Ontological arguments for God’s existence depend on assumptions about both the logic and the value of existence. Descartes’s much discussed argument has been pilloried, from Kant to Frege, for committing some kind of egregious category error. Two quite different categorial criticisms are often conflated, but once disentangled, jointly they are decisive against Descartes’s rather crude version of the argument. Like Descartes’s argument, Anselm’s Proslogion II argument has also been much discussed and analysed, almost to the exclusion of the far more promising and succinct argument presented in Proslogion III. By applying insights from Tichý’s ontology for higher-order entities (otherwise known as Transparent Intensional Logic) the Proslogion III argument can be shown to be immune to the categorial criticisms that cripple Descartes’s, and render the Proslogion II argument highly dubious. Logically the Proslogion III argument is impeccable. This fact forces a re-examination of Anselm’s axiological assumption, concerning the value of existence. It turns out to be the axiology of existence, not its logic, that cripples the Anselmian project.