Tag Archives: Effectiveness

William Lane Craig on the unexpected applicability of mathematics to nature

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 apologists. You can read the whole thing here.

Positive arguments for Christian theism

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 apologists. You can read the whole thing here.

Positive arguments for Christian theism

Is sheltering children a bad thing? What are children for anyway?

Marriage and family
Marriage and family

Lindsay and Doug Harold are Christian super-parents who do recommend sheltering kids. But the way they do it is interesting. Lindsey writes about it on her Lindsay’s Logic blog.

She writes:

People often criticize parents who are careful about what their children watch, listen to, or read or who monitor their friends and influences very carefully. This criticism is very commonly made of homeschooling parents, though it has certainly been applied to others as well. The claim is that these parents are sheltering their children too much and that they won’t know how to deal with the real world when they enter it upon reaching adulthood. Some even claim that sheltered children will be more likely to go crazy with the sudden freedom than children who have grown up exposed to evil things of the world and are used to them.

There seems to be a misunderstanding about what sheltering is and what its purpose is.

There’s a big difference between knowing about evil things that can happen and knowing evil by being steeped in it. It is certainly possible to shelter one’s children too much so that they are ignorant of reality and have no idea how to function in society or how to address the wrong ideas of the world. But that’s very rare. The greater danger is in putting children in the midst of evil before they are prepared (developmentally and spiritually) to handle it. That is by far the more common scenario and the one more likely to result in problems.

You don’t send a soldier into battle until he’s trained, and you don’t send a child into the world until he’s trained either. Children are very vulnerable and need protection until they are prepared to fight evil on their own.

Dina sent me this Gospel Coalition interview with Francis and Lisa Chan, that talked about the importance of training kids to have a specific purpose, too.

It says:

How has parenting seven kids affected your marriage? What’s your biggest piece of advice for fellow parents with respect to their marriages?

Children change everything. I am convinced God uses our children to cleanse us from self-centeredness. Babies demand that you move your focus off yourself and onto them. That’s not necessarily a bad thing. It’s only bad when they’re 13 and still believe everyone should drop whatever they’re doing to tend to their needs. It’s hard enough to fight self-centeredness in ourselves, but parents are given the task of training their children to live God-centered lives as well (Deut. 6:4–9).

Our biggest piece of advice would be to view your kids as assets rather than burdens. It used to be that people envied couples with many kids. It meant they had more help on the farm, with the business, around the home, and so on. When people hear we have seven kids now, though, they feel sorry for us! Why is it that for thousands of years children were a blessing, yet in the past few decades we’ve come to view them as burdens? Poor parenting. We raise them to either be burdens or assets. Good parenting involves teaching them to love and serve others rather than expecting to be constantly served. While we will always serve our kids to some degree, we also expect them to serve each other and those around us. Our children have been our biggest assets in ministry. Rather than distracting from kingdom work, they multiply it. Nine servants are better than two.

One of the things that’s scary to me is that if I did get married, my wife might be too soft on the children, and always let them have their way. Women sometimes want to be the child’s friend and not his parent. Men have a different view of children. We want them to be independent and to not starve, and to make a difference for God. So on the one hand, I want to be protective of them and shelter them from things they are not old enough to see, and on the other hand I want them to grow their skills in order to serve God. What a difficult balancing act – I am not sure I understand children well enough to manage it. But, that’s what a wife is for, right? She’s the Director of Child Development.

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 apologists. You can read the whole thing here.

Positive arguments for Christian theism

J. Warner Wallace: influence the culture by encouraging young Christians

From the Cold Case Christianity blog.

Excerpt:

I came to faith at the age of 35. I didn’t have a deep relationship with any Christians at the time, and I had no strong Christian influences in my life. Without a mentor or role model, I felt like I had to work through the evidence and claims of Christianity on my own. Many years later however, as I was preparing to write my own book and start a modest journey as a public Case Maker, members of the apologetics community surrounded me with support and encouragement. While I wasn’t much younger than any of them (and was, in fact, older than some), they recognized I was the “new kid” on the block and surprised me with their generosity, wisdom and assistance. I was humbled by the response, and began to look at my own sphere of influence, searching for young men and women I could encourage in a similar way.

Those of us who hope to influence the culture for Christ typically think of our own efforts to communicate and reach the world. What can I write today? What can I say? How can I effectively use the internet to promote and defend the Christian worldview? Like others, I’m guilty of viewing my influence through the narrow lens of my own efforts. As a guy who started this season in my 50’s however, I’ve come to realize the limits of my own impact and the role I can play as an encourager. My questions are starting to change: Who can I inspire as a young Christian Case Maker? What small piece of wisdom can I provide to someone who is a few steps behind me in this journey? How can I impact the younger generation of Christian Case Makers? I know I won’t be writing and speaking 30 years from now, but there are men and women out there who will be. What can I do to make them even more effective?

I wanted to add to what he wrote and tell you a little bit about what I do. Through my blog, I have been able to meet young people in high school and college who are making decisions about what to study and where to work. I’m been able to help people in some specific ways:

  • helping them to know what to read/listen to/watch in order to build up their worldview
  • helping them learn how to debate with skeptics
  • helping them to decide between college and trade school
  • helping them to choose the right major
  • encouraging them to work in the summer instead of taking time off
  • helping them get funding for apologetics events that they organize
  • rewarding them for doing well in school or work
  • listening to the conflicts with teachers and professors
  • helping them make plans for their lives
  • helping them make good decisions with the opposite sex
  • spending time playing games with them or just talking
  • asking them about their classes, assignments and tests

It’s always rewarding to seem them studying hard subjects, getting good grades, entering competitions and getting summer/full-time jobs. I like to give rewards to people who do try to grow their skills and produce results. It can be small stuff like games or books, or bigger stuff, like sponsoring an apologetics event that they’ve organized. Sometimes I can get a young person connected with a mentor. For example, one young lady wanted to start a pro-life club, and I was able to connect her with someone who started a large pro-life organization and the office manager from that large pro-life organization. I also provided her with some helpful pro-life books.  It’s important that we not understimate how much good it does to try to be supportive when young people want to grow their skills and take on challenges.

I think that mentoring young people is especially for those of us who are not married with children. We typically have more disposable income and time than married people do, especially married people with children. Not only is it good for them to get the advice from someone more experienced, but it also gives you parenting practice, and that’s something that you can talk about in a courting situation. This is the kind of thing that signals to a candidate spouse that you are going to be interested in mentoring them, and in raising effective Christian children. The most challenging thing about doing this is that you really have to think about how to please God with your mentoring, and that means that you have to put yourself second a lot of the time. It’s good for singles to learn how to do that.