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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?

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  • The role of analyticity was to explain the conundrum that logic and mathematics do not seem to be empirically based, while nonetheless are indispensable in scientific work. Declaring them to be glorified conventions was a nice way to explain that without compromising the tenets of empiricism (no a priori input). To confirm a general theory empirically we need to be able to deduce its consequences, i.e. to unpack all the particulars that are (conventionally, according to them) packed into the theory. Analytic statements are the bridge conventions that enable such packing and unpacking.
    – Conifold
    Oct 14, 2020 at 22:12
  • Thanks for the response. I was wondering if you can elaborate a bit on a few things. What exactly do you mean by "the bridge between packing and unpacking"? Do you mean drawing logical conclusions from empirical observations? If we empirically observe A: All humans have eventually died, and B: I am human, then does the logic come in when we conclude that A and B => I will eventually die, exactly because this conclusion, (at least in my lifetime and from my perspective) will never be directly observable?
    – Mark
    Oct 15, 2020 at 2:24
  • It is not a bridge between packing and unpacking, it is a bridge between general and its instances, packing and unpacking are the movements along it. We can not empirically observe that all humans have eventually died, nor any general statement whatsoever. We can only deduce empirical instances from the general, and then confirm or infirm them by observations. As for generating general hypotheses to test, one needs more than logic for that. It is a "creative" process, although not that creative in cases of simple empirical induction like yours. Positivists were happy to leave it to psychology.
    – Conifold
    Oct 15, 2020 at 4:37
  • Thank you, I believe that helps me a bit more. If I may pose one more question, I would be very appreciative. When you say: "To confirm a general theory empirically we need to be able to deduce its consequences." Is that to say, for example, if my theory is "the sun is very hot", then in order to confirm that theory, I deduce that if the sun is hot, surrounding areas like the earth must be somewhat warm, too. Because I cannot go put a thermometer on the sun, but I can on the earth, having deduced this consequence gives me a way of "confirming" my theory.
    – Mark
    Oct 15, 2020 at 21:14
  • Yes, that is the general idea. Of course, "the earth must be somewhat warm" is still general and vague, so you make "very hot" more specific, deduce further that the average temperature taken at finitely many points must be within some range, and then test it. In addition to general theory this also involves some pragmatic propositions (that the instruments are adequate, that the points chosen are representative, etc.), so there is some room to "save" the theory even if it appears to be disconfirmed. But that is resolved also pragmatically, improving observations, using Bayesian updates, etc.
    – Conifold
    Oct 15, 2020 at 22:29

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