 The first volume concerned the equational logic of classes, the main result being Boole’s Elimination Theorem of 1854. Three rather complicated counter-examples to Peirce’s claim of distributivity appeared in an appendix to Vol. I, one of which involved nine-hundred and ninety identities for quasigroups. On the basis of this volume, Dedekind (1897) composed an elegant modern abstract presentation of lattices (which he called Dualgruppen); in this paper he presented a five-element counter-example to Peirce’s claim of the distributive law.