Transcript: Podcast 2- The Cosmological Argument

20 March 2007

Hello, and welcome to The Skeptical Christian Podcast, episode number 2. I’m your host, Kyle Deming.

Alright, well for today’s show we’re going to be taking a look at the Kalam Cosmological Argument for God’s existence for the main feature. We also have a couple of book`reviews- Letter to a Christian Nation by Sam Harris, and also The Kalam Cosmological Argument by William Lane Craig. Then for the audience question we’re going to take a look at Cantorian set theory, and the existence of an actual infinite in the real world. But before we get to any of that, let’s first discuss the news.

News

There is some very interesting news this week. First up, producer James Cameron of “The Titanic” is planning to make a new documentary supposedly proving that Jesus Christ was not raised from the dead. 1 Based on a discovery of 10 ossuary’s, which are bone boxes often used to hold the remains of the deceased in the First Century, Cameron is claiming not only that Jesus Christ was not resurrected, but also that he had a son with Mary Magdelene. Cameron claims to have amassed evidence through DNA tests, archaeological evidence and Biblical studies that demonstrates that the 10 ossuary’s belong to Jesus and his family.

Does this sound to anyone else like another overblown, sensationalistic archaeological discovery? Well, that does seem to be the case. According to an article at Breitbart.com, archaeologists have given these claims little credibility. 2 According to Amos Kloner, “It was an ordinary middle-class Jerusalem burial cave. The names on the caskets are the most common names found among Jews at the time.” Kloner also points out that Jesus’ father was a humble carpenter who could not afford a luxurious crypt for his family.

And, in fact, there may be no ossuary with Jesus’ name on it anyways. Stephen Pfann thinks that the name on the casket may have been misread, and should actually reflect the name “Hanun.”

But, as Kloner points out, even though the idea fails to hold up by archaeological standards, the sensational nature of the claims will make for profitable television. It’s unfortunate that this sort of hype gets built up so much, but thinking Christians will find no reason to give up their faith, despite Cameron’s bloated claims.

Also newsworthy, it appears that Walden Media, who released the Chronicles of Narnia in 2005, are planning to create an adaptation of C.S. Lewis’s The Screwtape Letters. The Screwtape Letters is a short book written from the perspective of a senior demon who instructs his nephew in a series of letters on how to undermine the faith and promote sin to an earthly man known only as “the Patient.” It is a terrific book, probably my favorite Lewis book, and I am excited to see how they adapt this odd book for the big screen. It is currently slated to be released some time early in 2008.

Main Feature: The Cosmological Argument

The main feature for today’s show is one of my personal favorites- We’re going to be having a look at the Cosmological Argument for God’s existence. The Cosmological Argument is one of the most famous arguments for God’s existence, with roots going all the way back to Plato and Aristotle. Actually, there are several forms of Cosmological Arguments. I am going to focus on one version of the argument known as the Kalam version. This is a deductive argument with the following premises:

1. Everything that begins to exist requires a cause.
2. The universe began to exist.
3. Therefore, the universe has a cause.

The defender of the Kalam Cosmological Argument needs to show that the first and second premise are more plausible than their contradictories. With this in mind, let’s take a look at the premises.

The First Premise

What sort of evidence is there for the first premise? I would like to offer two separate lines of evidence.

1. First of all, the 1st premise is intuitively plausible. It is a common sense notion that things which begin to exist require a cause. We recognize this intuition whenever we hear a noise in the background and we ask, “What caused that noise?” If someone were to answer: “Nothing caused that noise. It just happened.” we would consider his answer nonsensical. We all know that there is a cause for the noise.

Indeed, serious reflection about the principle confirms the initial plausibility we give it in everyday life. How could something come to exist literally for no reason? If the first premise is intuitively obvious, then we should believe it unless there is some sort of good evidence that it is false.

2. The premise that everything that begins to exist has a cause is constantly confirmed by our everyday experience, and never falsified. Whenever we search for the underlying cause of something, there always ends up being some sort of cause. In fact, virtually all scientific knowledge is based on the causal principle: scientists try to find the underlying causes of phenomenon that occur in the universe. But if the first premise enjoys so much empirical support and seems intuitively obvious, then why should we reject it?

Therefore, the first premise enjoys unrivaled empirical confirmation, and it is intuitively plausible, or, I would argue, obvious. Thus, if someone wishes to reject the first premise, they must raise very strong counterevidence.

At this point, I would like to consider some common objections to the first premise. Some have claimed that so-called ‘quantum vacuum fluctuations’ demonstrate that, actually, things begin to exist uncaused all the time.

However, the idea that quantum vacuum fluctuations entail something coming to be out of nothing is misleading. Although normal usage of the word “vacuum” implies nothing, the quantum vacuum is anything but. In actuality, the vacuum is a sea of fluctuating energy. Paul Davies, an acclaimed physicist, has said, concerning quantum fluctuations: “The processes described here do not represent the creation of matter out of nothing, but the conversion of pre-existing energy into material form.” 3 Basically, in these quantum vacuums energy briefly turns into matter, what is known as “virtual particles.”

Thus, virtual particle production in quantum vacuums does not counter the strong evidence for the first premise.

Second Premise

What about the 2nd premise? For a long time, scientists and philosophers have answered versions of the Cosmological Argument by countering that the universe has existed forever. By their thinking, if the universe has existed forever, then it does not require a cause.

However, scientific evidence has shown without a doubt that the universe has not existed forever. There are two general classes of evidence for a beginning to the universe: evidence for expansion of the universe and evidence from thermodynamics. I will consider both avenues of evidence here.

First: Evidence for the expansion of the universe. By analyzing galactic redshift, Edwin Hubble proved in 1929 that all galaxies are receding from ours at a velocity proportional to their distance from us. What’s more, the rate of recession is the same in all directions. This provides undeniable evidence that the universe is expanding.

You may be wondering, “What is galactic redshift?” Well, redshift occurs when visible light that is emitted from something is shifted towards the red end of the electromagnetic spectrum. This occurs when there is an increase in the wavelength of the light received compared to the wavelength when the light was first emitted. Even if these concepts are difficult to grasp, the upshot is this: the galaxies have redshift, therefore we know that the galaxies are getting farther away. And, if the entire universe is expanding, then, looking back in the past, the universe was smaller than it is now. If we continue to look back, eventually we reach a point at which the entire universe is rolled up into a single, infinitely dense point- known as the singularity. Therefore, a finite time ago, the universe began to expand from this singularity in what is commonly known as “The Big Bang.”

Now, the Big Bang theory obviously has some important physical implications. One important prediction of the theory is that the universe used to be extremely, extremely hot when it was very small. As the universe has expanded, it has cooled off. Based on the Big Bang model, physicist George Gamow predicted in 1946 that there would be a microwave background radiation still detectable in the universe as a result of this earlier, hotter time. In 1965 this background radiation was detected. 4 This provides excellent confirmation of the Big Bang theory, and, therefore, for a universe with a beginning.

The Second major form of evidence for a beginning to the universe is the evidence from thermodynamics. According to the second law of thermodynamics, processes taking place in a closed system always tend toward a state of equilibrium. This means that, if a system does not receive energy from an outside source, then differences in temperature, pressure, and density will tend to even out.

Now, the universe is clearly a closed system, since it is all that exists. Therefore, the universe is currently progressing towards complete thermodynamic equilibrium, known as ‘the heat death’ of the universe. Since the universe is expanding too fast to ever recontract, this entails that the universe will eventually run out of energy. All the stars will burn up, and the universe will keep expanding as space becomes an ever-more diluted soup of elementary particles.

Now, we must ask ourselves the natural question- if the universe has existed for an infinite amount of time, then why is it not already in this state of heat death? The answer: The universe has not existed forever; it had a beginning a finite time ago.

Either one of these evidences taken by themselves- evidence for the Big Bang cosmological model, and the evidence from thermodynamics, would be more than sufficient to establish the case for the second premise. As a result of these evidences, among others, virtually all scientists now concede the beginning of the universe.

At this point I would like to consider a few possible objections to the second premise. Some may claim that the Big Bang model is not the end-all, and, in fact, an oscillating model of the universe may be true. An oscillating model is similar to the Big Bang, except that the universe eventually begins to recontract until it is condensed again in what is commonly referred to as a “big crunch.” After this, the universe experiences another big bang, and the process repeats for all eternity. If this model is correct, then the universe never had a beginning- and we simply find ourselves in one of an infinite number of universe expansion periods.

However, almost everyone has given up on these models because they are so problematic. Here I will mention 4 problems with the oscillating model.

1.) There is no actual evidence in favor of oscillation. If oscillation is assumed merely to overcome the evidence for a Creator of the universe, then it is entirely ad hoc and unjustified.

2.) There is no known mechanism for a supposed “bounce back” after a theoretical “big crunch.” As the late Professor Tinley of Yale stated: “even though the mathematics say that the universe oscillates, there is no known physics to reverse the collapse and bounce back to a new expansion. The physics seems to say that those models start from the Big Bang, expand, collapse, then end.” 5

3.) Recent measurements have shown that the universe is expanding at “escape velocity”. This means that the universe is moving too quickly to ever collapse back into a “big crunch”, thus making the oscillating model impossible. According to scientists Sandage and Tammann, “Hence, we are forced to decide that . . . it seems inevitable that the Universe will expand forever”; they conclude, therefore, “the Universe has happened only once.” 6 In fact, scientists are concluding that the acceleration is actually increasing, destroying any hope for an oscillating model. 7

4.) Thermodynamic properties of the universe dictate that, even if the universe did oscillate, an eternal universe could not occur. This is because, the farther back in time one goes, the shorter the time span of oscillations, or rotations. Thus, the universe could not be eternal. A scientific team under Duane Dicus came to the following conclusion: “The effect of entropy production will be to enlarge the cosmic scale, from cycle to cycle. . . . Thus, looking back in time, each cycle generated less entropy, had a smaller cycle time, and had a smaller cycle expansion factor than the cycle that followed it.” 8 Based on this data, Novikov and Zeldovich stated: “The multicycle model has an infinite future, but only a finite past.” 9 Thermodynamics- the most overriding laws governing the universe, prevent oscillating models from working.

Thus, we see that the oscillating models are false, and we are stuck answering the stubborn question, what is the cause of the universe?

With both the second and first premise amply supported, we have now reached our conclusion that the universe has a cause. However, some may rightly point out that this conclusion doesn’t necessarily point to an intelligent creator. However, a philosophical analysis of the type of cause required to make the universe reveals just such a creator.

At this point it is important to mention that the Cosmological Argument does not need to demonstrate with absolute certainty that the Christian God exists in order to be a powerful evidence for theism. For example, the Cosmological Argument can obviously not tell us anything about the moral character of the Creator. But the argument does establish the existence of God, I think. Here I would like to distinguish between a ‘minimalist’ conception of God and a Christian conception of God. A minimalist conception is concerned with what qualities an entity must necessarily have in order to be reasonably called God. The Christian conception is much fuller and more detailed. But the minimalist conception of God is useful because it allows us to see what we really must demonstrate if we want to make an argument for God’s existence.

What attributes does God need to possess, minimally, to be considered God? I would argue that the being must 1.) exist outside of the physical universe, 2.) have existed for an eternity or timelessly and 3.) must be a personal being. If you are speaking of a timeless, personal being who exists outside of the universe, I think it is fair to say that you are talking about God.

So, now we must ask the important question- does the cause of the Cosmological Argument require at least these three important attributes? Let’s consider them in turn.

1.) Must exist outside of the physical universe.

Since the cause created the entire universe, it is impossible for the cause itself to be inside the universe. If it were, this would mean that the cause created itself, which is contradictory.

2.) Must exist eternally or timelessly.

We have already seen that, according to our first premise, everything which begins to exist requires a cause. Therefore, if the cause of the universe had a beginning, then we could sensibly ask the question, what caused the cause? We would then be asking for the ultimate cause of that cause. Eventually, we must reach a point in which the cause did not have a beginning. Therefore, the cause of the universe must exist timelessly in order to escape the need for causality.

3.) Must be a personal being.

This is probably the most controversial and important step in the argument. Once the nonbeliever has admitted the existence of a personal Creator, the game is up. If the cause of the universe can be shown to be a personal being, then we can be confident that the Cosmological Argument does prove that God exists.

“According to the Islamic principle of determination, when two different states of affairs are equally possible and one results, this realization of one rather than the other must be the result of the action of a personal agent who freely chooses one rather than the other. Thus, while it is true that no mechanical cause existing from eternity could create the universe in time, such a production of a temporal effect from an eternal cause is possible if and only if the cause is a personal agent who wills from eternity to create a temporally finite effect. For while a mechanically operating set of necessary and sufficient conditions would either produce the effect from eternity or not at all, a personal being may freely choose to create at any time wholly apart from any distinguishing condition one moment from another.” 10

So, remarkably, the Cosmological Argument demonstrates the existence of a personal Creator.

Well, we have now seen that both premises of the Cosmological Argument are persuasive, and the conclusion entails the existence of a personal Creator of the universe. However, a slew of other objections have been urged which challenge this provocative conclusion. I will now consider a healthy dose of these objections.

1.) Some may point to the Hartle-Hawking model of the universe as a refutation of the argument. This model was articulated in Stephen Hawking’s best seller, A Brief History of Time. This cosmology purports to eliminate the need for a First Cause, even while maintaining that the universe has not existed forever.

Unfortunately, the Hartle-Hawking model only works by plugging imaginary numbers, such as the square root of negative 5, into equations. Since there is no real number for the square root of – 5, it is referred to as an imaginary number. The Hartle-Hawking model uses these numbers in order to create a concept called “imaginary time”, which, when plugged into the equations, eliminates the need for a First Cause. 11 However, this whole line of thinking is just confused. The positing of imaginary time is bad metaphysics. What are we supposed to make of the concept of “imaginary time”? Those who promote the Hartle-Hawking model have the burden of proof to enlighten us as to what this combination of words really means. Otherwise, we might as well say that “blarks” eliminate the need for a First Cause. Hawking’s only real response to this charge is that imaginary time is supposedly a “well-defined mathematical concept.” Nevertheless, the fact that it is mathematically well-defined does not demonstrate its applicability in the real world.

Another problem with plugging imaginary numbers into the time dimension in these equations is that it forces one to recognize time as another spatial dimension. However, this is more bad metaphysics, since space and time are inherently different. According to William Lane Craig:

“Space is ordered by a relation of betweenness: for three points x, y, and z on a spatial line, y is between x and z. But time is ordered in addition by a unique relation of earlier/later than: for two moments t1 and t2 in time, t1 is earlier than t2, and t2 is later than t1.” 12

Thus, it is seen that time and space are distinct. Therefore, the Hartle-Hawking model receives a further blow. Given that the theory involves at least two metaphysical absurdities, we are justified in rejecting the Hartle-Hawking model as a valid cosmology.

2.) One more alternative cosmology should be considered here- so called Vacuum Fluctuation Models, first developed by Edward Tryon in the 1970s. These theories hold that what we consider the universe is really just a small part of a larger ‘universe-as-a-whole.’ This super-universe is thought to be a vacuum in a steady state, with sub-atomic energy fluctuations creating material particles out of the energy in the vacuum. According to this model, then, our universe never went back to an initial singularity as predicted in the Big Bang model, rather, it emerged supposedly uncaused out of this super-universe vacuum state, paralleling the creation of virtual particles previously discussed.

Beyond the shaky theoretical foundations undergirding these theories, there is another severe problem with the model that has prevented it from receiving a wide acceptance in the scientific community. The problem is that, given the super-universe vacuum, there is a certain probability of a universe popping into existence at any point in space. Thus, given infinite past time, universes would have emerged at every point in the vacuum, and their expansion would cause them to coalesce and collide with one another. These predictions completely contradict our actual findings in the real world, and so these vacuum fluctuation models have to be abandoned. 13

3.) Probably the most frequent response to the Cosmological Argument is- “If God caused the universe, what caused God?” However, while this response may work against some versions of the Cosmological Argument, the Kalam version escapes unscathed. Recall that the first premise does NOT claim that “everything requires a cause.” It only claims that “Everything that begins to exist has a cause.” Since God did not begin to exist, but rather existed timelessly without the universe, we do not need to explain the existence of God.

It is not question begging to assert that God is eternal, because atheists in the past used to identify the universe as eternally existing. As pointed out previously, this is frequently how they denied the Cosmological Argument. That was, of course, before the discovery of the numerous scientific evidences against the eternality of the universe. Therefore, the atheist has no valid ground to declare that pronouncing God as eternally existing involves special pleading.

Moreover, to argue that the theist is employing special pleading actually involves backwards thinking. It is actually the premises of the Cosmological Argument, along with a philosophical analysis of the type of cause necessary to create the universe, that necessitates the postulation of a timeless creator. So in the end, we see that this simplest of counters to the Cosmological Argument is groundless.

4.) A somewhat more rare objection to the argument claims that premise 1 involves circular reasoning since the only possible eternally existing entity is God.

The objection here is the claim that premise (1) (Everything which begins to exist requires a cause) is circular reasoning, since the set of all things that exist eternally (according to the theist) consists only of God. In other words, since God is the only eternally existing entity, the premise might as well state:

1’ Everything except God requires a cause.

The atheist then complains that this is nothing but circular reasoning or special pleading. However, it is not the theist’s contention that God is the only potential eternally existing entity. For instance, it is possible that there exists more than one god (obviously, this is just a theoretical possibility, not potential Christian doctrine). Or, it is possible that there are physical objects that have existed forever outside of the universe (for example, it is possible that God has a book, and that book has existed alongside Him forever). Therefore, since it is at least possible that something other than God has existed eternally, it is not circular reasoning to claim that everything which begins to exist requires a cause.

5.) Some will argue that the Cosmological Argument equally demonstrates the truth of polytheism, the existence of multiple gods. This is a rather strange objection, since most who make it don’t believe in multiple gods anyways! This is just a last ditch effort to try to undermine the monotheist’s faith.

Nevertheless, there is actually a compelling reason to accept the existence of one Creator. The principle of Ockham’s Razor tells us that we should prefer the simplest hypothesis to explain the relevant data. Since one Creator will do the job, it is absolutely unnecessary to postulate multiple Gods.

Notice also that the supporter of the Cosmological Argument does not need to absolutely prove that the Christian God exists. The argument shows that God exists, as defined by the minimalistic criteria earlier in this episode.

6.) The final objection I want to look at is the claim that it is impossible for the origin of the universe to have a cause, since the cause cannot be after the Big Bang, and it cannot be before the Big Bang, since the Big Bang marks the beginning of time itself. However, this objection overlooks the fact that the universe’s creation by God could be simultaneous with the Big Bang. In fact, this seems to be the most plausible view from the Christian perspective. Since we believe that God is omnipotent, why should we expect there to be any delay between God’s willing the universe to exist and the universe actually existing? Simultaneous causation is actually the most plausible view of the universe’s creation by God, and so this objection fails to undermine the Cosmological Argument.

Conclusion

So, in sum, we have looked at a very simple but powerful argument for God’s existence. To recap, the first premise, which states that everything which begins to exist requires a cause, is both intuitively plausible and confirmed by all experience. We also saw that attempts to undermine this premise with reference to quantum vacuum fluctuations involved a misunderstanding of the nature of the quantum vacuum and so do not furnish a true counterexample.

The second premise, which contends that the universe began to exist, was supported with reference to Big Bang theory and thermodynamics. Big Bang theory is remarkably well-supported by galactic redshift and cosmic microwave background radiation. In addition, thermodynamics implies that our universe cannot have been running forever. We also saw that a major attempt to avoid a beginning, the oscillating model, is scientifically untenable and cannot in any case escape the problem of thermodynamics.

The conclusion, that the universe has a cause, is found to be a stunning discovery once we philosophically analyze the type of cause required. The cause of the universe would need to be a personal being who exists timelessly outside of the physical universe.

Despite a slew of objections urged against this argument, none of them are at the end of the day very persuasive. The Kalam Cosmological Argument stands as a powerful and compelling proof of theism.

Book Reviews

Letter to a Christian Nation

Letter to a Christian Nation is a bestseller by Sam Harris released in 2006. In this very short book, Harris takes some of the more general criticisms of religious faith found in his first book (The End of Faith) and applies them to so-called fundamentalist Christians.

Unfortunately, Harris never deals with any of the arguments for the Christian faith given by intelligent believers. In fact, he seems to think it is a given that all Christians accept their beliefs on the basis of a blind leap of faith. For those Christians who do have good reasons for their beliefs, Harris’s work shouldn’t be considered a serious threat. One will look in vain for any sort of consideration of arguments for God’s existence or the Resurrection of Jesus Christ.

Actually, Letter to a Christian Nation is mostly a social critique of the actions of fundamentalist Christians. However, even if Harris’s main points hold sway, his conclusions don’t really affect the truth of Christianity. For example, take this quote from Harris on page 25-

“Religion allows people to imagine that their concerns are moral when they are not- that is, when they have nothing to do with suffering or its alleviation. Indeed, religion allows people to imagine that their concerns are moral when they are highly immoral- that is, when pressing these concerns inflicts unnecessary and appalling suffering on innocent human beings. This explains why Christians like yourself expend more ‘moral’ energy opposing abortion than fighting genocide. It explains why you are more concerned about human embryos than about the lifesaving promise of stem-cell research. And it explains why you can preach against condom use in sub-Saharan Africa while millions die from AIDS there each year.”

Well, first of all, I must beg to differ with Harris about the moral importance and energy I place on genocide. This aside, the point is that Christians fall on both sides of each of these issues. Some are pro-life, and some are pro-choice. Some are OK with embryonic stem cell research, and some aren’t. Some preach against condom use in Africa, but many do not. 14 At the end of the day, what does this have to do with the truth of Christianity? Absolutely nothing. At best, Harris is critiquing a certain type of morality held by certain Christians.

But at the end of the day, what can we really expect from a 95-page book that is supposed to undermine the Christian faith? Letter to a Christian Nation is, at best, a rant against the influence and morality of a particular type of Christian. Yet, Harris covers such a broad scope in such a small space that he never has a chance of developing any sort of substantive case against Christianity. My rating for this book: 1 star out of 5.

The Kalam Cosmological Argument

It seems only appropriate to review the The Kalam Cosmological Argument by William Lane Craig, written in 1979. This is a relatively advanced book that lays out in detail the case for the Kalam argument by one of its most persuasive advocates.

In addition to providing many of the arguments mentioned in this episode, Craig discusses the history of the argument through medieval Islamic theology to the present day. The book focuses almost entirely on the second premise of the argument, concerning the beginning of the universe. In addition to providing scientific evidence, Craig makes a convincing case for the philosophical impossibility of an actually infinitely old universe. Arguing that actual infinities cannot exist in the real world.

The biggest problem with the book is that it is somewhat dated. Craig does not put enough effort into defending the first premise, largely because he believes that scarcely anyone would deny it. However, this does not reflect current attitudes, where most people are forced to grant the beginning of the universe and so must critique the first premise in order to refute the argument. For those interested in reading Craig’s responses to more recent objections to the Cosmological Argument, other works should be pursued.

Nevertheless, Craig’s book is a well-written and compelling defense of the Cosmological Argument. My rating for The Kalam Cosmological Argument is 4 stars out of 5.

Audience Question

Ok, it’s time for the audience question for the week. Parvinder asks; Does Cantorian set theory demonstrate that it is possible for an actual infinite to exist?

This may seem like a rather esoteric question, but it actually has a lot of relevance for the main feature of this podcast. As I pointed out in my review of Craig’s book on the Cosmological Argument, there is a whole other line of evidence for the beginning of the universe that is completely independent of the scientific confirmation found in Big Bang theory and thermodynamics. This is based on the impossibility of an actual infinite in the real world. If it can be shown that an actual infinite cannot exist in the real world, then we can deduce that the universe had a beginning, since it would otherwise have already been through an infinite number of past events.

Now, some philosophers have argued that a real infinite cannot exist because it leads to the existence of absurdities. Without going into too much detail, basically, when you consider imaginary cases in which an infinite number of objects exist in the real world, you encounter situations in which it is impossible to add or subtract an object to that group, which is clearly absurd because there is nothing to physically stop us from, say, adding one more book to a library shelf.

In any case, some people claim that we know that it is possible for there to be an actual infinite because Cantorian set theory proves it is possible. What Cantor did was establish the possibility of conceiving of the infinite as a completed whole, which enables us to speak abstractly of infinite sets. He didn’t try to mentally synthesize the infinite by counting, he viewed the infinite series of natural numbers from outside and grasped them conceptually as a totality.

Basically, Cantor showed that it is possible to consistently talk about the infinite in the mathematical realm. But does this prove that it is possible for the actual infinite to exist in the real world? It does not, as many mathematicians have recognized. For example, mathematician Abraham Robinson stated that “Cantor’s infinities are abstract and divorced from the physical world.” 15 This point is easily recognizable once one realizes that three out of the four major systems of thought about the existence of universals does not grant mathematical entities any actual existence in the real world. These four views are Nominalism, Conceptualism, Formalism, and Platonism.

According to Nominalism, there are no abstract entities such as number or sets, there are only individuals. Conceptualism holds that abstract entities, including numbers and sets, are created by and exist only in the mind. They do not have any real ontological existence in the actual world. Formalism says that mathematical systems are nothing but formalized systems that have absolutely no counterparts in reality. According to formalists, the only true condition of mathematics is freedom from contradiction.

Platonism contends that mathematics involves discovery of numbers, properties, and sets which actually objectively exist independent of the thoughts of the mathematician. Therefore, if one grants the success of Cantorian set theory, then a Platonist view does guarantee that actual infinities exist as part of reality.

However, Platonism needs to be argued for- it cannot simply be assumed. Thus, those who say that Cantorian set theory in and of itself implies the actual existence of the infinite have to argue for the truth of Platonism. Yet, Platonism suffers from several antinomies which argue against the view. I’ll give one example known as Russell’s antinomy. In order to avoid butchering the explanation, I will simply quote at length from Craig’s book,

“Russell’s antinomy proceeds on the assumption that it is meaningful to ask whether a set is a member of itself. Some sets are clearly not members of themselves. For example, the set of all pigs is not itself a pig, and, hence, it is not a member of itself. But some sets appear to be members of themselves; for example, the set of all things mentioned in this chapter is itself mentioned in this chapter and so would seem to be a member of itself. But what about the set of all sets that are not members of themselves- is it a member of itself? Denoting this set by S, we discover that if S is a member of itself, then it cannot be in S, for S includes only sets that are not members of themselves. But if S is not a member of itself, then, since it fulfills the condition for being in S, it is a member of itself. Thus, we reach the contradictory conclusion that S is a member of S if S is not a member of S.” 16 This is clearly a huge contradiction.

In any case, these kinds of paradoxes are difficult to explain under the Platonist view, and less hard to explain under the other views which are not committed to accepting the real existence of numbers, properties, and sets.

Conclusion

Ok, well that about wraps up everything for today’s show. I would just like to remind everyone to please send in their questions to kyle@skepticalchristian.com. You can also leave comments or ask questions at the podcast blog which can be found in the upper navigation at skepticalchristian.com. I look forward to any feedback you can give me on this show.

That’s all for The Skeptical Christian Podcast, episode number two. Thanks for joining me.

NOTES:

1. McGirk, Tim Jesus: Tales from the Crypt Found at http://time-blog.com/middle_east/2007/02/jesus_tales_from_the_crypt.html?iid=chix-digg

2. Thompson, Marshall. Scholars Criticize New Jesus Documentary. Found at http://www.breitbart.com/article.php?id=D8NHFDRG3&show_article=1

3. Davies, Paul. God and the New Physics (New York: Simon & Schuster, 1983), pg. 31.

4. Craig, William Lane. The Kalam Cosmological Argument (Wipf & Stock Publishers, 1979)

5. Beatrice Tinsley, personal letter. Cited from Craig, William Lane at http://www.leaderu.com/truth/3truth11.html

6. Sandage, Alan and G.A. Tammann. Steps Toward the Hubble Constant. VII Astrophysical Journal 210 (1976): 23, 7.

7. See http://physicsweb.org/articles/news/2/11/3/1

8. Duane Dicus, et.al. Effects of Proton Decay on the Cosmological Future. Astrophysical Journal 252 (1982): l, 8.

9. I.D. Novikov and Ya. B. Zeldovich, Physical Processes Near Cosmological Singularities. Annual Review of Astronomy and Astrophysics 11 (1973): 401-2.

10. Craig, Kalam

11. Guthrie, Shandon. Theism and Contemporary Cosmology. Found at http://sguthrie.net/theism_and_contemporary_cosmology.htm

12. Craig, William Lane. Reasonable Faith (Wheaton: Crossway books, 1994) p. 112.

13. Guthrie, Theism

14. For example, I argue that birth control in the context of a marriage relationship is perfectly moral. See my article Is Birth Control a Sin?

15. Craig, Kalam

16. Ibid.



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