Philosophy Lexicon of Arguments

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.
Author Item Excerpt Meta data
Geach, Peter T.
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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".

Gea I
P.T. Geach
Logic Matters Oxford 1972

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Ed. Martin Schulz, access date 2017-04-26