"Children in school learn what we call definitions. A definition is an explanatory statement which tells us exactly what a certain thing is, as "an island is a tract of land completely surrounded by water." God also gives us definitions in His Word. We could cite hundreds of examples! He tells us exactly what certain things are. And in the passage quoted above God tells us exactly what the second death is. "And death and hell were cast into the lake of fire. THIS IS THE SECOND DEATH." Now let me make this a little plainer. Definitions of men can be given backward. For instance, the definition, "An island is a tract of land completely surrounded by water," can be given thus: "A tract of land completely surrounded by water is an island." This is but another way of stating the same fact. It does not, in any way, change the meaning."
"Now let us try this on the definition of the second death. The Bible states it thus: "Death and hell were cast into the lake of fire. This is the second death." Now let us turn this statement around for clarity. "The second death is death and hell cast into the lake of fire." Therefore we have exactly the same meaning either way it is stated. What is the second death? IT IS THE FIRST DEATH AND HELL CAST INTO THE LAKE OF FIRE! This fact is very important. Most Christians and nearly all preachers read the Word of God very superficially. They read and suppose that the second death is men being tortured forever in the lake of fire. Yet there is absolutely nothing in this passage about men! The verse that follows the one we are considering speaks of men being cast into the lake of fire. But not this one! It is the state of death and the condition of hell that are cast into the lake of fire. The second death is not men cast into the lake of fire, or men tormented or tortured forever. That’s not in the Book! The Holy Spirit has made it very simple and plain. The second death is the first death and hell cast into the lake of fire. That is the Holy Spirit’s definition, not mine."
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https://www.godfire.net/eby/Rev/rev231.html
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"All Bible statements prove that the two deaths are absolutely UNLIKE, and that the two are opposite and antagonistic. The second death undoes all the work of the first death in the same manner that the last Adam undid all the work of the first Adam. Not to nullify the purpose being wrought out by the plan of God in the firsts, but to bring a release from the firsts in a MUCH MORE manner of majesty and glory and power and scope of converge, into the greater and more glorious things of God. Creation was made subject to vanity for a purpose! Sin was allowed for wise ends, but when those ends have been secured it will have to cease to exist. The purpose is not nullified, but the means whereby the purpose has been executed shall be done away. Discipline is a means to an end, but not the end itself, it leads up to the ‘AFTERWARDS YIELDING THE PEACEABLE FRUIT OF RIGHTEOUSNESS.’
"The first Adam died to God and righteousness, and became alive unto sin. The last Adam died unto sin (Rom. 6:10), and liveth unto God, and so fulfilleth all righteousness. The first made all men sinners, the last makes all men righteous. The lives and the deaths of the two Adams are thus greatly contrasting the one to the other. The first death was a transition from life to death, whereas the second death is a transition from corruption to incorruption, from mortality to immortality. Transformed from the carnal mind to the spiritual mind, which is life and peace, which transformation is wrought by a dying out to the one realm, to become alive to the higher realm. Because — the second death is prepared to purge out and burn away sin and its results, and so doing cleanse all of God’s universe."