For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
ἐξαλείφω (eksaleíphō): Ek "wholly out from" + Aleipho "smear". (Rev 3:5, Acts 3:19, Col 2:14, etc)
It means to completely erase/wipe away/remove/obliterate completely - to remove totally from a previous state as if it never was (such as we might erase pencil marks). It was used in reference to the scraping out of a record of debt, rubbing out the impression of a wax seal, cancelling obligations or entitlements, etc.
It is interesting that the same word is used for the wiping out of our sins as the wiping out of our name from the book of life.
It's hard to comprehend that someone could think that an unbeliever gets blotted out of a book that they were never entered into and that a believer can't be blotted out because he was entered into it before the foundation of the world.
A lawyer or a prosecutor must get to the truth of a matter so it can be exposed before the court. It is necessary for us to judge for ourselves as to what the Scripture in context is really saying. If you were told that unless you came to the annual meeting your membership would be cancelled and you would have your name struck off the register. Then it's plain as day what this would mean.
To the Church in Sardis they are given a condition to meet so they would not be blotted out of the book of life. Failing to meet that condition would mean a cancellation of any part that the book promised for them. The same applies regarding the taking away from the truth of the Bible or the adding to it. This would also mean a cancellation of the person's future eternal destiny. A notion that an unbeliever is blotted out of the book of life because they did not believe is such a contradiction of terms it could never be accepted as truth. If an unbeliever is recorded in the book of life they would not need to believe the gospel and would go to heaven regardless.
Of course the truth is only believers are recorded in the book and only believers can be blotted out of that book. There is no other way around it. An honest look at these truths will suffice so that we don't uphold error and call it truth.
There actually is another way around it, Anthony. There is not one single member of the church, the body of Christ, that can lose their salvation. The book of Revelation is prophetic for Israel. However, believers today, during God's Ephesians 3:2 "dispensation of grace", are "sealed unto the day of redemption" upon belief (Eph 4:30). Faith alone is the requirement for ETERNAL salvation during this age of God's grace (Eph 2:8).
To imply that a believing member of Christ's body, who is COMPLETE in Him (Col 2:10), could lose their salvation completely undermines what the GRACE of God means for today. Those under God's grace will NEVER be appointed to God's wrath. They are appointed to obtain salvation by God's grace through faith (1 Thes 5:9).
Prophecy is not for the church, the body of Christ. Prophecy is for Israel. The "mystery" (not prophecy) that was revealed to Paul from Christ ascended in glory is where the church, the body of Christ, will find doctrine pertaining to it (Romans through Philemon). Rightly dividing the word of truth, the gospel of OUR salvation (Eph 1:13), is the key to understanding these truths.
2 Tim 2:15
"Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the word of truth."