Science is based on a glut of laws from physics, chemistry, mathematics, and other areas. The assumption of scientific materialism, as I understand it, is that science has explained or will explain everything. The final conclusion of scientific materialism, also known as scientism, is nicely captured in a question chemist Peter Atkins asked philosopher William Lane Craig in a debate: “Do you deny that science can account for everything?”

Scientism’s assumption that science can establish everything is self-refuting. Careful analysis shows that there is an infinite number of things that are true that we cannot prove scientifically and never will.

Stephen Hawking saw the tip of the iceberg of this truth when he said, “Up to now, most people have implicitly assumed that there is an ultimate theory, that we will eventually discover.” This Theory of Everything, as it is often called, would link together all physical aspects of the universe under one vast umbrella theory. Some are still searching. But Hawking abandoned the search. In defending his switch of position, he invoked Kurt Gödel (1906–1978):

Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I’m now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery. Without it, we would stagnate. Gödel’s theorem ensured there would always be a job for mathematicians.

STEPHEN HAWKING, “GÖDEL AND THE END OF PHYSICS” AT TEXAS A&M UNIVERSITY (PUBLIC LECTURE, MARCH 8, 2002)

Speaking of Metamathematics

Just as it is hard to talk about evolution without mentioning Charles Darwin, it’s hard to talk about metamathematics without mentioning Kurt Gödel. Hawking’s invocation of Gödel’s (first) incompleteness theorem has even deeper implications. Hawking is right in saying there are possibly many more discoveries in physics remaining. But Gödel also showed that there are unprovable truths and, more dramatically, there is an infinite number of unprovable truths forever beyond the reach of scientific proof.

Here is a result of Gödel’s incompleteness theorem supporting this. Given a finite set of assumptions (axioms), there will be revealed truths (theorems) that are unprovable. It sounds like an oxymoron, but these truths in Gödel’s proof are provably unprovable. The axioms can be thought of as inflating to a Gödelian bubble filled with provable proofs. There are also unprovable truths revealed within the bubble whose proof may lie outside the bubble.

One solution is to take an unprovable truth in Gödel’s bubble and add to the list of axioms as an assumed truth. We can’t prove it, so let’s assume it. If the bubble of truth was spawned from a billion axioms, the augmented axiom list now has a billion and one entries. This new list will birth an even bigger bubble. The bigger bubble subsumes the smaller. The larger bubble contains another truth that cannot be proved within the larger bubble. So, as before, we add this new unprovable truth to the set of axioms and now have a billion and two axioms. The bubble gets bigger. Continuing, we can add an unbounded number of axioms to the original list. The bubble will continue to expand with each new assumed axiom but will always contain new unprovable truths. There will always be a new unprovable truth to be added to the collection of axiomatic assumptions.

Read the rest at Mind Matters News, published by Discovery Institute’s Walter Bradley Center on Natural and Artificial Intelligence.