Arguments from Silence
This is an articulate example of employing the argument from silence. Arguments from silence always rely on an unstated premise (think about it, it's actually pretty funny).
This does not mean the conclusion of an argument from silence is always false. It means the argument is not logically valid. For example:
P1: They didn't say it
C: Therefore, they didn't know it
The conclusion might be true, but it does not follow from the premise. We need one more premise: If they knew it they would have said it.
The argument then takes the form:
P1: P => Q (if they knew it they would have said it)
P2: ~Q (they didn't say it)
C: ~P (they didn't know it)
The above is a valid argument. The question then revolves around the truth of the first premise.
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The Didache
The date of the composition of the Didache is not known with certainty, but a first-century date is certainly possible. However, I suggest it is a stretch to call it the oldest literary monument of Christian antiquity outside of the New Testament canon. Other viable contenders for that claim include 1 Clement, The Shepherd of Hermas, and the Epistle of Barnabas. Especially 1 Clement (see discussion in chapter ten here).
The Didache is more of a handbook of instructions than a library of creeds; the absence of a particular doctrine is not terribly surprising. Numerous doctrines taught in the New Testament are absent in the Didache--should they be discarded as well?
Please keep in mind that the name "Jehovah" is never mentioned in the Didache. In my view, this does not in any way diminish the significance of the name.
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The Old Roman Creed
The date is unknown. It might date to circa 100; it might be later. As noted in the article cited in the OP, it was quoted by Pope Julius in the 4th century, and statements similar to it are found in the late 2nd and in the 3rd centuries.
Given that Igantius' letter to the Ephesians does reference the Deity of Christ (definitely written during the reign of Trajan), an earlier-is-more-reliable battle between Ignatius and the Old Roman Creed is going to favor the views of Igantius.
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Applying a logical reduction
If the absence of a doctrine in a Christian document means Christians did not believe the doctrine when the document was written (we'll call this Proposition A), we don't even need to appeal to the Didache or the Old Roman Creed.
The Deity of Christ is not taught--even in the most veiled manner--in several books of the New Testament. Let's apply some reductive reasoning to the epistle 3 John:
- 3 John never mentions the Deity of Christ
- 3 John never mentions the Savior by name
- 3 John never mentions the title "Christ"
- 3 John says nothing about baptism
- 3 John says nothing about the Holy Ghost
- 3 John says nothing about grace
If we accept Proposition A, we must discard all of the doctrines noted above.
By reductio ad absurdum, I reject Proposition A.
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Parallels from the Gospels
But why? As noted in the OP, this is important. Why leave it out?
If I have offended readers thus far, please know my intent has been to be objective & fair, not to be rude. But I'll go ahead and say something that might offend everybody who hasn't yet been offended by my post: I claim that it is possible for a rational person to read the Gospel of Luke without inferring the Deity of Christ.
In context this shouldn't be surprising--Luke wrote to Greeks who had a plethora of gods; claiming Jesus is God wouldn't have meant the same thing to them that it meant to Jews.
Okay, now that I've successfully offended every reader of this post, I'll propose a reason why many Christian documents, including the Didache & The Old Roman Creed, fail to mention the Deity of Christ.
In this post I offered a defense of the Gospel of John against a similar criticism. The OP in that case asserted that the "I am" statements are so important that there is no reason the other Gospel authors wouldn't have mentioned them. Therefore (according to the questioner), we cannot trust the Gospel of John. I disagree.
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Milk before Meat
The “I am” statements of John are theologically potent; they carry huge ramifications and would be likely, along with other statements in John, to be over-the-top or offensive to those who did not already have a belief in Jesus.
This principle, that has been experienced by anyone who has done much work in proselyting, was expressed very well by Paul:
I gave you milk to drink, not meat; for you were not able as yet. (1
Corinthians 3:2)
If the synoptics are milk, John is the meat. Much of what Jesus said would have been overwhelming to those who did not have the foundation to understand who Jesus was and why He could say these things.
This is in fact expressly noted by John in chapter 6, during and after the bread of life sermon:
And Jesus said unto them, I am the bread of life: he that cometh to me
shall never hunger; and he that believeth on me shall never thirst.
(verse 35)
The Jews then murmured at him, because he said, I am the bread which
came down from heaven. (verse 41)
From that time many of his disciples went back, and walked no more
with him. (verse 66) (see John 6:26-69 for the full context)
Thus we see that people being overwhelmed—by the profound nature of Christian doctrine—has been a reality for a long time. The synoptic authors tended to stick to the basics—their message of who Jesus is develops over time and climaxes with the resurrection. In John, a much more exalted portrayal of Jesus comes right in the very first chapter.
The fact that John taught more profound doctrine (“a spiritual gospel”) than did the synoptics does not indicate one or the other author did not know what Jesus said, but rather that the Gospels were written for different audiences and for different purposes.
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A personal application
My effort has been to show that the absence of a doctrine in a Christian document does not necessarily invalidate the doctrine. Could this be used to argue that there may be things that are true that are not stated in the Bible? A humble consideration of the question must acknowledge the answer is yes. I personally look forward to learning much more from God.
(To use a trivial, non-controversial example, the planet Neptune was unknown to the ancients and is never mentioned in any ancient Christian writing. This does not mean Neptune isn't real).
As some are aware, I run a YouTube channel. At the time of this writing it hosts 83 videos. I'm too lazy to check how many hours of footage that amounts to. Yet there are things I believe--even things that are not trivial, but are very important to me--that are never stated on my channel.
There are things I believe that would make you angry if I said them. I find both writer and reader tend to be more edified by starting with common ground than by jumping into areas of the sharpest disagreement. Perhaps the author of the Didache felt similarly.
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Conclusion
The New Testament itself (to say nothing of the Apostolic Fathers) is rich with examples of potent doctrines being left out of one document or another.
The absence of references to the Deity of Christ in the Didache & The Old Roman Creed neither affirms nor denies the doctrine.