Can time exist as an actual infinite?

Can time exist as an actual infinite?

  • Yes.
  • No.
0 voters

If time passes by successive addition, then time is endlessly approaching infinity as a limit, but it can never actually reach an actual infinite. It can never reach infinity. If time passes by successive addition, then an actually infinite amount of time cannot exist.

Philosopher William Lane Craig concurs on this point:

“Sometimes it’s said that we can find counter-examples to the claim that an actually infinite number cannot exist, so that this claim must be false. For instance, isn’t every finite distance capable of being divided into 1/2, 1/4, 1/8,…, on to infinity? Doesn’t that prove that there are in any finite distance an actually infinite number of parts? The fallacy of this objection is that it once again confuses a potential infinite with an actual infinite. You can continue to divide any distance for as long as you want, but such a series is merely potentially infinite, in that infinity serves as a limit that you endlessly approach but never reach. If you assume that any distance is already composed out of an actually infinite number of parts, then you’re begging the question. You’re assuming what the objector is supposed to prove, namely that there is a clear counter-example to the claim that an actually infinite number of things cannot exist.”

Time does pass by successive addition. Seconds are always followed by another second, endlessly and successively. No matter how you slice time up, whether you measure it in years, seconds, or even fractions of a second, each unit of time is endlessly followed successively by another unit of time. Therefore, time cannot exist as an actual infinite, but only as a potential infinite. And that entails that the universe cannot be beginningless, but it must have began to exist. It must be finite.

  1. If time passes by successive addition, then an actually infinite amount of time cannot exist.

  2. Time does pass by successive addition.

  3. Therefore, an actually infinite amount of time cannot exist.

And that entails that the universe cannot be infinite, but it must be finite.

If an actually infinite amount of time has passed, then an infinite must have been reached by successive addition, because time passes by successive addition. But it is impossible to reach infinity by successive addition, therefore, the universe must be finite.

Time is not compatible as an actual infinite.

Do you see this as a valid argument? It seems to be valid to me. Any comments on it would be greatly appreciated.

successive addition begs the question and is invalid…

there is no logical reason to believe that a future second will exist


It is currently 7:51 on the dot. Now it is currently 7:51:20. 20 successive seconds have passed. Not one was skipped. Not one has ever been skipped. Therefore, due to the nature of time, and the consistency of time, there is a strong reason to believe that a future second will exist.

Only if you extrapolate into the future. That isn’t necessarily logical to do, but all that exercise demonstrates is the limitations of logic.

what is a second?
what is time?

time requires two points.

time requires a start and finish.

E=MC(squared) ~einstein

If one agrees with einstein,
energy or mass or mass and energy have always exist

there is no beginning, no start point, thus time does not exist

I never claimed that it always did, although in this case I believe it gives us strong evidence that a future second will exist.

Time doesn’t come into that equation as we see it, but, ironically, e=mc^2 is a consequence of the symmetry of space-time and time itself is a vital variable in maxwell’s equation (from which Einstein’s solution is derived).

Here is an article by philosopher Dr. William Lane Craig on this subject:

Subject: Forming an Actual Infinite by Successive Addition


Dear Dr. Craig,

I have a question concerning one of the philosophical arguments you offer in support of the view that the universe began to exist, namely the argument from the impossibility of forming an actual infinite by successive addition. You set up the argument as follows:

  1. A collection formed by successive addition cannot be actually infinite.
  2. The temporal series of past events is a collection formed by successive addition.
  3. Therefore, the temporal series of past events cannot be actually infinite.

This argument exposes a feature in the notion of an infinite series of events that I find bewildering. To set the situation up, we’ll assume the past is infinite. By virtue of a tensed conception of time, every event in the infinite past up to the present was a real event that had to be “lived” through. But, if that’s the case, how could all those events have been lived through, one by one, up till now? Just how, exactly, could we reach the end of that beginningless series? How could the present event arrive if, before it could arrive, an infinite number of previous events had to arrive first?

Like I said, this seems very puzzling. But I can’t quite put my finger on why. Is it simply that, on an intuitive level, I find the idea of traversing a beginningless series absurd? As you wrote in your reply to John Taylor, “The question is whether an infinite series of events, having no beginning and having an ending in the present, is metaphysically possible given a tensed view of time. Intuitively, this does not seem possible, for it seems that the present event could not arrive if its arrival had to be preceded by the successive arrival of an infinite number of prior events.” [“A Swift and Simple Refutation of the Kalam Cosmological Argument?” Religious Studies 35 (1999): 57-72. Footnote 26] This is exactly what impels me to accept the argument. But is there a way to analyze our intuition more deeply to find out exactly why such a traversal is impossible? Or is it somehow non-analyzable?

The “traditional objection” to this argument is that it is only impossible to traverse infinity if one begins at some point. But, whatever this reply manages to do, it doesn’t seem to rebut our intuition or reduce the apparent absurdity engendered by the situation; after considering the objection, I’m still genuinely perplexed as to how such a traversal could happen.

What underlies our intuition isn’t the argument that, for every number one counts, another number can always be counted before reaching infinity–is it? For this does seem to be susceptible to the traditional objection. Since, as Wes Morriston [“Must the Past Have a Beginning?” Philo, Vol. 2 (1999) no. 1, 5-19.] et al have pointed out, this observation seems only to involve counts that begin at some point, it doesn’t seem like it could be effectively used to support the notion that a beginningless series of events is impossible. Is our intuition dependent on or independent of this observation?

(Note: I’ve been considering this argument in its “bare bones” form only, leaving separate, e.g., discussion of the Tristram Shandy paradox(es). I wanted to see if the argument could be defended without the use of such puzzles and thought experiments.)


Dr. Craig responds:

Well, Michael, I obviously share your intuition! Basically, you’re asking about the warrant for premiss (1). You find that as you reflect on the idea of forming an actually infinite collection of things by successive addition the task seems impossible. You want to know if we can unpack this intuition a little more to see why such a task is impossible.

In the case of beginning with some finite quantity and adding finite quantities to it we can pinpoint the problem clearly: since any finite quantity plus another finite quantity is always a finite quantity, we shall never arrive at infinity even if we keep on adding forever. Infinity in this case serves merely as a limit which we never attain.

What becomes truly puzzling, even mind-boggling, is the suggestion that we can, by adding only finite quantities, form an infinite quantity or collection–say, a certain collection of baseball cards–by never beginning but ending at some time! Here the impossibility cannot be analyzed as due to the impossibility of adding finite quantities to finite quantities and getting an infinite quantity, for in this case the quantity to which finite additions are being made is always and already infinite. We are successively adding finite quantities to an already infinite quantity, so of course the sum is an infinite quantity. Here infinity is not functioning as a mere limit but as a collection of concrete elements.

Now notice that one still hasn’t explained how we are able to form our infinite collection of baseball cards by successive addition. For at any time in the past the collection is already infinite, and yet the total collection has not yet been formed. The total collection will not be formed until the last card is added. From any point in the past one need add only a finite number of cards to complete the collection. But that leaves unsolved the problem of how the entire infinite collection could have been formed by successive addition.

Here’s the problem, it seems to me: in order for the collection to be completed, we must have already enumerated, one at a time, an infinite number of previous cards. But before the final card could be added, the card immediately prior to it would have to be added; and before that card could be added, the card immediately prior to it would have to be added; and so on ad infinitum. So one gets driven back and back into the infinite past, making it impossible for any card to be added to the collection.

This way of putting the argument is somewhat akin to Zeno’s argument that before Achilles could cross the stadium, he would have to cross half-way; but before he could cross half-way, he would have to cross a quarter of the way; but before he could cross a quarter of the way, he would have to cross an eighth of the way, and so on to infinity. Therefore, Achilles could not arrive at any point. Zeno’s paradox is resolved by noting that the intervals traversed by Achilles are potential and unequal. Zeno gratuitously assumes that any finite interval is composed of an infinite number of points, whereas Zeno’s opponents, like Aristotle, take the interval as a whole to be conceptually prior to any divisions which we might make in it. Moreover, Zeno’s intervals, being unequal, add up to a merely finite distance. By contrast, in the case of an infinite past the intervals are actual and equal and add up to an infinite distance.

About the best that the critic of the argument can do at this point, I think, is to say that if one adds cards at a rate of, say, one card per second, then the collection can be completed because there has been an infinite number of seconds in the beginningless past. But clearly this response only pushes the problem back a notch: for the question then is, how can the infinite collection of past seconds be formed by successive addition? For before the present second could elapse, the one before it would have to elapse, and so on, as before. Because the problem is applicable to time itself, it cannot be resolved by appealing to infinite past time.

Of course, proponents of a static or tenseless theory of time will deny that moments of time really do elapse, but then their objection is actually to premiss (2), not premiss (1).

If one is not yet convinced by this argument, then I would offer a further defense of premiss (1) by arguing that if an actual infinite could be formed by succesive addition, then various absurditites would result. Consider the scenario imagined by al-Ghazali of our solar system’s existing from eternity past, with the orbital periods of the planets being so co-ordinated that for every one orbit which Saturn completes Jupiter completes 2.5 times as many. If they have been orbiting from eternity, which planet has completed the most orbits? The correct mathematical answer is that they have completed precisely the same number of orbits. But this seems absurd. Think about it: the longer Jupiter and Saturn revolve, the greater becomes the disparity between them, so that they progressively approach a limit at which Jupiter has fallen infinitely far behind Saturn. Yet, being now actually infinite, the number of their respective completed orbits is somehow magically identical. Indeed, they will have “attained” infinity from eternity past: the number of completed orbits is always the same. So Jupiter and Saturn have each completed an infinite number of orbits, and that number has remained equal and unchanged from all eternity, despite their ongoing revolutions and the growing disparity between them over any finite interval of time. This strikes me as nuts.

It gets even worse. Suppose we meet a man who claims to have been counting down from infinity and who is now finishing: . . ., -3, -2, -1, 0. We could ask, why didn’t he finish counting yesterday or the day before or the year before? By then an infinite time had already elapsed, so that he should already have finished. Thus, at no point in the infinite past could we ever find the man finishing his countdown, for by that point he should already be done! In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will already have finished. But if at no point in the past do we find him counting, this contradicts the hypothesis that he has been counting from eternity. This shows again that the formation of an actual infinite by never beginning but reaching an end is as impossible as beginning at a point and trying to reach infinity.

So in defense of premiss (1), I offer both the direct argument against the possibility of forming an actual infinite by never beginning but ending at a point and indirect, reductio arguments that if premiss (1) is denied, then various absurdities follow.

the only way that time can exist as an infinite is if energy/matter its self does . since time in the end is DEPENDENT on the existence of energy/matter and the movement of both , for infinity , so does time.

time is a consequence of the movement of energy/matter. it DOES NOT influence the movement of energy/matter. however.

if energy/matter is not infinite.
when did it come into ‘existance’
or set in motion?

energy/matter is infinite .

I’ll explain one reason why this cannot be true.

Scientists recognize that due to the Second Law of Thermodynamics, the universe will eventually come to a state of equilibrium, which means, all of matter will consist of a uniform composition, and nothing will happen anymore. All energy will be evenly spread out throughout the universe and will become completely useless, and the universe will be in a state of “heat death” and maximum entropy. Nothing can cause the universe to be changed into a different state after it has reached this point, because the universe is one gigantic closed system, and there is no outside force to alter it in any way (this is assuming that God doesn’t exist, I personally believe that He does). Inevitably, this would be the universe’s final state, and it would end up existing in an eternal state of equilibrium and maximum entropy (useless energy).

Steven Hawking concurs on this point:

“In fact, the theory that the universe has existed forever is in serious difficulty with the Second Law of Thermodynamics. The Second Law, states that disorder always increases with time. Like the argument about human progress, it indicates that there must have been a beginning. Otherwise, the universe would be in a state of complete disorder by now, and everything would be at the same temperature.”

As does physicist P. J. Zwart:

" . . . according to the second law the whole universe must eventually reach a state of maximum entropy. It will then be in thermodynamical equilibrium; everywhere the situation will be exactly the same, with the same composition, the same temperature, the same pressure etc., etc. There will be no objects any more, but the universe will consist of one vast gas of uniform composition. Because it is in complete equilibrium, absolutely nothing will happen any more. The only way in which a process can begin in a system in equilibrium is through an action from the outside, but an action from the outside is of course impossible if the system in question is the whole universe. So in this future state of maximal entropy, the universe would be in absolute rest and complete darkness, and nothing could disturb the dead silence. Even if there would by chance occur a small deviation from the state of absolute equalization it would of itself rapidly vanish again. Because almost all energy would have been degraded, i.e. converted into kinetic energy of the existing particles (heat), this supposedly future state of the universe, which will also be its last state, is called the heat death of the universe."

Now if matter and energy were eternal, then that would mean that the universe had no beginning. If the universe had no beginning, then that would mean that before this current point in time, an actually infinite amount of time has already passed (I believe this is impossible because you cannot reach an actual infinite by successive addition, but nevertheless, I will continue). If an actually infinite amount of time has already passed (then how did we reach the present if an actually infinite amount of events had to pass prior to the present?), then that means that the finite amount of time needed (however long it may be) in order for the universe to reach such a state of equilibrium has certainly already passed; an infinite amount of times I might add. Because within any infinite amount of time, any finite time span has passed an equally infinite amount of times. For example, given an infinite amount of time, the time span of 1 second has passed an infinite amount of times. Also, the time span of 10 years has passed an infinite amount of times. Also, the time span of however long it takes for the universe to reach a state of equilibrium has passed an infinite amount of times. Now if the finite amount of time required in order for the universe to reach a state of equilibrium must have already passed at some point in the infinite past (an infinite amount of times), then the universe would be in a state of equilibrium now. But that’s the problem. The universe isn’t in a state of equilibrium. Matter does not currently exist in one uniform composition, and energy is still useful; stars are burning, your body is producing heat and functioning, ect. Therefore, the finite amount of time required for the universe to enter into a state of thermodynamical has not passed, and it then follows, that if a finite amount of time has not passed, than an infinite amount of time has not passed. Therefore, the universe must be finite.

  1. Because time passes by successive addition, and it is mathematically impossible to reach an actual infinite by successive addition.

  2. If given that an infinite amount of time had passed, that would conflict with the Second Law of Thermodynamics in that the universe is not currently in a state of thermodynamical equilibrium.

The universe must be finite.

however each atom in and of itself has movement.

Even if that’s true, that doesn’t change the fact that at one point in the finite past, each atom must have begun to exist.

the point is that energy/matter always existed , are infinite , for the exact opposite will bring forth " absolutely nothing " non-existence for infinity . therefore this implies that time is also infinite , because again , energy/matter are infinite. and time is dependent on the existence of energy/matter.

If everything possible would happen, there is at least one thing that can cause time to stop-

If all matter were to be collected by an ultra-massive black hole. There would be no more time.

I’m not saying everything possible would happen, but I am saying that something that is scientifically inevitable must happen if the finite time required for it to happen has passed an infinite amount of times. Either the Second Law of Thermodynamics would be false, or the universe is finite. We know that the Second Law of Thermodynamics is true, and therefore, the universe must be finite.

Whether that is even possible or not is irrelevant. Is that an inevitable event based solidly on an established law of physics? Thermodynamical equilibrium is, and within an infinite universe, that scientifically inevitable event must have happened by now, but it hasn’t, and therefore, the universe must be finite.

What good reasons do you have to believe that this is true despite the fact that it is mathematically impossible and that it defies an established law of physics?

The exact opposite brings us inevitably to a Creator.