Tag Archives: Christian Apologetics

William Lane Craig on the unexpected applicability of mathematics to nature

Christianity and the progress of science
Christianity and the progress of science

You might remember that Dr. Craig used a new argument in his debate with Lawrence Krauss in Melbourne, Australia.

My notes on the debate record it thus:

The unreasonable effectiveness of mathematics:

  • The underlying structure of nature is mathematical – mathematics is applicable to nature
  • Mathematical objects can either be abstract objects or useful fiction
  • Either way, there is no reason to expect that nature should be linked to abstract objects or fictions
  • But a divine mind that wants humans to understand nature is a better explanation for what we see

And now Dr. Craig has expanded on it in the Q&A section of his Reasonable Faith web site.

The question:

Dear Dr Craig

Firstly can I thank you for all your work. My faith in Christ has been enormously strengthened through studying your work in apologetics in particular and I have grown in confidence in my Christian witness.

My question relates to numbers and mathematics as a whole. On the Defenders podcast you state that as God is the only self-existent, necessary being, numbers and mathematical objects, whilst being useful, don’t actually exist as these too would exist necessarily and independently of God. If this is the case, how can it be that mathematics is so easily applied to the natural world? Surely if mathematics only existed in our minds, we would expect to see no correlation between it and how the physical world actually is?


United Kingdom

Excerpt from the answer:

As philosopher of mathematics Mary Leng points out, for the non-theistic realist, the fact that physical reality behaves in line with the dictates of acausal mathematical entities existing beyond space and time is “a happy coincidence” (Mathematics and Reality [Oxford: Oxford University Press, 2010], p. 239). Think about it: If, per impossibile, all the abstract objects in the mathematical realm were to disappear overnight, there would be no effect on the physical world. This is simply to reiterate that abstract objects are causally inert. The idea that realism somehow accounts for the applicability of mathematics “is actually very counterintuitive,” muses Mark Balaguer, a philosopher of mathematics. “The idea here is that in order to believe that the physical world has the nature that empirical science assigns to it, I have to believe that there are causally inert mathematical objects, existing outside of spacetime,” an idea which is inherently implausible (Platonism and Anti-Platonism in Mathematics [New York: Oxford University Press, 1998], p. 136).

By contrast, the theistic realist can argue that God has fashioned the world on the structure of the mathematical objects. This is essentially what Plato believed. The world has mathematical structure as a result.

This argument was also made by mechanical engineering professor Walter Bradley in a lecture he gave on scientific evidence for an intelligent designer. You can read an essay that covers some of the material in that lecture at Leadership University.


The physical universe is surprising in the simple mathematical form it assumes. All the basic laws of physics and fundamental relationships can be described on one side of one sheet of paper because they are so few in number and so simple in form (see table 1.1).

[…]It has been widely recognized for some time that nature assumes a form that is elegantly described by a relatively small number of simple, mathematical relationships, as previously noted in table 1.1. None of the various proposals presented later in this chapter to explain the complexity of the universe address this issue. Albert Einstein in a letter to a friend expressed his amazement that the universe takes such a form (Einstein 1956), saying:

You find it strange that I consider the comprehensibility of the world to the degree that we may speak of such comprehensibility as a miracle or an eternal mystery. Well, a priori one should expect a chaotic world which cannot be in any way grasped through thought. . . . The kind of order created, for example, by Newton’s theory of gravity is of quite a different kind. Even if the axioms of the theory are posited by a human being, the success of such an enterprise presupposes an order in the objective world of a high degree which one has no a priori right to expect. That is the “miracle” which grows increasingly persuasive with the increasing development of knowledge.

Alexander Polykov (1986), one of the top physicists in Russia, commenting on the mathematical character of the universe, said: “We know that nature is described by the best of all possible mathematics because God created it.” Paul Davies, an astrophysicist from England, says, “The equations of physics have in them incredible simplicity, elegance and beauty. That in itself is sufficient to prove to me that there must be a God who is responsible for these laws and responsible for the universe” (Davies 1984). Successful development of a unified field theory in the future would only add to this remarkable situation, further reducing the number of equations required to describe nature, indicating even further unity and integration in the natural phenomena than have been observed to date.

The whole paper that started this off is called “The Unreasonable Effectiveness of Mathematics”, and it is a must read for advanced Christian defenders. You can read the whole thing here.

William Lane Craig lectures on the evidence for the resurrection of Jesus

Sherlock Holmes and John Watson: let's take a look at the facts
Sherlock Holmes and John Watson: let’s take a look at the facts

Here is Dr. William Lane Craig giving a long-form argument for the historical event of the resurrection of Jesus, and taking questions from the audience.

The speaker introduction goes for 6 minutes, then Dr. Craig speaks for 35 minutes, then it’s a period of questions and answers with the audience. The total length is 93 minutes, so quite a long period of Q&A. The questions in the Q&A period are quite good.


  • Many people who are willing to accept God’s existence are not willing to accept the God of Christianity
  • Christians need to be ready to show that Jesus rose from the dead as a historical event
  • Private faith is fine for individuals, but when dealing with the public you have to have evidence
  • When making the case, you cannot assume that your audience accepts the Bible as inerrant
  • You must use the New Testament like any other ancient historical document
  • Most historians, Christian and not, accept the basic minimal facts supporting the resurrection of Jesus

Fact #1: the burial of Jesus following his crucifixion

  • Fact #1 is supported by the early creed found in Paul’s first letter to the Corinthians (1 Cor 15)
  • Fact #1 is supported by the early Passion narrative which was a source for Mark’s gospel
  • Fact #1 passes the criterion of enemy attestation, since it praises one of the Sanhedrin
  • Fact #1 is not opposed by any competing burial narratives

Fact #2: on the Sunday following his crucifixion, Jesus’ tomb was found empty by some women

  • Fact #2 is supported by the early Passion narrative which was a source for Mark’s gospel
  • Fact #2 is implied by the early creed found in Paul’s first letter to the Corinthians (1 Cor 15)
  • Fact #2 is simple and lacks legendary embellishment, which argues for an early dating
  • Fact #2 passes the criterion of embarrassment, because it has female, not male, witnesses
  • Fact #2 passes the criterion of enemy attestation, since it is reported by the Jewish leaders

Fact #3: Jesus appeared to various people in various circumstances after his death

  • Fact #3 is supported by the early creed found in Paul’s first letter to the Corinthians (1 Cor 15)
  • Fact #3 is supported by multiple, independent reports of the events from all four gospels
  • Fact #3 explains other historical facts, like the conversion of Jesus’ skeptical brother James

Fact #4: the earliest Christians proclaimed their belief in the resurrection of Jesus

  • Fact #4 explains why the earliest Christians continued to identify Jesus as the Messiah
  • Fact #4 explains why the earliest Christians were suddenly so unconcerned about being killed

Dr. Craig then asks which hypothesis explains all four of these facts. He surveys a number of naturalistic hypotheses, such as the hallucination theory or various conspiracy theories. All of these theories deny one or more of the minimal facts that have been established and accepted by the broad spectrum of historians. In order to reject the resurrection hypothesis, a skeptic would have to deny one of the four facts or propose an explanation that explains those facts better than the resurrection hypothesis.

I listened to the Q&A period while doing housekeeping and I heard lots of good questions. Dr. Craig gives very long answers to the questions. One person asked why we should trust the claim that the Jewish leaders really did say that the disciples stole the body. Another one asked why we should take the resurrection as proof that Jesus was divine. Another asks about the earthquake in Matthewand whether it is intended to be historical or apocalyptic imagery. Dr. Craig is also asked about the Jewish scholar Geza Vermes, and how many of the minimal facts he accepts. Another questioner asked about the ascension.

If you are looking for a good book to read on this topic, the best introductory book on the resurrection is “The Case for the Resurrection of Jesus” and the best comprehensive book is “The Resurrection of Jesus“.

William Lane Craig lectures on naturalistic alternatives to the Big Bang

William Lane Craig lecturing to university students
William Lane Craig lecturing to university students

Here’s the lecture, which was given in 2004 at the University of Colorado, Boulder.

This lecture might be a little advanced for beginners, but if you stretch your mind first, you shouldn’t tear anything. (Note: standard disclaimers apply if you do tear something!)

The description of the video states:

This is quite simply one of the best lectures William Lane Craig (a philosopher of science) has given. Craig explores the origins of the universe. He argues for a beginning of the universe, while refuting scientific models like the Steady State Theory, the Oscillating Theory, Quantum Vacuum Fluctuation Model, Chaotic Inflationary Theory, Quantum Gravity Theory, String Theory, M-Theory and Cyclic Ekpyrotic Theory.

And here is the description of the lecture from Reasonable Faith:

A Templeton Foundation lecture at the University of Colorado, Boulder, laying out the case from contemporary cosmology for the beginning of the universe and its theological implications. Includes a lengthy Q & A period which features previous critics and debate opponents of Dr. Craig who were in attendance, including Michael Tooley, Victor Stenger, and Arnold Guminski.

Craig has previously debated famous atheists Stenger and Tooley previously. And they both asked him questions in the Q&A time of this lecture. Imagine – having laid out your entire case to two people who have debated you before and who know your arguments well. What did they ask Craig, and how did he respond?

The scientific evidence

The Big Bang cosmology that Dr. Craig presents is the standard model for how the universe came into being. It is a theory based on six lines of experimental evidence.

Scientific evidence:

  1. Einstein’s theory of general relativity (GTR)
  2. the red-shifting of light from distant galaxies implies an expanding universe
  3. the cosmic background radiation (which also disproves the oscillating model of the universe)
  4. the second law of thermodynamics applied to star formation theory
  5. hydrogen-helium abundance predictions
  6. radioactive element abundance predictions

It’s probably a good idea to be familiar with these if you are presenting this argument, because experimental science is a reliable way of knowing about reality.

Published research paper

This lecture by Dr. Craig is based on a research paper published in an astrophysics journal, and was delivered to an audience of students and faculty, including atheist physicist Victor Stenger and prominent atheist philosopher Michael Tooley, at the University of Colorado at Boulder.

Here’s the peer-reviewed article that the lecture is based on.

Here’s the abstract:

Both cosmology and philosophy trace their roots to the wonder felt by the ancient Greeks as they contemplated the universe. The ultimate question remains why the universe exists rather than nothing. This question led Leibniz to postulate the existence of a metaphysically necessary being, which he identified as God. Leibniz’s critics, however, disputed this identification, claiming that the space-time universe itself may be the metaphysically necessary being. The discovery during this century that the universe began to exist, however, calls into question the universe’s status as metaphysically necessary, since any necessary being must be eternal in its existence. Although various cosmogonic models claiming to avert the beginning of the universe predicted by the standard model have been and continue to be offered, no model involving an eternal universe has proved as plausible as the standard model. Unless we are to assert that the universe simply sprang into being uncaused out of nothing, we are thus led to Leibniz’s conclusion. Several objections to inferring a supernatural cause of the origin of the universe are considered and found to be unsound.

The whole text of the article is posted online here.

If you want something to post on your Twitter or Facebook that is much shorter than this lecture, then you should check out this quick 4-minute explanation of the kalam argument.

William Lane Craig discusses faith and reason with university students

William Lane Craig lecturing to university students
William Lane Craig lecturing to university students

This is an interview of Dr. William Lane Craig before college students at the University of Central Florida. (95 minutes)

You can get an MP3 of the lecture here. (33 MB)

Questions from the interviewer: (40 minutes)

  • What started you on his journey of studying faith and reason?
  • How would you define the word “faith”?
  • Are faith and reason compatible? How are they related?
  • How can reasonable faith help us to avoid the two extremes of superstition and nihilism?
  • Who makes the best arguments against the Christian faith?
  • Why are angry atheists like Dawkins and Hitchens more well known than better-informed academic atheists?
  • Does the Bible require Christians to give the unbeliever reasons for their faith?
  • How does faith spur Christians to think carefully about the big questions in life?
  • Should the American church prod churchgoers to develop their minds so they can engage the secular culture?
  • When talking about Christianity intellectually, is there a risk of neglecting the experience of being a Christian?
  • Which Christian apologist has shaped your thinking the most?
  • Which Christian philosopher has shaped your thinking the most?
  • Does the confidence that comes from apologetics undermine humility and reverence?
  • If you had to sketch out a 5 minute case for Christianity, what would you present?
  • Can non-Christians use their reason to arrive at truth?
  • Are there cases where atheists must affirm irrational things in order to remain atheists?
  • Can the universe have existed eternal, so that there is no need to explain who created it?
  • Even if you persuade someone that Christianity is true, does that mean they will live it out?

There is also a long period of questions, many of them hostile, from the audience of students (55 minutes).

  • Haven’t you said nasty things about some atheists? Aren’t you a meany?
  • What do you make of the presuppositional approach to apologetics?
  • Can a person stop being a Christian because of the chances that happen to them as they age?
  • Why did God wait so long after humans appeared to reveal himself to people through Jesus?
  • Can a person be saved by faith without have any intellectual assent to truth?
  • How do you find time for regular things like marriage when you have to study and speak so much?
  • How would you respond to Zeitgeist and parallels to Christianity in Greek/Roman mythology?
  • Do Christians have to assume that the Bible is inerrant and inspired in order to evangelize?
  • If the universe has a beginning, then why doesn’t God have a beginning?
  • Can you name some philosophical resources on abstract objects, Platonism and nominalism?
  • How can you know that Christianity more right than other religions?
  • Should we respond to the problem of evil by saying that our moral notions are different from God’s?
  • Define the A and B theories of time. Explain how they relate to the kalam cosmological argument.
  • How can Christians claim that their view is true in the face of so many world religions?
  • What is the role of emotions in Christian belief and thought?
  • Can evolution be reconciled with Christian beliefs and the Bible?
  • When witnessing person-to-person, should you balance apologetics with personal testimony?
  • Is there a good analogy for the trinity that can help people to understand it? [Note: HE HAS ONE!]
  • How can Christians reconcile God’s omniscience, God’s sovereignty and human free will?

This is a nice introductory lecture that is sure to get Christians to become interested in apologetics. As you watch or listen to it, imagine what the world would be like if every Christian could answer the questions of skeptical college students and professors like Dr. Craig. What would non-Christians think about Christianity if every Christian had studied these issues like Dr. Craig? Why aren’t we making an effort to study these things so that we can answer these questions?

It is really fun to see him fielding the questions from the skeptical university students. My favorite question was from the physics student who sounds really foreign, (at 1:19:00), then you realize that he is a Christian. I do think that Dr. Craig went a little far in accommodating evolution, but I put that down to the venue, and not wanting to get into a peripheral issue. I’m also surprised that no one asked him why God allows humans to suffer and commit acts of evil.

If you are looking for a good basic book on apologetics, then I would choose “Is God Just a Human Invention?” by Sean McDowell and Jonathan Morrow.

Who is William Lane Craig?

About William Lane Craig:

William Lane Craig is Research Professor of Philosophy at Talbot School of Theology in La Mirada, California.

Dr. Craig pursued his undergraduate studies at Wheaton College (B.A. 1971) and graduate studies at Trinity Evangelical Divinity School (M.A. 1974; M.A. 1975), the University of Birmingham (England) (Ph.D. 1977), and the University of Munich (Germany) (D.Theol. 1984). From 1980-86 he taught Philosophy of Religion at Trinity… In 1987 they moved to Brussels, Belgium, where Dr. Craig pursued research at the University of Louvain until assuming his position at Talbot in 1994.

He has authored or edited over thirty books, including The Kalam Cosmological ArgumentAssessing the New Testament Evidence for the Historicity of the Resurrection of JesusDivine Foreknowledge and Human FreedomTheism, Atheism and Big Bang Cosmology; and God, Time and Eternity, as well as over a hundred articles in professional journals of philosophy and theology, including The Journal of PhilosophyNew Testament StudiesJournal for the Study of the New TestamentAmerican Philosophical QuarterlyPhilosophical StudiesPhilosophy, and British Journal for Philosophy of Science.

Craig’s CV is here.

Craig’s list of publications is here.

William Lane Craig is, without a doubt, the top living defender of Christianity. He has debated all of the most famous atheists, including Christopher Hitchens, Sam Harris, etc. as well as academic atheists like Quentin Smith, Peter Millican, etc. if you search this blog, you’ll find many debates posted here, sometimes even with snarky summaries.

William Lane Craig debates Walter Sinnott-Armstrong: evil, suffering and God

Two bears fight it out, and may the best bear win!
Two bears fight it out, and may the best bear win!

This is one of the top 4 best debates that William Lane Craig has done in my opinion. (The other three are Craig-Millican debate and the first and second Craig-Dacey debates).

Sinnott-Armstrong is very courteous, respectful and intelligent scholar and he is very good at defending his side. This is a very cordial and engaging debate, and because it was held in front of a church audience, it was targeted to laymen and not academics. So if you are looking for a good first debate to watch, this is it!

The MP3 file is here.

The video is here:

There is also a book based on this debate, published by Oxford University Press. I was actually able to find a PDF of it online. I should also remind people that you can get the wonderful Craig-Hitchens debate DVD from Amazon.com if you are looking for a debate to watch, or show in your church, this is the one to start with.

The debaters:

The format:

  • WSA: 15 minutes
  • WLC: 15 minutes
  • Debaters discussion: 6 minutes
  • Moderated discussion: 10 minutes
  • Audience Q&A: 18 minutes
  • WSA: 5 minutes
  • WLC: 5 minutes


WSA opening speech:

Evil is incompatible with the concept of God (three features all-powerful, all-god, all-knowing)

God’s additional attributes: eternal, effective and personal (a person)

He will be debating against the Christian God in this debate, specifically

Contention: no being has all of the three features of the concept of God

His argument: is not a deductive argument, but an inductive/probabilistic argument

Examples of pointless, unjustified suffering: a sick child who dies, earthquakes, famines

The inductive argument from evil:

  1.  If there were an all-powerful and all-good God, then there would not be any evil in the world unless that evil is logically necessary for some adequately compensating good.
  2.  There is evil in the world.
  3.  Some of that evil is not logically necessary for some adequately compensating good.
  4. Therefore, there can’t be a God who is all-powerful and all-good.

Defining terms:

  • Evil: anything that all rational people avoid for themselves, unless they have some adequate reason to want that evil for themselves (e.g. – pain, disability, death)
  • Adequate reason: some evils do have an adequate reason, like going to the dentist – you avoid a worse evil by having a filling

God could prevent tooth decay with no pain

God can even change the laws of physics in order to make people not suffer

Responses by Christians:

  • Evil as a punishment for sin: but evil is not distributed in accordance with sin, like babies
  • Children who suffer will go straight to Heaven: but it would be better to go to Heaven and not suffer
  • Free will: this response doesn’t account for natural evil, like disease, earthquakes, lightning
  • Character formation theodicy: there are other ways for God to form character, by showing movies
  • Character formation theodicy: it’s not fair to let X suffer so that Y will know God
  • God allows evil to turn people towards him: God would be an egomaniac to do that
  • We are not in a position to know that any particular evil is pointless: if we don’t see a reason then there is no reason
  • Inductive evil is minor compared to the evidences for God: arguments for a Creator do not prove that God is good

WLC opening speech:

Summarizing Walter’s argument

  1. If God exists, gratuitous evil does not exist.
  2. Gratuitous evil exists.
  3. Therefore, God does not exist.

Gratuitous evil means evil that God has no morally sufficient reason to permit. WSA doesn’t think that all evil is incompatible with God’s existence, just gratuitous evil.

Everyone admits that there are instances of evil and suffering such that we cannot see the morally sufficient reason why God would allow it to occur.

The claim of the atheist is that if they cannot see that there is a moral justification for allowing some instance evil, then there is no moral justification for that instance of evil.

Here are three reasons why we should not expect to know the morally sufficient reasons why God permits apparently pointless evil.

  1. the ripple effect: the morally sufficient reason for allowing some instance of evil may only be seen in another place or another time
  2. Three Christian doctrines undermine the claim that specific evils really are gratuitous
  3. Walter’s own premise 1 allows us to argue for God’s existence, which means that evil is not gratuitous

Christian doctrines from 2.:

  • The purpose of life is not happiness, and it is not God’s job to make us happy – we are here to know God. Many evils are gratuitous if we are concerned about being happy, but they are not gratuitous for producing the knowledge of God. What WSA has to show is that God could reduce the amount of suffering in the world while still retaining the same amount of knowledge of God’s existence and character.
  • Man is in rebellion, and many of the evils we see are caused by humans misusing their free will to harm others and cause suffering
  • For those who accept Christ, suffering is redeemed by eternal life with God, which is a benefit that far outweighs any sufferings and evils we experience in our earthly lives

Arguing for God in 3.

  1. If God exists, gratuitous evil does not exist.
  2. God exists
  3. Therefore, gratuitous evil does not exist.

Four reasons to think that God exists (premise 2 from above):

  • the kalam cosmological argument
  • the fine-tuning argument
  • the moral argument
  • the argument from evil