Hume's Fork

Hume's division of all meaningful propositions into two categories: 'relations of ideas' (analytic, certain, non-empirical) and 'matters of fact' (synthetic, contingent, empirical) — with everything else dismissed as sophistry.

The fork: all genuine knowledge is either (1) relations of ideas — propositions whose truth is knowable by pure reason alone (mathematics, logic) — or (2) matters of fact — contingent truths known through experience. Any proposition fitting neither category — including most of metaphysics and theology — is 'sophistry and illusion.' Commit it to the flames. Directly inspired Kant's synthetic a priori problem, and the logical positivists' verification principle.