Mereomodal partialhood and fractional counting

Abstract When we count, we often count fractions, too. We contend that fractional counting involves partial entities, which are merely possible parts of entities of the counted kind. The size of these possible parts is measured with respect to the size of a possible member of that kind. Therefore, partialhood is mereomodal, and the logical form of fractional counting claims includes mereological predicates, modal operators, and a measurement functor. Different varieties of modality and forms of measurement are involved, depending on the kinds of entities to be counted and the context. The mereomodal account validates the idea that fractional counting is a way of counting by identity, in continuity with logic-based accounts of non-fractional counting, albeit more complex than them. Such an account also explains why some kinds of entities are not involved in partialhood and cannot be fractionally counted, while others only have marginal involvement in these phenomena. In the last part, we discuss some difficult cases and show that an integrity condition for partial entities is required in the logical form of some fractional counting claims.