A Note on Order

contains a second-order generalization, in addition to the first-order generalization. What the standard notation for generalization is designed to do, and indeed excels at, is displaying propositional structure. It graphically represents how the force, scope and order components interact to make up propositions expressing generalization, and it allows us to typify these propositions in a completely discriminable manner. On a glance, universal generalization can be distinguished from existential, first-order from second-order, firstorder universal from second-order existential, and so on for the various combinations of the parameters. The beauty of the notation is that the structure over which both the truthconditions and inferential capacities of generalizations are defined is represented as a single composition of force, scope and order, and it is this that explains its perseverant utility. It characterizes what we mean by the logical form of generalization. This representational success is a core part of the analytic story about generalization, but it does beg a foundational question: What is it that makes these representations logical representations? The answer is readily at hand: it is because they are made up of logical parts, put together in a logical way. Comprehending this answer, however, requires some prior information we need to know in what sense force, scope and order are logical notions.