According to one of the greatest mathematicians of our time, “there is no picture- or theory-independent concept of reality.”* What Stephen Hawking means by this is that we are all limited in our perception of reality. He compares all of us to a goldfish living in a bowl with curved sides. Gazing out, the fish has a distorted view of reality. He points out that if the goldfish had sufficient time and brain-power, it might be able to work out a series of laws that describe the way things appear from inside of a fish bowl. We, on the outside of the bowl would find these goldfish descriptions of the world overly complicated and would simply point out that the fish lives in a bowl and cannot see reality in its true form. Hawking says, “might not we ourselves also be inside some big goldfish bowl and have our vision distorted by an enormous lens. The goldfish’s picture of reality is different from ours, but can we be sure it is less real?” Hawking then suggests that we might be living unknowingly inside a virtual reality created by intelligent computers as described in the science fiction film, The Matrix. He adopts a view which he calls “model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations.”
Now I suppose it is not surprising that a mathematician would come up with a mathematical way of describing the universe. But that is just it, it is a mathematical description of the universe. The greatest strength of his argument ultimately makes it weak in explaining the hows and whys of the universe. For, his is just one way of seeing the universe as is the goldfish way of seeing the universe. He certainly can develop such a model and use it to describe the universe as he sees it. Where he strays too far is in saying that his is the only way to view the universe and that philosophers and theologians have nothing to add to the story. His mathematical models have great predictive value for describing how electrons, protons, neutrons, and quarks function in the universe. He would like this same model to predict how the universe came into existence and why the universe came into existence. Here his model is less helpful. Just as the goldfish in the fish bowl cannot be sure of the reality of her world-view (even if she could create models that described her observations), neither can Hawking be sure of the reality of his world-view. It is equally as possible that his model works inside of the universe (or even inside the multi-verse that Hawking goes on to describe) and also inside a greater, over-arching, plan of a creator God. Here is precisely where philosophy, theology, and epistemology come into the discussion. Despite what physicists and mathematicians might think, mathematics is not the only valid tool of inquiry or description that we can use to understand our universe.
*This and other quotes in this article are from Hawking, Stephen, and Leonard Mlodinow. The Grand Design. New York: Bantam Books, 2010, p. 39-43.