Tag Archives: 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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Correcting four myths about the history of the Crusades

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Here is an interesting article from Intercollegiate Studies Institute.

Intro:

The verdict seems unanimous. From presidential speeches to role-playing games, the crusades are depicted as a deplorably violent episode in which thuggish Westerners trundled off, unprovoked, to murder and pillage peace-loving, sophisticated Muslims, laying down patterns of outrageous oppression that would be repeated throughout subsequent history. In many corners of the Western world today, this view is too commonplace and apparently obvious even to be challenged.

But unanimity is not a guarantee of accuracy. What everyone “knows” about the crusades may not, in fact, be true. From the many popular notions about the crusades, let us pick four and see if they bear close examination.

The four myths:

  • Myth #1: The crusades represented an unprovoked attack by Western Christians on the Muslim world.
  • Myth #2: Western Christians went on crusade because their greed led them to plunder Muslims in order to get rich.
  • Myth #3: Crusaders were a cynical lot who did not really believe their own religious propaganda; rather, they had ulterior, materialistic motives.
  • Myth #4: The crusades taught Muslims to hate and attack Christians.

Here’s the most obvious thing you should know. The Crusades were defensive actions:

In a.d. 632, Egypt, Palestine, Syria, Asia Minor, North Africa, Spain, France, Italy, and the islands of Sicily, Sardinia, and Corsica were all Christian territories. Inside the boundaries of the Roman Empire, which was still fully functional in the eastern Mediterranean, orthodox Christianity was the official, and overwhelmingly majority, religion. Outside those boundaries were other large Christian communities—not necessarily orthodox and Catholic, but still Christian. Most of the Christian population of Persia, for example, was Nestorian. Certainly there were many Christian communities in Arabia.

By a.d. 732, a century later, Christians had lost Egypt, Palestine, Syria, North Africa, Spain, most of Asia Minor, and southern France. Italy and her associated islands were under threat, and the islands would come under Muslim rule in the next century. The Christian communities of Arabia were entirely destroyed in or shortly after 633, when Jews and Christians alike were expelled from the peninsula.6 Those in Persia were under severe pressure. Two-thirds of the formerly Roman Christian world was now ruled by Muslims.

What had happened? Most people actually know the answer, if pressed—though for some reason they do not usually connect the answer with the crusades. The answer is the rise of Islam. Every one of the listed regions was taken, within the space of a hundred years, from Christian control by violence, in the course of military campaigns deliberately designed to expand Muslim territory at the expense of Islam’s neighbors. Nor did this conclude Islam’s program of conquest. The attacks continued, punctuated from time to time by Christian attempts to push back. Charlemagne blocked the Muslim advance in far western Europe in about a.d. 800, but Islamic forces simply shifted their focus and began to island-hop across from North Africa toward Italy and the French coast, attacking the Italian mainland by 837. A confused struggle for control of southern and central Italy continued for the rest of the ninth century and into the tenth. In the hundred years between 850 and 950, Benedictine monks were driven out of ancient monasteries, the Papal States were overrun, and Muslim pirate bases were established along the coast of northern Italy and southern France, from which attacks on the deep inland were launched. Desperate to protect victimized Christians, popes became involved in the tenth and early eleventh centuries in directing the defense of the territory around them.

If you asked me what are the two best books on the Crusades, I would answer God’s Battalions: The Case for the Crusades by Baylor professor Rodney Stark and The Concise History of the Crusades by Professor Thomas F. Madden. If you get this question a lot from atheists, then I recommend you pick these up. Anything by Rodney Stark is useful for Christians, in fact.

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How to respond to an atheist who complains about slavery in the Bible

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I often hear atheists going on and on about how the Bible has this evil and that evil. Their favorite one seems to be slavery. Here are three things I say to atheists when they push this objection.

The Bible and slavery

First, you should explain to them what the Bible actually says about slavery. And then tell them about the person responsible for stopping slavery in the UK: a devout evangelical named William Wilberforce.

Here’s an article that works.

Excerpt:

We should compare Hebrew debt-servanthood (many translations render this “slavery”) more fairly to apprentice-like positions to pay off debts — much like the indentured servitude during America’s founding when people worked for approximately 7 years to pay off the debt for their passage to the New World. Then they became free.

In most cases, servanthood was more like a live-inemployee, temporarily embedded within the employer’s household. Even today, teams trade sports players to another team that has an owner, and these players belong to a franchise. This language hardly suggests slavery, but rather a formal contractual agreement to be fulfilled — like in the Old Testament.3

Atheism and moral judgments

Second, inform them that moral values are not rationally grounded on atheism. In an accidental universe, there is no way we ought to be. There is no design for humans that we have to comply with. There are no objective human rights, like the right to liberty (that would block slavery) or the right to life (that would block abortion). Although you may find that most atheists act nicely, the ones who really understand what atheism means and live it out consistently are not so nice.

Famous atheist Richard Dawkins has previously written this:

The total amount of suffering per year in the natural world is beyond all decent contemplation. During the minute that it takes me to compose this sentence, thousands of animals are being eaten alive, many others are running for their lives, whimpering with fear, others are slowly being devoured from within by rasping parasites, thousands of all kinds are dying of starvation, thirst, and disease. It must be so. If there ever is a time of plenty, this very fact will automatically lead to an increase in the population until the natural state of starvation and misery is restored. In a universe of electrons and selfish genes, blind physical forces and genetic replication, some people are going to get hurt, other people are going to get lucky, and you won’t find any rhyme or reason in it, nor any justice. The universe that we observe has precisely the properties we should expect if there is, at bottom, no design, no purpose, no evil, no good, nothing but pitiless indifference.

(“God’s Utility Function,” Scientific American, November, 1995, p. 85)

When atheists like Dawkins talk about morality, you have to understand that they are pretending. To them, morality is just about personal preferences and cultural conventions. They just think that questions of right and wrong are arbitrary. Things that are wrong in one time and place are right in another. Every view is as right as any other, depending on the time and place. That’s atheist morality.

What’s worse than slavery? Abortion!

Third, you should ask the atheist what he has done to oppose abortion. Abortion is worse than slavery, so if they are sincere in thinking that slavery is wrong, then they ought to think that abortion is wrong even more. So ask them what they’ve done to oppose the practice of abortion. That will tell you how sincere they are about slavery.

Here’s atheist Richard Dawkins explaining what he’s done to stop abortion:

That’s right. The head atheist supports killing born children.