I'm reading up on a bit of the ideas of logical positivism. It seems that the main components were the distinction of synthetic and analytic statements, and the verification principle. Without giving a definition of the verification principle, it seems that this principle implies that only purely analytic or purely synthetic statements make sense.
My questions is, they seem to view analytic statements as trivial, tautological, or making no positive claim about the world. I see where they are coming from on this, but then my question is: Why don't they just go pure empirical and discard analytic statements all together? Why do logical empiricists value them in their philosophy of science, and what role are they supposed to play?
My initial impression is the following, and I'd appreciate it if somebody could tell me if this is on the right track: We observe physical objects, and then can empirically observe and "confirm" properties that they possess, for example: Stars expend energy. Then, using these objects as if they were mathematical objects or symbols, we apply the rules of logic to them in order to formulate further reasonable hypothesis. For example: If we observe A: Stars expend energy, and B: Stars do not replenish energy, then we can logically conclude that C: Stars will one day run out of energy, which is a testable hypothesis as we can go out and observe dying stars.
Is this was the logic in logical positivism is used for? Using the objects of our empirical observations to formulate rational hypotheses?