PETER ROEPER FIRST- AND SECOND-ORDER LOGIC OF MASS TERMS

ABSTRACT. Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differ-ences in connection with the identification of argument places and the significance of the identity relation. KEY WORDS: identity, infinite divisibility, non-atomic domains of quantification, quantities The logic of mass terms is a generalisation of standard predicate logic. It allows for domains of quantification which have parts, but do not consist of individuals. The rules of inference are largely those of normal predicate logic. The main point of divergence concerns the identification of argument places (reflexivisation). As there may be no individuals, the idea that dis-tinct occurrences of the same variable always refer to the same individual cannot be applied in specifying the semantics. The first-order system is developed syntactically in Section 1, the second-order system in Section 2. Formal semantics for the logic of mass terms1 are arrived at indirectly by first translating the statements of the logic of mass terms into a standard first-order calculus, whose domain of quantification is the totality of quantities, i.e. the totality of parts of the domain of mass quantification. Soundness and completeness results for the first-order logic of mass terms are obtained in Section 3, for second-order logic in Section 4