"...no biblical passage teaches that Scripture is the formal authority or rule of faith in isolation from the Church and Tradition. Sola scriptura can’t even be deduced from implicit passages."
The assertion that Sola Scriptura is unbiblical is a standard Roman Catholic objection, and has been dealt with in a succinct fashion here:
One must also wonder why so many uniquely Roman Catholic doctrines contradict Scripture?
"Word in Holy Scripture often refers to a proclaimed, oral teaching of prophets or apostles. What the prophets spoke was the word of God regardless of whether or not their utterances were recorded later as written Scripture."
This argument does not work because Sola Scriptura does not deny that the Word of God was once communicated orally. All the principle says is that Scripture alone is the final (not only) standard of authority for the Christian church. Scripture alone is the only infallible rule of faith or spiritual standard for Christians to use. We should not endorse somebody's ideas just because he or she claims to be a prophet of God (Deuteronomy 13:1-5; 1 Thessalonians 5:21).
"Protestants often quote the verses in the Bible where corrupt traditions of men are condemned (e.g., Matt. 15:2–6; Mark 7:8–13; Col. 2:8). Of course, Catholics agree with this. But it’s not the whole truth. True, apostolic Tradition also is endorsed positively. This Tradition is in total harmony with and consistent with Scripture."
Tradition that is in perfect harmony with the teaching of Scripture poses absolutely no problem for Sola Scriptura. What needs to be proven beyond reasonable doubt is that inspired extra-biblical oral traditions exist and that Christ appointed an office which infallibly interprets Scripture.
Next, Dave Armstrong goes on to claim that Jesus and the apostles accepted oral tradition (in the same sense that Rome claims to possess inspired tradition). The Roman Catholic author cites four examples of what he considers as proof which are addressed as follows:
"The reference to “He shall be called a Nazarene” cannot be found in the Old Testament, yet it was “spoken by the prophets” (Matt. 2:23). Therefore, this prophecy, which is considered to be “God’s word,” was passed down orally rather than through Scripture."
The above claim has been soundly refuted by the New Advent Catholic Encyclopedia online:
"In the manuscripts of the New Testament, the name occurs in a great orthographical variety, such as Nazaret, Nazareth, Nazara, Nazarat, and the like. In the time of Eusebius and St. Jerome (Onomasticon), its name was Nazara (in modern Arabic, en Nasirah), which therefore, seems to be the correct name; in the New Testament we find its derivatives written Nazarenos, or Nazoraios, but never Nazaretaios. The etymology of Nazara is neser, which means "a shoot". The Vulgate renders this word by flos, "flower", in the Prophecy of Isaias (11:1), which is applied to the Saviour. St. Jerome (Epist., xlvi, "Ad Marcellam") gives the same interpretation to the name of the town."
So, Dave Armstrong's argument is with a Roman Catholic source and not any proponents of Sola Scriptura.
"In Matthew 23:2–3, Jesus teaches that the scribes and Pharisees have a legitimate, binding authority based “on Moses’ seat,” but this phrase or idea cannot be found anywhere in the Old Testament. It is found in the (originally oral) Mishnah, which teaches a sort of “teaching succession” from Moses on down."
Attempting to prove the Papal office from Matthew 23 is plagued with problems. There was no Papal office in Israel. When Jesus referred to the seat of Moses, He was simply referring to a position of authority. It was one that belonged to several people, not to a single person who was taken as supreme over them: "Then Jesus spoke to the crowds and to His disciples, saying: “The scribes and the Pharisees have seated THEMSELVES in the chair of Moses..." See this article for more details:
This footnote from the Roman Catholic New American Bible Revised Edition says the following regarding the seat of Moses:
"[2-3] Have taken their seat . . . Moses: it is uncertain whether this is simply a metaphor for Mosaic teaching authority or refers to an actual chair on which the teacher sat. It has been proved that there was a seat so designated in synagogues of a later period than that of this gospel."
"In 1 Corinthians 10:4, Paul refers to a rock that “followed” the Jews through the Sinai wilderness. The Old Testament says nothing about such miraculous movement. But rabbinic tradition does."
It is certainly true that the Apostolic writers appealed to extra-biblical sources. However, all this proves is that extra-biblical sources sometimes contained statements that the Apostles deemed useful in articulating their points.
"As Jannes and Jambres opposed Moses” (2 Tim. 3:8). These two men cannot be found in the related Old Testament passage (Ex. 7:8ff.) or anywhere else in the Old Testament."
Could it be that the Holy Spirit simply moved Paul to incorporate the two names into his inspired epistle? Sola Scriptura does not deny that other books or materials are of use in Scripture being written. So none of what Dave Armstrong is saying poses a problem.
"In the Council of Jerusalem (Acts 15:6–30), we see Peter and James speaking with authority. This Council makes an authoritative pronouncement (citing the Holy Spirit) that was binding on all Christians."
The Council of Jerusalem is actually supportive of Sola Scriptura and harmful to Roman Catholic claims of Papal supremacy. See this article for more details:
"Christianity was derived in many ways from the Pharisaical tradition of Judaism. The Sadducees, on the other hand, rejected the future resurrection of the soul, the afterlife, rewards and retribution, demons and angels, and predestinarianism. The Sadducees also rejected all authoritative oral teaching and essentially believed in sola scriptura. They were the theological liberals of that time."
The standard that corrects the theological errors of the Pharisees and Sadducees is Scripture. That is what Jesus used when confronting the two groups. It is also important to keep in mind that there was no infallible teaching Magisterium for the Jews. Despite the rejection of the resurrection of the dead by the Sadducees, the concept was still clearly attested to in the Old Testament (Job 19:25-26; Psalm 16:10; Daniel 12:2; Isaiah 26:19). Both the Pharisees and the Sadducees upheld corrupt oral traditions as having equal authority with Scripture.
"Old Testament Jews did not believe in Sola Scriptura. So the people did indeed understand the law (cf. Neh. 8:8, 12), but not without much assistance—not merely upon hearing. Likewise, the Bible is not altogether clear in and of itself but requires the aid of teachers who are more familiar with biblical styles and Hebrew idiom, background, context, exegesis and cross-reference, hermeneutical principles, original languages, etc."
The reason that the Jews in Babylon had difficulties in interpreting Scripture is that they were unfamiliar with pure Hebrew. After all, they were in captivity for seventy years and learned Aramaic. Nonetheless, some parts of the Bible are harder to understand than others. However, infallibility is not a requirement for accurately interpreting and applying Scripture. The people would have listened to the teaching of the Law because Ezra had judicial authority and not because he was bestowed some gift of infallibility. Should we reject the Papacy, Marian dogmas, and the Eucharist for the reason that such concepts were not believed by the Old Testament Jews?
"This passage [2 Timothy 3:16-17] doesn’t teach formal sufficiency, which excludes a binding, authoritative role for Tradition and Church. Protestants extrapolate onto the text what isn’t there. If we look at the overall context of this passage, we can see that Paul makes reference to oral Tradition three times (cf. 2 Tim. 1:13–14; 2:2; 3:14)."
None of the Bible verses that the author mentions tell us what or where we can get the specific statements of the Apostle Paul. The claim that extra-biblical oral tradition exists in those passages is assumed rather than proved. It other words, the Roman Catholic apologist is guilty of circular reasoning. Could it be that what Timothy had learned came from the Old Testament Scriptures themselves?
"If 2 Timothy 3 proves the sole sufficiency of Scripture, then, by analogy, Ephesians 4 would likewise prove the sufficiency of pastors and teachers for the attainment of Christian perfection. In Ephesians 4, the Christian believer is equipped, built up, brought into unity and mature manhood, and even preserved from doctrinal confusion by means of the teaching function of the Church. This is a far stronger statement of the perfecting of the saints than 2 Timothy 3, yet it does not even mention Scripture.
So if all non-scriptural elements are excluded in 2 Timothy, then, by analogy, Scripture would logically have to be excluded in Ephesians. It is far more reasonable to recognize that the absence of one or more elements in one passage does not mean that they are nonexistent. The Church and Scripture are both equally necessary and important for teaching."
The author's claims are fallacious, considering how the context of Ephesians 4 does not match that of 2 Timothy 3. 2 Timothy 3:16-17 specifically points us to a rule of faith. Ephesians 4:11-15 is discussing unity in Christ Jesus and the diverse gifts of the Holy Spirit. The text from Ephesians pertains to the administration of the principles found within the guide (Scripture), namely brotherly fellowship and edification in the faith. The context of 2 Timothy 3:16-17 identifies our spiritual standard of discernment. 2 Timothy 3 discusses the means by which edification in the faith is to be done. Thus, the authority of ministers does not extend beyond that authoritative written standard. Scripture equips the faithful man of God for every good work. 2 Timothy mentions no other rule of faith. So this Roman Catholic objection is actually a false analogy.
The author argues that Sola Scriptura is a circular position, which has been already been addressed here:
"This is similar to people on two sides of a constitutional debate both saying, “Well, we go by what the Constitution says, whereas you guys don’t.” The U.S. Constitution, like the Bible, is not sufficient in and of itself to resolve differing interpretations. Judges and courts are necessary, and their decrees are legally binding. Supreme Court rulings cannot be overturned except by a future ruling or constitutional amendment. In any event, there is always a final appeal that settles the matter."
This comparison is highly deceptive because the constitution and the appointed judges who provide interpretations for lawmakers are fallible (whereas the pope claims to have been bestowed a charisma of infallibility in proclaiming dogmas). Secondly, it is merely assumed by Catholics that the church must be governed by an earthly head. That idea cannot even be found in the New Testament. Moreover, God is perfectly capable of revealing His truth to children or even the uneducated. Human leadership can and has become corrupt (1 Samuel 8; 2 Kings 22:8-13). What we should be striving for is unity according to Scripture. God given revelation is the final court of appeal that should settle doctrinal disputes.