There is another problem with Hume’s reasoning, less obvious but equally serious. Ittook the genius of Immanuel Kant to point out an error that had completely escaped Hume’s attention. Contrary to Hume’s assertions, mathematical truths are not analytic. Consider the famous mathematical proposition in Euclidean geometry that “the shortest distance between two points is a straight line.” This seems self-evidently true, and yet it cannot be confirmed simply by examining the sentence. There is nothing in the definition of the terms that makes it true. So how do we know it is true? We have to check. It is only when we make two points on a piece of paper and then draw a line through them that we can observe that the shortest distance between them is a straight line. Kant showed that many other mathematical propositions are of this sort.

I mention Kant’s correction of Hume not to suggest that these mathematical axioms are wrong. What I am suggesting is that their veracity can be established only synthetically. We can proceed only by looking at the data. So mathematical laws are, in general, like scien- tific laws. We can verify them only by examining the world around us. When we examine the world around us, however, we make a disconcerting discovery first noted by Hume himself.

Scientific laws are not verifiable. They cannot be empirically validated. Science is based on the law of cause and effect, and that law cannot be validated in experience either. Hume’s argument was a bombshell. So far-reaching were its implications that very few people grasped them, and to this day Hume’s ghost continues to haunt the corridors of modern science. It is quite amusing to see educated people, including our community of self-styled “brights,” continue to make claims about science that were exploded two centuries ago by Hume.