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.
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.