There is no doubt that inductive logic and inductive arguments are vital to the formation of scientific theories. This thesis questions the use of inductive inferences within the sciences. Specifically, it will examine various perspectives on David Hume's famed "problem of induction". Hume proposes that inductive inferences cannot be logically justified. Here we will explore several assessments of Hume's ideas and inductive logic in general. We will examine the views of philosophers and logicians: Karl Popper, Nelson Goodman, Larry Laudan, and Wesley Salmon. By comparing the radically different views of these philosophers it is possible to gain insight into the complex nature of making inductive inferences. First, Popper agrees with Hume that inductive inferences can never be logically justified. He maintains that the only way around the problem of induction is to rid science of inductive logic altogether. Goodman, on the other hand, believes induction can be justified in much the same way as deduction is justified. Goodman sets up a logical schema in which the rules of induction justify the particular inductive inferences. These general rules are then in turn justified by correct inferences. In this way, Goodman sets up an explication of inductive logic. Laudan and Salmon go on to provide more specific details about how the particular rules of induction should be constructed. Though both Laudan and Salmon are completing the logic schema of Goodman, their approaches are quite different. Laudan takes a more qualitative approach while Salmon uses the quantitative rules of probability to explicate induction. In the end, it can be concluded that it seems quite possible to justify inductive inferences, though there may be more than one possible set of rules of induction.