This chapter develops some axioms that express the fundamental features of the among relationship. It shows that although among is interdefinable with one of on one understanding of the one of relation, there is reason to think that that is not the only understanding available for one of, and that will help to clarify some issues in the semantics of plurals, especially concerning the status of the plurally plural (the perplural). The relationships among theory to set theory and to second-order logic are considered, and the reasons to think of among as a logical relationship are discussed. The first-order plural theory of among may provide a base for a first-order way of talking about everything, contrary to Tim Williamson's claim that second-order logic is needed for such ‘generality absolutism’.
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