A bit of background: Hume was an empiricist, he thought that knowledge of the world comes from our experience of the world (i.e. experimentation) along with logical reasoning. But he was also concerned about the relationship between experience and knowledge, that is, why is it that we think some experiences produce knowledge and others do not.<p>This is where the problem of induction comes from: using the tools that produce knowledge (experience and reason), is it possible to prove-out the required connection between experience and knowledge and if it isn't what do we do?
This is a philosophical question about knowledge, what it is, and how we arrive at it OR it's a linguistic question about the meaning of the word 'knowledge' and what it implies.<p>In summary: It is not possible to determine the cause of an effect when you only know the effect. For instance, the theory of evolution is not certain because we can't go back and check if we are correct in our assumptions. So how can it offer knowledge if we can't prove it's true?
An honest question--because I don't know: Has the philosophy of science in its long history produced anything that has proven useful in the practice of science?<p>I do understand that some people may consider the philosophy of science intrinsically valuable.