In my last post, I discussed how the findings of modern science support the idea that the universe began to exist, and how this provides support for the Kalam Cosmological Argument for God’s existence:
- Everything that begins to exist has a cause.
- The universe began to exist.
- Therefore, the universe has a cause.
Now, science cannot prove absolutely that the universe began to exist. But even if we set aside scientific evidence that the universe began to exist, there are strong philosophical arguments for the universe beginning to exist that do not depend on any particular scientific theory.
Concrete Actual Infinities Are Impossible
First, there are arguments that concrete actual infinities are impossible; therefore, an infinity of past events is impossible. It is important to distinguish here between mathematical impossibility and metaphysical impossibility. Not everything that is mathematically possible is metaphysically possible. Abstract infinities are used frequently in the realm of mathematics, but this does not mean that concrete actual infinities are metaphysically possible.
Consider the thought experiment of “Hilbert’s Hotel,” conceived by mathematician David Hilbert. Imagine a hotel with an infinite number of rooms, each occupied by a single guest; thus, there are an infinite number of guests. If you wish to get a room at the hotel, there is none available, since every room is occupied. However, if the proprietor has each guest move up one room (the guest in room 1 move to room 2, the guest in room 2 move to room 3, and so on), there will suddenly be a room available for you, even though the number of guests and the number of rooms in the hotel remains unchanged.
Or, imagine that every guest in an odd-numbered room checked out. An infinite number of guests would leave, yet the number of guests in the hotel would remain unchanged; there would still be an infinite number of guests. If every guest in rooms 5 and above checked out, again, an infinite number of guests would leave. Yet, this time, even though the exact same number of guests checked out, there would only be four guests left in the hotel!
There are many more such absurdities that can be revealed through analysis of Hilbert’s hotel. Together, they show, through reductio ad absurdum, that it is metaphysically impossible for concrete actual infinities to exist.
A common objection to this claim is that any distance (of length or time) could be divided infinitely; therefore, there are, in fact, concrete infinities. However, we do not actually know for certain that space and time are infinitely divisible; there may, in fact, be indivisible units of space and/or time. But in any case, even if space and time are infinitely divisible, such division would only be a potential infinity, not a concrete infinity. That is, even if someone went on dividing a distance indefinitely, they would only divide it an increasingly large number of times; they would never reach an actual infinite number of divisions.
Some have questioned whether the paradoxes of the infinities of Hilbert’s Hotel are really applicable to the concept of an infinite past. But philosopher Andrew Ter Ern Locke has devised a similar thought experiment that is more clearly applicable to the concept of an infinite past. He asks us to imagine a “Christmas present generator” that has generated Christmas presents at fixed intervals during an infinite past, as well as a “person generator” that has generated persons at the same fixed intervals. “The presence or absence of leftover presents should be independent of each person grabbing one present produced at any particular instant, because each person grabbing one present from one temporal position rather than another has no causal power with respect to the presence of leftover presents.” However, if each person grabbed the present generated at the same time as them (person t-1 grabs present t-1, person t-2 grabs present t-2, etc.), there would be zero presents leftover. But if each person instead grabbed the present produced at time t-2x (person t-1 grabs present t-2, person t-2 grabs present t-4, etc.), there would be an infinite number of presents leftover. This is a metaphysical absurdity, showing again that it is metaphysically impossible for concrete actual infinities to exist.[1]Andrew Ter Ern Locke, God and Ultimate Origins: A Novel Cosmological Argument (Palgrave Macmillan. 2017), pages 56-61.
Traversing an Actual Infinite is Impossible
Second, there are arguments that traversing an actual infinite is impossible; therefore, an infinity of past events is impossible.
No matter how much you add to a potential infinite, it can never reach an actual infinite; no matter how long you go on successively adding, you will always be able to add more and still be infinitely far away from reaching an actual infinite. Thus, a collection formed by successive addition can never be an actual infinite. Now, the temporal series of past events is a collection formed by successive addition. Therefore, the temporal series of past events cannot be an actual infinite. The past cannot be infinite, and so the universe must have begun to exist at some point in the past.
One objection to this argument is that it assumes a dynamic theory of time, but does not work if one assumes a static theory of time (According to a dynamic theory of time, the universe is actually progressing through time; according to the static theory of time, moving through time is merely a subjective human experience within a static space-time reality). However, the argument can be reformulated so that it works within either a dynamic or static theory of time:
“1.If time is beginningless, then it would be the case that a causal series which has members being generated one after another as long as time exists would arrive at an actual infinite of generations of members at a particular point in time.
2.It is not metaphysically possible for a causal series which has members being generated one after another as long as time exists to arrive at an actual infinite of generations of members at a particular point in time.
3.Therefore, it is not metaphysically possible that time is beginning-less.”[2]Andrew Ter Ern Locke, 68.
This version of the argument is successful even on a static theory of time, since it only relies on the idea of a causal series, not the idea of time being formed by successive addition.
The Kalam-Thomist Argument
Even if one is not persuaded by the arguments that concrete infinities are impossible and that traversing an actual infinite is impossible, a successful version of the cosmological argument can still be formulated. This involves combining the Kalam cosmological argument with the Thomist cosmological argument, which is not based on the idea of the universe beginning to exist.
We know that everything that begins to exist has a cause. We also know that there are entities that begin to exist and are members of a temporal causal series. Now, if every member of this series lacks the ability to exist without a prior cause, then, regardless of how many members this series has, they all must lack the ability to exist without a prior cause (0+0+0+. . . =0). Consider the analogy of a series of train cars, each of which needs to be pulled to move; there must be an engine to move them, even if there are an infinite number of train cars. Therefore, there must be an uncaused, beginningless entity that can provide a causal explanation for the existence of this temporal causal series. Nothing can exist prior to an uncaused, beginningless, entity, and so it is a First Cause.[3]Andrew Ter Ern Locke, 94.
Some have objected that the claim that the universe must have had a cause commits the fallacy of composition: the error of assuming that what is true of a member of a group is true of the whole. But this cosmological argument does not commit the fallacy of composition. It is based on the claim that anything that begins to exist must have a cause. If universes could begin to exist uncaused, then, logically, smaller things could begin to exist uncaused as well, and we would see things beginning to exist uncaused all the time around us.
Demonstrating that a First Cause exists does not get us all the way to the Christian concept of God. But it does get us partway there. It tells us that there is a Being that is extremely powerful, uncaused, and beginningless, which is the source of nature and its laws. This resonates with much of the Christian concept of God.