|Element relation, element relationship: the existence of a number within a set. In the broader sense the existence of an object (urelement) within a set. The element relation is to be distinguished from the subset relation. See also sets, classes, subsets, elements, set theory, empty set, universal class, paradoxes.|
|Geach, Peter T.
Books on Amazon
|Element Relation||I 53
Two-class theory/GeachVs: even worse than the Two-names theory: E.g. the general term "philosopher" denote "class of philosophers" - Socrates is then only a member of the class. Vs: the element relation is very different from the subclasses relation: E.g. A parliamentary committee is not a member of Parliament - but: "a philosopher" means the same in both applications - copula: fallacy of division: as if two varieties existed: one for "is a philosopher" and one for "is an element of the class of philosophers" - Geach: equivalent sets must not be divided into equivalent subsets - "every logician" is not equivalent to "class of logicians".
Logic Matters Oxford 1972