= Solution
Necessary connections would matter if they provided an independently knowable bridge from observed cases to unobserved ones. Their mere existence would not provide that bridge. In <David Hume>'s <problem of induction>, observations of past regularities do not deductively entail that the same regularities continue. Appealing to the past reliability of <inductive reasoning> uses the very kind of inference whose justification is at issue.<An Enquiry Concerning Human Understanding by David Hume>[section IV, part II]{ref}
Suppose, for example, that a particular <causal power> necessarily makes an isolated system respond in a certain way. If we knew independently that the power exists, that it remains present and that the relevant conditions obtain, a prediction could follow by <deduction>. But repeated agreement with the prediction does not itself establish those premises without further <inductive reasoning>. The proposal can relocate the epistemic burden rather than discharge it. A guarantee that every cause has some necessary effect also fails to identify which cause and effect our observations instantiate.
This separates <metaphysical necessity> from access to it. A scientist might posit <causal powers> because they unify otherwise separate regularities, explain counterfactual responses and guide successful interventions. An experimentally supported molecular mechanism can make the behaviour of a material intelligible across varied conditions. That supplies a comparative scientific reason to prefer a structured causal model over a bare catalogue. It does not demonstrate that the model captures a connection whose violation is impossible in every relevant world, or that its scope extends beyond the tested domain.
<Hume>'s discussion of <necessary connection> challenges the idea that inspecting one cause discloses such a connection directly; repeated experience instead explains our expectation.<An Enquiry Concerning Human Understanding by David Hume>[section VII, parts I–II]{ref} A defender of <causal powers> can reject that account, but must explain both the powers and how we know them. Mathematical necessity in a model is insufficient: the <deduction> is conditional on the model applying to the physical system.
The defensible conclusion is conditional. Independently warranted knowledge of stable necessary connections could justify particular projections. Simply adding them to one's account of nature does not solve the <problem of induction>. Scientific support for a causal account can remain strong, comparative and fallible without becoming a noncircular deductive foundation for every future inference.
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