Quantifiers in Frege's Grundgesetze like are not well-defined because the part Fx & Gx stands for a concept but the yoking conjunction is horizontalised and must stand for a truth-value. This standard interpretation is rejected in favor of a substitutional reading that, it is argued, both conforms better to the text and is well-defined. The theory of the horizontal is investigated in detail and the composite reading of Frege's connectives as made up of horizontals is rejected. The sense in which (...) the Grundgesetze has a many-valued but classical logic is explained by proving that its propositional fragment (under the standard interpretation) and Bochvar's 3-valued logic are instances of the same metatheoretic methods. Historically, the paper argues for a more naive but well-defined reading of the text. Theoretically, it provides a formally adequate statement of that semantics, as well as developing the abstract metatheory which embraces Bochvar's language and the Fregean fragment. (shrink)