Short answer
No. The verse before it speaks of the scriptures Timothy had known "from a child". When Timothy was a child, no book of the New Testament had been written. So the writer meant the Hebrew scriptures (the Old Testament). The list of 27 books of the New Testament first appears in the year 367, about three centuries after Paul. Using the verse to prove the whole Bible is also circular. The letter is trusted because it is in the Bible, and the Bible because the letter says so. Some Christians say only the first, original writings were inspired. But the verse speaks of the copies Timothy knew as a boy. Paul himself marks some of his words as his own, not the Lord's. Islam teaches that God (﷾) sent scripture to earlier prophets. The Qur'an is His word to the Prophet Muhammad (ﷺ), and it asks to be tested (4:82).
Full explanation
How Christians use the verse
For many Christians this is the key verse on the Bible's authority: all scripture is given by inspiration of God (﷾). They read it as covering every book of the Old and New Testaments. The leading statement of evangelical Christians (those who treat the Bible as the final authority) adds that inspiration strictly applies to the original writings. It holds that these can be recovered from the copies.
“And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:”
The best-known evangelical statement on the Bible. It affirms that Scripture is without error in all it teaches, and that inspiration, strictly speaking, applies only to the original manuscripts (the autographs), which no longer exist. Copies and translations are the word of God only so far as they faithfully represent the original.
Read the verse before it
The writer tells Timothy to keep to what he has learned, since "from a child" he has known the holy scriptures. The scriptures a Jewish-raised child knew were the Law, the Prophets and the Writings, the three parts of the Hebrew scriptures. Acts already calls Timothy a disciple when Paul, a Christian missionary of the first century, met him. That was around the year 49 or 50. Paul's earliest surviving letter dates from about 50. So when Timothy was a child, not one book of the New Testament existed.
“But continue thou in the things which thou hast learned and hast been assured of, knowing of whom thou hast learned them;”
“And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:”
“Then came he to Derbe and Lystra: and, behold, a certain disciple was there, named Timotheus, the son of a certain woman, which was a Jewess, and believed; but his father was a Greek:”
“Him would Paul have to go forth with him; and took and circumcised him because of the Jews which were in those quarters: for they knew all that his father was a Greek.”
A standard textbook. It dates Paul's earliest letters to around 50 CE, Mark to about 65-70, Matthew and Luke to about 80-85, and John to about 90-95, and notes that Jesus spoke Aramaic while the Gospels were written in Greek by authors who do not name themselves. It also says Paul did not know Jesus during Jesus' lifetime and came to faith only after the crucifixion.
Who wrote 2 Timothy
The letter names Paul as its writer. Most critical scholars, however, hold that 1 and 2 Timothy and Titus were written after Paul's death by a follower using his name. On either view the point about Timothy's childhood stands. Either way, the verse is being asked to vouch for books it never names.
Argues that 1 and 2 Timothy and Titus were not written by Paul but by a later follower writing in his name, a view Ehrman reports is held by most critical scholars.
There was no New Testament to mean
The churches disagreed for three centuries about which books belonged. Some read the Shepherd of Hermas, an early Christian writing, as scripture. Some rejected Hebrews, James or Revelation. Eusebius, a church historian writing around 325, still listed James, Jude, 2 Peter and two letters of John as disputed. The first surviving list of exactly the 27 books of today's New Testament comes from a letter of Athanasius, a bishop, in the year 367.
Traces how the churches came to agree on the New Testament. For three centuries books such as Hebrews, James and Revelation were disputed, and some read the Shepherd of Hermas as scripture. Athanasius' letter of 367 is the first surviving list of exactly the twenty-seven books; councils at Hippo (393) and Carthage (397) confirmed it; the Syrian churches long used a shorter set.
Eusebius sorts the Christian writings of his day into those accepted by all, those disputed, and those rejected. Among the disputed he lists the letters of James and Jude, the second letter of Peter, and the second and third letters of John.
Athanasius, bishop of Alexandria, lists the books he counts as scripture. His New Testament list is the twenty-seven books of today's New Testament, the earliest surviving list of exactly these books and no others.
Not the originals either
Some Christians answer that only the original writings were inspired. But the verse says nothing about originals. It speaks of the scriptures Timothy had in his hands as a boy, and those were copies. By Timothy's day the books of the Old Testament were centuries old. People read them in copies, not in the first scrolls. So the verse Christians use for the "originals" is not about the originals at all.
“And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:”
The best-known evangelical statement on the Bible. It affirms that Scripture is without error in all it teaches, and that inspiration, strictly speaking, applies only to the original manuscripts (the autographs), which no longer exist. Copies and translations are the word of God only so far as they faithfully represent the original.
A circle, not a proof
When this verse is offered as the proof that the Bible is inspired, ask why the letter should be trusted. The only answer it can give is that it is in the Bible. That is a circle. And Paul himself separates what the Lord commanded from what he says on his own judgment. Paul writes, "to the rest speak I, not the Lord", and "I have no commandment of the Lord: yet I give my judgment". He adds only, "I think also that I have the Spirit of God" (7:40). The Bible keeps his own judgment in the book called God's (﷾) word. The Qur'an does not ask to be believed on its own word. It challenges anyone in doubt to produce a chapter like it (2:23), and to search it for discrepancy (4:82).
“And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:”
“But to the rest speak I, not the Lord: If any brother hath a wife that believeth not, and she be pleased to dwell with him, let him not put her away.”
“Now concerning virgins I have no commandment of the Lord: yet I give my judgment, as one that hath obtained mercy of the Lord to be faithful.”
“But she is happier if she so abide, after my judgment: and I think also that I have the Spirit of God.”
“And if ye are in doubt as to what We have revealed from time to time to Our servant, then produce a Sura like thereunto; and call your witnesses or helpers (If there are any) besides Allah, if your (doubts) are true.”
“Do they not consider the Qur'an (with care)? Had it been from other Than Allah, they would surely have found therein Much discrepancy.”
Some Christians offer 2 Timothy 3:16 as proof that the whole Bible is God's (﷾) word: “All scripture is given by inspiration of God”.
Why trust 2 Timothy?
Because it is in the Bible.
Why trust the Bible?
Because 2 Timothy says all scripture is inspired. The argument has gone round in a circle.
Which scripture did the verse mean?
The verse before it speaks of the holy scriptures Timothy had known “from a child”. When Timothy was a child, not one book of the New Testament had been written.
So the verse cannot vouch for the New Testament. The first surviving list of its 27 books dates from the year 367, about three centuries after Paul.
Verse by verse
2 Timothy 3:15-16 — Second Epistle to Timothy, chapter 3, verses 15-16
“And that from a child thou hast known the holy scriptures, which are able to make thee wise unto salvation through faith which is in Christ Jesus. All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:”
Cited for
Christians read "all scripture" as the whole Bible, New Testament included.
The response
The verse before says these are the scriptures Timothy had known "from a child". No New Testament book existed in his childhood. So the writer means the Hebrew scriptures.
Where it lands — The verse cannot refer to a New Testament that did not yet exist.
2 Peter 3:16 — Second Epistle of Peter, chapter 3, verse 16
“As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction.”
Cited for
Christians point to 2 Peter, which puts Paul's letters beside "the other scriptures", to show that the New Testament was already counted as scripture.
The response
Eusebius records that 2 Peter was itself one of the disputed books in the early church. Using it to prove Paul, and Paul to prove the Bible, is the same circle. It also names no list of books. The 27-book list came three centuries later.
Where it lands — A disputed letter cannot settle which books are scripture.
1 Timothy 5:18 — First Epistle to Timothy, chapter 5, verse 18
“For the scripture saith, Thou shalt not muzzle the ox that treadeth out the corn. And, The labourer is worthy of his reward.”
Cited for
Christians point to 1 Timothy 5:18, which calls "The labourer is worthy of his reward" scripture, a saying also found in Luke 10:7.
The response
The verse quotes one saying, which Jesus used and which may have circulated on its own. It names no Gospel and no list of books. The 27-book list came three centuries later.
Where it lands — One quoted saying does not make a New Testament that did not yet exist.
Perspectives
Evangelical Christian
All scripture, Old and New Testament, is breathed out by God. 2 Timothy 3:16 states it. Inspiration belongs strictly to the original writings, which can be recovered from the copies.
2 Timothy 3:16 says all scripture is given by inspiration of God.
Rebuttal
Islam agrees that God (﷾) sent down scripture. But the verse does not say which books are scripture. It follows the scriptures Timothy knew "from a child", and no New Testament book existed then.
Evangelicals read the verse as covering the New Testament as well, and apply inspiration strictly to the original writings.
Rebuttal
A general rule still needs a list, and the verse names none. The 27-book list first appears in 367, and 2 Peter was among the books still disputed around 325. The verse also speaks of the copies Timothy knew as a boy, not of originals.
The Islamic perspective
The verse speaks of the Hebrew scriptures Timothy knew as a child. It cannot vouch for a New Testament that did not exist, and using it to prove the Bible is circular.
The verse before refers to scriptures Timothy had known from childhood, before any New Testament book was written.
The 27-book New Testament was first listed in 367, and several of its books were still disputed around 325.
Proving the Bible inspired from a verse inside the Bible is circular reasoning.
Paul marks some of his own instructions as his judgment rather than a command of the Lord.
Most critical scholars hold that 2 Timothy was written in Paul's name after his death.