The Concept of Proof (part 1)

"We cannot pretend to offer proofs. Proof is an idol before whom the pure mathematician tortures himself: In physics, we are generally content to sacrifice before the lesser shrine of plausibility." Arthur Stanley Eddington


Proof is a seriously misunderstood word. This probably accounts for its rare usage in the natural sciences. In one important sense no one can "prove" the theory of evolution, or the big bang theory, or relativity, or string theory, or whatever theory you want to talk about. But, and this is an important but, that does not mean that there is not sufficient evidence to warrant thinking these are good theories. To use Eddington's word, we can say they are plausible. In some cases, very plausible. What makes the word proof tricky is that it is sometimes used in philosophy in the one area you'd think everyone would be wary of using it: to prove the existence of God. Many people believe that God's existence cannot be proven. Let's stipulate to that for the sake of argument and vow only to use the word proof in areas where certainty appears attainable, like mathematics. The parallel postulate can be proven.


So what do we do with areas of empirical research? What do we do about God? Let's look for evidence and evaluate theories based on their plausibility and efficacy in explaining and accounting for that evidence. We need a set of criteria to evaluate theories to determine which best account for the evidence we have. A good suggestion comes from a critical thinking text titled How to Think About Weird Things by Theodore Schick and Lewis Vaughn. In it, they outline five points to use in the evaluation of theories. Let's look at them.


First a theory should be testable. If you can’t even figure out how to go about determining if your theory explains the evidence you don't have a good theory. As they point out testable means your hypothesis "predicts something more than what is predicted by the background theory alone." In short, we need this criterion because if there's no way to tell whether a theory is true or false it's really no good to us.


Second, a theory should be fruitful. What this means is that a good theory should make novel predictions. It should not only account for the evidence at hand but be able to address evidence that comes in later and even predict such new evidence. They point out that Einstein's theory of relativity is a good example of a fruitful theory because it made the novel prediction that light would be visible from a star behind the sun because the light would be bent by the gravitational field around the sun to be visible on earth. And, with reference to criterion number one this was a testable claim. Once tested, it was verified.


Third, a theory should have a wide scope. That is, a good theory explains a wide field of evidence. One of the differences between theories and hypotheses is their scope. Hypotheses address specific questions whereas theories attempt to provide a broad explanatory device. Theories that can explain a wide array of things are preferred, other things being equal, to more narrow theories.


Fourth, a theory should be simple. This term should not be confused with simplistic. Many scientific theories are complex in terms of our ability to understand them but simple in the sense that they postulate fewer underlying entities or assumptions. A good example of this is the difference between Copernicus and Ptolemy. Ptolemy's geocentric theory could explain the orbits of the planets but it was quite complex whereas Copernicus' theory explained the same observable phenomena with less complexity. So, other things being equal, that theory was the better theory. Think of it this way. Suppose I come up with a theory to explain how the lights in my house work but it involves little gremlins running inside the light bulbs. Someone else is able to explain the same phenomenon but without postulating gremlins. So, their theory is simpler than mine. It should also be pointed out that my gremlin theory may fail on other criteria as well such as being testable.


Finally, a theory should be conservative. Not in the political sense of the word. Rather, it should fit in with other things we know. If we have an explanation for something that we think is fairly certain and accurate then a new theory should fit in with that prior explanation. If it doesn't fit that may indicate our prior knowledge is flawed. We have to be open to that possibility but the burden of proof is on the new theory.