Well, by looking at the history! Its not rocket science. But there is also the biblical evidence regarding indefectibility, strongly implying that God will preserve His Church in faithfulness to true doctrine, which in turn implies infallibility.
8. Prior to Irenaeus' comments, Papias' search for apostolic tradition leads him to consulting eyewitnesses and contemporaries of Jesus and the apostles, without any reference to an infallible source of such information in the church.
Again, Jason commits the fallacy of fighting a straw man. We wouldn't expect to see the discussion framed in those terms at such an early stage.
Justin Martyr and Trypho discuss some of the New Testament documents, and Justin discusses the church to some extent (what happens during baptism, the eucharist, etc.), but church infallibility has no role in his argumentation or that of his Jewish and Gentile opponents. Though they often criticize the New Testament documents as sources of Christian authority, I'm not familiar with any reference to church infallibility among the earliest enemies of Christianity. Men like Trypho and Celsus comment on the Biblical documents, but they say nothing of a Pope, infallible councils, or church infallibility in general. Hegesippus' comments on the corruption of the church (Eusebius, Church History, 3:32, 4:22) wouldn't lead one to conclude that he held a view of church infallibility like what's advocated by Catholics and Orthodox today.
This displays Jason's lack of understanding of the Catholic view of development. He tries to make this elaborate argument from silence. But he misses the forest for the trees. Cardinal Newman, in his Essay on the Development of Christian Doctrine gives several proposed (and quite plausible) explanations for the relative early silence or lack of specificity: things that are perfectly consistent with his theory and altogether to be expected:
Let us see how, on the principles which I have been laying down and defending, the evidence lies for the Pope's Supremacy.
As to this doctrine the question is this, whether there was not from the first a certain element at work, or in existence, divinely sanctioned, which, for certain reasons, did not at once show itself upon the surface of ecclesiastical affairs, and of which events in the fourth century are the development; and whether the evidence of its existence and operation, which does occur in the earlier centuries, be it much or little, is not just such as ought to occur upon such an hypothesis.
2.For instance, it is true, St. Ignatius is silent in his Epistles on the subject of the Pope's authority; but if in fact that authority could not be in active operation then, such silence is not so difficult to account for as the silence of Seneca or Plutarch about Christianity itself, or of Lucian about the Roman people. St. Ignatius directed his doctrine according to the need. While Apostles were on earth, there was the display neither of Bishop nor Pope; their power had no prominence, as being exercised by Apostles. In course of time, first the power of the Bishop displayed itself, and then the power of the Pope. . . .3.
. . . St. Peter's prerogative would remain a mere letter, till the complication of ecclesiastical matters became the cause of ascertaining it. . . .
When the Church, then, was thrown upon her own resources, first local disturbances gave exercise to Bishops, and next ecumenical disturbances gave exercise to Popes; and whether communion with the Pope was necessary for Catholicity would not and could not be debated till a suspension of that communion had actually occurred. It is not a greater difficulty that St. Ignatius does not write to the Asian Greeks about Popes, than that St. Paul does not write to the Corinthians about Bishops. And it is a less difficulty that the Papal supremacy was not formally acknowledged in the second century, than that there was no formal acknowledgment on the part of the Church of the doctrine of the Holy Trinity till the fourth. No doctrine is defined till it is violated.
And, in like manner, it was natural for Christians to direct their course in matters of doctrine by the guidance of mere floating, and, as it were, endemic tradition, while it was fresh and strong; but in proportion as it languished, or was broken in particular places, did it become necessary to fall back upon its special homes, first the Apostolic Sees, and then the See of St. Peter.
5.Moreover, an international bond and a common authority could not be consolidated, were it ever so certainly provided, while persecutions lasted. If the Imperial Power checked the development of Councils, it availed also for keeping back the power of the Papacy. The Creed, the Canon, in like manner, both remained undefined. The Creed, the Canon, the Papacy, Ecumenical Councils, all began to form, as soon as the Empire relaxed its tyrannous oppression of the Church. And as it was natural that her monarchical power should display itself when the Empire became Christian, so was it natural also that further developments of that power should take place when that Empire fell. Moreover, when the power of the Holy See began to exert itself, disturbance and collision would be the necessary consequence. . . . a new power had to be defined; as St. Paul had to plead, nay, to strive for his apostolic authority, and enjoined St. Timothy, as Bishop of Ephesus, to let no man despise him: so Popes too have not therefore been ambitious because they did not establish their authority without a struggle. It was natural that Polycrates should oppose St. Victor; and natural too that St. Cyprian should both extol the See of St. Peter, yet resist it when he thought it went beyond its province. . . .
It will be said that all this is a theory. Certainly it is: it is a theory to account for facts as they lie in the history, to account for so much being told us about the Papal authority in early times, and not more; a theory to reconcile what is and what is not recorded about it; and, which is the principal point, a theory to connect the words and acts of the Ante-nicene Church with that antecedent probability of a monarchical principle in the Divine Scheme, and that actual exemplification of it in the fourth century, which forms their presumptive interpretation. All depends on the strength of that presumption. Supposing there be otherwise good reason for saying that the Papal Supremacy is part of Christianity, there is nothing in the early history of the Church to contradict it.
8.. . . Moreover, all this must be viewed in the light of the general probability, so much insisted on above, that doctrine cannot but develope as time proceeds and need arises, and that its developments are parts of the Divine system, and that therefore it is lawful, or rather necessary, to interpret the words and deeds of the earlier Church by the determinate teaching of the later.
(2nd edition, 1878, Part I, Chapter IV, Section 3: "Papal Supremacy")
Even long after the time of Irenaeus, we find sources like Augustine making comments about church authority that are inconsistent with a Catholic or Orthodox view (On Baptism, Against The Donatists, 2:2-4).
To the contrary, On Baptism, 2:2-4 contradicts Protestant notions more than it does the Catholic rule of faith. So, for example, he writes in 2:2:
For no one of us sets himself up as a bishop of bishops, or, by tyrannical terror, forces his colleagues to a necessity of obeying, inasmuch as every bishop, in the free use of his liberty and power, has the right of forming his own judgment, and can no more be judged by another than he can himself judge another.
The same contra-Catholic argument is made about St. Gregory the Great's denial of being a universal bishop (that has a perfectly orthodox Catholic explanation), but the sense appears to be the same in both cases: a bishop has jurisdiction in his own domain, and is not merely an agent of the pope. The same Gregory who eschewed the title "universal bishop" also made many explicit proclamations of papal supremacy. And this is true of St. Augustine as well. But Jason, in true anti-Catholic hyper-selective fashion, wants to dwell on these few passages (that don't prove at all what he asserts), and ignore the context of Augustine's overall teaching. Rather than cite the numerous Augustine utterances concerning Roman primacy, J. N. D. Kelly's assessment will suffice for our purposes:
It goes without saying that Augustine identifies the Church with the universal Catholic Church of his day, with its hierarchy and sacraments, and with its centre at Rome.
(Early Christian Doctrines, HarperSanFrancisco, revised edition of 1978, 412-413)
Elsewhere even in the passage cited by Jason, Augustine asserts things that are blatantly contrary to Protestantism, while nothing can be proven to be contrary to Catholicism:
. . . the Councils themselves, which are held in the several districts and provinces, must yield, beyond all possibility of doubt, to the authority of plenary Councils which are formed for the whole Christian world . . .
Protestantism denies the binding "authority of plenary councils." That was expressly part of Luther's revolt. In the very next clause, Augustine refers to development of doctrine between Catholic councils: precisely as Catholics hold:
. . . and that even of the plenary Councils, the earlier are often corrected by those which follow them, when, by some actual experiment, things are brought to light which were before concealed, and that is known which previously lay hid, . . .
Note his very strong Catholic (and most "unProtestant") statement in 2:4:
Nor should we ourselves venture to assert anything of the kind, were we not supported by the unanimous authority of the whole Church, to which he himself would unquestionably have yielded, if at that time the truth of this question had been placed beyond dispute by the investigation and decree of a plenary Council.
The truth of a question is "placed beyond dispute" by a council? How is that different from infallibility? I don't see any distinction. And this occurs in the passage that Jason brings out supposedly in support of a position supposedly "inconsistent with a Catholic or Orthodox view," as he claims. Later in this same chapter he refers to a doctrinal matter "brought to the full illumination and authoritative decision of a plenary Council."
It's not as if all high views of church authority or all forms of belief in an infallible church are equivalent to a Catholic or Orthodox view on the subject.
Really? An "infallible church" besides Catholicism or Orthodoxy is a contradiction in terms, since sola Scriptura rules it out by definition (being itself the only infallible authority). So let Jason produce an example of that which he refers to here. Where is it?
I see no reason to assume that the views of somebody like Irenaeus were equivalent to those of Catholics or Orthodox,
I know; this is the problem. Tunnel vision and historical revisionism have this blunting effect after so many years of doing that. By this I mean "equivalent" in terms of being consistent with Catholicism in kernel form, and inconsistent with Protestantism. It's not equivalent in terms of his views being as fully developed as they were later on. But that is our view, so it is no problem for us.
I don't see any reason to think that his views would naturally develop into a Catholic view or an Orthodox view,
More inability to comprehend, caused by years of forcing the facts into an interpretive grid that is impossible to maintain, once all the relevant facts are considered . . .
and I see no reason to assume that men like Papias and Augustine agreed with Irenaeus' view.
They agreed on the general outlines of Church hierarchy and authority, and that is all that is required in our viewpoint.
Some elements of Irenaeus' view were popular among patristic Christians, but I see no reason to conclude that his view of church reliability (which isn't the same as infallibility) was as widespread as acceptance of the Protestant canon.
I see. So now apostolic succession and a high view of authoritative tradition had not achieved the consensus that the canon had by A. D. 200 (around the time of St. Irenaeus' death)? It's fascinating then, that Protestant historian Philip Schaff writes of the views of the pre-Nicene period of the Church as follows:
The fathers of our period all saw in the church, though with different degrees of clearness, a divine, supernatural order of things, in a certain sense the continuation of the life of Christ on earth, the temple of the Holy Spirit, the sole repository of the powers of divine life, the possessor and interpreter of the Holy Scriptures, the mother of all the faithful . . .
Equally inseparable from her is the predicate of apostolicity, that is, the historical continuity or unbroken succession, which reaches back through the bishops to the apostles, from the apostles to Christ, and from Christ to God. In the view of the fathers, every theoretical departure from this empirical, tangible, catholic church is heresy, that is, arbitrary, subjective, ever changing human opinion; every practical departure, all disobedience to her rulers is schism, or dismemberment of the body of Christ; either is rebellion against divine authority, and a heinous, if not the most heinous, sin. No heresy can reach the conception of the church, or rightly claim any one of her predicates; it forms at best a sect or party, and consequently falls within the province and the fate of human and perishing things, while the church is divine and indestructible.
This is without doubt the view of the ante-Nicene fathers, even of the speculative and spiritualistic Alexandrians . . .
(History of the Christian Church, Vol. II: Ante-Nicene Christianity: A.D. 100-325, Grand Rapids, Michigan: Eerdmans Publishing Company, 1976, from the revised fifth edition of 1910. Chapter IV, section 53, "The Catholic Unity," pp. 169-170, 172)
"Divine and indestructible"? "Every theoretical departure from this empirical, tangible, catholic church is heresy"? "All disobedience to her rulers is schism"? That sure sounds a heck of a lot like something akin to infallibility, and this is a non-Catholic expert on patristics summarizing the views then held by the fathers, prior to 325 A. D. And just as surely, it is in no way consistent with the later Protestant novel view of sola Scriptura.
Jason now begins his infallibility / canon of the Bible disanalogy. He claims that there was more consensus on the latter than the former. In fact, development proceeded in both cases, rapidly in the fourth century. Most of the explicit elements of the historic papacy were in place by the reign of Pope St. Leo the Great (440-461), which was not long after the formulation of the canon. The true late (and radical) development here was when Protestants decided to demote the Deuterocanon over a thousand years later.
9. We have many lines of evidence for the widespread acceptance of the books of the Protestant canon, such as Eusebius' comments about the degree of acceptance of the books among the churches.
We also have a huge amount of patristic support for the Deuterocanon: the books that Protestants demoted from the Bible, but Jason conveniently omits that, because it doesn't fit with the playbook. One could go in a million directions with this: so wrong is Jason and the Protestant opposition to those books. As usual, the fathers (with some exceptions, as always) overwhelmingly favor the Catholic position. I wrote in my third dialogue with Jason on development and the canon:
St. Athanasius was the first Church Father to list the 27 NT books as we have them today, and no others, as canonical, in 367. What is not often mentioned by Protestant apologists, however, is the fact that when he listed the Old Testament books, they were not identical to the Protestant 39:As Athanasius includes Baruch and the 'Letter of Jeremiah' . . . so he probably includes the Greek additions to Daniel in the canonical book of that name, and the additions to Esther in the book of that name which he recommends for reading in the church, . . . Only those works which belong to the Hebrew Bible (apart from Esther) are worthy of inclusion in the canon (the additions to Jeremiah and Daniel make no appreciable difference to this principle . . . In practice Athanasius appears to have paid little attention to the formal distinction between those books which he listed in the canon and those which were suitable for the instruction of new Christians [he cites Wisdom of Solomon, Wisdom of Sirach, Esther, Judith, and Tobit] . . . and quoted from them freely, often with the same introductory formulae - 'as it is written', 'as the scripture says', etc. [footnote 46: He does not say in so many words why Esther is not included in the canon . . . ]Bruce notes that the Council of Hippo in 393 ("along the lines approved by Augustine") and the Third Council of Carthage in 397:
(F. F. Bruce, The Canon of Scripture, Downers Grove, Illinois: InterVarsity Press, 1988, 79-80). . . appear to have been the first church councils to make a formal pronouncement on the canon. When they did so, they did not impose any innovation on the churches; they simply endorsed what had become the general consensus of the churches in the west and of the greater part of the east . . . The Sixth Council of Carthage (419) re-enacted the ruling of the Third Council, again with the inclusion of the apocryphal books . . . Throughout the following centuries most users of the Bible made no distinction between the apocryphal books and the others: all alike were handed down as part of the Vulgate . . . The two Wycliffite versions of the complete Bible in English (1384, 1395) included the apocryphal books as a matter of course.
(Ibid., 97, 99-100)
Bruce also noted:
Throughout the following centuries most users of the Bible made no distinction between the apocryphal books and the others: all alike were handed down as part of the Vulgate . . .
(Bruce, ibid., 99)
Other Protestant scholarly sources concur:
A council probably held at Rome in 382 under St. Damasus gave a complete list of the canonical books of both the Old Testament and the New Testament (also known as the 'Gelasian Decree' because it was reproduced by Gelasius in 495), which is identical with the list given at Trent.St. Athanasius included Baruch (and other additional Greek chapters) but not Esther, in the Old Testament. I wrote in a paper of mine about the Deuterocanon, citing my good friend Gary Michuta at length regarding St. Athanasius:
(The Oxford Dictionary of the Christian Church, 2nd edition, edited by F. L. Cross & E. A. Livingstone, Oxford Univ. Press, 1983, 232)
This canon [of Carthage] remained undisturbed till the sixteenth century, and was sanctioned by the council of Trent at its fourth session.
(Philip Schaff, History of the Christian Church, Vol. III: Nicene and Post-Nicene Christianity, Grand Rapids, Michigan: Eerdmans, 1974 [orig. 1910], 609-610)
St. Athanasius is one of the favorites of Protestants (probably second to St. Augustine in that regard). It's true that he did seem to lower the status of the deuterocanonical books somewhat, but not to a sub-biblical level, as noted by my good friend Gary Michuta, in his excellent book, Why Catholic Bibles are Bigger (Port Huron, Michigan: Grotto Press, 2007, 110-112; footnote numbering my own):Athanasius quotes both Baruch and Susanna right along passages from Isaiah, Psalms, Romans, and Hebrews; he makes no distinction or qualification between them . Wisdom also is used as an authentic portion of sacred Scripture . . .:But of these and such like inventions of idolatrous madness, Scripture taught us beforehand long ago, when it said, 'The devising of idols, as the beginning of fornication, and the invention of them, the corruption of life . . .' [Ws 14:12] And later in the same work:For since they were endeavouring to invest with what Scripture calls the incommunicable name . . . This reference to the "incommunicable name" comes from Wisdom 14:21 . . .
Athanasius quotes another passage from Wisdom as constituting the teachings of Christ, the Word of God. He undoubtedly uses it to confirm doctrine.  In another argument against Arians, he calls both the Protocanonical Proverbs and the Deuterocanonical Wisdom "holy Scripture" . . .  . . .
Athanasius also quotes the book of Sirach without distinction or qualification, in the midst of several other scriptural quotations.  . . . Athanasius calls the Book of Judith Scripture.  Tobit is cited right along with several Protocanonical quotations  , and even introduced with the solemn formula "it is written." 
 Four Discourses Against the Arians, Discourse 1.12.
 Against the Heathen, 11.1. Emphasis added.
 Against the Heathen, 1, 17.3.
 On the Incarnate Word, 4.6; 5.2.
 Defense Against Arius, 1, 3.
 Life of Anthony, 28 and Apology Against the Arians, 66.
 Four Discourses Against the Arians, Discourse 2.35 . . .
 Defense of Constantius, 17. Tobit is cited after Matthew and Isaiah.
 Defense Against Arius, Part 1, 11.
I continue in the same paper regarding St. Jerome, citing Gary Michuta's superb research:
But even with Jerome, there were several anomalies (or changes of mind or vacillations?), of such a nature that the would shock many a Protestant who rely on him as a "champion" in opposing the Deuterocanon. Gary Michuta enumerates several of these curious inconsistencies:He . . . flatly denies that Tobit is part of the canon,  although elsewhere he cites it without qualification!  . . . Jerome adopts the popular convention in his Letter to Oceanus by quoting Baruch as a voice made by "the trumpets of the prophets."  Sirach is both rejected and quoted as Scripture,  although it is formally quoted  and occasionally used without qualification.  Wisdom is also occasionally formally quoted.  Jerome even attributes the passages from Wisdom to the Holy Spirit.  Maccabees is used without distinction.  Jerome at times alludes to the Deuterocanonical sections of Daniel in his letters.  Deuterocanonical passages from Esther are likewise quoted.  . . . he lists Judith as one of the virtuous women of sacred Scripture . . . .
 Prologue to John.
 Commentary in Eccles. 8.
 Letter 77:4.
 Commentary on Isaiah, Book 2, 3:12; Letters 77:6: 108:22; 118:1; 148:2,16,18.
 Commentary on Jeremiah, Book 4, 21:14; Commentary on Ezekiel, Book 6, 18:6; and Letter 64:5.
 Commentary on Isaiah, Book 8, 24:4; Commentary on Ezekiel, Book 6, 18:6; Letter 57.1 To Pammachius; and Letter 125.19, To Rusticus.
 Commentary on Isaiah, Book 1, 1:24; Commentary on Zechariah, Book 3, 14:9; and Commentary on Malachi, 3:7 ff.
 Commentary on Galatians, Book 1, 3:2 . . . and Breviarium in Psalmos, Ps 9.
 Against Pelagians, Book 2:30; Letter 7, To Chromatius, Jovinus and Eusebius.
 Letter 3, 1 To Rufinus the Monk; Letter 22,9-10, To Eustochium; Letter 1, 9 to Innocent.
 Letter 48, To Pammachius, 14.
 Letter 65,1.
(Michuta, ibid., 149-150; again, my own footnote numbering)
Jason wants to casually mention Eusebius? He wrote about the book of Revelation (Apocalypse):
Among the books which are spurious should be reckoned . . . the Apocalypse of John, should it seem right. For, as I said, some reject it, while others count it among the acknowledged books.
(in Bruce, ibid., 199)
St. Cyril of Jerusalem, Sr. John Chrysostom, and St. Gregory Nazianzen all disputed the canonicity of Revelation. At the Council of Nicaea, according to Protestant apologist Norman Geisler (How we Got the Bible, with co-author William E. Nix, Chicago: Moody Press, 1974, 109), the books of James, 2 Peter, 2 and 3 John, and Jude, were "named as disputed." Geisler seems, however (based on his comments on p. 111), to merely be talking about the time period of 325-340, and to base his conclusion on Eusebius' summary in Ecclesiastical History (III, 25, 3), which reads:
Among the disputed writings, which are nevertheless recognized by many, are extant the so-called epistle of James and that of Jude, also the second epistle of Peter, and those that are called the second and third of John, whether they belong to the evangelist or to another person of the same name.
But the date of Eusebius' famous book on Church history is itself a matter of dispute. G. A. Williamson, translator of the 1965 Penguin edition, surmised in the Introduction that it was somewhere between 311 and 325, and noted that some placed the first eight (of ten) books (or "chapters") as early as 305 (whereas Geisler was apparently extrapolating to the date of his death: around 340). So the basis for Geisler's conclusions in his chart on p. 109 seem a bit questionable and must be taken with a grain of salt. In any event, there is considerable evidence that all these books were disputed by not a few until late into the 4th century: some of which I have discussed in other installments of this four-part reply.
The Codex Sinaiticus manuscript from the late fourth century included the Epistle of Barnabas and the Shepherd of Hermas. The Codex Alexandrinus in the early fifth century included 1 and 2 Clement.
Even John Calvin joins the fun. He referred to Baruch as a "prophet" more than once, and also applied that noble title to Sirach. For documentation and more on his deuterocanonical citations, see my paper: John Calvin's Citations of Deuterocanonical Books (So-Called "Apocrypha"): Documented Instances.
This is a strange place for Jason to try to make some sort of case for proto-Protestantism in the fathers, for the canonical disputes of those times are exceedingly complicated. The disputes are at the "edges" of the canon (mostly about books other than the Gospels and Paul's epistles).
In the same fashion, the disputes about the papacy and Roman primacy and the authority of same are about the "edges" and particulars: but not about the thing itself. There was such a thing as a central authority in the Church and an apostolic See and a pope: how the authority was exercised in particulars, and its exact extent and nature were debated, as we would fully expect. The thing itself is clearly there and it develops. In the same fashion, everyone knew there was such a thing as a Bible that was inspired, but the debates had to do with the actual contents.
If Jason wants to dichotomize the development of the canon with the development of the papacy and Roman primacy (and infallibility), he is in a no-win situation. Either he will prove the validity of the former by analogy (once the broad scope of facts are examined, rather than Jason's carefully hand-picked prooftexting), as no less indicated than the canon, or he will show that the process concerning the canon has more difficulties than the ecclesiology questions, in which case it is a counter-productive argument for him.
But above and beyond all that, always lurking in the background in the canon dispute, is the question of the deuterocanonical books, where he loses (in terms of disputational "points") again, because the Church accepted these books that Protestants reject. Everywhere he turns, Church history is his enemy, or at the very least, a frustrating "nag," reminding him of innumerable anomalous facts.
Where's the comparable evidence for the degree of acceptance of belief in an infallible church?
An authoritative, binding Church is all over the place in the fathers. I don't have time to reproduce all that again. It is displayed in many other papers of mine, and books. My most succinct presentation or overview is found in the paper, The Witness of the Church Fathers With Regard to Catholic Distinctives (With Examples of Protestant Corroboration of Catholic Doctrines or Clear Contradiction of Patristic Consensus) (see section X: the last one, that comprises about one-quarter of the very long paper).
In my experience, advocates of an infallible church tend to group together a variety of patristic affirmations about different subjects (church reliability, the evidential value of apostolic succession, etc.), act as if all such comments are equivalent to belief in the infallibility of a single church that we today can identify, and assign belief in that church's infallibility to the patristic Christians in general.
Here again is Jason's games of not understanding how development works, that I discussed in my Introduction. This is very clever sophistry. It is implied that unless Catholics can locate explicit statements about infallibility in every jot and tittle (as was done in 1870), that somehow this proves that development did not occur at all, or that it is an illegitimate concept. I've already shown, citing Cardinal Newman, how it is quite unreasonable to expect this. But what we do find is quite compelling proof of development in this regard.
It's in Jason's interest to discount a whole host of closely related considerations from the discussion, because he knows that his case collapses if that is done. He wants to separate everything into airtight compartments, so that if we discuss apostolic succession and the certainty claimed to be obtained thereof, he simply dismisses that as off-topic, as if it has nothing to do with felt certainty, that is the very essence of infallibility and its reason for existence. His game-playing only reveals, in the end, how shallow and revisionist his analysis is.
In contrast to the dubious steps in that form of argumentation, we have many detailed accounts of the widespread acceptance of the 27 books that Protestants accept in their canon.
Since we agree with that, it is irrelevant to the discussion. I have already shown that there are many difficulties in that discussion, too. Note how Jason restricts the canon argument to the New Testament, so he can sidestep the whole Deuterocanonical dispute. Clever, again, but no dice.
When patristic sources refer to the gospel of Matthew or the second epistle of Peter, we have detailed knowledge of what they're referring to. When Eusebius, Jerome, or some other source comments on how widely accepted such a document is, we're being given a relatively specific assessment of the acceptance of a specific document. A reference to the church isn't as specific. Irenaeus, Cyprian, and John Chrysostom may all refer to the church, but have three different definitions in mind.
How so? This is another technique of Jason's: throw out the second-hand, subjective description of some notion that he wishes to convey, without any documented details. Why would I trust him for what these men believe? He's no scholar. He has shown himself consistently shoddy with arguments and sources, as I have demonstrated time and again in my debates with him, and again now. The reader can see how I copiously document everything. I don't expect anyone to accept my bald word, as if I am any kind of expert, as Jason does. So here he throws out a doubtful assertion, with no documentation.
Moreover, these are very strange choices for fathers with regard to the papacy and primacy of Rome. Few of these men are more vociferous in their support of the papacy as St. John Chrysostom. I could cite reams and reams of stuff, but instead, I'll send readers to Phil Porvaznik's excellent survey, St. John Chrysostom on the Apostle Peter. The evidence is manifestly overwhelming. Likewise, see his paper, St. Cyprian on the Church and the Papacy. We have already examined St. Irenaeus at some length. His beliefs do not help Jason's case at all. See also the excellent related papers:
Rome has Spoken, the Case is Closed, Dom John Chapman
St. Athanasius, Arianism, and the Holy See, Dom John Chapman
St. Jerome and Rome, Dom John Chapman
We also see how St. John Chrysostom regarded the papacy, in the ways he interacted with popes. He appealed to Pope Innocent I over against eastern bishops who opposed him, and Empress Eudoxia of Constantinople, after he had been deposed from his see in 404. Innocent I had also aided St. Jerome in his battles against John, Bishop of Jerusalem. Earlier, Pope Julius I reversed the sentence of an eastern council against St. Athanasius after the saint appealed to him (thus illustrating the nature of papal jurisdiction once again). Later, St. Cyril appealed to Pope Celestine against Nestorius (as did Nestorius too!). The heretic lost. This is what popes did and continue to do: enforce orthodoxy.
However, if all three refer to the gospel of Matthew, we can be confident that they're referring to the same document and that we possess it today.
Indeed, we can, but that is neither here nor there in this discussion. We can also refer to Pope Victor in the late second century determining the date of Easter, and know exactly what we are dealing with: the successor of Peter and the head of the Church. It's easy as pie to pick out Matthew: which was scarcely disputed at all, rather than comparing the papacy to the entire canon issue. But it is a double standard (extremely common in anti-catholic polemics).
Any argument for widespread belief in church infallibility would have to involve more than just vague references to "the church", "apostolic succession", the evidential value of agreeing with what Christians have historically believed, etc.
There is much, much more than vague references, and without question Jason is too informed about history to not know that. He's been arguing for these absurd things for so long I think he actually believes them himself. But this is how anti-Catholics reason. The devil is in the details, so they remain deliberately vague and sophistical, and engage in constant obfuscation and obscurantism. One might think I am being very judgmental and/or cynical. But I have almost twenty years of experience in dealing with the anti-Catholic mentality. I've seen it all. I know what I am talking about, from firsthand experience. All the old debates remains online, on my blog. These kinds of things are among the several reasons why I no longer debate them, and why this reply is an exception to my norm, as I stated in the beginning.
In other words, in my experience, Protestants are citing highly specific and convincing evidence for a highly specific conclusion,
That's certainly not evident in this display of "argumentation" from Jason!
whereas advocates of church infallibility are being much more vague in their argumentation and conclusions.
Right. You, the reader, can judge. Read his side, and mine, and make up your own mind: who is dealing with the relevant facts and who is not, and who is interacting with whom.
The gap between the patristic data and a specific system of church infallibility like Catholicism or Orthodoxy is large. The patristic evidence is too vague to lead us to the specific systems of infallibility that are popularly advocated today.
Polemical pablum . . . It is time to cite Cardinal Newman again, in conclusion of Part II. Newman biographer Ian Ker recounted what the Cardinal thought about Catholic historian Joseph Dollinger's defection in 1870, when the latter refused to accept the dogma of papal infallibility. I also cite Letter to the Duke of Norfolk at length, with regard to the issue of the proper relationship of history to Catholic faith and dogma:
But he wondered why 'private judgment' should 'be unlawful in interpreting Scripture against the voice of authority, and yet be lawful in the interpretation of history?' The Church certainly made use of history, as she also used Scripture, tradition, and human reason; but her doctrines could not be 'proved' by any of these 'informants', individually or in combination. No Catholic doctrine could be fully proved (or, for that matter, disproved) by historical evidence -- 'in all cases there is a margin left for the exercise of faith in the word of the Church.' Indeed, anyone 'who believes the dogmas of the Church only because he has reasoned them out of History, is scarcely a Catholic'.
(John Henry Newman: A Biography, Oxford University Press, 1988, p. 684; citing Difficulties of Anglicans, II [Letter to the Duke of Norfolk, 1875], 309, 311-312)
As regards the relation between history and theology, Newman is unequivocal in his criticism of Dollinger and his followers . . . 'I think them utterly wrong in what they have done and are doing; and, moreover, I agree as little in their view of history as in their acts.' It is not a matter of questioning the accuracy of their historical knowledge, but 'their use of the facts they report' and 'that special stand-point from which they view the relations existing between the records of History and the communications of Popes and Councils'. Newman sums up the essence of the problem: 'They seem to me to expect from History more than History can furnish.' The opposite was true of the Ultramontanes, who simply found history an embarrassing inconvenience.
(Ibid., 684-685; same primary source)
Towards Dollinger, whose quarrel with the Council had become a quarrel with the Church, Newman was still sympathetic, but critical. Characteristically, he diagnosed Dollinger's crisis as fundamentally a failure of imagination. Dollinger was not a 'philosophical historian', in the sense that 'He does not throw himself into the state of things which he reads about -- he does not enter into the position of Honorius, or of the Council 40 years afterwards. He ties you down like Shylock to the letter of the bond, instead of realizing what took place as a scene.' Newman could not understand how Dollinger could accept the council of Ephesus, for example, which was notorious for intrigue and violence, and not the recent one. Perhaps, he shrewdly guessed, 'by this time the very force of logic, to say nothing of philosophy, has obliged him to give up Councils altogether'.
(Ibid., p. 665; citing Letters and Diaries, Vol. XXVI, 120)
. . . The other main objection made to the Council is founded upon its supposed neglect of history in the decision which its Definition embodies. This objection is touched upon by Mr. Gladstone in the beginning of his Pamphlet, where he speaks of its "repudiation of ancient history," . . .
But it is not every one that can read its pages rightly; and certainly I cannot follow Mr. Gladstone's reading of it. He is too well informed indeed, too large in his knowledge, too acute and comprehensive in his views, not to have an acquaintance with history, far beyond the run of even highly educated men; still when he accuses us of deficient attention to history, one cannot help asking, whether he does not, as a matter of course, take for granted as true the principles for using it familiar with Protestant divines, and denied by our own, and in consequence whether his impeachment of us does not resolve itself into the fact that he is Protestant and we are Catholics. Nay, has it occurred to him that perhaps it is the fact, that we have views on the relation of History to Dogma different from those which Protestants maintain? And is he so certain of the facts of History in detail, of their relevancy, and of their drift, as to have a right, I do not say to have an opinion of his own, but to publish to the world, on his own warrant, that we have "repudiated ancient history"? He publicly charges us, not merely with having "neglected" it, or "garbled" its evidence, or with having contradicted certain ancient usages or doctrines to which it bears witness, but he says "repudiated." He could not have used a stronger term, supposing the Vatican Council had, by a formal act, cut itself off from early times, instead of professing, as it does (hypocritically, if you will, but still professing) to speak, "supported by Holy Scripture and the decrees both of preceding Popes and General Councils," and "faithfully adhering to the aboriginal tradition of the Church." Ought any one but an oculatus testis, a man whose profession was to acquaint himself with the details of history, to claim to himself the right of bringing, on his own authority, so extreme a charge against so august a power, so inflexible and rooted in its traditions through the long past, as Mr. Gladstone would admit the Roman Church to be?
. . . [referring to the Old Catholics] Extensive as may be their historical knowledge, I have no reason to think that they, more than Mr. Gladstone, would accept the position which History holds among the Loci Theologici as Catholic theologians determine it; and I am denying not their report of facts, but their use of the facts they report, and that, because of that special stand-point from which they view the relations existing between the records of History and the enunciations of Popes and Councils. They seem to me to expect from History more than History can furnish, and to have too little confidence in the Divine Promise and Providence as guiding and determining those enunciations.
Why should Ecclesiastical History, any more than the text of Scripture, contain in it "the whole counsel of God"? Why should private judgment be unlawful in interpreting Scripture against the voice of authority, and yet be lawful in the interpretation of history? There are those who make short work of questions such as these by denying authoritative interpretation altogether; that is their private concern, and no one has a right to inquire into their reason for so doing; but the case would be different were one of them to come forward publicly, and to arraign others, without first confuting their theological præambula, for repudiating history, or for repudiating the Bible.
. . . Historical evidence reaches a certain way, more or less, towards a proof of the Catholic doctrines; often nearly the whole way; sometimes it goes only as far as to point in their direction; sometimes there is only an absence of evidence for a conclusion contrary to them; nay, sometimes there is an apparent leaning of the evidence to a contrary conclusion, which has to be explained;. . . There is nothing of bondage or "renunciation of mental freedom" in this view, any more than in the converts of the Apostles believing what the Apostles might preach to them or teach them out of Scripture.
What has been said of History in relation to the formal Definitions of the Church, applies also to the exercise of Ratiocination. Our logical powers, too, being a gift from God, may claim to have their informations respected; and Protestants sometimes accuse our theologians, for instance, the medieval schoolmen, of having used them in divine matters a little too freely. Still it has ever been our teaching and our protest that, as there are doctrines which lie beyond the direct evidence of history, so there are doctrines which transcend the discoveries of reason; and, after all, whether they are more or less recommended to us by the one informant or the other, in all cases the immediate motive in the mind of a Catholic for his reception of them is, not that they are proved to him by Reason or by History, but because Revelation has declared them by means of that high ecclesiastical Magisterium which is their legitimate exponent.
What has been said applies also to those other truths, with which Ratiocination has more to do than History, which are sometimes called developments of Christian doctrine, truths which are not upon the surface of the Apostolic depositum—that is, the legacy of Revelation,—but which from time to time are brought into form by theologians, and sometimes have been proposed to the faithful by the Church, as direct objects of faith. No Catholic would hold that they ought to be logically deduced in their fulness and exactness from the belief of the first centuries, but only this,—that, on the assumption of the Infallibility of the Church (which will overcome every objection except a contradiction in thought), there is nothing greatly to try the reason in such difficulties as occur in reconciling those evolved doctrines with the teaching of the ancient Fathers; such development being evidently the new form, explanation, transformation, or carrying out of what in substance was held from the first, what the Apostles said, but have not recorded in writing, or would necessarily have said under our circumstances, or if they had been asked, or in view of certain uprisings of error, and in that sense being really portions of the legacy of truth, of which the Church, in all her members, but especially in her hierarchy, is the divinely appointed trustee.
Such an evolution of doctrine has been, as I would maintain, a law of the Church's teaching from the earliest times, and in nothing is her title of "semper eadem" more remarkably illustrated than in the correspondence of her ancient and modern exhibition of it. As to the ecclesiastical Acts of 1854 and 1870, I think with Mr. Gladstone that the principle of doctrinal development, and that of authority, have never in the proceedings of the Church been so freely and largely used as in the Definitions then promulgated to the faithful; but I deny that at either time the testimony of history was repudiated or perverted. The utmost that can be fairly said by an opponent against the theological decisions of those years is, that antecedently to the event, it might appear that there were no sufficient historical grounds in behalf of either of them—I do not mean for a personal belief in either, but—for the purpose of converting a doctrine long existing in the Church into a dogma, and making it a portion of the Catholic Creed. This adverse anticipation was proved to be a mistake by the fact of the definition being made.
(A Letter Addressed to the Duke of Norfolk on Occasion of Mr. Gladstone's Recent Expostulation [Certain Difficulties Felt by Anglicans in Catholic Teaching] --online; Chapter 8: "The Vatican Council", [book and chapter both linked to the left], Volume 2, 1874; reprinted by Longmans, Green, and Co., London, 1900, 299, 301-305, 308-315, 339-340; see also Chapter 9, "The Vatican Definition," for an excellent discussion of many epistemological and ecclesiological aspects of infallibility)