Tuesday, February 10, 2009
The Kalam Cosmological Argument
Disclaimer: There is very little that can be known with absolute certainty. Logical and mathematical proofs might be among them, but almost any proposition can be shot down with enough hyperskepticism. I could deny many propositions that virtually everyone else would agree are true; that other minds exist, that the outside world is real, that George Washington was the first US President. While there is no absolute proof that these things I might be trying to deny are true, there is good reason to believe them, because the evidence better supports them than it supports their negations.
Deductive logic operates on deriving a conclusion from premises. If each premise is more plausible than its negation, and the connection between the premises and the conclusion is valid, then the conclusion follows logically and inescapably.
Here are the Big Four arguments in natural theology and what they attempt to demonstrate:
Kalam Cosmological Argument: There cannot be an actually infinite number of past events, therefore, matter cannot be eternal. There was a first event. The first event had to be caused. The cause for the first event had to be uncaused, nonphysical and had to have the properties of volition and causal potency
Teleological Argument: That from which reality came had to possess intelligence, volition, and causal potency
Ontological Argument: That which is greater than anything that can be conceived actually exists in all possible worlds
Moral Argument: Objective morality exists, and that from which objective morality came had to possess the property of morality
The Kalam Cosmological Argument
1. Whatever begins to exist has a cause
2. The universe began to exist
The universe has a cause
Premise 1 is supportable both philosophically and scientifically. Philosophically, this is a first principle of metaphysics. Out of nothing, nothing comes. None of us believes that a raging Bengal tiger will pop into existence behind us and devour us while we try to read this post. No one believes that a piano will pop into existence 5 stories above their car and crush it. The idea of things popping into existence uncaused out of nothing is worse than magic. With magic, at least you have a magician and a hat! If things could could come into being uncaused out of nothing, then it is inexplicable why anything and everything doesn't just pop into being. Why doesn't a giant roll of $100 bills pop into my pocket out of nothing? I sure would like that!
Scientifically, this principle has been repeatedly verified and never been falsified. How could we even do science if things could just come into existence without a cause? Evolutionary biologists believe that all life evolved from a single-celled lifeform because they observe a pattern of fossils in the ground and similarities in the genetic code. If the fossils and genes could have come into existence without a cause, then all the evidence for evolution is undermined.
A common objection to this premise is that virtual particles seem to pop into existence out of nothing. This is part of quantum physics, which has a mathematical core, and many competing conceptual models. The Copenhagen interpretation states that particles appear out of a quantum vacuum, which is this sea of fluctuating energy, still governed by physical laws, not out of nothing. When quantum fields line up in a certain way, particles come into existence. This is no more mysterious than when I rearrange my fingers in a certain way, fists come into existence. The particles also cannot stay in existence any longer than the Heisenberg Indeterminacy Principle allows. To do so would violate physics.
Therefore, we have better grounds for believing Premise 1 than its negation.
But what about the universe itself? Premise 1 is not a physical principle, it is a metaphysical principle, "being cannot come from nonbeing" and applies to all of reality. You cannot dismiss this principle like a taxicab when you get to the origin of the universe itself. Prior to the big bang, there isn't even the potentiality of the universe existing, as there was no space or time in which for events to work.
There are two philosophical arguments and two scientific arguments for Premise 2
Philosophical Argument 1
An actually infinite number of things cannot exist.
A beginningless series of events involves an actually infinite number of things
Therefore, a beginningless series of past events cannot exist
An Actually Infinite Number of Things Cannot Exist
Now, actual infinity, represented by aleph, is different than potential infinity, represented by the lazy eight. A potential infinite is a collection which is at every point, finite, but always growing toward infinity as a limit. It is finite at every point, but it grows, ceaselessly, without limit. It is used in calculus. By contrast, an actual infinite is a collection with an actual infinite number of members, which exceeds any natural number. It is not growing toward infinity, it is actually infinite.
The distance between any two points can be divided in half, and then in half again, on and on without limit. This is a potential infinite, not an actual infinite. To presuppose that any distance is composed of an actually infinite number of parts is begging the question.
In fact, if an actually infinite number of things could exist, it would violate the law of non-contradiction.
For example, if you could have an actually infinite number of things in reality, you could subtract various quantities from your infinite collection. Suppose we have the numbers, 1,2,3... to infinity. If we subtracted all of the odd numbers, we would have all of the even numbers. We have subtracted an infinite number of odd numbers from an infinite number of actual numbers, and we got an infinite number of even numbers. Infinity - infinity = infinity. What if we subtracted from this set all numbers greater than 4. We have four natural numbers left. Infinity - infinity = 3. You will any number you want, even though in each case, you have subtraced identical quantities from identical quantities. This is a self-contradiction, which is why in mathematics, you are prohibited from subtracting from actual infinity.
If an infinite number of things existed in reality, you could not prevent someone from taking some of them away. If I had an infinite number of marbles, I could give some to you. I could give you all the odd numbered marbles, or I could give you a few handfuls, or all of them. Self-contradictions will result.
This concept was developed by David Hilbert, one of the greatest mathematicians of the 20th century. He also demonstrated this absurdity with his paradoxical Hilbert Hotel.
The typical objection is that modern set theory proves that an actually infinite number of things can exist. Set theory states that an actually infinite number of natural numbers can exist in the set aleph-null. This is the typical refutation, and it collapses, because:
1. Not all mathematicians agree that actual infinites exist, even in the mathematical realm
2. Existence in the mathematical realm does not imply existence in the real world
When mathematicians say there are an infinite number of numbers in a set, they are postulating a realm of discourse, governed by certain arbitrarily adopted axioms and rules. There is no guarantee that all the axioms and rules are true in the real world.
3. The existence of an actually infinite number of things in the real world would violate the rules of set theory. Subtraction with infinite quantities leads to self-contradictions and therefore infinite set theory prohibits these kinds of operations. You cannot subtract or divide with these numbers because it leads to contradictions, but there is nothing preventing you from doing so in the real world.
A beginningless series of events involves an actually infinite number of things
This is pretty uncontroversial. A beginningless series of events is an actually infinite number of events. An event is a thing. Do I really need to defend it?
Philosophical Argument 2
This argument is wholly independent of Philosophical Argument 1, and does not presuppose it. It is based on the possibility of forming an actually infinite nubmer of things through successive addition.
An actually infinite collection of things cannot be formed by successive addition
The series of past events is a collection of things formed by successive addition
Therefore, the series of past events cannot be actually infinite
An actually infinite collection of things cannot be formed by successive addition, meaning adding one at a time, one after another.
This is called the impossibility of counting to infinity. No matter how high you count, you can always count one higher number. This is also called the impossibility of traversing, or crossing, the infinite. no matter how far you run, you can always take one more step.
Some people have responded to this argument by stating that you cannot form an actually infinite collection of things by beginning at a point and trying to reach infinity, but you can form an actually infinite collection of things by never beginning and ending at a point, but this would be like trying to count down all the negative numbers from negative infinity. It would be like forming an actual infinite by successive subtraction. There are deeper absurdities involved in this method of counting down the negative numbers.
Suppose we meet someone who claims to have finished counting down all the negative numbers, and has just finished today. We might as ourselves "why did he finish his countdown today? Why didn't he finish yesterday, or the day before?" If he has been counting down from infinity, there have been just as many days prior to yesterday as there were prior to today. If he is counting one number per minute, or per hour, given that there were an actually infinite number of hours prior to today as there were yesterday, or why didn't he finish counting down a trillion years ago, or any time in the finite past? At any point, an infinite amount of time would have passed. No matter how far back in the past, you will never find the person finishing. At any point your reach, the man would have already finished his countdown, but if at no point in the finite past, could you find the man finishing his countdown, then it is not true that he has been counting down from eternity.
Therefore, in modern set theory, any notions of successive addition has been done away with. In a set, all members are given simultaneously. They are not formed through successive addition or subtraction.
The series of past events is a collection of things formed by successive addition
The past is not given whole and entire. Events are formed sequentially, one after another. Nor are events formed by subtracting events from the present. Sometimes we speak of an infinite regress of events into the past. Technically, it is our minds that regress into the past, the events are not regressing. They are progressing. One event occurs after another in the direction of the future. The past is a collection of things formed by adding one event after another, until we have arrived at today.
If time had to traverse an actual infinite number of events, it would never get to today.
The scientific arguments exist independently of the philosophical arguments do not presuppose them.
In 1917, Albert Einstein applied his general theory of relativity to cosmology. Einstein initially believed in a steady state theory of the universe. However, he noticed that his equations based on general relativity would not permit such a static universe. Alexander Friedman had used Einstein's formulas to predict that the universe is growing apart.
In 1929, Edwin Hubble, showed that the light emanating from distant galaxies appears redder than it should, because distant galaxies are moving away from us faster than galaxies closer to us. However, he noticed that every galaxy had a red shift. He had noticed the expansion of the universe. Also, according to general relativity, matter is not expanding into pre-existing space, but space itself is expanding. The galaxies are thought to be at rest relative to space, but the space in between the galaxies is stretching.
If you glue buttons to a balloon, and blow up the balloon, the buttons will become farther apart from one another. As you go back in time, everything gets closer and closer, until the entire universe is contracted down to a mathematical point, before which the universe did not exist. That initial point is called a singularity and represents the edge of space and time. On this view, the big bang represents the creation event of all the matter in the unvierse, but of space and time as well. This is now the controlling paradigm for contemporary cosmology. Under this model, the universe came into being at some point in the finite past.
As Barrow and Tipler emphasized: "At this singularity, space and time came into existence, literally nothing existed before the singularity. If the universe originated at such a singularity, we would have a creation ex nihilo."
Argument From Entropy
According to the second law of thermodynamics, processes taking place in a closed system tend toward states of higher entropy as their energy is used up. For example, if you placed a hot cup of water in a room, the heat will be dispersed from the water to the rest of the room until the water and the room reach the same temperature. You would not expect to place a cup of water that is room temperature into a room and come back an hour later to find that the water is now boiling hot.
What happens when the law is applied to the universe as a whole? The result is grim. Scientists believe that in time, the universe will use up all of its energy and become cold, dark and dead. All the stars will burn out, and then protons will decay into positrons and electrons until the universe is nothing but a thin gas that the distance between a positron and an electron will be the size of our present galaxy, growing ever more dilute as it expands into the infinite darkness.
If in a finite amount of time, the universe will achieve this state, why then, given an infinite past, isn't the universe already in such a state?
Objections to the Scientific Argument
The history of cosmology in the 20th century is a history of failed attempts to avoid an absolute beginning to the universe.
The steady state theory was proposed in 1948 by Fred Hoyle. According to this theory, the universe is in a state of cosmic expansion, but as the universe expands, new matter appears in order to fill in the void created by the retreating galaxies. This violates the first law of thermodynamics. This theory never secured a single piece of experimental verification. It was always trying to explain away evidence that contradicted it. Also, the discovery of farther and farther radio galaxies undermined the theory by showing that the universe was different in the past than it is today. The nail in the coffin came when two other confirmations came of the big bang model, namely the synthesis of the light elements (hydrogen and deuterium) in the big bang, as well as the microwave background radiation. While heavier elements are synthesized in the stars, lighter elements could not have been synthesized in them because the temperatures are not high enough. In order to explain these lighter elements, only the big bang could produce enough heat to create these elements. With regard to the microwave background radiation, in 1965 R.W. Wilson discovered that the entire universe is bathed with a background of microwave radiation. This radiation background of a very hot and very dense state of the universe. Under the steady state model, no such condition could be possible, the steady state model was discredited.
The oscillating models of the universe state that if the universe is dense enough, then the internal pull of gravity would eventually overcome the expansion of the universe and pull everything back together again into a big crunch. If the universe were not exactly even in its matter distribution, it was theorized that some of the matter would pass by during the crunch so that the universe would appear to re-expand again. It would bounce back to a new expansion, on and on. This theory was extraordinarily speculative. In 1970, the prospects for this model were severely dimmed thanks to Roger Penrose and Stephen Hawking formulated singularity theorems. They are equations about how singularities form. Under these theorems, an initial cosmological singularity is inevitable for a universe that is under gravitational self-collapse. The universe's matter would not pass each other by, it would collapse into a singularity.
Despite the fact that no spacetime path can go through a singularity, and therefore a singularity marks an edge of space and time, this model persisted, due to its metaphysical implications. Then, three further strikes were lodged against it. First, there are no known physics which could cause a collapsing universe to bounce back into another expansion. It would require a whole new physics, which is completely unknown. Physics predicts that a universe collapsing on itself would not bounce, but would collapse into a singularity. Second, the observational evidence has continued to indicate that the density of the universe is not sufficient to generate a gravitational attraction to halt the expansion of the universe. The most recent evidence indicates that the expansion appears to be accelerating rather than slowing down. Third, the thermodynamic properties of an oscillating model predict the very origin of the universe that proponents of this model sought to avoid. The thermodynamic properties of this model indicate that entropy is conserved from cycle to cycle, making each successive big bang, bigger than the previous one. As you trace this model back in time, each big bang gets smaller and smaller until you come to a smallest cycle and an origin of the universe.
To quote the Russian scientist Sergei Petrovich Novikov: "The multicycle model has an infinite future but only a finite past"
The physicist Joseph Silk estimated that based on the current entropy levels in the universe, the universe could not have gone through more than 100 previous oscillations.
Quantum Fluctuation Models
The next class of models are vacuum fluctuation models, that require the use of quantum physics in addition to general relativity. On the quantum model, certain particles called virtual particles are thought to arise through a release of the energy that is locked up in the quantum vacuum. They exist for a fleeting moment and then dissolve back into this vacuum.
In 1973, a scientist named Edward Tryon speculated whether the universe itself might be a long-lived virtual particle. This led to the vacuum fluctuation models. On these models, the universe that we observe is not the whole universe, rather, it is just a tiny part of a wider, mother universe. This wider mother universe is a vacuum that is filled with energy at a subatomic level. By these fluctuations, many universes are born within the womb of this mother universe. These models did not outlive the 1980s among professional cosmologists. In addition to theoretical problems, these models faced a deep, internal incoherence. According to these models, it is impossible to specify just where and when a fluctuation would occur that would produce a universe. At every point in space, there is a positive probability within a finite interval of time that a universe will form there and grow. If there is a positive probability, given enough time, that a universe will form, then given an infinite past, universes will have formed at every point in the cosmic vacuum, and then will collide with one another and coalesce, forming one infinitely old universe, completely contradicting observation.
Christopher Isham called this problem "fairly lethal to vacuum fluctuation models, which is why they did not find wide acceptance. The only way to avert this problem is to posit an expansion of the cosmic vacuum itself, which reintroduced the singularity problem.
One of the most fertile of the inflation theorists has been Andre Linde, who created the chaotic inflationary model. According to this model, as the universe expands, certain domains in it begin to blow up and expand in a super rapid way. When these domains reach a certain size, they also produce inflation. Imagine a Mickey Mouse balloon where blowing up the main balloon causes ears to spring out of it, and then ears to spring out of those ears, ad infinitum. Under this model, the universe has an infinite future.
However, Linde writes about the problem regarding the past: "The most difficult aspect of this problem is not the singularity itself, but the question of what was before the singularity. This problem lies somewhere at the boundary between physics and metaphysics."
In 1994, Arvin Borde and Alexander Vilenkin developed a theory that showed that any universe that is eternally inflating into the future cannot have a beginningless past. "A model in which the inflationary phase has no end naturally leads to this quesiton. Can this model be extended to the infinite past? This is in fact not possible. In future eternal inflationary spacetimes, such models must, necessarily produce initial singularities."
In response to this, and other problems including the weak gravity conjecture, Linde abandoned the chaotic inflationary theory.
If that was not enough, in 2001 and then again in 2003, Vilenkin and Borde, in cooperation with Alan Guth, the founder of inflationary theory, were able to strengthen their theorem to show that any universe that has been expanding throughout its history must have an inital boundary point in the past.
Hawking Hartle Model
Stephen Hawking and James Hartle formulated a theoretical model to avoid the initial singularity by plugging imaginary numbers into the time variable in Einstein's equations, rounding off the beginning of space and time. It is an irrelevant objection, because it only avoids the singularity, but not the finitude of time. Time is still divisible into a finite number of hours. Also, imaginary numbers are used to grease the math, and have to be converted to real numbers in order to apply to reality. Once the numbers are converted back to real numbers, the singularity reappears.
These models are based upon an alternative to the standard model of elementary particle theory. On the standard model, the fundamental building blocks of matter are quarks. On the string model, the building blocks of matter are tiny, vibrating strings of energy. String theory is so embryonic that its equations have not all been stated yet, much less solved. This has not thwarted cosmologists from attempting to avoid the beginning of the universe by standard big bang cosmology. One of the most popular models is the Ekpyrotic model developed by Paul Steinhardt.
These ekpyrotic scenarios have undergone numerous revisions as deficiencies have been exposed. In the cyclic revision, we are asked to imagine two 3-dimensional membranes existing in a 5 dimensional space. The membranes approach one another and collide, then recede, approach, collide, and recede. Each time the membranes collide, it causes one of the membranes to expand. That membrane is our universe. With each collision, the expansion of our universe is renewed. This model is so highly speculative that it resembles science fiction more than science. It is built on speculation which is built on speculation. There are numerous problems with it. One is that this cyclic model is the oscillating model writ large in 5 dimensions. There is no known physics for the universe to go through a singularity and bounce back. Andre Linde has complained that while this cyclic model has been popular among journalists, it is very unpopular among scientists.
In September of 2001, Borde and Vilenkin, in cooperation with Alan Guth, were able to generalize their model which shows that inflationary models cannot be eternal in the past, to apply to other models including cosmology in higher dimensions.
Conclusion to the Scientific Argument
Science is always provisional, and its conclusions are always tentative. Alternative models will continue to be proposed. As they come and go, with each successive failure, they confirm the beginning of the universe as predicted in the standard big bang model.
There is no other model of the universe which is as mathematically consistent, nor as consistently corroborated by the evidence as the standard model.
As P.C.W. Davies said: "What caused the big bang, one might consider some supernatural force beyond space and time as being responsible for the big bang, or, one might prefer to regard the big bang as an event without a cause. It seems to me that we don't have too much choice. Either something outside the physical world or an event without a cause."
So overwhelmed was the atheist philosopher Quentin Smith that he concluded: "The most rational thing to believe is that the universe came from nothing, by nothing, and for nothing"
This is hyperskepticism at its finest.
Therefore, Premise 2 is more plausible than its negation.
Therefore, there is good reason to believe the universe had a cause.
Implications of the Kalam Cosmological Argument
What could cause the first event? What properties would it have?
It had to be uncaused, or else its cause would be the first event.
It would have to be causally potent, obviously.
It had to be nonphysical, because matter, time, and space came into existence with the big bang
It had to be immutable, or else it would lead to an actually infinite number of past events
It also had to have the property of volition, since only volition can cause without being caused.
Hence, there is good reason to believe:
There cannot be an actually infinite number of past events, therefore, matter cannot be eternal. There was a first event. The first event had to be caused. The cause for the first event had to be uncaused, nonphysical and had to have the properties of volition and causal potency
For further reading on this subject, the Blackwell Companion to Natural Theology will be released in May of this year.
Update: Dan's Disastrous Downfall
The Kalam Cosmological argument is one of the most misunderstood arguments out there. Dan Barker in particular, whose arguments the atheist side borrowed, badly misunderstands why something that begins to exist needs a cause. First, let me lay out three assumptions that I share with Barker.
1. An event is a change in the state of affairs. When an electron moves around a nucleus, that is an event. When light moves through space, that is an event. When a mind produces a thought, that is an event.
2. Time is a sequence of events occurring one after another. When there are no events, there is no time.
3. There is not an infinite number of past events. The past is finite, meaning that there was a first event.
Barker's booming blunder is his assumption that because time began to exist, there is no state of affairs before the first event, and therefore the universe can exist necessarily because there was no time before the universe was. "Asking what existed before the first event is like asking what is north of the north pole." Barker confuses the fact that there was no time before the first event (indeed, the idea of events before the first event is self-contradictory) with the notion that there was no state of affairs before the first event. In fact, if there was a first event, then there had to be some unchanging and therefore timeless state of affairs prior to it. The question is: what was that state of affairs?
On an atheistic view, there was nothing, except perhaps abstract objects such as numbers. How then did this state of affairs give rise to matter, energy, time, and space? If the cause was an impersonal set of sufficient conditions, then it can't exist timelessly, as it is inseparable from its effect. Only a personal agent, an unembodied consciousness can exist timelessly, and then act.
Once you realize this, then admission to those three assumptions leads necessarily and inescapably to a personal creator.