Aspects of the Grammar and Logic of Relative Terms - Simons, Peter (Przegląd Filozoficzny. Nowa Seria, 2020)
We are familiar with the grammar and logic of relational predicates in predicate calculus, chiefly as transmitted through Whitehead and Russell. In natural languages however, relations are frequently expressed using what Peirce called relatives, that is, expressions like brother, gift, head, effect, successor, which require completion by one or more definite terms to yield general names or terms. Peirce developed a logic of such relatives which influenced Schröder and Tarski. Later, Leśniewski used relative terms such as part, overlapper, class etc. to formulate his mereology, rather than the predicates and operators subsequently and more standardly used. In this paper I con-sider aspects of the grammar and logic of such relative terms, particularly in regard to several areas of general logico-philosophical interest: cardinality; functions; abstrac-tion; the order problem of relations; and Russell’s multiple relation theory of belief and judgment.
Keywords: term; relative; C.S. Peirce; B. Russell; function; multiple relation theory of belief