Tag Archives: Philosophy

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?


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.


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 apologists. You can read the whole thing here.

Positive arguments for Christian theism

Six reasons why you should believe in non-physical souls

This podcast is a must-listen. Please take the time to download this podcast and listen to it. I guarantee that you will love this podcast. I even recommended it to my Dad and I almost never do that.


In this podcast, J. Warner examines the evidence for the existence of the mind (and inferentially, the soul) as he looks at six classic philosophical arguments. Jim also briefly discusses Thomas Nagel’s book, Mind and Cosmos and discusses the limitations of physicalism.

The MP3 file is here. (67 MB, 72 minutes)


  • Atheist Thomas Nagel’s latest book “Mind and Cosmos” makes the case that materialism cannot account for the evidence of mental phenomena
  • Nagel writes in this recent New York Times article that materialism cannot account for the reality of consciousness, meaning, intention and purpose
  • Quote from the Nagel article:

Even though the theistic outlook, in some versions, is consistent with the available scientific evidence, I don’t believe it, and am drawn instead to a naturalistic, though non-materialist, alternative. Mind, I suspect, is not an inexplicable accident or a divine and anomalous gift but a basic aspect of nature that we will not understand until we transcend the built-in limits of contemporary scientific orthodoxy.

  • When looking at this question, it’s important to not have our conclusions pre-determined by presupposing materialism or atheism
  • If your mind/soul doesn’t exist and you are a purely physical being then that is a defeater for Christianity, so we need to respond
  • Traditionally, Christians have been committed to a view of human nature called “dualism” – human beings are souls who have bodies
  • The best way* to argue for the existence of the soul is using philosophical arguments

The case:

  • The law of identity says that if A = B’ if A and B have the exact same properties
  • If A = the mind and B = the brain, then is A identical to B?
  • Wallace will present 6 arguments to show that A is not identical to B because they have different properties

Not everyone of the arguments below might make sense to you, but you will probably find one or two that strike you as correct. Some of the points are more illustrative than persuasive, like #2. However, I do find #3, #5 and #6 persuasive.

1) First-person access to mental properties

  • Thought experiment: Imagine your dream car, and picture it clearly in your mind
  • If we invited an artist to come and sketch out your dream car, then we could see your dream car’s shape on paper
  • This concept of your dream car is not something that people can see by looking at your brain structure
  • Physical properties can be physically accessed, but the properties of your dream care and privately accessed

2) Our experience of consciousness implies that we are not our bodies

  • Common sense notion of personhood is that we own our bodies, but we are not our bodies

3) Persistent self-identity through time

  • Thought experiment: replacing a new car with an old car one piece at a time
  • When you change even the smallest part of a physical object, it changes the identity of that object
  • Similarly, your body is undergoing changes constantly over time
  • Every cell in your body is different from the body you had 10 years ago
  • Even your brain cells undergo changes (see this from New Scientist – WK)
  • If you are the same person you were 10 years ago, then you are not your physical body

4) Mental properties cannot be measured like physical objects

  • Physical objects can be measured (e.g. – use physical measurements to measure weight, size, etc.)
  • Mental properties cannot be measured

5) Intentionality or About-ness

  • Mental entities can refer to realities that are physical, something outside of themselves
  • A tree is not about anything, it just is a physical object
  • But you can have thoughts about the tree out there in the garden that needs water

6) Free will and personal responsibility

  • If humans are purely physical, then all our actions are determined by sensory inputs and genetic programming
  • Biological determinism is not compatible with free will, and free will is required for personal responsibility
  • Our experience of moral choices and moral responsibility requires free will, and free will requires minds/souls

He spends the last 10 minutes of the podcast responding to naturalistic objections to the mind/soul hypothesis.

*Now in the podcast, Wallace does say that scientific evidence is not the best kind of evidence to use when discussing this issue of body/soul and mind/brain. But I did blog before about two pieces of evidence that I think are relevant to this discussion: corroborated near-death experiences and mental effort.

You might remember that Dr. Craig brought up the issue of substance dualism, and the argument from intentionality (“aboutness”), in his debate with the naturalist philosopher Alex Rosenberg, so this argument about dualism is battle-ready. You can add it to your list of arguments for Christian theism along with all the other arguments like the Big Bang, the fine-tuning, the origin of life, stellar habitability, galactic habitability, irreducible complexity, molecular machines, the Cambrian explosion, the moral argument, the resurrection, biological convergence, and so on.

William Lane Craig debates Walter Sinnott-Armstrong: evil, suffering and God

This is one of the top 4 best debates that William Lane Craig has done in my opinion. (The other three are Craig-Millican debate and the first and second Craig-Dacey debates).

Sinnott-Armstrong is very courteous, respectful and intelligent scholar and he is very good at defending his side. This is a very cordial and engaging debate, and because it was held in front of a church audience, it was targeted to laymen and not academics. So if you are looking for a good first debate to watch, this is it!

The MP3 file is here.

There is also a book based on this debate, published by Oxford University Press. I was actually able to find a PDF of it online. I should also remind people that you can get the wonderful Craig-Hitchens debate DVD from Amazon.com if you are looking for a debate to watch, or show in your church, this is the one to start with.

The debaters:

The format:

  • WSA: 15 minutes
  • WLC: 15 minutes
  • Debaters discussion: 6 minutes
  • Moderated discussion: 10 minutes
  • Audience Q&A: 18 minutes
  • WSA: 5 minutes
  • WLC: 5 minutes


WSA opening speech:

Evil is incompatible with the concept of God (three features all-powerful, all-god, all-knowing)

God’s additional attributes: eternal, effective and personal (a person)

He will be debating against the Christian God in this debate, specifically

Contention: no being has all of the three features of the concept of God

His argument: is not a deductive argument, but an inductive/probabilistic argument

Examples of pointless, unjustified suffering: a sick child who dies, earthquakes, famines

The inductive argument from evil:

  1.  If there were an all-powerful and all-good God, then there would not be any evil in the world unless that evil is logically necessary for some adequately compensating good.
  2.  There is evil in the world.
  3.  Some of that evil is not logically necessary for some adequately compensating good.
  4. Therefore, there can’t be a God who is all-powerful and all-good.

Defining terms:

  • Evil: anything that all rational people avoid for themselves, unless they have some adequate reason to want that evil for themselves (e.g. – pain, disability, death)
  • Adequate reason: some evils do have an adequate reason, like going to the dentist – you avoid a worse evil by having a filling

God could prevent tooth decay with no pain

God can even change the laws of physics in order to make people not suffer

Responses by Christians:

  • Evil as a punishment for sin: but evil is not distributed in accordance with sin, like babies
  • Children who suffer will go straight to Heaven: but it would be better to go to Heaven and not suffer
  • Free will: this response doesn’t account for natural evil, like disease, earthquakes, lightning
  • Character formation theodicy: there are other ways for God to form character, by showing movies
  • Character formation theodicy: it’s not fair to let X suffer so that Y will know God
  • God allows evil to turn people towards him: God would be an egomaniac to do that
  • We are not in a position to know that any particular evil is pointless: if we don’t see a reason then there is no reason
  • Inductive evil is minor compared to the evidences for God: arguments for a Creator do not prove that God is good

WLC opening speech:

Summarizing Walter’s argument

  1. If God exists, gratuitous evil does not exist.
  2. Gratuitous evil exists.
  3. Therefore, God does not exist.

Gratuitous evil means evil that God has no morally sufficient reason to permit. WSA doesn’t think that all evil is incompatible with God’s existence, just gratuitous evil.

Everyone admits that there are instances of evil and suffering such that we cannot see the morally sufficient reason why God would allow it to occur.

The claim of the atheist is that if they cannot see that there is a moral justification for allowing some instance evil, then there is no moral justification for that instance of evil.

Here are three reasons why we should not expect to know the morally sufficient reasons why God permits apparently pointless evil.

  1. the ripple effect: the morally sufficient reason for allowing some instance of evil may only be seen in another place or another time
  2. Three Christian doctrines undermine the claim that specific evils really are gratuitous
  3. Walter’s own premise 1 allows us to argue for God’s existence, which means that evil is not gratuitous

Christian doctrines from 2.:

  • The purpose of life is not happiness, and it is not God’s job to make us happy – we are here to know God. Many evils are gratuitous if we are concerned about being happy, but they are not gratuitous for producing the knowledge of God. What WSA has to show is that God could reduce the amount of suffering in the world while still retaining the same amount of knowledge of God’s existence and character.
  • Man is in rebellion, and many of the evils we see are caused by humans misusing their free will to harm others and cause suffering
  • For those who accept Christ, suffering is redeemed by eternal life with God, which is a benefit that far outweighs any sufferings and evils we experience in our earthly lives

Arguing for God in 3.

  1. If God exists, gratuitous evil does not exist.
  2. God exists
  3. Therefore, gratuitous evil does not exist.

Four reasons to think that God exists (premise 2 from above):

  • the kalam cosmological argument
  • the fine-tuning argument
  • the moral argument
  • the argument from evil

Does God’s omniscience conflict with human free will?

Here’s the setup for the question, from Come Reason ministries.



Christian doctrine holds that God is all knowing (1 John 3:20), and humans have free will (Deuteronomy 30:19 is my favorite example). however, at my favorite apologetics debate board, I have seen skeptics raise an objection to these points several times. the basic logic behind their arguments is this:

  1. A being with free will, given two options A and B, can freely choose between A and B.
  2. God is omniscient (all-knowing).
  3. God knows I will choose A.
  4. God cannot be wrong, since an omniscient being cannot have false knowledge.
  5. From 3 and 4, I will choose A and cannot choose B.
  6. From 1 and 5, omniscience and free will cannot co-exist.

I have read many counter-arguments from apologetics sites, but they were either too technical (I couldn’t understand them), or not satisfying. so, I was wondering what would your input be on this issue?

Thank you,


Ever heard that one? I actually had that one posed to me by a guy I used to work with who had a Ph.D in computer science from Northwestern. So this is an objection you may actually here.

Here’s Lenny Eposito’s answer:

Hi Justin,

Thanks for writing. This is a great question as it shows how even those who appeal to logic can have biases that blind them. Let’s examine this argument and see if it follows logically.

Premises 1 and 2 in your outline above are the main premises to the argument and are not disputed. The Christian worldview argues that every human being is a free moral agent and is capable of making choices simply by exercising their will, not under compulsion or because of instinct. Also, it is a long held doctrine of Christianity that God is all-knowing. The Bible says that God knows “the end from the beginning (Isaiah 46:10).” For omniscience to be truly knowledgeable it must be correct knowledge, so premise number 4 is also granted.

However, point number 5 is where the logic falters. Those who argue in this manner make the mistake of thinking that because God possesses knowledge about a specific matter, then he has influenced it. That does not follow at all. Just because God can foresee which choice you will make, it does not mean you couldn’t still freely choose the other option.

Let me give you an example. I have a five year old son. If I were to leave a chocolate chip cookie on the table about a hour before dinner time and my son was to walk by and see it, I know that he would pick up the cookie and eat it. I did not force him to make that decision. In fact, I don’t even have to be in the room at all. I think I know my son well enough, though, to tell you that if I come back into the kitchen the cookie will be gone. His act was made completely free of my influence, but I knew what his actions would be.

In examining the argument, the assumption is made in premise 3 that because God knows I will choose A somehow denies me the choice of B. That is the premise that Christianity rejects. Omniscience and free will are not incompatible and it is a non-sequitor to claim otherwise.

Thank you Justin for this interesting question. I pray that you will continue to defend the gospel of our Lord and may He continue to bless you as you seek to grow in Him.

That’s a great answer and should work in ordinary conversations.

More technical

J.W. Wartick maps out the arguments more fully with symbolic logic here on his Always Have A Reason blog. But I’ll just excerpt the gist of it.


It is necessarily true that if God knows x will happen, then x will happen. But then if one takes these terms, God knowing x will happen only means that x will happen, not that x will happen necessarily. Certainly, God’s foreknowledge of an event means that that event will happen, but it does not mean that the event could not have happened otherwise. If an event happens necessarily, that means the event could not have happened otherwise, but God’s foreknowledge of an event doesn’t somehow transfer necessity to the event, it only means that the event will happen. It could have been otherwise, in which case, God’s knowledge would have been different.

[…]Perhaps I could take an example. Let’s say that I’m going to go to classes tomorrow (and I do hope I will, I don’t like missing classes!). God knows in advance that I’m going to go to classes tomorrow. His knowledge of this event means that it will happen, but it doesn’t mean that I couldn’t choose to stay in and sleep for a while, or play my new copy of Final Fantasy XIII, or do something more useless with my time. If I chose to, say, play Final Fantasy XIII (a strong temptation!), then God simply would have known that I would play FFXIII. His knowledge does not determine the outcome, His knowledge is simply of the outcome.

If we choose A, God would foreknow A. If we choose B, God would foreknow B. His foreknowledge of our choices is contingent on our making free choices.

Dan Barker debates Casey Luskin on academic freedom

Two ninjas face off at sundown
Two ninjas face off at sundown

The Michael Medved show is a national radio show broadcast out of Seattle, Washington. According to Talkers magazine, he has the fifth largest radio audience.

The MP3 file is available for download. (38 minutes)

The description is:

On this episode of ID the Future, the CSC’s Casey Luskin and atheist Dan Barker of the Freedom From Religion Foundation debate academic freedom and free speech on the Medved Show. This debate was inspired by the ongoing case of Professor Eric Hedin, a physicist at Ball State University who is being threatened by the Freedom From Religion Foundation for favorably portraying intelligent design in the classroom.

Topics: (note that I am paraphrasing Dan Barker for the sake of humor, and he will probably sue me, since that is his entire contribution to the search for truth in this debate)

  • Michael Medved: untenured Ball State University professor Eric Hedin is under fire for teaching both sides of intelligent design in a college course
  • Dan Barker: this complaint against professor Hedin came to our attention from Jerry Coyne not from students of Professor Hedin
  • Dan Barker: professors are not allowed to question the presuppositions atheism, materialism, naturalism in the physics classroom
  • Dan Barker: this is a science course and you cannot question the religion of naturalism in class or else it’s teaching religion
  • Dan Barker: we need to use the power of the courts to stifle any dissent from of my religion (naturalism)
  • Dan Barker: the classroom of a university is not the proper place for students to inquire about both sides of scientific disputes
  • Dan Barker: even if students are paying their money and choosing this course of their own free will, they can’t be allowed to hear both sides
  • Casey Luskin: this course is not a science course, it is open to non-science students
  • Casey Luskin: the course evaluations from students of all majors is overwhelmingly positive
  • Casey Luskin: the course features people on both sides
  • Casey Luskin: the course features brilliant scholars like Lennox and Penrose, both from Oxford University
  • Casey Luskin: the course features opponents of intelligent design like Francis Collins and Karl Gilberson
  • Casey Luskin: the course features non-Christians like Lee Spetner, Paul Davies, Roger Penrose and Gerald Schroeder
  • Dan Barker: (taking over the host) you cannot study scientists like Francis Collins who mapped the human genome, that is “creationism”
  • Michael Medved: academic freedom allows professors to put a slant on what they are teaching
  • Dan Barker: if the professor’s slant is against my religion of naturalism, then I have to put them in jail and inquisition them
  • Dan Barker: you cannot teach science like the Big Bang and fine-tuning  as if it is science because it contradicts naturalism
  • Casey Luskin: Even radical atheist PZ Myers says that professors have the right to academic freedom
  • Dan Barker: I’ll burn that creationist at the stake, too! And smash his filthy microscopes and telescopes!
  • Michael Medved: Casey, would you use state power to fire a professor who disagreed with you because you were offended?
  • Casey Luskin: no, I had to take tons of courses from professors who had a slant against my views and I learned a lot from different views
  • Dan Barker: you will address me as the Holy Father, please! Every professor who disagrees with my religion must burn!
  • Casey Luskin: Barker has no idea what is going on in the class, he never attended it
  • Casey Luskin: The atheists students who took his class gave him high ratings and said he graded fairly
  • Dan Barker: I don’t have to look through the telescope to know the Earth is flat – Hedin is a traitor! Off with his head!
  • Dan Barker: Creationist PZ Myers is wrong, and I’ll burn him at the stake for creationist heresy against my Holy Church!
  • Dan Barker: Oxford professors like John Lennox are creationists because his Big Bang religion is grounded on experimental data like the cosmic background radiation, the hydrogen/helium abundances and the redshifting of light from distant galaxies
  • Dan Barker: I have a degree in Religion and I write hymns, which makes me smarter than John Lennox since he is a “creationist”
  • Dan Barker: I haven’t published any scientific research myself, but I have written some atheist praise hymns, so I am qualified to burn the heretics!
  • Michael Medved: The course is taught by someone with a PhD in Physics, and the syllabus says that it investigates science and religion
  • Michael Medved: Why is it wrong to investigate the science that questions philosophical assumptions like naturalism and materialism?
  • Casey Luskin: The syllabus features amazing readings from all the latest science relevant to that question from both sides
  • Michael Medved: What will Ball State U do to the professor?
  • Casey Luskin: So far no action from Ball State U, but people need to sign the petition to protect the professor
  • Michael Medved: Isn’t academic freedom being applied inconsistently here?
  • Casey Luskin: Yes and science is supposed to move forward by disagreement and debate
  • Casey Luskin: How confident can intelligent design censors really be if their contribution to the debate is coercion and intimidation?
  • Michael Luskin: Is Dan Barker right to say that Oxford professor John Lennox is a “creationist”?
  • Casey Luskin: Creationism starts with the Bible, but intelligent design starts with scientific data

And there is a period of questions from the callers. This episode features a debate, so it is not to be missed.

Now Dan Barker sounded pretty confident in that debate, so you might be surprised by his academic background:

Dan became a teenage evangelist at age 15. At 16 he was choir librarian for faith-healer Kathryn Kuhlman’s Los Angeles appearances. He received a degree in Religion from Azusa Pacific University and was ordained to the ministry by the Standard Community Church, California, in 1975.

[…]Dan preached for 19 years. He maintained an ongoing touring musical ministry, including eight years of full-time, cross-country evangelism. An accomplished pianist, record producer, arranger and songwriter, he worked with Christian music companies such as Manna Music and Word Music. For a few years, Dan wrote and produced the annual “Mini Musicale” for Gospel Light Publications’ Vacation Bible School curriculum.

I’m not sure if Dan Barker has the right background for disputing whether intelligent design belongs in a classroom or not. Remember, the bulk of his life was spent writing and singing feel-good, happy-clappy songs. In his debates with Christians, it’s quite clear that he is totally unequipped to assess scientific evidence from the Big Bang, the fine-tuning, the origin of life, the Cambrian explosion, or habitability. It’s just not his thing, and I don’t think that musicians have what it takes to understand those arguments enough to feel comfortable using the courts to suppress people with actual PhDs in science.

You can read more about my opinion about how Dan Barker arrived at his atheism through a mistaken view of the Christian life.

I subscribe to the ID the Future podcast, and I really recommend that you do as well!