Mathematical Proof That Naturalism Is Incorrect?

John Lennox has three earned doctorates and is a professor of mathematics at the University of Oxford and teaches Philosophy of Science at Green Templeton College in England. So in the area of mathematics and how it applies to science, I think he would qualify as an expert. In Lennox’ book God’s Undertaker: Has Science Buried God? he deals with many things related to science and religion, including an idea called “reductionism.” Reductionism is the concept that that any given system, up to and including the universe, can be explained by breaking the system up and into simpler components that are individually easier to investigate. Of course, this is how most all complex problems are attacked. But reductionism teaches that the the entire system can be adequately explained by explaining the operation of all the parts. Atheistic scieintists believe that since we have adequately explained many complex problems up to this point, then there is no reason why we will not explain more complex problems later. Eventually, given enough time and brain power, science will explain anything to which it sets its mind, including the operation of the universe. No God is in the machine to make it work; pure matter and physics have explained everything so far, therfore they will explain everything eventually. 

Naturalism is the worldview that supports reductionism and most of modern science. Naturlism says that all that exists is nature…the only things in existence are matter and energy. Those who believe in a God as a divine creator are neanderthals who are in the way of progress.

But Lennox shows how this is false. Not only does Lennox show how reductionism is untrue, he states that it is mathematically impossible. In Lennox own words:

In a piece of mathematics that stands as an intellectual tour-de-force of the first magnatude, [Kurt] Godel demonstrated that the arithmetic with which we are all familiar is incomplete: that is, in any system that has a finite set of axioms and rules of inference and which is large enough to contain ordinary arithmetic, there are always true statements of the system that cannot be proved on the basis of that set of axioms and those rules of inference. This result is known as Godel’s First Incompleteness Theorem. (p.53)

Now what Lennox is saying is this: Godel’s First and Second Incompleteness Theorems are accepted mathematical proofs that demonstrate that we cannot investigate a complex system and explain all of it. No matter how long we investigate the workings of the clock, we will never be able to explain everything there is to learn about the machine. Mathematics is the language by which physicists demonstrate things. According to Lennox, Godel’s theorem proves mathematically that we cannot fully explain any complex system, let alone the whole universe.  

It strikes me that this point is monumental. We are told by atheist scientists that a theistic worldview has no place in science. We are told that belief in God gets in the way of progress, and that the only way to further knowledge is to assume that there is no God, and that everything in the natural world is merely working from natural laws. We are told that if we bring God into the picture, we have stopped doing science and have brought religion into the classroom. But if Lennox point is true, the naturalistic worldview is disproved mathematically. Science clings to naturalistic materialism and methodical reductionism as the only allowable tools, yet according to proven mathematical models, these tools will never be able to fully explain the universe or any complex system.

Now I am a self-proclaimed mathematical basket case, and do not have the capacity to evaluate Godel’s Theorems or Lennox’ application of them. I’m sure the atheists will have some response to show that their position is accurate, for they must at all costs keep God’s foot out of the door so that they do not have to answer for the way they live. But Lennox is a professor of mathmatics at Oxford, so I’ll have to take his word for it.