Science cannot end. For science to end would mean that we had made a set of observations, from which we could logically predict the results of all other observations. At any given moment, the set of observations is finite, as is the set of rules of logical inference. This is therefore a formal system of inference. And it is, of course, complicated enough to encompass basic arithmetic. But Gödel proved that every formal system of inference complicated enough to encompass basic arithmetic must be incomplete: There are statements in any such system whose truth value cannot be determined within the system. At which point we will need more observations to expand our system.