Tag Archives: Christian Apologetics

Polemics

William Lane Craig on the unexpected applicability of mathematics to nature

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Christianity and the progress of science
Christianity and the progress of science

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.

Videos

William Lane Craig debates Austin Dacey: Does God Exist?

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Two tough rams butt heads, and may the best ram win!
Two tough rams butt heads, and may the best ram win!

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

Are Mormon doctrines supported by philosophy, science and history?

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A conflict of worldviews
A conflict of worldviews

This post presents evidence against Mormonism/LDS in three main areas. The first is in the area of science. The second is in the area of philosophy. And the third is in the area of history.

The scientific evidence

First, let’s take a look at what the founder of Mormonism, Joseph Smith, believes about the origin of the universe:

“The elements are eternal. That which had a beggining will surely have an end; take a ring, it is without beggining or end – cut it for a beggining place and at the same time you have an ending place.” (“Scriptural Teachings of the Prophet Joseph Smith”, p. 205)

“Now, the word create came from the word baurau which does not mean to create out of nothing; it means to organize; the same as a man would organize materials and build a ship. Hence, we infer that God had materials to organize the world out of chaos – chaotic matter, which is element, and in which dwells all the glory. Element had an existance from the time he had. The pure principles of element are principles which can never be destroyed; they may be organized and re-organized, but not destroyed. They had no beggining, and can have no end.”
(“Scriptural Teachings of the Prophet Joseph Smith”, p. 395)

A Mormon scholar named Blake Ostler summarizes the Mormon view in a Mormon theological journal:

“In contrast to the self-sufficient and solitary absolute who creates ex nihilo (out of nothing), the Mormon God did not bring into being the ultimate constituents of the cosmos — neither its fundamental matter nor the space/time matrix which defines it. Hence, unlike the Necessary Being of classical theology who alone could not not exist and on which all else is contingent for existence, the personal God of Mormonism confronts uncreated realities which exist of metaphysical necessity. Such realities include inherently self-directing selves (intelligences), primordial elements (mass/energy), the natural laws which structure reality, and moral principles grounded in the intrinsic value of selves and the requirements for growth and happiness.” (Blake Ostler, “The Mormon Concept of God,” Dialogue: A Journal of Mormon Thought 17 (Summer 1984):65-93)

So, Mormons believe in an eternally existing universe, such that matter was never created out of nothing, and will never be destroyed. But this is at odds with modern cosmology.

The Big Bang cosmology is the most widely accepted cosmology of the day. It denies the past eternality of the universe. This peer-reviewed paper in an astrophysics journal explains. (full text here)

Excerpt:

The standard Big Bang model thus describes a universe which is not eternal in the past, but which came into being a finite time ago. Moreover,–and this deserves underscoring–the origin it posits is an absolute origin ex nihilo. For not only all matter and energy, but space and time themselves come into being at the initial cosmological singularity. As Barrow and Tipler emphasize, “At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo.”

[…]On such a model the universe originates ex nihilo in the sense that at the initial singularity it is true that There is no earlier space-time point or it is false that Something existed prior to the singularity.

Christian cosmology requires such a creation out of nothing, but this is clearly incompatible with what Mormons believe about the universe. The claims about the universe made by the two religions are in disagreement, and we can test empirically to see who is right, using science.

Philosophical problems

Always Have a Reason contrasts two concepts of God in Mormonism: Monarchotheism and Polytheism. It turns out that although Mormonism is actually a polytheistic religion, like Hinduism. In Mormonism, humans can become God and then be God of their own planet. So there are many Gods in Mormonism, not just one.

Excerpt:

[T]he notion that there are innumerable contingent “primal intelligences” is central to this Mormon concept of god (P+M, 201; Beckwith and Parrish, 101). That there is more than one god is attested in the Pearl of Great Price, particularly Abraham 4-5. This Mormon concept has the gods positioned to move “primal intelligences along the path to godhood” (Beckwith and Parrish, 114). Among these gods are other gods which were once humans, including God the Father. Brigham Young wrote, “our Father in Heaven was begotten on a previous heavenly world by His Father, and again, He was begotten by a still more ancient Father, and so on…” (Brigham Young, The Seer, 132, quoted in Beckwith and Parrish, 106).

[…]The logic of the Mormon polytheistic concept of God entails that there is an infinite number of gods. To see this, it must be noted that each god him/herself was helped on the path to godhood by another god. There is, therefore, an infinite regress of gods, each aided on his/her path to godhood by a previous god. There is no termination in this series. Now because this entails an actually infinite collection of gods, the Mormon polytheistic concept of deity must deal with all the paradoxes which come with actually existing infinities…

The idea of counting up to an actual infinite number of things by addition (it doesn’t matter what kind of thing it is) is problematic. See here.

More:

Finally, it seems polytheistic Mormonism has a difficulty at its heart–namely the infinite regress of deity.

[…]Each god relies upon a former god, which itself relies upon a former god, forever. Certainly, this is an incoherence at the core of this concept of deity, for it provides no explanation for the existence of the gods, nor does it explain the existence of the universe.

Now let’s see the historical evidence against Mormonism.

The historical evidence

J. Warner Wallace explains how the “Book of Abraham”, a part of the Mormon Scriptures, faces historical difficulties.

The Book of Abraham papyri are not as old as claimed:

Mormon prophets and teachers have always maintained that the papyri that was purchased by Joseph Smith was the actual papyri that was created and written by Abraham. In fact, early believers were told that the papyri were the writings of Abraham.

[…]There is little doubt that the earliest of leaders and witnesses believed and maintained that these papyri were, in fact the very scrolls upon which Abraham and Joseph wrote. These papyri were considered to be the original scrolls until they were later recovered in 1966. After discovering the original papyri, scientists, linguists, archeologists and investigators (both Mormon and non-Mormon) examined them and came to agree that the papyri are far too young to have been written by Abraham. They are approximately 1500 to 2000 years too late, dating from anywhere between 500 B.C. (John A. Wilson, Dialogue: A Journal of Mormon Thought, Summer 1968, p. 70.) and 60 A.D. If they papyri had never been discovered, this truth would never have come to light. Today, however, we know the truth, and the truth contradicts the statements of the earliest Mormon leaders and witnesses.

The Book of Abraham papyri do not claim what Joseph Smith said:

In addition to this, the existing papyri simply don’t say anything that would place them in the era related to 2000BC in ancient Egypt. The content of the papyri would at least help verify the dating of the document, even if the content had been transcribed or copied from an earlier document. But the papyri simply tell us about an ancient burial ritual and prayers that are consistent with Egyptian culture in 500BC. Nothing in the papyri hints specifically or exclusively to a time in history in which Abraham would have lived.

So there is a clear difference hear between the Bible and Mormonism, when it comes to historical verification.

Further study

If you want a nice long PDF to print out and read at lunch (which is what I did with it) you can grab this PDF by Michael Licona, entitled “Behold, I Stand at the Door and Knock“.