The Infinitude of Time
Michael Huemer advances a provocative thesis: the past must be infinite. His central argument rests on a simple but powerful intuition — whenever something begins, there must be an explanation for that beginning. Yet any explanation requires time to already exist. This creates a vicious circle that cannot be broken.
### Objections to the Infinite Past
Some philosophers argue that the past cannot be infinite because actual infinities are impossible. The reasoning goes like this: if the past were infinite, every event in history would be fully actualized — a completed infinity. And completed infinities are paradoxical. Additionally, an infinite series cannot be completed. Counting to infinity is absurd; one cannot count through all natural numbers.
Aristotle and Aquinas advanced a related argument: everything actual must be fully determinate. Infinity is not a determinate quantity and cannot be compatible with having a determinate quantity. People also cite Hilbert's Hotel as a reason to deny actual infinities. In this scenario, a hotel with infinitely many rooms is completely full, yet new guests can still be accommodated by shifting every existing guest to the next room. The result seems counter-intuitive — how can infinitely many additional guests fit in an already-full hotel?
A counterargument might note that Hilbert's Hotel is a mathematical abstraction. Real physical systems do not behave this way, and the paradox depends on assuming infinite divisibility without practical constraint.
### Replies to Objections
Zeno's Paradox reveals these objections to be flawed. Consider an object moving from point A to point B. It must first go half the distance, then half the remaining distance, and so on — an infinite series of steps. Yet the object still reaches its destination. These are actual infinities that are completed every time movement occurs. Each step is actually completed by the time the object reaches its destination; they are not merely capable of being completed.
Regarding Aristotle and Aquinas' argument: to say the past is infinite, we need not claim there is any particular attribute whose measure is infinity. We only need to say such things as "for every time, there is a time before it" and "for any duration d, there is a past duration longer than d." We do not have to say there is a duration called \"infinity\".
Regarding Hilbert's Hotel: the allegedly counterintuitive result may simply be correct. It is possible to accommodate all new guests while still providing rooms for existing guests.
### The Big Bang Theory
The traditional understanding of the Big Bang holds that time itself began approximately 14 billion years ago, making it nonsensical to ask what happened before the Big Bang. This view was held by Stephen Hawking and others — philosophers should listen to physicists.
However, there are also cyclical models in cosmology with an infinite past, such as Roger Penrose's Conformal Cyclic Cosmology. The Hawking version of Big Bang cosmology proposes an extremely improbable initial state happening for no reason: the universe starts in an extremely low-entropy state with a huge amount of energy concentrated in a tiny region, moving outward at the first moment of time. There could be no causal explanation for this initial state.
Critics might note that Huemer's alternative theory (that the universe appeared already in 1950) is equally speculative and does not solve the problem of initial conditions. The entropy argument remains compelling regardless of which year one cites as a starting point.
A better theory might be that the universe did not begin from nothing — perhaps it appeared already in a particular state, for no reason. This is actually more likely than the standard Big Bang theory because the entropy of the universe was much higher than at the time of the Big Bang.
### Intuitions About Limits
Consider someone proposing there is an edge of space. You go up to the edge of space and try to stick your hand past it — maybe your hand would just stop, no matter how hard you push. However, it still seems you could ask about what is on the other side of this invisible barrier. Intuitively, there must be an answer, even if the answer is that nothing exists there.
Similarly, imagine someone proposing time just started. It seems you could ask what happened before this, and there must be an answer — even if the answer is that no events were occurring. It seems impossible for time itself to not exist.
The idea of a beginning of time is not formally contradictory, nor is that of an edge of space. There are coherent mathematical structures for time with a beginning (like non-negative real numbers) and for space with an edge (like a sphere). But intuitively, these seem that they could not be the actual structure of space and time.
### What Could Explain the Beginning of Time?
If we posit a beginning of time, we should want an explanation of why time began. Not everything requires an explanation, but something like the beginning of time is weird enough that it seems to require one — especially if it started with the universe in a really improbable state.
But there could not be an explanation. God, existing \"outside time,\" cannot create time because creation is an action occurring in time. If there was no time, or if God was not in time, then God could not perform any actions. Creation is also a causal notion — to create is to cause something to exist. But causation requires time; if time did not already exist, nothing could cause anything.
Creation is also a change from a state where a thing does not exist to a state where it exists. To create time would require there first to be a time when time did not exist, followed by a time when time exists. But there could not be such a time.
Some might argue that this argument assumes too much about what counts as an \"explanation.\" Perhaps divine action or quantum tunnelling events could explain beginnings without requiring temporal sequence.
Even if God's action occurs simultaneously with the first instant, avoiding the objection that actions require time to exist, there remains a problem of metaphysical priority. The ability to act depends upon one's existing in time. It cannot also be the case that existence of time depends upon some particular action — dependence relations cannot be circular.
If no secular cause could create time if time did not already exist, then nothing else could do so either. No event or state of affairs could cause time to begin. Any explanation would presuppose the existence of time.
Are there any facts outside time? Purely abstract facts, such as that seven is a prime number, are outside time — no time at which this \"happens.\" However, such purely abstract facts could not explain something contingent and concrete like the beginning of time.
### Past/Future Symmetry
Almost everyone agrees there can be no end of time; time must continue forever into the future. Even if all physical processes freeze, that will not be an end of time — it will just be a time when things are static.
It is not inconsistent to hold an asymmetric view where you posit a beginning but not an end of time. But it is odd. If one thinks an end of time is impossible, shouldn't a beginning of time be similarly impossible?
The \"no actual infinity\" people say the future is an infinite potential, whereas the past is actual — and that is why their view rules out an infinite past but not an infinite future. However, this does not explain why an end of time is impossible; it only explains why an end of time is not required by the \"no actual infinity\" view.
If one thinks an end of time is impossible on intuitive grounds, there is likely a parallel intuition about a beginning of time. When thinking about the alleged last moment of time, it seems there must be an answer to what happens after this moment — just as, when thinking about the alleged first moment of time, there must be an answer to what happened before it.