Ryan Reyes asks a very good question on the Facebook page, "Brothers, how can I argue for 'eternity' against a secularist who believe [sic] that there's none?" If I am to give a helpful answer, it is necessary to determine what is meant by "eternity," which is a notoriously difficult concept. I will begin by saying what it is not.
First, "eternity" is not referring to the eternity of the world. Classical Roman and Greek authors generally agreed that the universe existed from all eternity. Aristotle, for example, argued for the eternity of the world based upon the ideas that time had no beginning and that change comes from other change and so on to infinity past. This of course was a cause for disputation throughout the medieval period, as theologians from Boethius to Thomas Aquinas to William of Occam wrestled with whether this idea could be reconciled with Christian teaching that the heavens and the earth had a beginning and were created ex nihilo. Thomas Aquinas's solution was that neither creation ex nihilo nor eternity of the world were demonstrable. Creation is an article of faith. Jewish philosopher Moses Maimonides argued along similar lines saying that a proposition that cannot be demonstrated, such as creation ex nihilo, is better accepted on authority.
Second, "eternity" is not referring to either mathematical eternity or infinity. Mathematical eternity or infinity is most famously represented by Zeno's paradoxes, which have been preserved for us in Aristotle's and Diogenes Laertius's writings. The three most relevant ones are the Achilles and the Tortoise, the Dichotomy, and the Arrow Paradoxes. The first two relate to space showing that in order for one to get from point A to point B one must first get through an infinite amount of points along the way. How can one ever reach his or her destination, or, in the case of Achilles, if he gives the tortoise a head start, how can he ever overrun the tortoise? The third deals with time. An arrow that is shot from a bow to a target is at every point occupying a space. At every instant in time the arrow is neither moving to where it is nor to where it is not. Each instant is a point on a line. And each instant the arrow is at rest because it is occupying a space, and it cannot move because at each instance no time is elapsing. Like those trying to go from point A to point B, an arrow has to travel through an infinite amount of points or instances of time to reach it's target, and at each point it is at rest occupying space. Now, as fascinating as these paradoxes are to think about, they do not establish any irrefutable metaphysical conclusions.
Now is probably a good place to make the point that infinity and eternity are not synonymous terms. Infinity refers to limitless extension of being, whereas eternity refers to limitless duration of existence.
Now to a more positive explanation of eternity. "Eternity" could be referring either to the duration of God's existence throughout endless ages, or the duration of our existence throughout the age to come. The existence of God is without any limitation. He not only exists as Psalm 90:2 says, "from everlasting to everlasting," but, since he is the creator of time, he exists beyond the bounds of time.
We who are creatures were born in time, and are bound by time. When we, by the grace of Christ, enter the age to come after the glorious return of Christ and the resurrection of the body, we have an endless existence to look forward to, but we will still be limited creatures. We had a beginning, and we will still occupy space and time. God is both infinite and eternal. That is, his being has no limits and his existence has no beginning and no end.
Getting to your question, Ryan, how can we prove eternity to one who doesn't believe in eternity? You call this person a "secularist." I assume you mean by that a person who affirms the material universe and nothing more. If he is such a one, then even he has to acknowledge the possibility of eternity based upon the notions of the eternity of the universe or of mathematical eternity or infinity. As a materialist he may affirm with modern cosmology the origin of the universe in the big bang and the end of the universe in the big crunch. He may also affirm with some scientists that the big bang and the big crunch are part of an endless cycle of beginnings and endings. Whether one big bang and one big crunch or an endless cycle of big bangs and crunches, he will have to come to the conclusion that matter always existed, and if he affirms this, you need to press him to irrefutably prove the logical possibility of the endless existence of matter, which he will not be able to. In fact, he will not be able to irrefutably demonstrate that the big bang is, in fact, the origin of the universe or that the big crunch is its end. It is a theorem based upon mathematical observations. Sure, the theorem makes sense, but it is based upon limited observations. To say that the big bang or the big crunch is irrefutable is saying too much. We're back to what both Thomas Aquinas and Moses Maimonides argued, vis., that creation by God is not demonstrable--neither is the big bang or the big crunch!
"But," he might say, "the mathematical proofs!!!!" Yes, they make sense as far as they go, but can they be said to have irrefutably proven how the universe began, or that they even make sense outside of the system of our universe? The dirty little secret of the big bang theory is that it is based upon certain assumptions. Assumptions, which I'm sure your materialist friend takes for granted. Assumptions such as that this universe is a closed system, that the universe is expanding at a uniform rate, and that the universe doesn't need a divine being to uphold it. Don't forget, too, that I haven't even dealt with the question of where the notion of logic and mathematics comes from, let alone the very idea that the universe operates by laws. How do laws exist apart from a lawgiver? It's a sticky question for the materialists. The fact that the universe is orderly not chaotic remains a problem for the strict materialists. No one has yet given any conclusive proof that laws, mathematical or otherwise, can exist apart from a lawgiver.
Never forget that eternity, whether you are talking about the eternality of God or our endless existence in the age to come, is a matter of faith. True, it cannot be demonstrated that God is eternal or that we will live forever in the age to come, but the assumptions of the materialists cannot be demonstrated either. What's more logical, to believe in God or to believe in a materialistic universe? We accept the authority of Scripture, and we confess what Scripture teaches: the eternity of God and the saecula saeculorum.
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