Current Status of the Inductive Reasoning

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I'm very interested in economics. But I've decided that before studying any actual science I need to have a solid background in methodology and philosophy of science. And this specially true for economics, since it's a field where people seem to have no idea on what they are building upon, hence the multiple radically different schools of thought.

Now I've already read some history of science and some philosophy, but I got stuck. It is consensus that the induction does not render justified knowledge, but also that without it, science would not be possible (Popper claimed to have ditched it but he didn't, since you need induction to create an hypotesis, you can't just dream of a 'bold hypotesis'). However the last attempt of formally developing or fitting the induction into a formal model of science I could find was Hempel's and Carnap's, which failed, and some related bayesian confirmation bullshit of attributing arbitrary probabilities.

Do any of you homos can point me any directions, authors an so on?

Thanks very much.

Also no scientific relativism/feyerabend bullshit in this thread.