Jesus is the Author AND Finisher of our faith, therefore OSAS.
Sure... and what do you do with verses that indicate the loss of faith, like Matthew 18, where the guy is forgiven all his debts (corresponding to the righteousness of faith, defined as being forgiven Ro 4:6-8), but, afterward, the forgiveness is rescinded (meaning his righteousness of faith has been forgotten--as God says, He is able to forget not only sin but also righteousness)?
You see, I need an explanation that is able to account for all that is taught in the Bible, not just one or two strips of Scripture here and there.
That said, I used to interpret the concept of this Book of Life as only including those saved and that this book of eternally saved individuals existed in the beginning of Creation. In God's mind, since He knows all, that is true. But for us, we only see life from birth to death in time, day by day, year by year. So to us, it is a book with our names added when we are born and kept there or blotted out depending on what happens in life (we receive Christ and persevere or not). At the end of time when all have been accounted for, it is for us The Eternal Book of Life; but not before since one can be blotted out. So what does this mean? The Book of Life (how Gid wants us to understand it since we do not possess omniclscience), therefore starts with everyone's name who ever lived life, written in as all unbelievers when we are born but then ends with only the saved believers. And that's my perspective, not God's, for He sees the end from the beginning. My two cents ... go figure.
My issue with this interpretation is that "God's Book", "the Lamb's Book of Life", etc, is only mentioned where God's people are concerned : in Exodus, after God's people sinned a great sin, Moses said, "No, blot me out of Your Book", and the answer is, "No, the one who has sinned against Me I will blot out of My Book"; in Revelation 3, it is mentioned with regard to the Church, where those who have defiled their garments are those who will be blotted out (because they are contrasted against those who are worthy, who will walk with Christ in White, who He will never blot out of His Book), as it always has been said, "the one who has sinned against Me I will blot out".
So, what does all of this mean?
Righteousness is what corresponds with life.
Unrighteousness is what corresponds with death.
Therefore, the righteous are in His Book of the living.
When Hosea 1 says "No Mercy" and "Not My People", it means that God's People are, by definition, those upon whom God has mercy, this is the source of life--mercy. Those who retain faith in Christ, and who walk in faith, are those upon whom God has mercy, and this is righteousness of faith (Ro 4:6-8) whereby they overcome the world.
Those who are "blotted out of God's Book" are those who are "cut off" from God's people (eg, Ro 11:17+) for not retaining faith, but, also, not
walking in faith (Ro 1:17, 14:5, 23), is what it seems.
So, when someone is "cut off", "blotted out", then it
becomes that God
never said to them "I will not lose you", because their righteousness of faith has been "forgotten"--therefore, still, Christ will "lose none", but, also, people can be blotted out/forgotten/lose salvation (which, from another perspective, they don't "lose" salvation, because, from that other perspective, God "forgets", so it becomes that they never have had it).
The conclusion, then--the practical application--is that we should trust God like OSAS says.