James Anderson offers a concise synopses of the problem of induction.
I recall as a child being struck by the fact that if a monkey were placed at a typewriter, the chimp would eventually type the works of Shakespeare given enough time.
Soon after becoming a believer it occurred to me that if the unbeliever were consistent with his worldview, which entails pure randomness, he would concede that up until the present moment he had been living in a random slice of time, not unlike that in which a monkey might type the works of Shakespeare. Yet he’d have no rational basis for assuming the future would be like the seemingly ordered past. Salt dissolving in water everyday, just like yesterday, would be as likely as Bonzo typing great literature given the assumptions of unbelief. Little did I know then, I was dealing with the age old problem of induction. (A problem for a non-Revelational epistemology and naturalistic metaphysic.)
But as any astute parlour game aficionado realizes, probability has no memory, (an insight I learned as a young boy from my father as I pondered discrete events). So, if black were to come up on the roulette wheel twenty times in a row, the odds of black coming up a 21st time would still be 50% (if there weren’t two green slots of 0 and 00 on the wheel, and assuming no other anomalies, like the wheel was rigged etc.). We oughtn’t think red is overdue or black is running a hot streak. Given the uniformity of nature, we may expect red and black to occur equally over time and with equal probability at each consecutive spin.
However, the unbeliever can have no such expectation if true to his espoused presuppositions. The unbeliever should no sooner bet on the future results of past science (e.g. a streak of seemingly consistent pattern of salt dissolving in water) than on the pure randomness of non-science, if he were consistent. Bonzo’s uncontrolled predictability is as dependable as the scientific method.