Back in ancient history, when I was a graduate student we did not have a computer on every desk. We prepared decks of computer cards and trotted them down to the computer center and waited for the printed output. No getting upset if you did not have two-second response on you monitor. Anyway, I was calculating the same quantity in two different ways. One way involved a complicated calculation solving the Schrodinger equation for many different states and doing an obscure averaging. The other was a much simpler calculation using what is known as semi-classical approximations (to find out more, read my thesis). Relating the two involved a lot of math – calculus, differential equations, Laplace transforms, and various other techniques named after august, dead people. As I sat there looking at the numbers coming out the same, I thought: Egad, you know, math really does work. But, is it correct to say I had faith in the validity of mathematics?
Similarly, is my belief in the utility of Newton’s laws of motions a matter of faith? But, you say, in this case, my belief or faith is misplaced because the laws are not absolutely correct. So? Where they work, they work extraordinarily well: planetary motion, cars, books, baseballs (except when I am trying to catch them), chalk thrown by an irate teacher (it missed), etc. I do not worry about books starting to move by themselves. Is my belief in the continuing validity of other well-established models and techniques of science a matter of faith or something else? What about evolution, global warming, renormalization techniques, quantum mechanics, and the second law of thermodynamics? Are they all or any of them matters of faith?
The answer to the above question depends on what one means by faith. But if the above are examples of faith it is a rather trite use of the word. Indeed, it is a stretch to claim that any of these are examples of faith at all—certainly not in the same sense that faith is used in religious circles: Now faith is the assurance of things hoped for, the conviction of things not seen (Hebrews 11:1). To a large extent, faith, in this latter sense, is absent from science. The rules of engagement are well laid out and there is little need for a conviction of things not seen.
But, faith does come into science in two ways: one fundamental to science and the other optional and probably spurious. The spurious one is when science is taken beyond it legitimate bounds and claims are made about the ultimate nature of reality: claims about materialism, naturalism and realism. Here, indeed, we have a conviction of things not seen. These are not really a part of science but rather metaphysics and a matter of faith as discussed in a previous post, The Limits of Science. But what about things like atoms, electrons and quarks: things that are not seen in the normal sense of the word but are inferred? They are internal parts of the models science builds and taking them to be definite parts of reality is an act of faith. Like the ether they may go poof at some point in the future. Following Poincaré, I rather take their existence as a matter of convention and convenience. Are they really there? Who knows. If the math works out the same does it really matter?
At one point faith does play a key role in science. It could be called the fundamental axiom of science or science’s Nicene Creed: Patterns observed in the past enable us to predict what will happen in the future. The seriousness of the problem was originally pointed out by David Hume (1711 –1776) in his critique of scientific induction. His claim was that scientific induction does not exist. There is no logical reason for tomorrow to be the same as today. Hume had no answer to the problem other than to ignore it. Immanuel Kant (1724 – 1804), responding to Hume, tried to solve the problem and failed.
The fundamental axiom of science lies behind all of science and provides the foundation on which the scientific method rests. We build models based on past observations to predict future observations. This only works if the fundamental axiom is true. The scientific method is just the practical application of this idea. In terms of Aristotle’s four types of causes, the scientific method is the formal cause, the scientists the effective cause, and final cause (the why) is to build models that will correctly predict the future based on the past. The ability to achieve the final cause rests entirely on the fundamental axiom. The formal cause, the scientific method, follows from trying to put the final cause into action. Since the constructs of science are abstract there is no material cause.
The fundamental axiom is a sophisticated version of the “Mount Saint Helens fallacy.” This was named after a person who refused to leave Mount Saint Helens because he did not believe it would blow up. It had not blown up in living memory so why would it blow up now? I am not sure his body was ever found. Today does not have to be like yesterday. But in science we assume the rules will be the same or at least change in predictable ways. Not as naively as the poor guy on Mount Saint Helens but the assumption is the same: the sun will rise tomorrow (in Vancouver in the winter that is, indeed, a thing not seen). Do the laws of physics tomorrow have to be the same as today? Will mathematics be different tomorrow? Maybe, just maybe, when I look at the two answers on my computer screen[1] tomorrow they will be different. It is possible, but I have faith
Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod
[1] Note computer screen, not computer printout; things have changed.
