 Peirce started his research into the algebra of logic in the late 1860s. In his paper “On an Improvement in Boole’s calculus of Logic” (Peirce 1867), he arrived independently at the same conclusion that Jevons had reached earlier, that one needed to replace Boole’s partial operation of addition with the total operation of union (see CP 3.3.6). In his important 1880 paper, “On the Algebra of Logic”, Peirce quietly broke with the traditional extensional semantics and introduced a usual assumption of modern semantics: the extension of a concept, understood as a class, could be empty (as well as the universe), and stated the truth values of the categorical propositions that we use today. For example, he said the proposition “All \(A\) is \(B\)” is true if \(A\) and \(B\) are both the empty class. Conversion by Limitation, that is, the argument “All \(A\) is \(B\)” therefore “Some \(B\) is \(A\)”, was no longer a valid inference. Peirce said nothing about the reasons for and merits of his departure from the traditional semantic assumption of existence.