A Brief Doctrine of Scripture
In setting out to write a summary of the doctrine of scripture, it is necessary first to note that this is not a summary of the teachings within scripture but rather what the teachings within scripture say about scripture. There are, of course, many who view this to be circular logic, but it is no more circular than someone appealing to reason to explain the principles of reason.
There are several elements to the doctrine of scripture that I will list and explain in brief below.
"All Scripture is inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness; so that the man of God may be adequate, equipped for every good work." - 2 TIMOTHY 3:16-17 NASB
The term inspired here literally translates God-breathed. Just as we see in the Garden of Eden when God breathed the breath of life into Adam, and he became a living soul, God breathed His truth into human writers the result of which is inspired scripture.
In Millard J. Erikson's book Christian Theology: 3rd Edition he defines inspiration as follows:
"the supernatural influence of the Holy Spirit on the scripture writers that rendered their writings an accurate record of the revelation or that resulted in what they wrote being the Word of God." (169)
He goes on to say that this is simply a preliminary definition that requires amplification.
It is essential concerning the inspiration of scripture to see that the New Testament writers believed themselves to be writing scripture. For example when Paul writes in 1 Timothy 5:18 and says "you shall not muzzle an ox when it treads out the grain" he is not quoting the Old Testament but from Jesus in Luke 10:7. More commonly used in this argument is 2 Peter 3:15-16 in which Peter, defending the Apostle Paul, says that ignorant and unstable people twist Paul's words to their own destruction "as they do the OTHER scriptures." (emphasis mine)
It is also my view that an understanding of inspiration necessarily speaks to the authority of scripture. As we have already seen in 1 Timothy 3, scripture is inspired or God-breathed and is thus used for correction and training in righteousness. The reason why the scriptures correct and train us is because of authority, and the reason they have authority is that they are inspired.
Inerrancy and Infallibility
Basically, inerrancy means the Bible is valid in all that it teaches. This is closely connected with infallibility, which is roughly understood as incapable of erring as God cannot lie.
"Sanctify them in the truth; Your word is truth." - JOHN 17:17 NASB
"The sum of Your word is truth, And every one of Your righteous ordinances is everlasting." - PSALMS 119:160 NASB
In conjunction with the case made about inerrancy, we see in John's gospel that God's word is truth. In Numbers, Titus, and Hebrews, we see that God cannot lie. The Psalmist adds that the sum of God's word is truth. Therefore together, we have God's revelation, which is true in all that it teaches and without error.