The paradox of induction is the problem that in all scientific reasoning we form conclusions, called laws, that are of a general nature; however, the evidence we have for those laws is based upon particular 

experiences. For example, we form the conclusion that all rays of light will be bend as the pass from air into glass, but we have only ever observed a finite number of instances of this law. On further reflection we see that there is no necessary connection between something happening on one occasion and the same thing happening in like circumstances on another occasion. We are not directly acquainted with the “power” behind events that ensures the uniformity of nature throughout space and time.

Another illustration of this might concern the uniformity of space. Imagine that a space mission is about to be sent to the nearest star, Alpha Centauri. People might be queuing up to volunteer to be the first people to witness life on a distant planet. On the other hand, there might be anxious reluctant passengers, desperate not to be dragged on the fool-hardy mission. Why? Because there is no guarantee that the laws of nature operate in the same way in outer space as they do in our solar system. It is entirely conceivable that once the space ship passes beyond the perimeter of our solar system, that entirely different laws of physics will apply, and the space ship could be destroyed by chaotic forces that cannot be anticipated. We have no way at present of being sure that universe is uniform. We have only sampled physical nature in our own limited portion of the universe. We might regard the fear of the passengers as outlandish, but it is not an irrational fear. Just because things have happened at one point of space and at a given time in a certain way is no guarantee that they always will happen that way.

This, then, is the paradox. Every day we reason from particular instances to generalities, and such inference is essential to our way of life; but there is no guarantee that such an inference is valid, and, indeed, very often such inferences prove to be fallacious — as in the case of the chicken that reasoned that its master would always feed it just because its master always has!

A schematic representation of the inductive inference is as follows.

The general law encompasses a potentially infinite number of instances that no amount of observation could possibly affirm. The problem is usually expressed as a problem of inference from past to future, but strictly this is only an instance of the problem; unobserved past events are also subject to the paradox of induction — we can never be sure that any general law has applied uniformly even in the past. No general law can ever be certain.