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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!

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Why do so many atheist historians think that 1 Corinthians 15 is reliable history?

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Which passage of the Bible is the favorite of Christians who like to defend the Christian worldview? I don’t mean which one is most inspirational… I mean “which one is the most useful for winning arguments?” Well, when it comes to the historical Jesus, the most important passage has to be 1 Corinthians 15:3-7.

The tradition in 1 Corinthians 15 is an early creed that was received from the eyewitnesses Peter and John when Paul visited them several times in Jerusalem, as documented in Galatians 1 and 2, where Paul meets the eyewitnesses. And of course, Paul records his own eyewitness experience, documented in 1 Cor 15:8.

So, is this passage accepted as historically reliable by all ancient historians? Or only by the Bible-believing ones?

Here’s something posted by Dr. William Lane Craig about the 1 Corinthians 15 passage:

The evidence that Paul is not writing in his own hand in I Cor. 15.3-5 is so powerful that all New Testament scholars recognize that Paul is here passing on a prior tradition. In addition to the fact that Paul explicitly says as much, the passage is replete with non-Pauline characteristics, including, in order of appearance: (i) the phrase “for our sins” using the genitive case and plural noun is unusual for Paul; (ii) the phrase “according to the Scriptures” is unparalleled in Paul, who introduces Scriptural citations by “as it is written”; (iii) the perfect passive verb “has been raised” appears only in this chapter and in a pre-Pauline confessional formula in II Tim. 2.8; (iv) the phrase “on the third day” with its ordinal number following the noun in Greek is non-Pauline; (v) the word “appeared” is found only here and in the confessional formula in I Tim. 3.16; and (vi) “the Twelve” is not Paul’s nomenclature, for he always speaks of the twelve disciples as “the apostles.”

Now the visit during which Paul may have received this tradition is the visit you mention three years after his conversion on the road to Damascus (Gal. 1.18). This puts the tradition back to within the first five years after Jesus’ death in AD 30. So there’s not even an apparent inconsistency with Paul’s appropriating the language of the formula to encapsulate the Gospel he was already preaching during those first three years in Damascus.

Ancient historian Gary Habermas loves to read non-Christian scholars… and then he writes about what THEY think about Jesus in peer-reviewed articles, published in academic journals. Let’s look at this one: Dialog: A Journal of Theology, Vol. 45; No. 3 (Fall, 2006), pp. 288-297; published by Blackwell Publishing, UK.

He writes:

(1) Contemporary critical scholars agree that the apostle Paul is the primary witness to the early resurrection experiences. A former opponent (1 Cor. 15:9; Gal. 1:13-14; Phil. 3:4-7), Paul states that the risen Jesus appeared personally to him (1 Cor. 9:1; 15:8; Gal. 1:16). The scholarly consensus here is attested by atheist Michael Martin, who avers: “However, we have only one contemporary eyewitness account of a postresurrection appearance of Jesus, namely Paul’s.”[3]

(2) In addition to Paul’s own experience, few conclusions are more widely recognized than that, in 1 Corinthians 15:3ff., Paul records an ancient oral tradition(s). This pre-Pauline report summarizes the early Gospel content, that Christ died for human sin, was buried, rose from the dead, and then appeared to many witnesses, both individuals and groups.

Paul is clear that this material was not his own but that he had passed on to others what he had received earlier, as the center of his message (15:3). There are many textual indications that the material pre-dates Paul. Most directly, the apostle employs paredoka and parelabon, the equivalent Greek terms for delivering and receiving rabbinic tradition (cf. 1 Cor. 11:23). Indirect indications of a traditional text(s) include the sentence structure and verbal parallelism, diction, and the triple sequence of kai hoti Further, several non-Pauline words, the proper names of Cephas (cf. Lk. 24:34) and James, and the possibility of an Aramaic original are all significant. Fuller attests to the unanimity of scholarship here: “It is almost universally agreed today that Paul is here citing tradition.”[4] Critical scholars agree that Paul received the material well before this book was written.[5]

This is important:

The most popular view is that Paul received this material during his trip to Jerusalem just three years after his conversion, to visit Peter and James, the brother of Jesus (Gal. 1:18-19), both of whose names appear in the appearance list (1 Cor. 15:5; 7). An important hint here is Paul’s use of the verb historesai (1:18), a term that indicates the investigation of a topic.[6] The immediate context both before and after reveals this subject matter: Paul was inquiring concerning the nature of the Gospel proclamation (Gal. 1:11-2:10), of which Jesus’ resurrection was the center (1 Cor. 15:3-4, 14, 17; Gal. 1:11, 16).

He’s an eyewitness (verse 8), and he met with the other eyewitnesses, James and Peter. 1 Corinthians is early. Galatians is early. The creed is extremely early – right after the events occurred. There was no time for legends to develop.

And atheistic / critical historians agree, the creed is reliable:

Critical scholars generally agree that this pre-Pauline creed(s) may be the earliest in the New Testament. Ulrich Wilckens asserts that it “indubitably goes back to the oldest phase of all in the history of primitive Christianity.”[7] Joachim Jeremias agrees that it is, “the earliest tradition of all.”[8] Perhaps a bit too optimistically, Walter Kasper even thinks that it was possibly even “in use by the end of 30 AD . . . .”[9]

Indicating the wide approval on this subject, even more skeptical scholars frequently agree. Gerd Ludemann maintains that “the elements in the tradition are to be dated to the first two years after the crucifixion of Jesus. . . . not later than three years. . . . the formation of the appearance traditions mentioned in I Cor.15.3-8 falls into the time between 30 and 33 CE. . . .”[10] Similarly, Michael Goulder thinks that it “goes back at least to what Paul was taught when he was converted, a couple of years after the crucifixion.”[11] Thomas Sheehan agrees that this tradition “probably goes back to at least 32-34 C.E., that is, to within two to four years of the crucifixion.”[12] Others clearly consent.[13]

Overall, my recent overview of critical sources mentioned above indicates that those who provide a date generally opt for Paul’s reception of this report relatively soon after Jesus’ death, by the early to mid-30s A.D.[14] This provides an additional source that appears just a half step removed from eyewitness testimony.

(3) Paul was so careful to assure the content of his Gospel message, that he made a second trip to Jerusalem (Gal. 2:1-10) specifically to be absolutely sure that he had not been mistaken (2:2). The first time he met with Peter and James (Gal. 1:18-20). On this occasion, the same two men were there, plus the apostle John (2:9). Paul was clearly doing his research by seeking out the chief apostles. As Martin Hengel notes, “Evidently the tradition of I Cor. 15.3 had been subjected to many tests” by Paul.[15]

These four apostles were the chief authorities in the early church, and each is represented in the list of those who had seen the resurrected Jesus (1 Cor. 15:5-7). So their confirmation of Paul’s Gospel preaching (Gal. 2:9), especially given the apostolic concern to insure doctrinal truth in the early church, is certainly significant. On Paul’s word, we are again just a short distance from a firsthand report.

(4) Not only do we have Paul’s account that the other major apostles confirmed his Gospel message, but he provides the reverse testimony, too. After listing Jesus’ resurrection appearances, Paul tells us he also knew what the other apostles were preaching regarding Jesus’ appearances, and it was the same as his own teaching on this subject (1 Cor. 15:11). As one, they proclaimed that Jesus was raised from the dead (15:12, 15). So Paul narrates both the more indirect confirmation of his Gospel message by the apostolic leaders, plus his firsthand, direct approval of their resurrection message.

Now, some of the people he lists are really biased against the supernatural, and they really hate the idea that the claims of Christianity exclude other religions. And yet they don’t deny the historical reliability of 1 Corinthians 15, or that it is based on eyewitness testimony.

That’s why when you watch debates about the historical Jesus, you see skeptical historians like Bart Ehrman, Gerd Ludemann, James Crossley, Michael Goulder, etc. accepting that the disciples thought they saw Jesus after his death. They’re not just being nice to Dr. Craig when they give him that. They are forced to accept it, because it passes the historical tests. Every Christian ought to be aware of which passages of the New Testament are seen by the broad spectrum of ancient historians as “historical”, regardless of their various biases. You can believe everything in the Bible. But when you debate non-Christians, you have to use the historical core of Christianity which successfully passes historical analysis.

You can see the creed used as evidence in the debate between James Crossley and William Lane Craig.