The Beginning of the Universe

(Cross-posted at Rational Thoughts)

I’m currently working on a nine-part series on the kalam cosmological argument and I thought it would be nice to post this particular entry here.

Defenders of the KCA muster several different arguments in support of the premise that the universe began to exist.  These arguments are both philosophical and scientific in nature.  Arguments under the former category involve showing that the existence of an actually infinite number of things is metaphysically impossible. If the universe never began to exist, then its past duration would be actually infinite. Since actual infinities cannot exist, then the past duration of the universe must have been finite, implying that the universe must have begun to exist. Even if one grants that it is possible for an actual infinite to exist, it still cannot be formed by successive addition, and henceforth the past duration of the universe must still be finite. From a scientific perspective, the beginning of the universe is strongly supported by modern big bang cosmology. The proponent of the KCA thus finds himself comfortably seated in the midst of mainstream cosmology. Combined, these two reasons lend strong support to the truth of the second premise.

The Impossibility of Actual Infinities

It’s helpful to distinguish between actual and potential infinities.  Potential infinities are sets that are constantly increasing toward infinity as a limit, but never attain infinite status. A more accurate description would be to say that their members are indefinite. An actual infinite, by contrast, is a set x that contains a subset x’ that is equivalent to x.  That is, they are denumerable.  Phrased in layman’s terms, a set is actually infinite if a part of the set is as big as the whole set.  A potentially infinite set would thus be a set in which a part is less than the whole.  “The crucial difference between an infinite set and an indefinite collection would be that the former is conceived as a determinate whole actually possessing an infinite number of members, while the latter never actually attains infinity, although it increases perpetually. We have, then, three types of collection that we must keep conceptually distinct: finite, infinite, and indefinite. [1]  Because it leads to contradictions and absurdities, an actually infinite set cannot exist in reality.

There are several examples which illustrate the absurdity of the existence of an actually infinite number of things, the most famous of which is known as Hilbert’s paradox of the grand hotel. For the sake of clarity, however, I’ll use a simple example used by Craig:

Imagine I had an infinite number of marbles in my possession, and that I wanted to give you some.  In fact, suppose I wanted to give you an infinite number of marbles.  In that case I would have zero marbles left for myself.

However, another way to do it would be to give you all of the odd numbered marbles.  Then I would still have an infinite left over for myself, and you would have an infinite too.  You’d have just as many as I would — and, in fact, each of us would have just as many as I originally had before we divided into odd and even!  Or another approach would be for me to give you all the marbles numbered four and higher.  That way, you would have an infinite of marbles, but I would have only three marbles left.

What these illustrates demonstrate is that the notion of an actual infinite number of things leads to contradictory results.  In my first case in which I gave you all the marbles, infinity minus infinity is zero, in the second case in which I gave you all the odd-numbered marbles, infinity minus infinity is infinity; and in the third case in which I gave you all the marbles numbered four and greater, infinity minus infinity is three.  In each case, we have subtracted the identical number from the identical number, but we have come up with non-identical results. [2]

The point of this example is that arithmetical operations with actually infinite quantities yield contradictory answers, and thus it is metaphysically impossible for actual infinites to exist.  The notion of an actually infinite set is purely conceptual and has no relation to reality. It should be noted here that while one is able to work with actual infinities in set theory and calculus, they existence in re is metaphysically impossible.  Their existence is only permitted in mathematics because mathematical operations involving infinite quantities are prohibited. In reality, however, there is nothing stopping someone from adding or subtracting from an infinite quantity of marbles.

Suppose however, that actual infinities could exist in reality. Would this serve as a defeater for the second premise? It seems not, for even if actual infinities could exist in reality, they could not be formed by successive addition nor could they be navigated successfully.  It is impossible to form an actually infinite quantity by successive addition, as one can always add another number to what they have counted.  No matter how many times one adds a number to a finite quantity, one will never yield an infinite quantity.

Even if actual infinities were possible, it is unclear that they could be traversed.  Consider Bertrand Russell’s example of Tristram Shandy, who writes his autobiography at such a slow pace that it takes him a whole year to write about a single day.  If Shandy had been writing for eternity past, then he would be infinitely far behind. [3] Since it is impossible to traverse an actually infinite past, then we should not have arrived at this point.  But since we have, we can conclude that the past duration of the universe was finite.

Critics have sometimes compared the impossibility of forming an actual infinite to Zeno’s paradoxes of motion, which, though tricky and stubborn, are obviously wrongheaded.  But these comparisons are not accurate for several reasons:  First, the distances traversed in an infinite past are actual and equal, as opposed to being potential and unequal in Zeno’s paradoxes.  Second, the distances traversed in Zeno’s paradoxes sum to a finite distance, whereas the distances traversed in an infinite paste sum to an infinite distance.  Finally, it begs the question by presupposing the distance traversed as being composed of an infinite amount of points.  Critics of Zeno held that the existence of the line itself is prior to any divisions that are made in it.  Moreover, in regards to an infinite past, divisions such as a halfway, a quarter of a way, and a third of the way are unintelligible because there is no beginning, unlike in Zeno’s paradoxes. [4]

Scientific Pointers to a Beginning of the Universe

Due to the heavy influence of Aristotelianism, scientists and philosophers from the medieval periods up until the early 1900’s firmly believed in the eternality of the universe.  The first indications that the universe was not eternal started to surface in 1917 with the advent of Albert Einstein’s general theory of relativity. Einstein himself was a believer in an eternal universe, and when he saw that his theory of general relativity did not permit such a model, he introduced a “fudge factor” into his equations to maintain an eternal universe.   By exploiting the shortcomings of Einstein’s model, the Russian mathematician Alexander Friedman and the Belgian astronomer Georges Lemaitre independently developed an expanding model of the universe.  Further evidence came in 1929, when astronomer Edwin Hubble confirmed the expanding universe predicted by the Friedman-Lemaitre model through his discovery of redshift.  The fact that the universe was expanding implied that in some point in the past, it was compacted together tightly, for if one reverses the expansion of the universe backwards in time, the universe becomes more and more dense until it reaches a state of infinite density.  This had the jolting conclusion that the universe, over 14 billion years ago, had once been compressed to a size of an infinitely dense point known as a singularity.  Since space and time themselves came into existence at this singularity, it served as a boundary for space-time, as there was no moment “before” the big bang.  Hence, the origin posited by the standard big bang model is that of an absolute origin ex nihilo.

This lent strong support to the Judeo-Christian doctrine of creation ex nihilo. In fact, the bang theory, far from having atheistic implications, was actually criticized for being too religious when first proposed.

Further support came in 2001 with the advent of the BVG theorem.  Physicists Arvind Bord, Alan Guth, and Alexander Vilenkin were able to prove that any universe in a state of cosmic expansion must have an absolute beginning point.

Scientific verification for the second premise also comes from the second law of thermodynamics, one of the most verified laws in science.  According to the second law, the entropy of a closed system tends to increase over time.  In other words, the amount of energy required to do work constantly decreases as closed systems tend toward equilibrium.  If one drops a small amount of food coloring into a cup of water, for example, the food coloring will diffuse evenly throughout the water.

Applied to the universe, the second law implies that it will eventually attain maximum entropy.  This is known as the heat death of the universe.   At that point, there will be no energy available to do work, and the universe will be locked in a state of changelessness.  If the universe were eternal, however, then it should have already attained maximum entropy.  But since it has not yet attained maximum entropy, then it follows that the universe must be finite in its past duration.  Picture a toy that has been wound up.  If an infinite amount of time had passed, then the toy should have wound down.  The fact that it is still running indicates that it was wound up a finite time ago.  On the basis of the second law of thermodynamics, we may also conclude that the universe began to exist.


[1] — William Lane Craig and James D. Sinclair in William Lane Craig and J. P. Moreland (eds), The Blackwell Companion to Natural Theology (Blackwell: 2009) p.105
[2] — William Lane Craig, as interviewed by Lee Strobel in The Case for a Creator (Grand Rapids, MI: Zondervan 2004) p.103
[3] — For more on this, see Paul Copan and William Lane Craig, Creation Out of Nothing: A Biblical, Philosophical, and Scientific Exploration (Grand Rapids, MI: Baker Academic 2004)  p.213-216
[4] — Craig and Sinclair, “The Kalam Cosmological Argument”, inTBCNT, pp. 119

Os Guinness on the Essence of Apologetics (Part 3)

In Part 3 of this lecture series, Dr Guinness considers how to communicate effectively in apologetics. He discusses cross-cultural communication and how to contextualize your message to the language and world of your audience.

A "Grab Bag" of Self-Refuting Positions

In his Introduction to Logic, Harry Gensler defines a self-refuting statement as “[A] statement that makes negative claims so sweeping that it ends up denying itself.” [1] In other words, it results when an argument or position is undercut by its own criteria  (An example of this would be saying, “I cannot speak a word of English” in English).  Off the top of my head and in no particular order, here’s a grab-bag of several self-refuting positions which I’ve documented over the years:

  1. Truth does not exist (Is that a true statement?)
  2. Nothing is absolute (Is that absolutely true?)
  3. I do not exist (You must exist to deny that you exist)
  4. Science is the only way to know (Can you scientifically prove that?)
  5. Only what can be perceived by the five senses exists (Can you prove that by the five senses?)
  6. Nobody can know anything for sure (Do you know that for sure?)
  7. Nobody can know anything about God (How do you know that?)
  8. Talk about God is meaningless (Since it is a statement about God, this statement is meaningless too)
  9. Reality is just your interpretation, objective reality does not exist (That’s just your interpretation)
  10. “‘Everything we think and do is the function of our genes/nervous system'”: Is this belief itself just the result of genetic/neutral activity? If so, why trust it — or any belief we have? If your belief happens to be right, it’s just by accident” [2]
  11. There are no beliefs (You expect me to believe that?) [3]
  12. Everything is meaningless (So is that statement)

I’ll be adding to this as they keep coming to me, suggestions are welcome!


[1] – Harry J. Gensler, Introduction to Logic (New York, NY: Routledge 2002)p:396
[2] – Paul Copan, Loving Wisdom: Christian Philosophy of Religion (Danvers, MA: Chalice 2007) p.62
[3] – Victor Reppert, C. S. Lewis’s Dangerous Idea (Downers Grove, IL: InterVarsity 2003)p.75

Friday Night Miscellany

This week, we saw technology feature prominently in the headlines, with tens of thousands of New Zealand Telecom XT mobile customers losing their connections over the last few days. However, the big news of course was the announcement of Apple’s latest tech gadget, the iPad. Weighing in at one-and-a-half pounds (.68 kg) and a half-an-inch thick (13.4mm), with a 9.7-inch screen, the most surprising detail of the portable computer was the price: $499 USD. Will it change the world? At the very least, it will offer a serious challenge to Amazon’s Kindle. And Christians may wonder if it has the potential to revolutionize the virtual church movement.

Until then, here is some reading to take you into the final weekend of January.

Christianity and the Haiti disaster

Christianity and Theology

  • Douglas Wilson: “How shall we understand our afflictions? Our God sometimes strikes us, but only as the accomplished pianist forcefully strikes the keys.”
  • The Judgmental Jesus
    Matt’s column in the latest Investigate Magazine addresses one of the most quoted (and misunderstood) verses in the Bible: “Do not judge, or you too will be judged.”
  • Greg Beale discusses inerrancy
    Martin Downes interviews professor Greg Beale about the exegetical foundations of inerrancy and the status of the doctrine today among evangelical theologians and biblical scholars.
  • The Church and the surprising offense of God’s love
  • Inerrancy and its denial
    Jeremy Pierce discusses why inerrancy should be the starting point for our doctrine of Scripture and some of the implications of its denial.

Christianity and Ethics

Christianity and Philosophy

Christianity and Politics

Christianity and Fiction

  • Vampires and God
    An interview with a professor Emeritus of English Literature at the University of Central Missouri about vampires, folklore, literature, and the how these themes connect to death and religion.
  • More discussion about The Shack
    Yesterday, we posted Tim Keller’s impressions of the enormously popular novel by William Young. This week, Albert Mohler also considers the popularity of the book and what this means about the lost art of spiritual discernment within the Christian community. Fred Sanders, at the Scriptorium, also has some thoughts on how we can make the most of The Shack.

Christianity and Film

  • Exegeting Avatar
    Sophie Lister deftly analyzes James Cameron’s epic crowd-pleaser from a Christian perspective.

Do Christians and Muslims love the same God?

A panel discussion at the Evangelical Theological Society (ETS) Annual Meeting explores the common ground between Islam and Christianity. John Piper and Albert Mohler argue that while dialogue can occur, Muslims do not love and worship the God of the Bible.

Half a God is no God at all: Tim Keller on The Shack

Tim Keller, pastor of Redeemer PCA in Manhattan, offers his impressions of the best-selling novel, The Shack:

“Anyone who is strongly influenced by the imaginative world of The Shack will be totally unprepared for the far more multi-dimensional and complex God that you actually meet when you read the Bible. In the prophets the reader will find a God who is constantly condemning and vowing judgment on his enemies, while the Persons of the Triune-God of The Shack repeatedly deny that sin is any offense to them. The reader of Psalm 119 is filled with delight at God’s statutes, decrees, and laws, yet the God of The Shack insists that he doesn’t give us any rules or even have any expectations of human beings. All he wants is relationship. The reader of the lives of Abraham, Jacob, Moses, and Isaiah will learn that the holiness of God makes his immediate presence dangerous or fatal to us. Someone may counter (as Young seems to do, on p.192) that because of Jesus, God is now only a God of love, making all talk of holiness, wrath, and law obsolete. But when John, one of Jesus’ closest friends, long after the crucifixion sees the risen Christ in person on the isle of Patmos, John ‘fell at his feet as dead.’ (Rev.1:17.) The Shack effectively deconstructs the holiness and transcendence of God. It is simply not there. In its place is unconditional love, period. The God of The Shack has none of the balance and complexity of the Biblical God. Half a God is not God at all.”

Read the whole thing at the Gospel Coalition blog.

Five ways to argue like Jesus

We sometimes have a view of Jesus as a safe and gentle teacher but forget that the pages of Scripture reveal him as person of enormous controversy and debate. And many times it was Jesus himself who sought out that controversy – repudiating religious customs, upturning tables in temple markets, and castigating religious leaders for their moralism and hard-heartedness. For any Christian who thinks that we should always avoid confrontation or argument, Jesus’ life is a powerful reminder of the importance of discourse that embodies both truth and grace, salt and light.

Joe Carter and John Coleman have written a recent post at Relevant Magazine about how we can follow Jesus’ example and debate in a disarming and civil manner. If we want our communication to have the most impact, Carter and Coleman suggest that we should learn to be able to conduct a conversation that doesn’t raise voices or blood pressure.  The  “rules of rhetoric” they offer for effective communication have been distilled from their excellent book; How to Argue Like Jesus.  Joe Carter is the editor of the First Things magazine and an adjunct professor of journalism at Patrick Henry College. John Coleman is a former national public speaking champion pursuing a concurrent MBA/MPA at Harvard University.

You can read the whole post here. Crossway Books have also provided a brief overview on their blog:

  1. Start with examples your audience will understand: Always start with an example or concept your audience knows, understands, or finds interesting, and connect it to your core message.
  2. Speak your audience’s language: When you speak to an audience, to the extent possible, you must speak their language.
  3. Use witness: Consider the use of witnesses essential to the construction of an effective message based on narrative and ethos. Wherever possible, elicit testimonies.
  4. Know when to speak: There are a lot of important topics in the world, and it is not necessary that you have something to say about all of them—particularly if speaking on the topic would hurt your credibility or detract from your primary goal.
  5. And know when to be silent: Silence is one of the most powerful forms of communication. It shows that you are in control and gives the person or people a moment to think for themselves and consider how they will respond to your message

Assessing the euthanasia debate from a Christian perspective

Distinguished Professor of Philosophy at Biola University’s Talbot School of Theology, J. P. Moreland analyzes the different arguments used in the debate about euthanasia and sets the controversy in the larger context of broad, world view issues.

Indignity and indecency: Pascal on human nature

It is in vain, oh men, that you seek within yourselves the cure for all your miseries. All your insight has led to the knowledge that it is not in yourselves that you discover the true and the good. The philosophers promised them to you, but they were not able to keep that promise. They do not know what your true good is or what your nature is. How should they have provided you with a cure for ills which they have not even understood? Your principal maladies are pride, which cuts you off from God, and sensuality, which binds you to the earth. And they have done nothing but foster at least one of these maladies. If they have given you God for your object, it has been to pander to your pride. They have made you think you were like him and resemble him by your nature. And those who have grasped the vanity of such a pretension have cast you down in the other abyss by making you believe that your nature is like that of the beast of the field and have led you to seek your good in lust, which is the lot of animals.

Blaise Pascal, The Mind on Fire, ed. James M. Houston (Multnomah Pub, 1989), page 115.

A seamless garment with no holes: human persons and the failure of naturalism

Last year, the release of J. P. Moreland and William Lane Craig’s Blackwell Companion to Natural Theology saw a lot of attention. And quite rightly. The Companion marshalled some of most cutting-edge work in the field of the philosophy of religion and showed why natural theology is fast becoming an exciting scholarly domain again. But in the shadow of the Companion‘s release, another of Moreland’s works was published: The Recalcitrant Imago Dei: Human Persons and the Failure of Naturalism. Although it might not have got the same amount of attention, The Recalcitrant Imago Dei also represented an important entry in the contest of ideas and a powerful defense of theism. In it, Moreland argues for the theistic position by way of a stinging attack on naturalism and its failure to answer the problem of consciousness and account for the basic facts of human experience, such as free will, rationality, and intrinsic value.

The problem of consciousness is a deep mystery for philosophers and neuroscientists. This problem is the dilemma of how conscious states (thoughts, feelings, perceptions) arise from physical brain states. Ned Block, the American philosopher at NYU, has said that “researchers are stumped” and that we have “no conception” that enables us to explain subjective experience or conscious life. Colin McGinn, a professor at the University of Miami in the philosophy of mind, says that the emergence of consciousness “strikes us as miraculous, eerie, even faintly comic”. Even if we are sure that they arise from brains, we do not know the sorts of connections that conscious states (such as “seeing a tree”) have with brain states (such as “there are neurons firing at point A in the brain”). Hard materialists like Daniel Dennett have argued that conscious states are nothing more than brain states and brain behaviour, but Moreland argues that in both science and philosophy, a strict physicalist analysis of consciousness and the self has been breaking down since the mid-1980s.

For Christianity, the existence of such features basic to human experience are not metaphysically strange or inexplicable. For if in the beginning existed a supremely self-aware Being, then it is not difficult to see how consciousness could emerge. And if Christianity were true, Moreland also suggests one would predict that alternative worldviews whose basic entity or entities are not spiritual would find these things we take for granted recalcitrant – that is, hard to explain or explain away. In his book, Moreland shows that this is exactly the case with philosophical naturalism. Because naturalism posits particles at the beginning, one cannot adequately account for consciousness without mounting other reductive or eliminative strategies to explain their emergence. In The Recalcitrant Imago Dei, Moreland looks at these strategies and shows why they fail. Moreland therefore concludes that consciousness, freedom, rationality, a unified/simple self, equal and intrinsic value, and moral action of a certain sort, are all rebutting defeaters for naturalism and evidence for Judeo-Christian monotheism.

Bill Vallicella has written an excellent and thorough review of Moreland’s book, giving a summary of Moreland’s discussion of naturalism and his argument from consciousness for the existence of God.

Formally set out, Moreland’s argument looks like this:

1. Genuinely non-physical mental states exist.

2. There is an explanation for the existence of mental states.

3. Personal explanation is different from natural scientific explanation.

4. The explanation for the existence of mental states is either a personal or natural scientific explanation.

5. The explanation is not a natural scientific one.


6. The explanation is a personal one.

7. If the explanation is personal, then it is theistic.


8. The explanation [for the existence of mental states] is theistic.

In his review, Vallicella examines each of the premises, cataloguing additional reasons that Moreland offers in support for them. He writes:

Moreland makes a very powerful case, to my mind a crushingly powerful case, that [mental states] do not have a natural-scientific explanation. I would go further and claim that they cannot have such an explanation. (If a naturalist pins his hopes on future science, a science that can do what contemporary science manifestly cannot do, then I say our naturalist does not know what he is talking about when he bandies about the phrase ‘future science.’ He is merely gesturing in the direction of he knows not what. He is simply asseverating that somehow science will someday have all the answers. That’s as ‘theological’ as the assurance that, though now we see through a glass darkly, later we will see face to face. What do faith and hope have to do with science? Furthermore, why should anyone hope to have it proven to him that he is nothing more than a complex physical system?)

While Vallicella acknowledges that there are possible objections to Moreland’s argument (he raises some potential ones himself), he concludes that it renders belief in the Judeo-Christian God reasonable, and when combined with the rest of Moreland’s arguments, demonstrates why theism is more reasonable than naturalism.

It is worth reading his whole review (it can also be found on his own blog here). Also worth looking at is Moreland’s interview about the book on the Evangelical Philosophical Blog from last year (part 1 and 2) and Moreland’s post about the topic on his Amazon blog.

The Recalcitrant Imago Dei: Human Persons and the Failure of Naturalism, can of course, be picked up on Amazon.


“God, Naturalism and the Foundations of Morality” by Paul Copan in The Future of Atheism: Alister McGrath and Daniel Dennett in Dialogue, ed. Robert Stewart. Minneapolis: Fortress Press, 2008.

The gospel can do for Haiti what the media coverage cannot

Dan Cruver on the Gospel Coalition blog:

“One of the great dangers of living where I live is that I can easily adopt a hobbit’s way of thinking: “Well, it’s none of our concern what goes on beyond our borders. Keep your nose out of trouble and no trouble will come to you” (hobbit Ted Sandyman to Sam in The Fellowship of the Ring). In the face of that ongoing temptation, the media’s coverage confronts me daily with Haiti’s ongoing crisis, and for that I am grateful.

But the gospel does what media coverage cannot. It doesn’t merely awaken us to humanity’s need; it moves us out to meet it. We move out to meet the needs of others because God first came down to meet ours.

Long after the media coverage fades, after our nation’s attention has turned to other things, the gospel will still be moving us toward Haiti’s need. Therefore, it is critical that we as believers feast upon the gospel every day. It’s the only thing that will make what goes on beyond the borders of our own little Hobbiton our active concern. The gospel does what media coverage cannot: it mobilizes for long-term engagement.”

Read the whole thing here.

Glenn Sunshine on ‘What is a Worldview?’

Glenn S. Sunshine, the author of Why You Think the Way You Do: The Story of Western Worldviews from Rome to Home, explains what a worldview is (Source: The Koinonia Blog).