The Synthetic Relation in Hume

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Here we will see that contrary to the party line, Hume’s notion of a relation should be understood, in all cases, as a peculiar non-necessary synthetic relation; unique, but similar in a certain constructive sense to what I characterize as a mathematical notion of synthesis. And, most controversially, I argue that this non-necessary synthetic notion of a relation includes Hume’s arithmetical relations, which have typically been interpreted as either “analytic,” necessary, or both. In this general respect, Hume anticipates Quine’s attack on the analytic/synthetic distinction.
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