And what about Irenaeus's use of Acts? In Book Three at the end of chapter 15
And again he says, "For an hour we did give place to subjection, that the truth of the gospel might continue with you." If, then, any one shall, from the Acts of the Apostles, carefully scrutinize the time concerning which it is written that he went up to Jerusalem on account of the forementioned question, he will find those years mentioned by Paul coinciding with it. Thus the statement of Paul harmonizes with, and is, as it were, identical with, the testimony of Luke regarding the apostles.
I know the way people like you look at this statement. Irenaeus was using a variant of Galatians that had this submissive reference, blah, blah, blah. We no longer take Irenaeus's text of Galatians to be the correct one. But without it, surely our text of Galatians DISAGREES with Acts. How then is Acts with its blatant subordination of Paul to the apostles a "first century witness." Whether or not there was a "good text" of Galatians floating around somewhere Acts depends on Irenaeus's falsified text of Galatians. This is where it got the information that Paul subordinated himself to the other apostles. Without this falsification Acts would have had no historical information about Paul's subordination to the apostles. Even Irenaeus can only cite the second century falsified edition of Galatians in support of the ideas of Acts.
And I would argue furthermore than Clement of Alexandria's Paul, the hierophant of a mystery religion, is what Acts was developed to counter. So in what immediately follows in Irenaeus:
But that this Luke was inseparable from Paul, and his fellow-labourer in the Gospel, he himself clearly evinces, not as a matter of boasting, but as bound to do so by the truth itself. For he says that when Barnabas, and John who was called Mark, had parted company from Paul, and sailed to Cyprus, "we came to Troas;"(10) and when Paul had beheld in a dream a man of Macedonia, saying, "Come into Macedonia, Paul, and help us," "immediately," he says, "we endeavoured to go into Macedonia, understanding that the Lord had called us to preach the Gospel unto them. Therefore, sailing from Troas, we directed our ship's course towards Samothracia." And then he carefully indicates all the rest of their journey as far as Philippi, and how they delivered their first address: "for, sitting down," he says, "we spake unto the women who had assembled;"(11) and certain believed, even a great many. And again does he say, "But we sailed from Philippi after the days of unleavened bread, and came to Troas, where we abode seven days."(12) And all the remaining [details] of his course with Paul he recounts, indicating with all diligence both places, and cities, and number of days, until they went up to Jerusalem; and what befell Paul there,(13) how he was sent to Rome in bonds; the name of the centurion who took him in charge;(14) and the signs of the ships, and how they made shipwreck;(15) and the island upon which they escaped, and how they received kindness there, Paul healing the chief man of that island; and how they sailed from thence to Puteoli, and from that arrived at Rome; and for what period they sojourned at Rome. As Luke was present at all these occurrences, he carefully noted them down in writing, so that he cannot be convicted of falsehood or boastfulness, because all these [particulars] proved both that he was senior to all those who now teach otherwise, and that he was not ignorant of the truth. That he was not merely a follower, but also a fellow-labourer of the apostles, but especially of Paul, Paul has himself declared also in the Epistles, saying: "Demas hath forsaken me, ... and is departed unto Thessalonica; Crescens to Galatia, Titus to Dalmatia. Only Luke is with me."(1) From this he shows that he was always attached to and inseparable from him. And again he says, in the Epistle to the Colossians: "Luke, the beloved physician, greets you."(2) But surely if Luke, who always preached in company with Paul, and is called by him "the beloved," and with him performed the work of an evangelist, and was entrusted to hand down to us a Gospel, learned nothing different from him (Paul), as has been pointed out from his words, how can these men, who were never attached to Paul, boast that they have learned hidden and unspeakable mysteries?
I read these last words of course that "these men" i.e. Clement had a gospel which taught them that the apostle transmitted a mystery religion to them. Acts is perfectly suited for countering this understanding.
It is specifically against a "mystery gospel" that Luke was developed against too. As we read in the very next lines:
But that Paul taught with simplicity what he knew, not only to those who were [employed] with him, but to those that heard him, he does himself make manifest. For when the bishops and presbyters who came from Ephesus and the other cities adjoining had assembled in Miletus, since he was himself hastening to Jerusalem to observe Pentecost, after testifying many things to them, and declaring what must happen to him at Jerusalem, he added: "I know that ye shall see my face no more. Therefore I take you to record this day, that I am pure from the blood of all. For I have not shunned to declare unto you all the counsel of God. Take heed, therefore, both to yourselves, and to all the flock over which the Holy Ghost has placed you as bishops, to rule the Church of the Lord,(3) which He has acquired for Himself through His own blood."(4) Then, referring to the evil teachers who should arise, he said: "I know that after my departure shall grievous wolves come to you, not sparing the flock. Also of your own selves shall men arise, speaking perverse things, to draw away disciples after them." "I have not shunned," he says, "to declare unto you all the counsel of God." Thus did the apostles simply, and without respect of persons, deliver to all what they had themselves learned from the Lord. Thus also does Luke, without respect of persons, deliver to us what he had learned from them, as he has himself testified, saying, "Even as they delivered them unto us, who from the beginning were eye-witnesses and ministers of the Word."
It's deceptive not to see the concept of "mystery gospel" present in this long discussion of Luke. Luke proves that "short Mark" does not lead to a "mystery gospel." When Mark is expanded, it expands to Luke. Clearly it is Mark and Papias's criticism of Mark that Luke has in mind when he wrote the words cited in Irenaeus:
Forasmuch as many have taken in hand to draw up a narrative concerning those matters which have been fulfilled among us, even as they delivered them unto us, who from the beginning were eye-witnesses and ministers of the word, it seemed good to me also, having traced the course of all things accurately from the first to write thee in order, most excellent Theophilus; that thou mightest know the certainty concerning the things wherein thou wast instructed.
How then is Luke a first century text? Did Papias "really" live in the first century? Of course not. He lived in the early second century. As such, whoever wrote these words necessarily read Papias's criticism of Mark and - I would argue, knew the existence of a longer mystery gospel of Mark (but that is of no matter) - said that he was expanding the testimony of Mark in a good way. Instead of expanding it into a "mystery gospel" and all the things Irenaeus criticizes in Book Three in the section we've just cited, Luke "proves" IN THE SECOND CENTURY that, after reading Mark's gospel production that what follows is a "good expansion" of the original material of Mark. I see no other way than read Irenaeus and Luke walking in lockstep regarding (a) familiarity with Papias's criticism of Mark and (b) the idea that the orthodox "canon" solves the problems raised by Papias.
There is no way for Luke to be aware of Papias if he lived in the first century.