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The infinitude of time

Could time stretch back forever? The idea sounds absurd until you consider that every argument against it has a fatal flaw. Michael Huemer argues that traditional objections to an infinite past—dating back to Aristotle and Aquinas—are actually mistaken. He contends that Zeno's paradoxes demonstrate completed infinities are possible, and that Stephen Hawking's Big Bang theory faces a serious problem: positing an extremely improbable initial state for no reason.

The Impossibility of Actual Infinity?

One major objection holds that actual infinities cannot exist because infinity is not a determinate quantity. If the past were infinite, every event becomes fully actual as it happens—a completed infinite series. Critics also argue that infinite series cannot be completed: counting to infinity is absurd.

The infinitude of time

Yet Zeno's paradoxes prove otherwise. Consider an object moving from point A to point B. It must first cover half the distance, then half the remaining distance, and so on—an infinite series of steps. Yet when the object arrives at its destination, every step has actually been completed. The same applies to Hilbert's Hotel: a full hotel with infinitely many rooms can accommodate infinitely many new guests by shifting occupants to room n+1. These are actual infinities that are completed.

Why Big Bang Theory Fails

Hawking's traditional view holds that time began at the Big Bang, approximately 14 billion years ago, making questions about what came before meaningless. However, cyclical cosmologies like Roger Penrose's Conformal Cyclic Cosmology propose an infinite past.

More troubling is Hawking's specific theory. It proposes that the universe started in an extremely low-entropy state with massive energy concentrated in a tiny region—without any causal explanation. The probability of such a state, calculated by Penrose, is 1 in 10^10^124. Huemer argues this is less probable than a universe appearing already in its 1950 state, which had higher entropy. If the latter seems implausible, the former should too.

Intuitions About Limits

Consider an edge of space. Push your hand beyond it—your hand stops. Yet you can still ask what lies beyond that invisible barrier. Similarly, if time began at some moment, we can ask what happened before. It feels impossible for location or time itself not to exist.

The argument extends to explanations. If time began, we want to know why—but no explanation works. God cannot create time outside of time; actions require time. Causation requires time. Even abstract facts like mathematical truths cannot explain a contingent beginning.

You could never explain the start of time, because any explanation would already need time to exist.

Past and Future Asymmetry

Most philosophers agree time must continue indefinitely into the future—an end of time feels impossible. Yet if an end is impossible, shouldn't a beginning be equally impossible? The "no actual infinity" view permits infinite potential futures but prohibits infinite pasts. But this asymmetry has no intuitive ground: both feel equally impossible.

Critics might note that Huemer's argument assumes time must be comprehensible to us—a distinctly modern assumption. Medieval thinkers like Aquinas would have rejected the very framing of the question.

Bottom Line

Huemer's strongest move is showing that completed infinities exist in mathematics and motion—undermining the core objection to an infinite past. His vulnerability lies in assuming we should find Hawking's theory implausible, which requires accepting that improbable events happening for no reason is worse than alternative explanations. The philosophical stakes are high: if time has no beginning, neither does the universe.

Deep Dives

Explore these related deep dives:

  • The Beginning of Infinity Amazon · Better World Books by David Deutsch

    A physicist's argument that explanations are the key to progress — and that progress is infinite.

  • Cycles of Time Amazon by Roger Penrose

    Penrose proposes the universe cycles through infinite aeons — conformal cyclic cosmology explained.

  • Big Bang

    The excerpt discusses whether time has a beginning, and Big Bang cosmology is relevant to discussions of infinite past

  • Zeno's paradoxes

    Explicitly mentioned as two variants (endless series and beginningless series) showing how infinite series can be completed

  • Hilbert's paradox of the Grand Hotel

    The excerpt cites Hilbert's Hotel as a thought experiment about accommodating infinitely many guests in a full hotel

Sources

The infinitude of time

by Michael Huemer · Fake Nous · Read full article

Here, I argue that the past is infinite.*

1. Objections to the Infinite Past.

1.1. Completed, Actual Infinities.

Some people argue that the past cannot be infinite because

(i) There cannot be an actual infinity. If the past were to be infinite, it would be an actual infinity since every event becomes actual as of the time it happens (and stays actual). On this view, it’s okay to have an infinite future, because the future is never fully actualized, but all past events are fully actualized.

Or:

(ii) An infinite series cannot be completed. (Imagine the absurd idea of “counting to infinity,” or counting through all the natural numbers.) If the past were to be infinite, then the series of past events would constitute, as of now, a completed infinite series.

Why think there cannot be an actual infinity? Aristotle and Aquinas’ argument was basically this:

Everything actual must be fully determinate.

Infinity is not a determinate quantity (and is not compatible with having a determinate quantity).

Therefore, there cannot be an actual infinite.

People also like to cite paradoxes of the infinite, which allegedly can and should be avoided by denying the possibility of actual infinities. William Lane Craig likes to cite Hilbert’s Hotel:

Assume there is a hotel with infinitely many rooms, all of which are filled. A new guest shows up. Can he be accommodated (without kicking anyone out)? Yes. You tell each guest to move to room number (n+1), where n is their current room #. This leaves Room #1 free for the new guest.

Then an infinite number of new guests shows up. They can also be accommodated: move each guest to room #2n, where n is their current room number. This leaves rooms #1, 3, 5, and so on free for the new guests.

It’s counter-intuitive that you should be able to accommodate infinitely many additional guests in a hotel that is already full. To avoid this, we’re supposed to say “actual infinities are impossible”.

Replies:.

(a) This view is refuted by Zeno’s Paradox. Two variants of Zeno’s paradox:

Zeno’s endless series: For an object to move from point A to point B, it must first go half the distance, then half the remaining distance, and so on.

Zeno’s beginningless series: For an object to move from point A to point B, it must first go half the distance. But before it does that, ...