Hume notoriously maintains that contiguity, succession, and constant conjunction are individually necessary and jointly sufficient conditions of causation. While his arguments for the necessity of constant conjunction have been thoroughly dissected, his arguments for contiguity and succession have generally been either ignored or misstated. I hope both to correct this unfortunate state of affairs and to show some fatal defects in Hume's account.
The pertinent passages in Hume's writings acknowledge three conceivable ways in which the temporal relation between causes and effects might be construed: (i) as separated by some interval; (ii) as perfectly contiguous, so that the effect succeeds the cause in the very next moment; (iii) as perfectly contemporaneous, existing at the same moment. Hume defends the correctness of (ii) and denies the tenability of both (i) and (iii).
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