LECTURE #5: Theism and Big Bang Cosmology


Kalam Argument

The Beginning of the Universe

Universality of Causation

The Nature of the Creator

The Kalam Argument

The Kalam tradition of Muslim thought rejected Aristotelianism and, in particular, Aristotle's thesis of the eternity of the world of matter and motion. The Kalam thinkers, culminating in the work of al-Ghazali, attempted to prove that the universe had a beginning and therefore, was created in time. The basic Kalam argument takes the following form:

  1. The universe had a beginning.
  2. Everything that has a beginning has a cause.
  3. Therefore, the universe has a cause, which is God.
We will take up each of these points in this lecture: the beginning of the universe, the scope of causation, and the nature of the creator of the universe.

The Beginning of the Universe

The Kalam tradition had a number of arguments for the existence of a beginning of the universe. These arguments have been revived in recent years by William Lane Craig. In addition to these philosophical arguments, there is a body of physical evidence for the beginning of our universe. On the other side, there are philosophical arguments against the possibility of an absolute beginning. We will look at Kant's presentation of these arguments in the discussion of the antithesis of the First Antinomy in Kant's Critique of Pure Reason. Finally, in A Brief History of Time, Stephen Hawking offers a speculative model of a beginningless universe.

Philosophical Arguments for a Beginning

In the Kalam tradition, there were two types of philosophical arguments for a beginning of the universe. The first was based on the thesis (borrowed from Aristotle) that an actual infinity is impossible, together with the assumption that the elements of the past are still actual. The second is based on the idea that time is constructed by a process of "successive addition". Consequently, an infinite past would be possible only if an infinite series of successive additions could be completed, which is obviously impossible.

Aristotle believed that an actual infinite was impossible. Many philosophers, mathematicians and scientists, from Aristotle's time until the twentieth century, have agreed with him. However, a substantial number of philosophers and mathematicians believe that the development of the mathematics of the infinite in modern set theory (first formulated in the late 19th century by Georg Cantor) has shown that an actual infinite is possible. Cantor himself was a Christian, who believed that the existence of infinite collections (such as the collection of all natural numbers, or all real-valued functions) followed from the infinity of God's mind. It would be possible to pose a dilemma to the agnostic: if infinite sets are possible, this would seem to require an infinite mind through which these sets could exist. Alternatively, if infinite sets are impossible, then the past would have to be finite, forcing us to posit a cause of the beginning of time and motion.

William Lane Craig, following the lead of the Kalam thinkers, poses a number of paradoxes which are supposed to show that actual infinities are impossible. One example is that of Hilbert's hotel (invented by the mathematician David Hilbert). If Cantorian infinities were possible, there could exist a hotel with infinitely many rooms, one for each natural number. Suppose that at the end of the day, every room is occupied. After the No Vacancy sign is lit, a weary traveller arrives and demands accomodation. Since the traveller is a set theorist, he points out that the hotel has plenty of room: if every guest will move from his present room (room n) to the next room (n+1), every guest can still be accomodated, and in addition, room 1 will now be available. In fact, even if a party with infinitely many members arrive, all the visitors can be accomodated. Each present guest must move from room n to room 2n. As a result, all of the odd-numbered rooms become available, with plenty of room for all of the new arrivals.

Another example is mentioned by al-Ghazali. Suppose that the sun and moon have each been revolving around the earth throughout an infinite past. There are 12 revolutions of the moon for every revolution of the sun. As we go back in time, the gap between the number of months and years grows ever wider, yet, taken as a whole, there are an equal number of elapsed months and years (both infinite). Cantorian set theory agrees with this paradoxical result: the cardinal number of months and years is exactly the same.

Bertrand Russell discusses a similar paradox, which he called the Tristam Shandy paradox. Tristam is writing is own autobiography. He takes a whole year to write down the events of a single day. In an infinite amount of time, Shandy can complete the task. Here's a time-reversed version of the paradox: suppose that Tristam is clairvoyent -- he writes about his own future. Last year he wrote about today's events; in the year before last, he wrote about yesterday's events. Today, he has just completed an infinite autobiography, cover all the events of his infinite past, despite the fact that, as we go farther in the past, Shandy is every further behind in the task -- i.e., 1000 years ago, he was still writing about the events of only the last three days.

Aristotle agreed that an actual infinity is impossible. Nonetheless, he believed that the universe is infinitely old. Apparently, Aristotle did not believe that events in the very remote past are still in any sense actual. He clearly rejected the idea that future contingent events are already actual. Perhaps he would have said the same thing about past events that occurred so long ago as to leave absolutely no trace. The Kalam thinkers appealed to the fact that there seems to be a clear difference between the past and the future. The idea of affecting or influencing the past is odd in a way that that of influencing the future could never be.

A second Kalam argument was based on the idea that time is built up by a process of successive addition. In order to have an infinite past, reality would have to have just completed an infinite task. However, an infinite task cannot be completed in time, since if it were first completed at time t, then at time t - 1, the infinite task would have remained incomplete. However, since the difference between t and t-1 is finite, an infinite task was already completed at t-1. These two infinite task must differ only by the fact that the past completed at t is one day longer than the past completed at t-1. However, "one day longer" has no meaning when applied to infinite series.

What the Kalam argument seems to overlook is the difference between infinities of size (cardinal number) and infinities of order (ordinal number). It is an infinite series that is first completed at time t, namely, the series consisting of all times earlier than t. This series is distinct from the series first completed at time t-1, despite the fact that the size of the set of past times is exactly the same. The series ending at t includes time t-1, while the series ending at t-1 does not.

It is interesting to note one crucial difference between the Kalam arguments and the alternative Aristotelian tradition. The idea of an infinite regress plays no explicit role in the Kalam arguments. The existence of an infinite causal regress and of an infinite past are independent: we can have one without the other. For example, we can imagine an infinitely old universe in which all causal regresses are finite, tracing back to some eternal First Cause. Each neighborhood of the universe would be only finitely old, but the whole succession of neighborhoods could be infinite. Conversely, we could have infinite causal regresses without an infinite past. Suppose that for each real number r greater than 0, there is a moment of time and a distinct event occuring at time t+r. We could then regress through infinitely many events, starting at event t+1 and approaching ever closer to t (without ever arriving there).

Physical Evidence of a Finite Past

There are two kinds of physical evidence that point to the finitude of the past: thermodynamic considerations, and evidence of cosmic expansion. Thermodynamics dictates that the entropy (disorder) of the universe increases over time. Had the universe already existed for an infinite length of time, we would have reached the state of heat death -- the state in which all energy is uniformly distributed in the form of a constant temperature Second, we observe that the universe is expanding uniformly in all directions. Had the universe existed for an infinite period of time, the density of matter would have become zero. In fact, we have increasingly good scientific evidence of a physical singularity, an absolute beginning to space and time, about 16 billion years ago. From this singularity, our universe arose in a "Big Bang" event.

The weight of current evidence seems to be on the side of the hypothesis that the universe will go on expanding forever -- that the power of gravity is insufficient to bring about a reversal of the expansion. This seems to rule out the possibility of an eternally oscillating universe, one in which every Big Bang is eventually followd by a Big Crunch. Thus, the evidence suggest that the Big Bang is the very beginning of the universe.

There has been some speculation in recent years that our universe (which we can define as the cone of space and time emerging from the Big Bang) is only a small part of much larger physical realm. In some cases, the argument for a finite past applies with equal force to this larger multiverse. In other cases, the speculations are so vague that no definite conclusions about the origins of the multiverse are possible. When we reach the fourth point, the nature of the creator, the existence of such non-theistic explanations of the origin of the Big Bang will justify some caution in jumping too quickly to an identification of the Big Bang with the absolute beginning of creation.

Kant's First Antinomy

Immanuel Kant, the great German philosopher of the Enlightenment, believed that human reason is wholly unequal to the task of cosmology. Human reason is able to gain knowledge about the "phenomenal world" -- the realm of possible human experience. The "world" as a totality, Kant thought, is not a possible object of our experience. Consequently, any speculation about the nature of the world is futile. In particular, Kant believed that human reason falls into unavoidable self-contradictions whenever it attempts to investigate the nature of the cosmos. These contradictions he called "the antinomies". Kant's First Antinomy concerned the age and extent of the universe. According to the Thesis, the world is finite in age and in space. According to the Antithesis, the world is infinite in both respects. Kant believed that compelling arguments could be given for each side of the antinomy. Kant accepted and used one of the two forms of the Kalam argument in his proof of the Thesis: the argument from successive addition.

On the side of the antithesis, Kant argues that the idea of a beginning of the universe is incoherent, as is the idea of a spatial limit of the world. Kant assumes that if the universe begins to exist at time t, then before t there must lie an infinite expanse of "empty time", time during which nothing happened. Similarly, Kant believed that beyond the spatial limits of the universe would lie an infinite expanse of "empty space". Kant repeats Aristotle's argument that empty time is impossible, since nothing could differentiate one moment from another. Similarly, Kant insists that empty space is impossible.

Kant believed that science must treat the universe as infinite in space and time, without turning this operational or methodological principle into a metaphysical thesis. Modern cosmology seems to refute this claim of the scientific necessity of the Antithesis view. According to standard cosmology, the universe is finite in both time and space. At the same time, cosmology agrees with Aristotle and Kant in rejecting the idea of empty space and time. The reconciliation of these two views is possible because cosmology holds that space and time are themselves finite. Before the original singularity, there is no time. Space is finite but unbounded -- it curves back upon itself, like the surface of a finite sphere.

The failure of Kant's prescription of the Antithesis as the guiding principle of scientific cosmology should sound a cautionary note. We must be careful about dictating methodological rules to science, that constrain the theories or models that scientists are allowed to entertain. Scientists must be free to follow the evidence wherever it leads, even if it should lead in the direction of the supernatural.

Hawking's No-Singularity Model

In A Brief History of Time, Stephen Hawking presented a new model of a beginningless universe. Hawking does not challenge the idea that the universe is finite in space and time. Consequently, there is no time earlier than 16-10 billion years ago. Nonetheless, if the univese does eventually collapse back into a infinitesimal point, and if we use a mathematical technique known as "imaginary time", we can model space-time as a smooth, uneventful surface, with the Big Bang as the North Pole and the Big Crunch as the South Pole. Hawking's model involves "spatializing" time -- turning time into a spatial dimension, no different from the familiar three dimensions of space. Hence, his model involves a radical rejection of change and becoming: the universe is an unchanging, multi-dimensional whole, given once for all. Change is merely variation along a static dimension.

Hawking's model is highly speculative, based on what Hawking believes a quantum theory of gravity (which does not yet exist) must be like. In addition, mounting evidence against the eventuality of the Big Crunch spoils the symmetry of Hawking's model. However, the main problem with Hawking's model is its incorporation of an unbelievable view of time and change. When using physical theory in metaphysical investigation, one must be aware of a GIGO principle: garbage in, garbage out. When using a physical theory in metaphysics, one must be careful not to incorporate metaphysical absurdities in one's interpretation of that theory. Otherwise, any metaphysical conclusions one bases on this interpretation will be vitiated by these prior absurdities. In Hawking's case, he uses the technique of imaginary time, and interprets this technique as reflecting the true nature of the world. This means that Hawking starts out by assuming that time is no different from a spatial dimension, that there is no real becoming in the world. This is obviously false: physics can tell us many surprising things, but if a physicist tells us that there is no such thing as the passage of time, we have good grounds for concluding that a serious mistake has been made. As soon as we interpret Hawking's model in a way that treats time in a credible way, we find (as Hawking himself admits) that the initial singularity re-appears.

The Universality of Causation

The Kalam argument depends on the assumption that everything that begins to exist must have a cause of its coming-to-be. This is a principle that nearly everyone (even skeptics like Hume) admits is difficult to doubt. It is especially difficult to believe that a given thing that has begun to exist really happened through no cause whatsoever.

Nonetheless, Quentin Smith (a philosopher at Western Michigan) has argued that quantum mechanics provides us with some evidence that events can occur uncaused. It is true that Heisenberg's uncertainty principle guarantees that there are certain microscopic events that cannot be predicted in advance. Smith's argument depends on his identification of causation and predictability: where there is unpredictability, there is an absence of causation.

This is a highly controversial view of causation. In two weeks, we will spend some time considering a variety of conceptions of causation. For now, let me say that Smith seems to have confused causation with determinism. There is no absurdity in the idea of indeterministic, non-necessitating causation. The decay of a uranium atom is caused by the preceding state of the atom, whether or not anything about that state determined or necessitated that the decay should occur when it did. Similarly, my power of will is the cause of my free actions, even if those actions were not predetermined by any state of that will.

Others have used the creation of virtual particles from the vacuum as evidence that things can begin to exist without a cause. If the energy involved is small enough, and the period of existence is short enough, Heisenberg's uncertainty principle allows particles to emerge from "nothing" and to disappear shortly thereafter. However, this argument fails to distinguish between something containing no energy or particles and sheer nothingness. In quantum mechanics, the vacuum is not a nothing. It is the indeterministic cause of the temporary existence of the virtual particles.

Smith has a second argument, one that suggests that the original singularity could not have been caused. In general, causes precede their effects in time. According to the standard model of cosmology, there is no time prior to the singularity. Consequently, we have good reason to believe that the singularity was uncaused.

Of course, the fact that the singularity could not have been caused by any preceding physical state is exactly what the defender of the Kalam argument needs to argue for the existence of a supernatural cause. The issue is: does the impossibility of a physical cause provide any reason for doubting the exitence of any cause whatsoever? This is another crucial issue that we will take up in two weeks.

In thinking about the relationship between time and creation, a number of important questions emerge:

Let us let t = 0 represent the time of the singularity, at which the volume of the universe was zero. Did the universe begin at t = 0, or at some point thereafter. Some have argued that the singularity was not a real event, but only the ideal limit of a process of expansion. The main reason for this opinion is the suspicion that zero volume and infinite density and temperature are not physically possible states of our universe. On this view, the universe begins to exist immediately after t = 0.

This possibility opens again the question of an infinite temporal regress. Were there infinitely many different stages of the universe, each corresponding to positive values of t, closer and closer to 0. If we reject the possibility of infinite regresses, then we must say that there have been only finitely many distinct states of the universe, each taking place during some finite interval of time. Consequently, there must have been some earliest stage of the universe's existence, which endured during the period from t=0 until t=r, for some positive r.

When did the action of God's creating the universe occur? There are four possibilities:

  1. At some time before t = 0.
  2. At time t = 0.
  3. At some time after t = 0.
  4. At no time, from eternity.
If we adopt the first hypothesis, we must distinguish between two kinds of time: physical or measurable time (that begins with the singularity), and metaphysical or supernatural time (that extends for some period, perhaps eternally, prior to the singularity).

The choice between the first three hypotheses presents us with a version of Zeno's paradox. If we say that the cause occurs before t = 0, then it would seem that God's action was ineffectual, since the universe did not come into being until t = 0. Alternatively, if we say that the cause occurred at or after t = 0, it would seem that God's action was redundant, since the universe already existed at the time of God's action.

Zeno's paradox is a problem, not just for the creation, but for any theory of instantaneous action. For example, suppose that one billiard ball causes a second to move, via an event of physical contact. If we say that the second ball is already moving at the time of contact, then the action of the first ball seems to be redundant. However, if we say that the second ball is not yet moving at the time of contact, then the action of the first ball seems to have failed to have any effect.

The most common solution to the paradox takes the following form. Think of the cause and the effect as taking place over finite intervals, not at instantaneous points. Causes and events should be adjacent events -- sharing a common boundary-point. At the boundary point, neither event is taking place, although one is in state of ceasing-to-be, and the other in a state of beginning-to-be. For example, at the point of contact, the second ball is not yet moving, but it is in a state of beginning-to-move. Similarly, we could say that at time t = 0, the universe does not yet exist, but it is in a state of beginning-to-exist. As I suggested before, the first stage of the universe's existence is an interval beginning at t = 0.When, then, does God's act of creation take place? We must locate it either at t=0 (as an instantaneous event), or outside of our time dimension altogether.

Can an event or situation in timeless eternity have an effect in time? Can there be other time dimensions, unrelated to our own, and can events in one dimension affect those in others? Once again, we find ourselves confronting deep questions about the relation of time and causation?

Assuming that the universe begins to exist at t = 0, what "precedes" the universe (in the causal order)? Again, there are several possibilities:

  1. An infinite regress empty time.
  2. An infinite regress of time, filled by a variety of states of the Divine Mind.
  3. An infinite regress of time in another dimension, filled by a variety of states.
  4. A timeless state of eternity.
Someone who accepts the Kalam arguments against the possibility of an infinite past will be forced to accept either (1) or (4). Al-Ghazali and William Lane Craig both seem to opt for (4). Hugh Ross, in contrast, seems to embrace option (3). He argues that that time is, by definition, the dimension of causal order. Consequently, if there is no temporal priority, there can be no causal priority.

Options (2) and (3), if they both include a God whose mental past is infinitely long, both run afoul of the Aristotelian/falsafa cosmological argument, since they would commit us to an infinite causal regress involving the internal states of God's mind.

Some early Moslem thinkers, including al-Kindi, adopted option (1). They argued that only the exercise of God's free will could explain why the universe came into being when it did, rather than earlier or later. All of these moments of empty time were equivalent, and al-Kindi argued that it is the function of the will to choose between indistinguishable options.

The Nature of the Creator

If the Kalam argument is successful, we reach the conclusion that the universe has a cause. This cause must itself be without beginning (since otherwise, it would be merely part of the universe, and not its cause). The cause must have immense power, in order to bring the universe into existence. However, it is difficult to see how the Kalam argument can give us the existence of an infinite or necessary being. It also has some difficulty in establishing the personality of the cause.

As I mentioned above, some defenders of Kalam have argued that the cause of the universe must be a personal creator, endowed with free will, since otherwise it would be impossible to explain how the universe could have come into existence when it did, rather than earlier. These thinkers introduced the concept of "determination" to describe this indeterministic relation between God and the beginning of the universe.

William Lane Craig argues that only a personal, omnipotent being could, acting from a timeless eternity, bring into being a world of time. Craig imagines a divine act of fiat ("Let there be time..") occurring contingently in the realm of timelessness, thereby bringing about the dimension of time. He concludes that we can best explain the universe by postulating a personal creator.

Does the idea of a creation ex nihilo, the contingent bringing-into-existence of a world, entail that the world have a beginning in time? Some have thought so -- Maimonides and Hawking, to mention two we have discussed. Hawking clearly assumes that if there is no beginning of the world, then the world could not have been created by a personal God. Aquinas, in contrast, disagreed. He contended that God's act of freely creating occurs in eternity. The world resulting from this free act could have a beginning or not, as God chose. As it happens, it seems to have had a beginning, but this is not a necessary condition of creation.