Existence And Life

The concept of existing and the concept of being alive in a biological sense are not identical.  It does not matter whether there is an afterlife of any kind, but unless the concept of existing in an afterlife or existing as an uncaused cause prior to the universe was the same as the concept of ordinary life, they could not be distinguished or addressed as anything except the same idea.  Clearly, these ideas are not the same.  The relevance beyond the fundamental metaphysics of consciousness and the logical possibility of a certain type of afterlife pertain to explicitly Christian theology.  If basic existence as a consciousness and biological life are not synonymous concepts, does this mean that the Biblical descriptions of humans in hell do allow for eternal conscious torment for all unsaved beings despite using the language of death, destruction, and annihilation?

Not at all!  Whether or not the word soul refers to consciousness, restricted to a body or not, or to the mind-body composite that humans live as in daily life, the Biblical language still describes the nonexistence of the soul, rather than just a biological death that leads to eternal life with or without salvation.  The soul dies, not just the body and the mind's tie to it (Ezekiel 18:4, Matthew 10:28).  God is the only conscious being that does not depend on another being for its continued existence, which means the existence of human souls is metaphysically dependent on the divine consciousness.  Humans are not immortal by nature (1 Timothy 6:16).  The wicked are said to be dismissed from reality as one leaves a dream upon waking from it (Psalm 73:18-20).  The unsaved will perish (John 3:16).  Even if someone has not yet realized that Biblical ideas like the wages of sin being death (Romans 6:23) are actually in part affirmations of annihilationism, these other verses make it clear that the unsaved are not only said to biologically die, but to metaphysically cease to exist as conscious beings altogether.

One could cease to live as a biological creature and still hypothetically exist as an unembodied consciousness.  However, the Bible simply does not teach that this is the default for all unsaved beings.  All references to eternal life and death are rightly understood in light of the verses that explicitly say the wicked will cease to exist as conscious beings, like Ezekiel 18:4, 2 Peter 2:4, Matthew 10:28, and even John 3:16 of all verses.  Then, even if the Biblical teachings on hell were not as clearly affirmative of annihilationism as words can be without bypassing language, without looking straight into an author's actual mind to focus on concepts without the ambiguity of words, it would still be obvious that the wording of every verse about the ultimate punishment of unsaved beings other than those about the mark of the beast or a demonic entity (like Revelation 20:10) directly suggests annihilationism, or is at least consistent with it.

The concepts of existence as a conscious being and living as a biological creature are plainly distinct, even if experience as a biological creature requires existence as a conscious being, and this still does not logically establish that the Biblical promise of eternal life to those committed to Christ means that the unsaved will all still exist forever, as opposed to just having temporary life on Earth and a temporary existence in hell before permanent destruction.  In fact, some passages make it very plain that permanent, cosmic death of consciousness is the grand wages of sin for fallen humankind (with the possible exception of a group of people who receive a "mark of the beast").  Even with the aforementioned distinction, annihilationism is still the obvious Biblical teaching about the general fate of the unsaved once a reader makes no assumptions about the text and evaluates relevant philosophical ideas without fallacies.