accept its fundamental postulates...
These postulates, at least in the Western world, have been challenged in recent years on many grounds... But it is one thing to reject religion altogether, and quite another thing to try to save it by pumping out of it all its essential substance...
That, it seems to me, is what the Modernists have done... What they have left, once they have achieved their imprudent scavenging, is hardly more than a row of hollow platitudes, as empty of psychological force and effect as so many nursery rhymes...
Religion is something else again... Dr. Machen tried to impress that obvious fact upon his fellow [Presbyterians]. He failed - but he was undoubtedly right.
--H.L. Mencken, "Dr. Fundamentalist," The Baltimore Evening Sun, January 18, 1937; 2nd Section, p. 15.
But better than reading Lippmann or Mencken is to read Machen himself. His 1923 book Christianity and Liberalism is available in its entirety on-line here and here. Note Machen's emphasis upon doctrine:
In my little book, Christianity and Liberalism, 1923, I tried to show that the issue in the Church of the present day is not between two varieties of the same religion, but, at bottom, between two essentially different types of thought and life. There is much interlocking of the branches, but the two tendencies, Modernism and supernaturalism, or (otherwise designated) non-doctrinal religion and historic Christianity, spring from different roots. In particular, I tried to show that Christianity is not a "life," as distinguished from a doctrine, and not a life that has doctrine as its changing symbolic expression, but that--exactly the other way around--it is a life founded on a doctrine.
--J. Gresham Machen, "Christianity in Conflict," in D.G. Hart, ed., J. Gresham Machen: Selected Shorter Writings (P & R Publishing, 2004), pp. 563-564.
My point, again, is that when the Presbyterian Church of America chose to rename itself the Orthodox Presbyterian Church, what was primarily in mind in 1939 was orthodoxy of belief, correct doctrine, and not "correct worship" (although it is admitted that correct worship is founded upon correct doctrine).
Thank you again for your note. If you have further questions or would like to interact further on this matter, please feel free to drop me a note. And may our God graciously grant to us a true orthodoxy in doctrine and in life, in faith and in practice, and to Him be the glory!
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