 The problem is even starker for universal truths: there’s no truth-table for them because there is no set of atomic formulae whose truth determines that a universally quantified formula is true too. Why so? Because whatever true atomic formulae we light upon (Fa, Fb… Fn), it doesn’t follow from them that ∀xFx is true. To extract the general conclusion one would need to add to the premises that a, b… n are all the things there are; that there’s no extra thing waiting in the wings to appear on stage that isn’t F. But this extra premise is itself universally quantified, not atomic. So it can’t be argued that the truth-makers for Fa, Fb… Fn put together already discharge the task of making ∀xFx true because they entail it (Russell 1918–9: 236–7; Hochberg 1969: 335–7).