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Definition.com

Necessary connection (n.) depends ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠on the inference, instead of the inference depending on the necessary connexion.

Definition.com

Necessary connection (n.) is ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠what turns mere contiguity and succession into cause — and it cannot be found in any quality or relation of the objects themselves.

Definition.com

Necessary connection (n.) exists ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠at least in that we think of it; Hume muddled the importance of an idea with the fact that we entertain it.

Definition.com

Necessary connection (n.) is ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠never seen in any single case: one billiard ball strikes, the other moves, and that is the whole that appears to the outward senses.

Definition.com

Necessary connection (n.) is ⁠​‌​​​‌​​​‌​‌‌​​​​‌​‌​​‌‌​‌​​‌​​​​​‌‌​​‌​​​‌‌​‌‌​⁠felt in the mind, not found in the world: it is the customary transition of the imagination from one object to its usual attendant, projected onto things.