Philosophy Dictionary of ArgumentsHome
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| Subsets, set theory: subsets are not to be confused with elements of sets which are not themselves sets. Individual sets can be formed from individual elements if additional assumptions are introduced. On the other hand, subsets may consist of 0 or more elements. Subsets are in each case related to a set whose subset they are. The cardinality of a set results from the counting of its elements and not from the counting of its subsets, since these can overlap. The set of all subsets of a set is called a power set. The empty set {0} is a subset of each set, but not an element of it. See also set theory, sets, power set, element relation._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. | |||
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P. Geach on Subsets - Dictionary of Arguments
I 53 Two-class theory/GeachVs: this theory is even worse than the Two-names theory. >Two-names theory. Two-class theory: E.g. the general term "philosopher" denotes "class of philosophers". - Socrates is then only a member of the class. >General term, >Denotation. GeachVs: the element relation is very different from the subclasses relation: E.g. A parliamentary committee is not a member of Parliament. >Element relation, >Subsets. 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". >Copula/Geach. Geach: equivalent sets must not be divided into equivalent subsets - "every logician" is not equivalent to "class of logicians". >Equivalent class._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition. |
Gea I P.T. Geach Logic Matters Oxford 1972 |
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Ed. Martin Schulz, access date 2024-04-16