Tag Archives: Christian Apologetics

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William Lane Craig on the unexpected applicability of mathematics to nature

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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?

Michael

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.

Excerpt:

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.

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William Lane Craig debates Austin Dacey: Does God Exist?

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Here is the video and summary of a debate between Christian theist William Lane Craig and Austin Dacey at Purdue University in 2004 about the existence of God.

The debaters:

The video: (2 hours)

The video shows the speakers and powerpoint slides of their arguments. Austin Dacey is one of the top atheist debaters, and I would put him second to Peter Millican alone, with Walter Sinnott-Armstrong in third place. This is the debate to show people who are new to apologetics. The debate with Peter Millican is better for advanced students, and that’s no surprise since he teaches at Oxford University and is familiar with all of Dr. Craig’s work. The Craig-Dacey debate is the one that I give to my co-workers.

By the way, you can get the DVDs and CDs for the first Craig-Dacey debate and the second Craig-Dacey debate and the second Craig-Sinnott-Armstrong debate. The Peter Millican debate is not available on DVD, but the link above (Peter Millican) has the video and my summary.

Dr. Dacey’s 5 arguments below are all good arguments that you find in the academic literature. He is also an effective and engaging speaker, This is a great debate to watch!

SUMMARY of the opening speeches:

Dr. Craig’s opening statement:

Dr. Craig will present six reasons why God exists:

  1. (Contingency argument) God is the best explanation of why something exists rather than nothing
  2. (Cosmological argument)  God’s existence is implied by the origin of the universe
  3. (Fine-tuning argument) The fine-tuning of the universe for intelligent life points to a designer of the cosmos
  4. (Moral argument) God is the best explanation for the existence of objective moral values and objective moral duties
  5. (Miracles argument) The historical facts surrounding the life, death and resurrection of Jesus
  6. (Religious experience) God’s existence is directly knowable even apart from arguments

Dr. Dacey’s opening argument:

There are two ways to disprove God’s existence, by showing that the concept of God is self-contradictory, or by showing that certain facts about ourselves and the world are incompatible with what we would expect to be true if God did exist. Dr. Dacey will focus on the second kind of argument.

  1. The hiddenness of God
  2. The success of science in explaining nature without needing a supernatural agency
  3. The dependence of mind on physical processes in the brain
  4. Naturalistic evolution
  5. The existence of gratuitous / pointless evil and suffering

One final point:

One thing that I have to point out is that Dr. Dacey quotes Brian Greene during the debate to counter Dr. Craig’s cosmological argument. Dr. Craig could not respond because he can’t see the context of the quote. However, Dr. Craig had a rematch with Dr. Dacey where was able to read the context of the quote and defuse Dr. Dacey’s objection. This is what he wrote in his August 2005 newsletter after the re-match:

The following week, I was off an another three-day trip, this time to California State University at Fresno. As part of a week of campus outreach the Veritas Forum scheduled a debate on the existence of God between me and Austin Dacey, whom I had debated last spring at Purdue University. In preparation for the rematch I adopted two strategies: (1) Since Dacey had come to the Purdue debate with prepared speeches, I decided to throw him for a loop by offering a different set of arguments for God, so that his canned objections wouldn’t apply. I chose to focus on the cosmological argument, giving four separate arguments for the beginning of the universe, and on the evidence for Jesus’ resurrection. (2) I reviewed our previous debate carefully, preparing critiques of his five atheistic arguments. In the process I found that he had seriously misunderstood or misrepresented a statement by a scientist on the Big Bang; so I brought along the book itself in case Dacey quoted this source again. I figured he might change his arguments just as I was doing; but I wanted to be ready in case he used his old arguments again.

[…]The auditorium was packed that night for the debate, and I later learned that there were overflow rooms, too. To my surprise Dr. Dacey gave the very same case he had presented at Purdue; so he really got clobbered on those arguments. Because he wasn’t prepared for my new arguments, he didn’t even respond to two of my arguments for the beginning of the universe, though he did a credible job responding to the others. I was pleased when he attacked the Big Bang by quoting the same scientist as before, because I then held up the book, specified the page number, and proceeded to quote the context to show what the scientist really meant.

Dr. Craig is always prepared!

Polemics

What should Christians bring up when discussing truth with Muslims?

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I have some experience dicussing Islam because my mother’s side of the family is all Muslim. My go-to argument has always been to confront them about the Qur’an’s claim that Jesus did not die of crucifixion. But I noticed a different argument from Laura Powell, who knows far more about this topic than I do. Do you think her approach is the best one?

She writes about it over at her blog, An Affair with Reason:

The crux of the argument is this: The Qur’an affirms the inspiration, authority, and preservation of the New Testament Gospels;[2] yet the Qur’an also contradicts the Gospels on major theological and historical points. Therefore, the Qur’an cannot be reliable.

According to the Qur’an, the Gospel is the trustworthy, reliable revelation of God given as a guidance for mankind (Qur’an 3:3-4). These Scriptures from God were available and trustworthy when the Qur’an was revealed in the 7th century A.D., and those who had access to them were repeatedly told to obey them, judge by them, submit to their teaching, and stand fast upon them. In other words, according to the Qur’an, the Gospels are the inspired and authoritative words of God.

Qur’an 5:47 says, “And let the People of the Gospel judge by what Allah has revealed therein. And whoever does not judge by what Allah has revealed—then it is those who are the defiantly disobedient.”

Furthermore, Qur’an 5:68 states, “Say, ‘O People of the Scripture, you are [standing] on nothing until you uphold [the law of] the Torah, the Gospel, and what has been revealed to you from your Lord’” (see also 6:114; 3:3-4).

What I like about her argument is that she’s just taking the words of the Qur’an seriously, and asking the Muslims who claim to believe it what’s going on here. Why say that the gospels are unreliable today, when the Qur’an said that the gospels were reliable, yesterday.

My argument about the death of Jesus requires us to ask Muslims “where is the non-Muslim historian who thinks that Jesus did not die?” There isn’t one.

But my argument requires that the Muslim know something about historical scholarship, to know what non-Muslim historians think.Laura’s argument has wider appeal, because it doesn’t require that the Muslim have any knowledge about history – only knowledge about what their own holy book says.

She concludes with this:

What we see here is that the Qur’an teaches the inspiration, authority, and preservation of the Gospels. The Qur’an was intended as an Arabic version of the message of truth found in the Jewish and Christian Scriptures, but this presents a huge problem for Muslims because the Qur’an contradicts the Christian Scriptures on essential doctrines. Most notably, the Qur’an teaches that Jesus was not God incarnate, he did not die on a cross, and he was not raised from the dead (Qur’an 4:157; 5:116).

Here’s the dilemma for Muslims: If the Gospels are not trustworthy, then the Qur’an is false because it teaches that the Gospels are the inspired, perfectly preserved, authoritative words of God. But if the Gospels are trustworthy, then the Qur’an is false because it teaches contradictory, mutually exclusive facts about key issues. Either way, the Qur’an is false.

This, of course, is a huge problem for Muslims. The validity of Islam rests upon the reliability of the Qur’an, just as Christianity rests upon the truth of the divinity, death, and resurrection of Jesus. If the Qur’an is unreliable, then Islam is a false religion.

I like that she’s comfortable having disagreements with people. That’s not very common in the church today, in my experience.

By the way, this is the same Laura who wrote that really good article about how she found a better way to discuss her Christian worldview when she moved on from sharing her testimony. I blogged about it here.