 We conclude this section by presenting a number of prominent examples from these remainder of Volume I, with their intuitive meaning, location in PM, definition in PM, and a modern version. (Some of these numbers are theorems rather than definitions.) Note, however, that the modern formulations will sometimes logically differ from the original version in PM, such as by treating relations as classes of ordered pairs, etc. More prominent is the practice in PM of defining notions as relations, or higher order relations between relations, rather than as functions determined by those relations. In his account of the logic of Principia, W.V. Quine (1951) objects to the complexity and even redundancy of much of this symbolism in comparison with axiomatic set theory. These formulas can be worked out, however, with a step by step application of the definitions. 