The Endless Horizon: Distinguishing Eternity from Infinity
1. Infinity: The Endless Count
Infinity (∞) is a mathematical and physical concept. It is not a "large number," but rather the property of a set that never ends.
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The Mathematical View: In mathematics, infinity describes a limit. This is famously illustrated by Zeno’s Paradox. Zeno of Elea argued that to walk across a room, you must first travel halfway. To finish the remaining half, you must travel half of that distance, and so on. Mathematically, you are dividing space into an infinite number of points. How can a finite person traverse an infinite number of points? We "solve" this in calculus, but the philosophical tension remains.
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The Physical View: Astronomers grapple with whether the universe is infinite. As Galileo once noted, infinity behaves counter-intuitively: if you have an infinite number of integers, and you square every one of them, you have the same "amount" of numbers, even though you’ve skipped all the non-squares.
2. Eternity: The Timeless Now
Eternity is often misunderstood as "a very long time," but philosophically, it is the absence of time.
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The "Everlasting" vs. "Eternal": If something is "everlasting," it exists within time and simply never stops. If something is "eternal," it exists outside of time altogether. The philosopher Boethius defined eternity as "the total and simultaneous possession of unending life."
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The Vertical Dimension: If time is a horizontal line moving from past to future, eternity is the vertical point that exists independent of that line. It is a state where "before" and "after" lose their meaning. As the Islamic philosopher Al-Ghazali explored, if time were infinite in the past, we could never have arrived at "now," because an infinite number of moments would have had to pass first. This suggests that eternity must be a different kind of existence entirely—one where "now" is the only thing that exists.
3. Where They Meet
The bridge between these two is the human attempt to map the unmappable. We use infinity to try to measure the physical world and eternity to describe the spiritual or metaphysical realm. Infinity is a journey that never reaches a destination; eternity is the realization that there was never a journey to begin with because time is an illusion.
As we look at the stars or dive into equations, we realize that infinity is what we count, but eternity is what we inhabit.
This video provides a deep dive into how philosophers like Al-Ghazali used logical arguments to challenge the idea of an infinite duration of time, which helps clarify the difference between a mathematical sequence and the concept of eternity.