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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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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The importance of having a narrative when confronting the assumption of naturalism

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How do you present theism as a rational belief to a person who thinks that the progress of science has removed the need for God?

Canadian science writer Denyse O’Leary writes about the history of cosmology at Evolution News.

Excerpt:

What help has materialism been in understanding the universe’s beginnings?

Many in cosmology have never made any secret of their dislike of the Big Bang, the generally accepted start to our universe first suggested by Belgian priest Georges Lemaître (1894-1966).

On the face of it, that is odd. The theory accounts well enough for the evidence. Nothing ever completely accounts for all the evidence, of course, because evidence is always changing a bit. But the Big Bang has enabled accurate prediction.

In which case, its hostile reception might surprise you. British astronomer Fred Hoyle (1915-2001) gave the theory its name in one of his papers — as a joke. Another noted astronomer, Arthur Eddington (1882-1944), exclaimed in 1933, “I feel almost an indignation that anyone should believe in it — except myself.” Why? Because “The beginning seems to present insuperable difficulties unless we agree to look on it as frankly supernatural.”

One team of astrophysicists (1973) opined that it “involves a certain metaphysical aspect which may be either appealing or revolting.” Robert Jastrow (1925-2008), head of NASA’s Goddard Institute for Space Studies, initially remarked, “On both scientific and philosophical grounds, the concept of an eternal Universe seems more acceptable than the concept of a transient Universe that springs into being suddenly, and then fades slowly into darkness.” And Templeton Prize winner (2011) Martin Rees recalls his mentor Dennis Sciama’s dogged commitment to an eternal universe, no-Big Bang model:

For him, as for its inventors, it had a deep philosophical appeal — the universe existed, from everlasting to everlasting, in a uniquely self-consistent state. When conflicting evidence emerged, Sciama therefore sought a loophole (even an unlikely seeming one) rather as a defense lawyer clutches at any argument to rebut the prosecution case.

Evidence forced theorists to abandon their preferred eternal-universe model. From the mid 1940s, Hoyle attempted to disprove the theory he named. Until 1964, when his preferred theory, the Steady State, lost an evidence test.

Here is a quick summary of some of the experimental evidence that emerged in the last few decades that caused naturalists to abandon the eternal universe that they loved so much when they were younger.

The importance of having a narrative

Now I want to make a very, very important point about Christianity and the progress of science. And that point is that it is very important that Christians present the evidence in exactly the way that Denyse presented it in that article – in its historical context, featuring the conflict between naturalists and the experimental evidence.

All Christians should be familiar with the following basic pieces of evidence which fit the war between science and naturalism narrative:

  1. The origin of the universe
  2. The cosmic fine-tuning
  3. The origin of life (biological information)
  4. The sudden origin of the Cambrian phyla
  5. The habitability/observability correlation

When you talk about these evidences as a Christian theist to non-Christians, you have to have cultivated a genuine interest in reconciling your beliefs with science. You have to accept that there are two books that reveal God’s character and attributes. The book of nature, and the book of Scripture. And you need to be flexible about getting these two books to fit together. The book of nature gives us natural theology (see Romans 1). It tells us that God is Creator and Designer. The book of Scripture tells us that God stepped into history as a man to save us by taking the punishment for our headlong rush away from God, which the Bible calls sin. Science is one way that humans can recover some of basic knowledge about God. Knowledge that is only possible because God created and designed the universe (and us) in such a way that we are capable of making discoveries, and that the universe is capable of being explored and understood.

It’s very important to present these five basic evidences to non-Christians in the historical context. And here is the story you must tell: “In the beginning, there was the naturalism, and the naturalism tried to argue from ignorance that God was not Creator and God was not Designer. And then came the science, and now people have to give up their naturalism in order to account for the science”. That’s the narrative you use when talking to non-Christians about science.

In the beginning was the naturalism:

  1. In pre-scientific times, atheists maintained that the universe was eternal
  2. In pre-scientific times, atheists maintained that a life-permitting universe was as likely as a life-prohibiting universe
  3. In pre-scientific times, atheists maintained that the cell was a simple blob of Jello that could spontaneously emerge in some warm pond
  4. In pre-scientific times, atheists maintained that the sudden origin of the Cambrian phyla would be explained by subsequent fossil discoveries
  5. In pre-scientific times, atheists maintained that there was nothing special about our galaxy, solar system, planet or moon

But then science progressed by doing experiments and making observations:

  1. Scientists discovered redshift and the cosmic microwave background radiation (evidence for a cosmic beginning) and more!
  2. Scientists discovered the fine-tuning of gravity and of the cosmological constant and more!
  3. Scientists discovered protein sequencing and exposed the myth of “junk DNA” and more!
  4. Scientists discovered an even shorter Cambrian explosion period and the absence of precursor fossils and more!
  5. Scientists discovered galactic habitable zones and circumstellar habitable zones and more!

And now rational people – people who want to have true beliefs about reality – need to abandon a false religion (naturalism).

Now naturally, science is in a state of flux and things change. But you have to look at the trend of discoveries, and those trends are clearly going against naturalism, and in favor of Christian theism. No one is arguing for a deductive proof here, we are simply looking at the evidence we have today and proportioning our belief to the concrete evidence we have today. People who are guided by reason should not seek to construct a worldview by leveraging speculations about future discoveries and mere possibilities. We should instead believe what is more probable than not. That’s what a rational seeker of truth ought to do. Proportion belief to probabilities based on current, concrete knowledge.

Atheism, as a worldview, is not rooted in an honest assessment about what science tells us about reality. Atheism is rooted in a religion: naturalism. And the troubling thing we learn from looking at the history of science is that this religion of naturalism is insulated from correction from the progress of science. Nothing that science reveals about nature seems to be able to put a dent in the religion of naturalism, at least for most atheists.

It falls to us Christian theists, then, to hold them accountable for their abuse and misrepresentation of science. And that means telling the story of the progress of science accurately, and accurately calling out the religion of naturalism for what it is – a religion rooted in blind faith and ignorance that has been repeatedly and convincingly falsified by the progress of science in the modern era.

Positive arguments for Christian theism