Restricting to actual causal history avoids the problem that counterfactual theories otherwise treat all logically possible worlds equally, making normative distinctions arbitrary.

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Causal history(what the Inheritance View focuses on): The chain of events and causes that led to something happening; in this case, all the things that happened to cause you to have a particular belief.
Counterfactual theories(as theories about how causation works): Philosophical theories that explain causation by asking 'what if?' questions—like 'if the cause hadn't happened, would the effect still occur?'
Logically possible worlds(the domain across which strict implication operates): Imaginary scenarios or alternative realities that don't contradict the laws of logic itself—even if they're wildly different from our actual world.
Normative distinctions(normative distinctions between correct and incorrect belief attributions): Differences between what is considered correct or right versus incorrect or wrong according to some standard or rule.

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