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    Operational frameworks successfully define probabilities ... — Carmelics
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    Challenges→In contextual models, apparatus settings and outcomes are not cleanly separable variables, making the probability function's domain ill-defined for the parameter/outcome distinction.

    Operational frameworks successfully define probabilities P(outcome|settings,initial-state) with perfectly well-defined domains, showing the separation problem is solvable rather than fundamental.

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    Key Terms

    Operational frameworks(as used in physics and philosophy of science)
    A practical system or set of rules for how to measure and test something in the real world, rather than just thinking about it theoretically.
    P(outcome|settings,initial-state)(as used in mathematics and physics)
    Mathematical notation meaning 'the probability of a particular result, given specific experimental conditions and starting point'—the vertical line means 'given that.'
    Probabilities(as used in discussing whether actions have fixed chances of occurring)
    Numerical chances or likelihoods that something will happen (like a 50% chance of rain).
    The separation problem(as used in quantum mechanics philosophy)
    A debate in quantum physics about whether we can cleanly separate what's happening in the experiment from how the experimenter measures it, or if they're always tangled together.

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    Well-defined domains(as used in mathematics and logic)
    Clear boundaries or limits on what situations and inputs a system can actually work with—knowing exactly when and where the rules apply.
    fundamental(as used in metaphysics)
    Basic, primary, or most essential—the deepest level of something, not derived from anything else.

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    In contextual models, apparatus settings and outcomes are not cleanly separable ...

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    In contextual models, apparatus settings and outcomes are not cleanly separable ...

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