You do realize that Hume held that induction cannot be logically justified? He noticed there is a "problem of induction". That problem was exploded by Karl Popper. Have you read what he has to say and taken seriously his ideas? Have you read and taken seriously the ideas of philosophers like David Deutsch, David Miller, and Bill Bartley? They all agree with Popper that:

Induction, i.e. inference based on many observations, is a myth. It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure - Karl Popper (Conjectures & Refutations, p 70).