Tag Archives: Christian Apologetics

William Lane Craig on the unexpected applicability of mathematics to nature

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.

Christian woman finds a way to discuss her faith with non-Christians

I found an interesting article where a Christian woman explains how she used to share her testimony with non-Christians. But that wasn’t working. So she decided to try something different.

She writes:

I’ll never forget the first time I shared my personal testimony with a non-Christian.

When the opportunity arose and I shared my story with an unbelieving friend, she replied, “That’s so cool. I’m so happy you found something that works for you.”

For me?

“It’s not about what works for me,” I said, trying to hide my discouragement. “It’s about what’s true for everyone.”

“That doesn’t make sense,” she responded. “That’s your experience, not mine. I had a similar revelation when I realized I could leave the church, and I’ve become a better person for my decision. Just as you were freed from your heaviest burdens by finding God, I was freed from mine by leaving God behind.”

I was devastated but I chalked it up to my friend’s hardheartedness. I decided to shake the dust off my feet and look forward to the next opportunity.

But time after time of sharing my testimony resulted in similar responses. People expressed enthusiasm that I was happy, that Christianity worked for me, and that I had “found my niche.” Yet no one considered my experience as anything more than just that—my own personal experience.

[…]I had been taught that sharing what God had done in my life was the ideal way to witness to non-Christians. A personal testimony was interesting yet non-confrontational, compelling but inoffensive. And yet, despite having shared my testimony with dozens of unbelievers, not a single person felt challenged to consider the truth claims of Christianity.

She noticed that her approach wasn’t actually in the Bible. There was a different approach being demonstrated by Jesus, and later by his disciples.

She writes:

When Jesus called his first disciples, he taught truth and provided evidence (miracles) to support his claims, then he asked people to follow him (Luke 5:1–11). In fact, this was his method whenever he went into new regions (see Luke 4:14–44; John 4:7–26). People decided to follow Jesus not on blind faith or a subjective feeling, but based on the evidence they had seen and heard.[i]

Jesus also used evidence to assuage the doubts of even those who had been with him a long time. John the Baptist was Jesus’ cousin, who leapt in the womb during Mary’s visit (Luke 1:39–45), baptized Jesus in the Jordan River, heard God’s voice from heaven, and saw the Holy Spirit descend on Jesus in bodily form like a dove (Luke 3:21–22). Yet when John experienced unexpected suffering, he began to doubt.

Jesus didn’t respond as many do today, by insisting that John “just believe” or “have faith” or “prayer harder.” Rather, he responded with more evidence, saying, “Go and tell John what you hear and see: the blind receive their sight and the lame walk, lepers are cleansed and the deaf hear, and the dead are raised up, and the poor have good news preached to them. And blessed is the one who is not offended by me.” (Matt. 11:2–6).

[…]At Pentecost, the apostle Peter offered signs and wonders, fulfilled prophecy, and relayed eyewitness testimony to persuade people from all over the Roman Empire that the most reasonable explanation for what they were seeing was not morning drunkenness, but a risen Messiah (Acts 2:1–41).

On his missionary journeys, the apostle Paul reasoned with the Jews from the Scriptures, explaining and proving that Jesus was the Messiah who needed to suffer and rise from the dead (Acts 17:1–3, 17). And he reasoned with the Gentiles from outside the Scriptures, making a case with their own accepted beliefs to convince them (Acts 17:17–34).

In fact, in describing his mission, Paul told the Philippians, “I am put here for the defense of the gospel” (1:7, 16). This word translated defense is the same word from which we get our English word “apologetics,” meaning to make reasoned arguments or to provide evidence as justification. Using this same word, Peter commanded believers to “always [be] prepared to make a defense to anyone who asks you for a reason for the hope that is in you”(1 Pet. 3:15).

So, she decided to dump the testimony approach, and try the Biblical approach. But she had to change it a little bit, since she couldn’t perform miracles herself:

We are not eyewitnesses to Jesus’s life and resurrection, but we have the accounts of those who were. We don’t typically see miracles, but we have millennia of biblical scholarship and archaeology that provide reasons to believe the accounts are trustworthy. We don’t often hear God speaking audibly or see him parting seas, but we have significant scientific evidence that shows the universe had a beginning, and millennia of observation to confirm the scientific principle that everything that begins to exist has a cause.

I think a lot of Christians never move on from approach she described that wasn’t getting results. And there’s a reason for that – studying evidence is hard work. But I can tell you from my experience as a software engineer, there is no better way to convince other people to adopt your view than to show them working code that produces results. If they have a prototype, they will adopt your design. Similarly with Christianity. If you have evidence, then you will be persuasive.

When talking about spiritual things with non-Christians, always remember the joke about the two men walking in the woods who meet a bear. One man starts to put on his running shoes. The other man says “what are you doing? you can’t outrun a bear!” And the first man says “I don’t have to. I only have to outrun you”. It’s the same with apologetics. You don’t have to be William Lane Craig to talk about your faith to non-Christians. You just have to know more than your non-Christian opponent knows about evidence.

The way things are going these days with the public schools and the mainstream news media, this is actually pretty easy to do. One or two introductory books on the origin of the universe, the fine-tuning for intelligent life, the origin of biological information, the origin of body plans, the historical reliability of the New Testament, the minimal facts case for the resurrection, etc. will do the job. You might need another one on philosophical challenges like evil, suffering, divine hiddenness, etc. But we’re talking no more than 5 books, and you’ll be effective in the vast majority of your conversations. If you can only get one book, I like Sean McDowell and Jonathan Morrow’s “Is God Just a Human Invention?” best.

Theologian R.C. Sproul asks: “If there’s a God, why are there atheists?”

Brian Auten has a book review posted up at Apologetics 315.

The book is “If There’s A God, Why Are There Atheists?”, by theologian R.C. Sproul. R.C. Sproul is one of my favorite theologians. The book in question has a very, very special place in my heart, because I think that it is one of the major reasons why I was able to resist pernicious ideas like religious pluralism and postmodernism for so long. Once you put on the glasses of Romans 1 and see for the first time what man is really doing with respect to God, you can never see things the same again. I’ll say more about this at the end, but let’s see what Brian wrote first.

The review

So often, you hear atheists complaining about religion is nothing but wish-fulfillment or some sort of crutch for people who are frightened by a variety of things. They think that God is invented to solve several problems. 1) how does the world work?, 2) is there meaning to suffering and evil?, 3) why should I be moral?, and 4) what will happen to me and my loved ones when I die?. On the atheistic view, God is just a crutch that people cling to out of weakness and ignorance. But is this really the case?

Sproul starts the book by investigating three atheists who sought to explain religious belief as a result of psychological factors.

Brian writes:

Before tackling the psychology of atheism, Sproul spends a chapter on the psychology of theism, from the perspective of Freud’s question “If there is no God, why is there religion?” What follows is an overview of various psychological explanations of theistic belief: Feuerbach’s “religion is a dream of the human mind.” Marx’s belief that religion is “due to the devious imagination of particular segment of mankind.” And Nietzche’s idea that “religion endures because weak men need it.” The author properly reiterates: “We must be careful to note that the above arguments can never be used as proof for the nonexistence of God. They can be useful for atheists who hear theists state that the only possible explanation for religion is the existence of God.” That being said, Sproul also reveals what these arguments presume:

Their arguments already presupposed the nonexistence of God. They were not dealing with the question, Is there a God? They were dealing with the question, Since there is no God, why is there religion?16

Sproul points out the weaknesses of each of these approaches and says “there are just as many arguments showing that unbelief has its roots in the psychological needs of man.”

Wow, could that really be true? What are the real reasons why people reject God? Does the Bible have anything to say about what those reasons are?

Brian cites Sproul’s contention:

The New Testament maintains that unbelief is generated not so much by intellectual causes as by moral and psychological ones. The problem is not that there is insufficient evidence to convince rational beings that there is a God, but that rational beings have a natural hostility to the being of God.

[…]Man’s desire is not that the omnipotent, personal Judeo-Christian God exist, but that He not exist.

In Romans 1:18-23, the apostle Paul explains what is really going on:

18The wrath of God is being revealed from heaven against all the godlessness and wickedness of men who suppress the truth by their wickedness,

19since what may be known about God is plain to them, because God has made it plain to them.

20For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that men are without excuse.

21For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened.

22Although they claimed to be wise, they became fools

23and exchanged the glory of the immortal God for images made to look like mortal man and birds and animals and reptiles.

On this blog, I regularly present many, many arguments for theism in general, and Christian theism in particular:

Sproul explains why atheists cannot allow themselves to live according to the evidence that is presented to them:

The cumulative effect of this knowledge that is clearly seen is to leave men ‘without excuse.’ Herein lies the basis of the universal guilt of man. No one can claim ignorance of the knowledge of God. No one can cite insufficient evidence for not believing in God. Though people are not persuaded by the evidence, this does not indicate an insufficiency in the evidence, but rather an insufficiency in man.

[…]The basic stages of man’s reaction to God can be formulated by means of the categories of trauma, repression, and substitution.

[…]If God exists, man cannot be a law unto himself. If God exists, man’s will-to-power is destined to run head-on into the will of God.

And this is the force that is animating atheists today. They don’t want to be accountable to God in a relationship, no matter what the evidence is. They have to deny it, so that they can be free to get the benefits of a universe designed for them, without having to give any recognition or acknowledgement back. If they have to lie to themselves to deny the evidence, they will do it. Anything to insulate themselves from the Creator and Designer who reveals himself in Jesus Christ.

The rest of the book review, and the book, deals with explaining in detail how atheists respond to an all-good, all-powerful, all-knowing Creator/Designer. I encourage you to click through and read the whole book review. You can read the review, and the book, and then investigate for yourself whether atheists really are like that.